ON THE DETAILED FLOW STRUCTURE AND THE CORRESPONDING DAMAGE TO TEST SPECIMENS IN A CAVITATING VENTURI Marion John Robinson A dissertation submitted in partial fulfillment of the requirements for the degree of Doctor o.f Philosophy in the University of Michigan 196-5 Doctoral Committee: Professor Frederick G. Hammitt, Chairman Associate Professor William P. Graebel Associate Professor Terry Kammash Professor William Kerr Professor Clarence A. Siebert Professor George L. West

AC KtNOWLEDGMENTS The author would like to acknowledge the financial support of The National Aeronautics and Space Administration under Grant NsG-39-60 which provided the bulk of the equipment for this work. The guidance and assistance of Professor F. G. Hammitt during the term of this investigation is gratefully appreciated. The loan of the Linear Proficorder by the manufacturer, Micrometrical Division, The Bendix Corporation of Ann Arbor, to the University, and the cooperation of the Mechanical Engineering Department and Professor Lo V. Colwell during its use is gratefully appreciated. Also, many thanks are due the numerous fellow candidates and research assistants who worked on this grant for their valuable assistance and helpful suggestions. Finally, thanks are due my wonderful wife, Sonja, for the beneficial environment which she created during the period during which this dissertation was conducted. ii

TABLE OF CONTENTS Page ACKNOWLEDGMENTS..ii LIST OF TABLES........................ v LIST OF FIGURES...... vi NOME NC LATU RE..xiii Chapter I. INTRODUCTION AND LITERATURE SURVEY....1 A. Introduction............. B. Summary Review of Cavitation Literature 3 C,. Material Selection Criterion. 7 D. Flow Regime Investigation...... II. EXPERIMENTAL APPARATUS AND PROCEDURES 9...... 9 A. Water Test Facility. 9 B. Mercury Test Facility........... 9 C. Test Specimens. 12 D. Damage Test Venturis.. 12 E. Associated Experimental Apparatus and Techniques. 16 1. Pressure Profile Measurement 2. High-Speed Photography 3. Electrical Probe Technique 4. Damage Specimen Examination 5. Fluid Purity Observations and Operating Conditions III. CAVITATING FLOW STRUCTURE IN VENTURI. 34 A. Measurement of Venturi Pressure Profiles.34 1. General 2. Motivation 3. Data Reduction 4, Velocity and Number of Test Specimen Effects iii

Chapter Page B. High-Speed Photography of Cavitation Regime.... 60 1. General 2. Motivation 3. Qualitative Observations 4. Quantitative Observations C. Specimen-Fluid Contact Measurements During Cavitation...... 85 1. General-Motivation 2. Data Reduction Analysis 3. Discussion IV. CAVITATION TEST SPECIMEN DATA ANALYSIS.......... 99 A. General... 99 B. Mechanical Property Measurements... 99 C. Specimen Preparation.... 107 D. Typical Damage to Specimens in Mercury Facility 110 E. Typical Damage to Specimens in Water Facility. 117 F. Comparison of Damage Pattern to Pressure Profiles 117 G. Detailed Examinations of Damage...... 127 1. Mercury Specimens 2. Water Specimens 3. Comparison of Damage in Mercury and Water V. CAVITATION DAMAGE DATA CORRELATIONS........... 169 A. Mercury Damage Data Analysis Versus Mechanical Properties....... 169 1. General 2. Single Property Correlations 3. Multiple Property Correlations B. Water Damage Data Analysis Versus Mechanical Properties...173 1-. General 2. Single Property Correlations 3. Multiple Property Correlations C. Discussion and Conclusions..180 VI. CONCLUSIONS.. 186 APPENDICES.191 A. Definition of Cavitation Conditions B. Computer Analysis of Pressure Profile Data C. Computer Analysis of Cavitation Damage Data D. Computer Regression Analysis of Damage Data Versus Mechanical Properties REFERENCES........................... 228 iv

LIST OF TABLES Table Page 1. Actual Pressure Above Vapor Pressure on Test Specimen Surface for Standard Cavitation in Mercury and Water.. 50 2. Percent of Time Mercury is in Contact with Surface.89 3. Mechanical Properties of Test Specimen Materials...... 100 4. Comparison of Mercury and Water Damage Data..... 124 5. Actual Pressure Above Vapor Pressure on Test Specimen Surface for Standard Cavitation in Mercury for Two Specimen Symmetrical Versus Unsymmetrical Arrangement.. 126 6. Depth to Diameter Ratio for Mercury Cavitation Pits.... 151 7. Depth to Diameter Ratio for Water Cavitation Pits.... 164 8. Mechanical Property Versus Damage Correlations for Mercury Data................... 171 9. Mechanical Property Versus Damage Correlations for Water Data...................... 176

LIST OF FIGURES Figure Page 1. Schematic of Water Cavitation Damage Facility (Only Two of the Four Loops Are Shown)...... 10 2. Photograph of Water Cavitation Damage, Closed Loop, Venturi Facility.................... 11 3. Photograph of a Typical Plexiglas Test Venturi Installed in the Water Loop.................. 11 4. Schematic Drawing of Overall Mercury Facility Layout... 13 5. Photograph of Mercury Facility with Top Half of Heater Sections Removed................... 14 6. Schematic Drawing of the Damage Test Venturis Showing Nominal Flow Passage, Axial Specimen Location, Cavitation Termination Points, etc. 15 7. Cross Section Schematic Drawing of Damage Venturi as Modified for Pressure Profile Measurements... 17 8. Schematic Drawing of Plexiglas Specimen-Holder Combination for Measuring Pressures on Specimen Face.... 18 9. Photograph of Plexiglas Specimen-Holder Combination for Pressure Measurements.20 10. Schematic Drawing of Transparent Specimen-Holder Combination for High-Speed Photography....... 21 11. Photograph of the Transparent Photographic Specimen-Holder Combination....................... 23 12. Mercury Loop Plexiglas Venturi with Photo and Pressure Measurement Test Specimens Installed.......... 24 13. Schematic Drawing of Plexiglas Electrode Specimen-Holder Assembly for Contact Measurements............ 26 14. Photographs of the Electrode Specimen-Holder Combination. 27 vi

Figure Page 15. (a) Single Channel, (b) Three-Channel Mercury Contact Indicator Circuit.................... 29 16. Photograph of Electrode Specimen-Holder, Stainless Steel Venturi Center Section (No Test Specimens in Place), Boxes Containing Circuitry..... 30 17. Normalized Pressure Profile for "Visible Initiation" With Three Specimens in "Dry'" Mercury at Various Velocities. 39 18. Normalized Pressure Profile for "Standard Cavitation" With Three Specimens in "Dry" Mercury at Various Velocities. 40 19. Normalized Pressure Profile for Velocity of 22.9 ft./sec. in "Dry" Mercury, With Three Specimens at Various Cavitation Conditions...41 20. Normalized Pressure Profile for Velocity of 33.1 ft./sec. With Three Specimens in "Dry" Mercury at Various Cavitation Conditions............... 42 21. Normalized Pressure Profiles for "Visible Initiation," Three Specimens in Water, at Various Velocities.... 43 22. Normalized Pressure Profile for "Cavitation to Nose" With Three Specimens in Water at Various Velocities 44 23. Normalized Pressure Profile for "Standard Cavitation" With Three Specimens in Water at Various Velocities..... 45 24. Normalized Pressure Profile for 64,5 ft./sec. With Three Specimens in Water at Various Cavitation Conditions.. 46 25. Normalized Pressure Profile for 9604 ft./sec. With Three Specimens in Water at Various Cavitation Conditions o.. 47 26. Normalized Pressure Profile for 199.5 ft./sec. With Three Specimens in Water at Various Cavitation Conditions.. 48 27. (MDP/MDPmax) Versus Cavitation Condition for Various Materials in Mercury and Water............. 51 28. Normalized Pressure Profile for Velocity of 64.5 ft./sec. for "Standard Cavitation" in Water With One, Two and Three Specimens... 53 vii

Figure Page 29. Normalized Pressure Profile for Velocity of 96.4 ft./sec. for "Standard Cavitation; in Water With One, Two and Three Specimens... 54 30. Normalized Pressure Profile for Velocity of 199.5 ft./sec. for "Standard Cavitation" in Water With One, Two and Three Specimens................. 55 31. Normalized Pressure Profile for Velocity of 22.9 ft./sec. for "Visible Initiation" in "Dry" Mercury With One, Two and Three Specimens............ 56 32. Normalized Pressure Profile for Velocity of 33.1 ft./sec. for "Visible Initiation" in "Dry' Mercury With One, Two and Three Specimens............ 57 33. Normalized Pressure Profile for Velocity of 22.9 ft./sec. for "Standard Cavitation" in "Dry" Mercury With One, Two and Three Specimens...... 58 34. Normalized Pressure Profile for Velocity of 33.1 ft./sec. for "Standard Cavitation" in "Dry" Mercury With One, Two and Three Specimens................... 59 35. Normalized Fluid Density and Core Void Fraction Versus Centerline Axial Position for "Standard Cavitation" in Mercury at a Throat Velocity of 34 ft./sec........ 61 36. Typical Sequence of Pictures of Cavitating Flow on Specimen in Mercury at 34 ft./sec................ 65 37. Typical Sequence of Pictures of Cavitating Flow on Specimen Surface in Mercury at 34 ft./sec............. 66 38. Typical Sequence of Frames of Cavitating Flow on Specimen Surface in Mercury at 34 ft./sec............ 67 39. Typical Sequence of Frames of Cavitating Flow on Specimen Surface in Mercury at 34 ft./sec............ 68 40. Typical Sequence of Frames of Cavitating Flow on Specimen Surface in Mercury at 34 ft./sec............. 70 41. Typical Sequence of Frames of Cavitating Flow on Specimen Surface in Water at 97 ft./sec........... 73 42. Typical Sequence of Frames of Cavitating Flow from Side in Water at 97 ft./sec.... 76 * * 0

Figure Page 43. Bubble Number Distribution Versus Axial Position on Test Specimen Surface in Mercury at 34 ft./sec. 79 44. Photomicrographs of Cavitation Damage on Copper-Nickel Alloy (H.HoTrt.), for "Standard Cavitation" in Water at One Hour Duration, (a) 65 ft./sec., (b) 97 ft./sec., (c) 199 ft./sec.........84 45. Typical Oscilloscope Traces of Signal From Electrode Specimen........... 87 46. Percent Contact Time of Mercury to Surface Versus Axial Position on Surface for Various Cavitation Conditions in Mercury at Two Velocities for the Two Specimen Symmetrical Arrangement in the SS Venturi.... 91 47. Percent Contact Time of Mercury to Surface Versus Axial Position on Surface for Various Cavitation Conditions in Mercury at Two Velocities for the One Specimen Arrangement in the SS Venturi......... 93 48. Percent Contact Time of Mercury to Surface Versus Axial Position on Surface for "Standard Cavitation" in Mercury at Two Velocities Comparing One Specimen Versus Two.. 94 49. Percent Contact Time of Mercury to Surface Versus Axial Position on Surface for Various Cavitation Conditions in Mercury at Two Velocities Comparing One Specimen Versus Two.......................... 95 50. Photomicrographs and Proficorder Traces of Original Surface Characteristics of Specimen Nos. 39-1 (1008 Carbon Steel), 13-F (Tenelon), and 188-3 (304 Stainless Steel)... 103 51. Photomicrographs and Proficorder Traces of Original Surface Characteristics of Specimen Nos. 10-A (Ta-1OW), 10-B (Ta-8W-2Hf), and 9-E (Mo-1/2Ti).... 104 52. Photomicrographs and Proficorder Traces of Original Surface Characteristics of Specimen Nos. 23-2 (1100-0 Aluminum), 79-2 (2024-T351 Aluminum), 154-2 (6061-T651 Aluminum). 105 53. Photomicrographs and Proficorder Traces of Original Surface Characteristics of Specimen Nos. 34-cz (As Rec'd Brass), 104-cz (Low Ht.Trt. Brass), 258-cz (Bi.Ht.Trt. Brass). 106 54. Photomicrographs and Proficorder Traces of Original Surface Characteristics of Specimen Nos. 72-cu (As Rec'd Copper), 148-cu (Low Ht.Trt. Copper), 221-cu (Hi.Ht.Trto Copper).......................... 107 ix

Figure Page 55. Photomicrographs and Proficorder Traces of Original Surface Characteristics of Specimen Nos. 69-cn (As Rec'd CopperNickel), 149-cn and 223-cn (Low and Hi. Ht. Trt. CopperNickel)........................ 108 56. Photomicrographs and Proficorder Traces of Original Surface Characteristics of Specimen Nos. 17-ni (As Rec'd Nickel), 91-hi (Low Mt. Trt. Nickel), 175-ni (Hi. Ht. Trt. Nickel)................. 109 57. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Mercury Cavitation Damage Test of (a) Spec. No. 10-Cb-lZr at 0 Hours, (b) 10-Cb-lZr at 10 Hours, (c) 3-Cb-lZr at 50 Hours........... 111 58. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Mercury Cavitation Damage Test of (a) Spec. No. 37-1, Carbon Steel, at 0 Hours, (b) 37-1 at 10 Hours.1.................. 112 59. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Mercury Cavitation Damage Test of (a) 177-3, 304 SS at 0 Hours, (b) 177-3 at 10 Hours... 113 60. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Mercury Cavitation Damage Test of Spec. No. 8-B, Ta-8W-2Hf, (a) 0 Hours, (b) 10 Hours... 114 61. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Mercury Cavitation Damage Test of (a) Spec. No. 89-ni, Low Ht. Trt. Nickel, at 0 Hours, (b) 89-ni at 0L Hours, and (c) 85-ni at 50 Hours.... 115 62. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Water Cavitation Damage Test of Spec. No. l-F, Tenelon, (a) at 0 Hours, (b) at 1 Hour, and (c) at 100 Hours.. 118 63. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Water Cavitation Damage Test of Spec. No. 2-Cb-lZr at (a) 0 Hours, (b) 1 Hour, and (c) 100 Hours....................... 119 64. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Water Cavitation Damage Test of Spec. No. (a) 10-ni at 100 Hours, (b) 83-ni at 100 Hours, (c) 170-.i at 100 Hours............ 120 x

Figure Page 65. Full Surface Photomicrographs of the Polished Surface at Various Stages in the Water Cavitation Damage Test of Spec. No. (a) 139-3, 304 SS, (b) l-E, Mo-1/2Ti, and (c) 8-cn, All at 100 Hours........ 121 66. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 39-1 (Carbon Steel)........ 129 67. Schematic of Polished Surface Showing Areas Covered by Transverse and Longitudinal Traces......... 132 68. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 11-F (Tenelon)........... 133 69. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 22-SS (304 Stainless Steel).134 70. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 23-SS (Stainless Steel)....... 135 71. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 4-Cb-lZr............. 136 72. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 10-Cb-lZr.... 137 73. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 10-Cb-lZr... 138 74. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 10-Cb-lZr........ 139 75. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 9-A (Ta-lOW)........... 140 76. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 9-A (Ta-lOW)............ 141 77. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 9-A (Ta-lOW)........... 142 78. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 8-B (Ta-8W-2Hf)......... 143 79. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 8-B (Ta-8W-2Hf)......... 144 80. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 8-B (Ta-8W-2Hf)......... 145 xi

Figure Page 81. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 24-E (Mo-1/2Ti)........... 146 82. Photomicrograph and Corresponding Proficorder Traces of Surface of Specimen 13-ni (As Rec'd Nickel).149 83. Pit Size Density Versus Pit Diameter for Stainless Steel Tested at "Standard Cavitation" in Mercury at 34 ft./sec.............. 154 84. Pit Size Density Versus Pit Diameter for Carbon Steel Tested in Mercury at "Standard Cavitation" at 34 ft./sec...................... 155 85. Typical Photomicrographs and Typical Axial Proficorder Traces of Cavitated Surface of Specimen No. 139-3 (304 SS)........................ 157 86. Typical Photomicrographs and Typical Axial Proficorder Traces of Cavitated Surface of Specimen No. 1-F (Tenelon)..................... 158 87. Typical Photomicrographs and Typical Axial Proficorder Traces of Cavitated Surface of Specimen No. 2-Cb-lZr (Columbium- % Zirconium)............... 159 88. Typical Photomicrographs and Corresponding Transverse Proficorder Traces of Cavitated Surface of Specimen No. 8-cn (As Rec'd Copper-Nickel)............. 160 89. Typical Photomicrographs and Typical Axial Proficorder Traces of Cavitated Surface of Specimen No. 8-cn (As Rec'd Copper-Nickel)............... 161 90. Typical Photomicrographs and Typical Axial Proficorder Traces of Cavitated Surface of Specimen No. 85-ni (Low Ht. Trto Nickel). 162 91. Pit Size Distribution for Stainless Steel Tested in Water at 200 ft./seco for "Standard Cavitation....... 167 92. Comparisons of Predicted Values of MDP from the Prediction Equation Listed to the Actual Values Observed in Mercury for all Materials Tested.......... 174 xii

NOMENC LATURE A Area Acl, AcImp Acoustic impedance Al (2)*Y Aluminum As Rec'd As received (material condition, GO/ cold-worked) BHN Brinell hardness CbZr (CbZr)* Columbium-l17 zirconium cn (cn)> Copper-nickel alloy cs (1)K Carbon steel cu (cu<) Copper cz (cz)* Copper-zinc alloy (brass) D, d Diameter E Elastic modulus El, I1 Percent elongation ESE Engineering strain energy Degrees Fahrenheit fps Feet per second g Conversionr unit Hi. Ht. Trt. Highest heat treatment or annealing temperature 1 Length L. Ht. Trt. Lowest heat treatment or annealing temperature xiii

MDP Mean depth of penetration MHD Magnetohydrodynamic Mo-1/2Ti (E) Molybedenum and titanium alloy ni (ni)* Nickel p Pressure P Load or force ppm Parts per million pps Pictures per second 7ORA Percent reduction of area SS (ss) Stainless steel STP Standard temperature and pressure t Subscript denoting values at venturi throat Ta-lOw (A)* Tantalum and tungsten alloy Ta-8w-2Hf (B)* Tantalum, tungsten and hafnium alloy TBS True breaking stress TS Tensile strength TSE True strain energy V Velocity, volume v Subscript denoting vapor properties, velocity YS Yield strength Et True strain 10 Density (ic Cavitation number Y-t True stress Symbols and numbers in brackets indicate designation stamped on test specimens for material identification. xiv

CHAPTER I INTRODUCTION AND LITERATURE SURVEY A. Introduction For the past two hundred years, the phenomenon of cavitation has been known and the accompanying losses of component performance and the material damage done to the cavitating fluid enclosure or liner has been of considerable importance to the furtherance of scientific and technological progress in the fluid machinery field foi approximately sixty-five years. This phenomern has been the subject of numerous investigations and contributions to a partial understanding of this phenomeni have been made by many people. However, controversies and disagreement as to the actual basic mechanisms of damage which are inflicted by the cavitating flow regime still exist at this time and probably will for some time into the future. Comparatively little is known evern today about the prediction of damage by a cavitating flow regime other than in a few specific and simplified systems that have been carefully investigated. In the earliest considerations of the cavitation phenomenon the primary fluid of importance was water, as this was the basic fluid used in fluid machinery until recent times. At the present, however, liquid metals, cryogenics, organics and other fluids have come into prime 1

2 consideration as working fluids, in heat transfer systems, various process systems, as working fluids in thermodynamic cycles, etc. With the advent of liquid metals as heat transfer fluids for nuclear reactor power plants, and as working fluids in various power generating plants especially, at present, those for space vehicles, the prediction of cavitation performance and damage in a variety of fluid-material environments and at various temperatures becomes of great importance. The high developmental costs for the component machinery, and the difficult handling problems encountered with liquid metals, makes the full scale component testing and the materials-screening programs, which have had to be used in many cases, highly undesirable and very costly. In addition, the desire to design very high-performance components, as for space vehicle power plants, requires that the fluid handling components utilize higher velocity flows and minimum suppression heads so that they may have to operate under some degree of cavitation to obtain optimum weight to power performance. In addition, long unattended life is desired for many such units. Thus it becomes increasingly more important to define precisely the method of attack of the cavitation flow regime and to determine those physical and mechanical properties of materials which are important in resisting attack~ Once this goal is accomplished it will be possible to intelligently choose and/or develop materials for these purposes, and permit more aggressive and still reliable designs to be -made. The current investigation sheds more light on the basic damage mechanisms and helps in determining a relationship between measurable mechanical properties of materials,

3 and their resistance to cavitation damage in a variety of fluids. In order to gain some constructive insight into the complex damage mechanisms of cavitating flow, it is necessary that the laboratory test conditions match as closely as possible the actual operating conditions of fluid-handling machines. However, certain compromises become necessary for reasons such as budgetary requirements, flexibility for the handling of multiple and differing test specimens, ability to handle different test fluids under differing conditions of velocity, temperature, pressure, gas content, etc., and to obtain reproducible results which are susceptible to analysis, both in terms of knowledge of the flow regime and of the test materials properties. With these requirements in mind the closed loop cavitating venturi test section facility was selected for the present investigation. This system lends itself well to the requirements of multiple test specimen insertion, temperature and velocity variation and control, susceptibility of results to careful analysis, and very close similarity to flow-induced cavitation in actual field equipment. B. Summary Review of Cavitation Literature The concept of cavitation was first postulated by Leonhard 1 Euler in 17.54 in his theory on hydraulic turbines. However, the major 2 3 early analyses of importance were those by Rayleigh and Besant. Shortly thereafter the accompanying loss of component performances and the destructive action of cavitation were discovered by many of other early investigators of fluid handling machinery such as with propel4,5 6 lors, and turbines. In the 1930's, the laboratory testing of

4 materials for their resistance to cavitation damage came into wide use and several different means of such testing were developed. Schroeter, in 1932, used a constricted-tube type of water tunnel to produce cavitation, the extent and intensity of which could be controlled, and made to occur in a region where a test specimen could be inserted. Gaines, in 1932, and Kerr, in 1937, first used the vibratory method of cavitation testing. Other investigators have used devices as a high velocity liquid jet impinging on multiple test specimens mounted on a rotating 10 disk (Hobbs), and a rotating disk with through-holes which is rotated in a chamber of fluid to produce cavitation on the disk downstream of 11 the holes (Rasmussen). To the present time, each of the above-mentioned laboratory tests has received considerable attention from several investigators in the cavitation field and there are several current materials-screening programs underway throughout the world. With the advent of cavitation damage testing in the laboratory and the resulting interpretation of results in order to rank materials as to their relative resistance to cavitation damage, many ir.estigators postulated the physical properties of materials of significance in 7 their susceptibility to cavitation damage. Schroeter presented a correlation of his data with Brinell Hardness and other early investiga12 13 tors, such as Boetcher, and Mousson, postulated surface hardening *It has long beern known that the damage caused by an impinging jet resembled cavitation damage, but only recently has the connection become reasonably clear.

5 effects, fatigue failures (due to the pounding of the surface with many impacts from the collapsing bubbles), and showed results of slip lines in the material surfaces resulting from the cavitation action. Since then, many investigators have put forward their results in terms of a correlation with a single mechanical property of the materials tested. The list of investigators in this category is too lengthy to list. Several of these have shown correlations with hardness, yield strength and tensile strength. The actual mode of the material attack by the cavitation flow regime has also been the subject of numerous hypotheses. Classically, it has been assumed that shock waves from bubble implosions impinge on 14,etc. adjacent solid structures. Under ideal fluid assumptions, in an incompressible fluid with an empty bubble, and assuming spherical symmetry, infinitely high pressures at the mathematical point of bubble collapse can result. Recent theoretical studies by Hickling and Plesset, and by Ivany, in our own laboratory, throw doubt on the likelihood of this mechanism in that it was shown in both cases that if the bubble collapse center remains stationary (which of course it would not in detail, being perturbed by the nearness of the solid member to be damaged), the pressures applied to the wall would in general not reach damaging magnitudes. Damaging pressures could be created, how42 ever, by bubble rebounds, which have been observed by Ivany and others. More recently, evidence of the possible importance of nonspherical collapses resulting in a central liquid jet which impacts on the material has accrued. This mode of collapse was first suggested by

6 deHaller and Ackeret, and Suverov. Recent evidence to support its 17 significance has been furnished by Naude and Ellis, Shutler and 18 19 Mesler, and Benjamin and Ellis. Fatigue failure due to the repeated exposure to forces resulting from either of the already discussed mechanisms has been proposed 9,11,13,15,20,21,22,23,24,25,26,28,etc. by many invrestigators~ Direct failure due to the imposition of sufficiently high forces from either 17,18,19,26,28,etc. of the above mechanisms has been postulated by many (undoubtedly, both fatigue and cratering failure occur in most real cases to differing extents, depending on the intensity of the cavitation). Since corrosion is often present with cavitation, the interrelation has been discussed by many, assuming that the combined action 27 28,29,30,31,etc. creates damage more readily than either separately. Other less probable theories have also been advanced in the past as chemical disassociation of the liquid producing very reactive 32 fluid corrosion, etc. The above impressive list of possible mechanisms is an indication of the very complex nature of the cavitation phenomena and serves to illustrate that an attempt to understand the mechanism of attack must include an attempt to isolate the particular mechanism which is under investigation, although this cannot be done rigorously, or completely, in any system.

C. Material Selection Criterion In light of the above-mentioned modes of attack and in view of the high emphasis of earlier work on the mechanical aspect of the cavitation damage, most of the materials for the present investigation have been chosen for the following reasons: 1. Low susceptibility to chemical attack (corrosion) in the fluid environment in which they are to be tested. 2. Wide range of mechanical properties so that the existence of a possible material properties correlation could be tested. 3. Flexibility of the material state (i.e., ability to be coldworked) so that the same material could be examined in different states, i.e., several materials were tested in three different heat treatment states so that variations on grain size, mechanical properties as strain energy, tensile strength, etc. could be examined on the same material. Since in the very early stages of the investigation it was noted that the available materials mechanical property data in manufacturers' handbooks, engineering handbooks, etc. gave wide variations (order of + 25%) in the reported properties for supposedly the same alloys and materials, a program was initiated to measure the applicable mechanical properties of the particular materials used from the same piece of stock from which the test specimens for the analysis were to be made and at the actual test temperature. This has been done in all but a very few cases where sufficient material was not available. The results of the complete material property tests are reported in detail elsewhere,9 aand the pertinent data only are reproduced herein.

8 D. Flow Regime Investigation The investigation of the cavitating flow behavior and the resulting damage was conducted in three main phases. First, the effects of small changes in degree of cavitation, velocity, pressure, specimen orientation to flow, etc., on the final results were examined. Then, high-speed movies of the flow and an electrical probe technique, to be described later, were utilized to obtain detailed information on the actual flow pattern existing, and thus to help interpret the observed damage. Also envisioned was the determination of a bubble size spectrum to be compared with the subsequent pit size spectrum on the test specimens. The final phase consisted of constant duration cavitation damage tests on many different materials with the flow, temperature and gas content and other cavitation parameters kept the same. In all cases, more than one specimen of a material was tested for statistical interpretation of the data. The specimens so exposed were examined in detail, as described later.

CHAPTER II EXPERIMENTAL APPARATUS AND PROCEDURES The two venturi test facilities used in the present investiga33 tion have been described in complete detail in an earlier report. However, the pertinent equipment and modifications utilized in this investigation will be summarized below for convenience. A. Water Test Facility This facility is a multiple-venturi closed-loop system with a maximum capability of four test venturis in a parallel combination. It includes equipment for deaerating and purifying the water, and has been designed for operation with a minimum of operator attention. The maximum venturi throat velocity obtainable is slightly in excess of 200 feet per second. Figure 1 is a schematic drawing of this facility, and Figures 2 and 3 respectively are photographs of the facility and of a venturi test section. The general operational procedure for testing specimens in this facility was to run three such venturis in parallel with three specimens in each venturi so that nine specimens were tested at one time, under identical flow conditions. B. Mercury Test Facility This facility is a single-venturi closed-loop system which was operated with mercury at room temperature for this particular 9

HIGH PRESSURE TA NK CAVIT ATION TEST VENTURI I \ FLOW STRAIGHTENER FLOW DIR ECT ION I LOW DIVERTOR GAS PRESSURE FLOW MEASURING ORIFICE LOW PRESSURE TANK SURGE TANK VARIABLE SPEED(PESR MOTOR AND MAGNETIC CLUTCH DRIVE UNIT SCREEN (PRESSURE CONTROL) PUMP Fig. l. —Schematic of water cavitation damage facility (only two of the four loops are shown).

11 Fig. 2. —Photograph of water cavitation damage, closed loop, venturi facility. Fig. 3. —Photograph of a typical plexiglas test venturi installed in the water loop.

12 investigation. For the general damage correlation two specimens were run at the same time, and of the same material. The effects of specimen insertion geometry, and number of test specimens in a single venturi were also studied in this venturi, to be described later. A schematic drawing of the facility is shown in Figure 4, and a photograph which includes the heater section for higher temperature operation (not included in the present study), is shown in Figure 5. In this photograph the top half of the heater sections have been removed to facilitate the viewing of the loop components. C. Test Specimens The damage test specimens are thin flat plates with tapered ends. The nominal dimensions are 1/16" wide by 5/8" high by 3/4" long. They are inserted into the walls of the diffuser portion of the venturi with suitable specimen holders so that the longest dimension is parallel to the fluid flow and only about 0.200" of the test specimen height is submerged in the fluid. Figure 6 (a) is a schematic drawing of a typical specimen. D. Damage Test Venturis All of the cavitation damage tests have been conducted in venturis with identical flow paths, although the number and respective orientation of the test specimen insertion has been varied. The nominal flow path dimensions are shown in Figure 6, along with the variations of venturi-specimen geometry. All of the damage tests in the water facility were conducted in a venturi arrangement as Figure 6 (c), the venturi

176 DRIVE PULLEY BEARING HOUSING STUFFING BOX THROTTLING VALVE VENTURI TEST SECTION "MEASRING VENTURI COOLER COOLING WATER OUT I COOLING WATER IN THROTTLING VALVE 1006 TO STORAGE TANK TO STRAESTORAGE TANK (OUT OF LOCATION) TO MAIN LOOP DRAIN Fig. 4. —Schematic drawing of overall mercury facility layout.

14.:::i:,::::::::iii~~~~~~~~~ii~~i::'i~~~ai~~i~~ il!!!iii~:i::iii-ii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iiiiii:,~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~~iiiiiii~iii — p~~~~~~~a~~~~asa~~~~~~P~ ~~~~~~~ i~~~iii~~~~~~~ ~~~~~;r~~~~~~~~~~~~~i~~~~~a~~~i~~~~~~(n:~~~~~~~:~~~~~~::: ~~ ~ ~ ~?~!!!iii!17ii~iii~ i:: I 1~~~~~~~13 i~ig. 5. —Photograph of mercury facility with top half of heater sections removed.

0. 200" i ~~~~~~~~~~~~~~1800 0.740"' Ns 0.745's 281, ~ ~~0.060 (a)~ —Polished Surf ace b 1 200 c~\ \ 200 VI, 1.2 —- BI_ x 3 STUD (c)~~~~~~~~~V ONS SPECIMEN HOLDER 4 TANDARD CCAV TO BACK CAV TO IST MK.11 ooo ~~~~~~~~(d) VISIBLE INITIATION ~ ~\~~~\~~~/ CAVTO 2ND MK SECTION B-B 1L~~~~~~~~~~~~~~~~~~~~~~~~~~~.5.7 3 S C IO 0550 4

16 being constructed from plexiglas, while all of the damage tests in the mercury facility were conducted in a stainless steel venturi as shown in Figure 6 (b). Comparisons of damage between venturi arrangements (b) and (d) were made in mercury and between (c) and (d) in water in order to be able to observe the specimen orientation effect and thus be able to compare the mercury and water results. It would have been preferable to use identical venturis and test specimen geometries throughout. However, cost and time limitations did not permit the fabrication of the required numbers of venturis (with the differing end attachments required for the two loops), so that existing equipment was used. Arrangements (b) and (c) have a symmetrical flow path with specimens inserted, and arrangement (d) is nonsymmetrical. E. Associated Experimental Apparatus and Techniques 1. Pressure Profile Measurements A special pressure tapped venturi was modified to enable use in either of the two closed-loop facilities described earlier in this report. It is essentially identical to the damage venturis in the water loop although the ends were turned down to fit the mercury loop venturi holders and special adaptors then made to enable use again in the water loop. A schematic drawing of this venturi is shown in Figure 7, indicating the location of the pressure tap points, a typical pressure tap dimension and the possible specimen insertion ports. The flow path dimensions are identical to the ones used for the damage studies. Figure 8 is a schematic drawing of the special plexiglas specimen-holder

17 0040' 0250" 00 SPECMEN HOLDER A A-A AWEAlR SPECIMEN LOOP ADAPTER so; 1625 i/Z7~~~~84'~- I \CAV/TA T/ON O I st MaRK 1//'///66 ||\ CAV/I ATON rTO BACK / // 5A < - SUANDARD CAVrATi/ON \ -- CAV/TAr/ON ro NOSE / tl:. —-,' 4.131VI/S/BLE /N/T/AT/ON P5 Ps 3 /-.___. - PsFP3 and Ps2 P12 ) Pressure Tap Locations P1 PO p o Fig. 7. —Cross section schematic drawing of damage vencuri as modified for pressure profile measurements.

18 GLUED JOINT 1/8" DIAMETER-3 HOLES CD1 fr~ -de 0.030" D, 3 HOLES SECTION A-A / A / I~ A -~ 0.750,11438 Fig. 8. —Schematic drawing of plexiglas specimen-holder combination for measuring pressures on specimen face.

19 combination used to measure the actual pressures existing on the test specimen polished surface in conjunction with the axial pressure profile measurements. There are three pressure taps located on the polished surface, symmetrically located in an axial direction. With this system it was possible to utilize either one, two or three specimen insertion geometries by filling the other ports with flush inserts. Also, it was possible to visually observe the cavitation cloud on the surface between the pressure taps in order to verify the methods used for setting the degree of cavitation (extent of cavitating cloud). A photograph of this apparatus is shown in Figure 9. 2. High-Speed Photography Due to the opacity of the mercury it is impossible to observe the flow around the cavitation damage test specimens as can be done in the water loop. However, the mercury provides an advantage in that any activity observed in an opaque fluid through a transparent wall must be occurring adjacent to that wall, whereas in water, a transparent fluid, the precise location of an event is not so easily established. Hence, a device was designed and fabricated to allow viewing of the polished surface (labelled in Figure 6) of a transparent test specimen through the specimen, i.e., from the back. This device is a specimen and holder combination of plexiglas, suitably polished, so that the underside of the surface of the test specimen can be viewed through the plexiglas holder (Figure 10). The plexiglas test specimen polished surface to mercury interface (Figure 6 [a]) can be viewed quite clearly, and in fact all of the high-speed movies have been taken through a device of

20 Fig. 9.- Photograph of plJexiglas specimlent..holider combinatio) n for pressttre measuttrements.

21 ~ I,o + /93;4tS,0v —4 1 1628 Fig. 10. —Schematic drawing of transparent specimen-holder combination for high-speed photography.

22 this kind. The first feasibility model was not contoured to match the inside tapered curvature of the venturi. After the photographic technique was demonstrated, however, a subsequent model, contoured to match file inside surface of the venturi, was constructed. It was necessary to use two pieces, glued together. After many trials, this was accomplished with no loss of clarity to the view. After a time in the cavitating mercury field, mercury penetrated the glued interface so that a replacement unit was necessary. Special adaptors were required to seal the unit into place in all three types of venturis (water test venturis and mercury, plexiglas and stainless steel, test venturis). Figure 11 shows the adaptors and the transparent test specimen. Figure 11 (c) shows a grid of lines on paper at the location which would ordinarily constitute the mercury-test specimen interface, serving to illustrate the clarity of the view obtained and the field of view for the pictures in the following sections. Figure 12 (a) is a photograph of the plexiglas venturi with both of the special plexiglas specimen-holder combinations installed. In this manner it was possible to record the pressures on the surface, the extent of the cavitating cloud (degree of cavitation), and the highspeed movies simultaneously. In Figure 12 (b) is the same photograph with the Fastax camera, camera control unit, flash holder and pressure measuring manifold in place. A 1:1 image to actual view was obtained with this set-up. Any further enlargement of the image was prevented by the camera lens to subject distance required to allow the direction of sufficient light cnto the mercury-specimen interface.

23 (a) (b) (c) Fig. 1l. —(a) Photograph of the transparent photographic specimen-holder combination, (b) adaptors for different venturis, (c) view through this unit illustrating view obtained in high-speed motion pictures.

24 (a) Fig. 12. —(a) Photograph of mercury loop plexiglas venturi with photo and pressure measurement test specimens installed, and (b) camera set-up and pressure measuring equipment.

25 With this arrangement high-speed motion pictures were taken at a framing rate of 16,000 pictures per second with two different frame exposure times. The first light source used was a Sylvania FF-33 Flood Flash Lamp in a 6" hemispherical reflector. In this case framing was controlled by the rotating prism in the Fastax camera, and the corresponding exposure time per frame was on the order of 21 microseconds. The second light source used was an Edgerton, Germerhausen and Grier, Type 501 High-Speed Stroboscope, which was synchronized with the camera to give an exposure time of 1.2 microseconds per frame. Ir this latter case the maximum framing rate was limited by the maximum flashing rate of the light source to about 8,000 frames per second. 3. Electrical Probe Technique It was observed from the high-speed movies that, in some cases, the mercury appeared to lift free of the specimen surface, recontacting the surface further downstream. A rather unique method of further investigating this phenomenon was developed, which consists of electrically measuring.he physical contact between the mercury and specimen surface using a plexiglas test specimen-holder combination, somewhat similar to those already described. Figure 13. a schematic dra:iang of the apparatus and Figure 14 is a photograph. Three 0.019" wires pass through the holder, terminatinrg flush with the surface of the test. specimen, and located at three axial positions on the surface. These wires are sealed with glue to prevernt mercury leakage. A good visual observation of the surface can still be made through the holder, so that the extenrt of the cavitation zone on the surface can be noted.

26 K B A A B. *200"' 0.200" V-i0 75 0.060'AI TY.1..i 0.375" 2" 0.019" insulated Cu wire) 1634 View A- A View B - B Fig. 13. —Schematic drawing of plexiglas electrode specimenholder assembly for contact measurements.

27 1635 (a) (b) (C) Fig. 14. —Photographs of the electrode specimen-holder combination, (a) side view showing wires in holder, (b) angle view showing wire termination points, (c) end view showing axial location of termination points.

28 Figure 15 (a) shows the preliminary electrical circuit used to establish the feasibility of the technique. A 6 volt, 200 ma lamp was used in series with a 6 volt battery to give a visual indication of mercury contact with the wires. Oscilloscope output was taken from the lamp terminals. An improved circuit, Figure 15 (b), was later used to monitor all three probe positions at the same time, using the lamps. Also, any two could be connected to the dual beam oscilloscope (Tetronix 502A), for instantaneous comparison. The transformer in the circuit is used only for visual monitoring of the cavitation condition via the lamps, as the output has a strong 60 cycle component. The battery circuit is used only for data taking, to conserve battery life. The circuit in Figure 15 (b) was not optimum as there was interference between the oscilloscope outputs from the different probes, to be explained in detail later. To avoid this, a combination of the two circuits, Figure 15 (a) and (b) was finally used and proved to be quite satisfactory. Each oscilloscope beam trace was then from an independent circuit and battery. Figure 16 is a photograph of this experimental set-up. 4. Damage Specimen Examination In general, test specimen preparation and post-test examination were conducted as follows: 1. Metallographic polish performed on the flat surface parallel to the venturi centerline ("polished surface" labelled in Figure 6). Typical before-exposure photomicrographs and roughness profiles of this surface are shown and described in the next section~

To Probe (a) t Symbol Meaning S1 S1 Transformer Power Switch | O S2 Selector Switch 4110 VG I1 Transformer Indicator #47.4 T'I S2 I 12 -I4 Probe Indicators #44 B Lantern Type #TW1 ( 6 V) I I1 12 3 L'-l1 Grd _#2 Id #3 I 1636 Scope outputs (b) Fig. 15. —(a) Single channel, (b) three-channel mercury contact indicator circuit.

30 I. a...:....N........_. i...... i~~~ii~~~i~~ii;'''"''''::-:i':i~~~~~~~~~~~~~~~ci::::: ~~l~~~~~~~~~~iil'l~~~~~lz:5 ~~~~~~:;:i~~~~iii':ii~~~~~~iiiiliiii~~~~~~ziz;E: _:. _::., n~~~~~r~:i::ii::~~~~~~~~~~~~soXS s:: -::.::~~~~~~~~~~~~~~~~~~~~~~~~~~f._::}:~i::::: _:i~l~i:::::: _:_::::: 1B:: B_::~: X::: ~:: "::_::::EI - _ Z Z _ s:.: iJ: S iiiii: i: i': _ii iiiiiiiii:,::. l I -g'..2-';;~i"EiE'E i::' iX' 0'.:::::'::':::-:::2:E:E:.::...........................':.::.:'-'.-i.'S...''.O fi l 1637 Fig. 16. —Photograph of electrode specimen-holder, stainless steel venturi center section (no test specimens in place), boxes containing circuitry.

31 2. Initial specimen weight recorded to a precision of 10 5 grams on electronic balance. 3. Original surface pits and imperfections examined at 100X under microscope and tabulated into several size categories by two observers. 4. Photomicrographs taken, in some cases, of full surface at 40X, and selected areas of probable damage at 100X before exposure. 5. After exposure to cavitation of selected condition and duration items (2), (3) and (4) repeated. 6. After (5) in the mercury runs only the specimens were baked at a temperature of 500~F for a period of 5 hours in a vacuum chamber in order to remove any mercury on the surfaces that was not removed by the normal cleaning operation in N-Heptane. Experience showed that this was necessary. By this process, as explained below, it was possible to determine the existence of possible chemical attack or chemical corrosion as opposed to purely mechanical damage. A few materials exhibited large weight gains after cavitation but before baking, and large weight losses after baking. This was taken to be an indication of the existence during the cavitation test of chemical formation of amalgamations, etc. However, most materials exhibited very small weight changes after baking due primarily to vaporization and removal of mercury droplets from the surfaces. 7. Selected areas of typical cavitation damage were photographed at several magnifications and detailed proficorder traces made in

32 several cases. The results of these investigations will be described in a later section. 8. In a few cases, metallographic cross-section through typical damaged areas were performed. 5. Fluid Purity Observations and Operating Conditions a. Water Conditions The water used in these tests was normal tap water at a temperature of 80~F + 10OF, with a nominal total gas content of 2.5 *.5 percent by volume at STP as determined by Van Slyke measurements, and an impurity content of 8.0 ~ 0.5 grains per gallon (about 140 ~ 10 ppm solids), as measured by an RDE4 Solubridge and VSO216 Dip Cell manufactured by Industrial Instruments in New Jersey. b. Mercury Conditions The mercury installed in the cavitation damage facility for these tests was triple-distilled laboratory grade mercury, at a temperature of 75~F + 5~F, with an entrained gas content of r, 0.2 ppm by mass as determined by a modified Van Slyke apparatus, and a water vapor content below 10 to 15 ppm by mass. The required instrumentation was designed and developed in this laboratory. During the investigation, it was noted that sealing water used in the pump had contaminated the mercury to about 500 ppm by mass. Subsequently, a means of measuring the water content of the mercury was developed. The water was removed from the mercury by operating the loop for a prolonged period at 5000F. Henceforth, the tests were conducted

33 in "dry" mercury (established by the sensitivity limitation of the instrument to be less than 15 ppm by mass, and probably zero).

CHAPTER III CAVITATING FLOW STRUCTURE IN VENTURI The cavitating flow structure in the venturis used in this investigation has been experimentally observed in three different ways. In each case the observation has included the effects of velocity, degree of cavitation, and the number and orientation of the test specimens. The following three sections describe these methods, and the possible relation between the variation of the above-mentioned parameters and the observed damage. A. Measurement of Venturi Pressure Profiles 1. General Axial wall pressure profiles have been used in this laboratory 34 for investigations of scale effects in the flow and currently an extensive effort is being made to examine the scale effects phenomenon of cavitating flow. However, the walls of the venturi were smooth during these measurements and no test specimens were inserted. Since the test specimens projecting into the venturi constitute significant obstructions, it is presumed that the local pressures seen by the test specimens will not be the same as the wall pressure at that point. Hence, a test specimen assembly was fabricated in order to measure the 34

35 actual pressures existing on the test specimen polished surface at the same time as conventional wall pressure profiles were measured. The equipment for this has already been described. 2. Motivation The motivation for conducting this particular type of measurement stems from two considerations. First, it was necessary to know the actual pressures or pressure gradients existing on the test specimen surfaces to be able to compare the observed bubble size and number distribution, to be obtained photographically, with observed pitting and theoretical treatments of forces imposed on the surface by bubble collapse. Secondly, it was desired to determine the local flow environmental changes produced by variations of velocity, degree of cavitation (see Appendix A for definitions of degrees of cavitation), and number and geometry of test specimen insertion, since the comparison of the mercury and water damage depends on knowing this relationship. 3. Data Reduction The pressure profile data has been normalized by dividing the observed pressure above vapor pressure ("suppression pressure") by the kinetic pressure at the appropriate flow conditions, i.e., P P - Pv norm. 2 1Pvt/2g where p = the normalized pressure = the observed or measured pressure = the fluid vapor pressure

36 vt = the mean venturi throat velocity = the liquid density When this method of normalization (i.e., not a true normalization, since the maximum values exceed 1.0) is used, the minimum value of normalized pressure is the conventional cavitation number, i.e., Pmin - Pv L-c v2/2g The data reduction was facilitated by the use of a computer program written for the IBM 7090 facility, described in Appendix B. 4. Velocity and Number of Test Specimen Effects 36 (rotating disk), obbs10 (jet or droplet impacting Lichtman (rotating disk), Hobbs (jet or droplet impacting 24 device), and Knapp (ogive in a water tunnel), all reported a considerable effect of velocity upon damage rate. It is the author's opinion that the existence of such an effect, not observed previously in general 37 in the venturi arrangements herein used, and the small dependence of damage on velocity noted in this investigation, i.e., a very large increase in damaging capabilities of a particular laboratory or field device with velocity, is due indirectly to the effect of velocity on the location, pressure environment, and distribution of the cavitating bubble cloud produced by the device. Thus it is not evident that there can be a generally applicable, simplified velocity effect "law" as, n 10,24,36 e.g., Damage Rate cx V as previously suggested. In many systems, when velocity is increased, the system pressures and pressure

37 gradients, influencing the violence of bubble collapse, are increased. In addition, the departure from classical scaling laws involving fluid flow parameters can also be produced by these changes in velocity, and thus indirectly influence damage. Finally, the presently undefined mode of attack and material failure from the cavitation flow regime could be influenced indirectly in some presently unknown manner by a change in velocity through a change in intensity of cavitation attack. If, as described later, the intensity level of the cavitation flow regime is such that the forces resulting have the effect of producing a fatigue failure of the material, then an increase in velocity could produce an increase in intensity of cavitation level which would in turn influence the relative importance of failure mechanisms and cause proportionately more damage by single blow failure, cratering, e.g. This would also apply to change of fluid, as discussed later. In the present case, it is believed that the major effect of velocity upon damage is due to the increase of collapse pressure and/or the increase in pressure gradient in the collapse region of the cavitation cloud due to an increase in velocity. In the particular venturi system used in this investigation, the degree of cavitation is variable and several such "degrees" are defined in Appendix A. For the less developed conditions as "visible initiation," a substantial portion of the specimen, somewhat downstream of the collapse region of the apparent cavitation cloud, is under pressures considerably higher than vapor pressure. Thus these pressures influencing the collapse of the larger bubbles which do most of the damage are proportional to velocity squared.

38 Conversely, for the well-developed cavitation conditions, the entire specimen is under pressures near vapor pressure, regardless of the velocity. As expected, the damage shows a maximum when plotted against degree of cavitation, since the numbers of bubbles increase as the cavitation condition becomes more fully developed, but the pressure differential causing collapse decreases. The maximum cavitation condition for damage ("standard cavitation," Appendix A) was selected for this investigation. Consideration of Figures 17 through 26 illustrates the applicability of the above-described effect of velocity on damage. Normalized static pressure profiles reduced, as previously described, from the same venturi in mercury and in water, are shown. From these profiles, it is observed that the pressures on the test specimen surface are slightly lower than the wall pressures measured at the same axial location. For the well-developed cavitation conditions the wall pressure adjacent to the nose of the specimen is apparently increased by a kinetic component of the flow due to the flow pattern around the specimen. It can also be observed that the pressure gradient on the specimen surface decreases as the degree of cavitation is increased towards the more fully developed condition, where the entire surface of the specimen is under pressure only slightly in excess of vapor pressure. The normalized profiles for different velocities are almost identical (Figures 177 18, 21, 22, 23). Hence, the actual pressure differentials above vapor pressure on the surface are higher for the higher

i-2 a.2 WL 0.8 ct ~~~~~~~~~~~~~~~I ~~~~~~~Te s 7Specimen W~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ix I a. 0.6 a r/ W ~~Throat' Cl) 0.4 0 0 Visible,3 Specimens,2293 fps z EJ Some, 33.14 fps 0.22 0 WALL TAP * SPECIMEN TAP 1428 0 1.0 2.0 3.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (Inches) Fig. 17. —Normalized pressure profile for "visible initiation" with three specimens in "dry" mercury at various velocities.

1.4 i.2 0.8, 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1.0,,.t~ CL a~~~~~~~~~~~~~O ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~,. cnLL) Test m ~ ~~~~~~~~~~~~~Specimenre0 i o. 0.6,W~~~~~~~~~~~~~~~~~~~ LC N/ C~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I~ 0.4 n-;-. Throat Standard, 3 Specimen# 0 Z 22.93fps jl ~~~~~~~I I I,iE Standard, 3 Specime 0.2' I' 33.14 fps WALL TAP I SPECIMEN TAP 1429 0 ---— __0 0 1.0 2.0 $.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 18.- Normalized pressure profile for "standard cavitation" with three specimens in "dry" mercury at various velocities.

-4t.~lLSpeciBcnks_ r 1020304 a. 0.6 ~ V,N0.. / S x~ o'_ _',...Z1 DISTANCE OFI THROAT ENTRANCE (inches) oVlsec.,ndr", in"dry" urywith three spapecimen rious cavitation conditions. DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 19. —Normalized pressure profile for velocity of 22.9 ft./ conditions.

i.2 A 0~ W 0.8, LIJ co Test n- /, Specimen/ / o 0.6 I~~~~~~~~~~~~ 2-. 0 0.4 I z~~ ~ ~~I Standard, same 0.2 - Back, same'I. n-Y ~~ ~ ~ ~ 3~E WALL TAP II SPECIMEN TAP 0'P"""1 "__________________ 1 1431 0 1.0 2.0 3.0 4.0O DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 20. —Normalized pressure profile for velocity of 33.1 ft./ sec. with three specimens in "dry" mercury at various cavitation conditions.

1.4 IN 0%t0~ O.8 k'Q cn Test Slpeecimeni9a w a.0.6 0.4 0 0 Visible, 3 SpecImens, 64.55 fps Z ESame, 96.43fps 0.2 A Same, 199.46 fps 0 WALL TAP * SPECIMEN TAP 0 1432 0 1.0 2.0 3.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 21. —Normalized pressure profiles for "visible initiation," three specimens in water, at various velocities.

1.4 1.2 L 0.86 ~cfcwi three spcmn in wae at vario S ecimmens,6.0.6 - 4 - I4 N I,,a: 0~~~~~~~~~~O ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~4.433 A Sme,199.46 fps ] WALL TAP A............'~......~.......~ II SPECIMEN TAP 0.$ Q 0 _______ 0 1.0 2.0 3.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 22. —Normalized pressure profile for'Lavitation to nose" with three specimens in water at various velocities.

1.4 1.2 0. 0.8 co w W Specimee a0.6. 9 N -JI 0.4 n- l~ ~~~~~~Throat " Throat I Q Stondard,3 Specimens,6455fps Z I I 1 3 Same, 96.43 fps ~~0.21 A I I i A Same, 199.46 fps _II: 1 ~0 WALL TAP ~........ -"- - -~ I~ SPECIMEN TAP.........___ 1434 0 0 1.0 2.0 30 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 23. —Normalized pressure profile for "standard cavitation" with three specimens in water at various velocities.

1.4 1.2 Co W O-8 cn ~~~~~~~~~~~~~~~Test -A xo cl -iSpecimen ao0.6 ox~~~~~~~~~~~~w N Q0.4 Cr ~~~~~~Throat o 1 OVisIble, 3 Speclmens,64.55fps Z: I I ~'4I ANose, Same 0.2 El OStandardSame.............~~~~~.~.. [ O WALL TAP * SPECIMEN TAP 0 1435 0 1.0 2.0 3.0 4.0O DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 24. —Normalized pressure profile for 64.5 ft./sec. with three specimens in water at various cavitation conditions.

1.4 O.'. 1. C!, o0.6 X 0.8 / ot -*1Testf P | tThroat I OVisible, 3 Specimens, 96.43 fps 0.2A Nose, Same,,, — wl T0~eli//' WALL TAPv' ot wv =,'.. Ur~g 9/ SPECIMEN TAP three specimens in water at various cavitation conditions. three specimens in water at various cavitation conditions.

1.4 _ _ 1.2 "J 0.8'..c) Test the -piSiecblmens Sem /w99e4 t vn a. 0.6 _IEl' " oo < 0.4I'.':1 Fig. Nom e pThroat threespecime wat at vrios cvit n c tiOVn sibls3 Specimins,in9.4 0.2' 1 I. / Standard,Same. "WALL TAP I SPECIMEN TAP 1437 0 1.0 2.0 $.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 26. —Normalized pressure profile for 199.5 ft./sec. with three specimens in water at various cavitation conditions.

49 velocities approximately according to the square of the velocity. This differential becomes substantial for the less-developed cavitation conditions. The measured specimen surface pressures minus vapor pressure for mercury and for water and for three specimens in the venturi, with a variation in velocity, are shown in Table 1, illustrating the foregoing comments. Figure 27, reproduced from a previous investigation from this 37 system, shows the actual effects of degree of cavitation on the observed damage for different materials, at different velocities, in both water and mercury. The ordinate values, MDP/MDPmax. are normalized values (simply divided by the maximum) of the damage received at the different conditions. The damage data for all materials is reported as mean depth of penetration (MDP), which is a "specific volume loss," i.e., the weight loss is divided by the total exposed area and density of the specimen so as to make the comparison of damage received by all materials directly and correctly comparable. An important observation apparent from this plot is that the maximum damaging condition for mercury is "standard cavitation," where the cavitation cloud on the surface appears to end at the center of the specimen, while the most damaging for water is also "standard cavitation," however, the cavitation cloud here appears to end at the tail of the specimen. As discussed in more detail later, it is believed that these two conditions are similar, in that bubbles are thought to exist in the mercury at a small distance above the surface, and are not visible due to the opacity of the mercury. Although the same terms are used to describe the cavitation

50 TABLE 1 ACTUAL PRESSURE ABOVE VAPOR PRESSURE ON TEST SPECIMEN SURFACE FOR STANDARD CAVITATION IN MERCURY AND WATER Velocity No. of Spec. Pressure (psi) Fluid Ft./Sec. Specs. Tap No. Run No.1 Run No.2 Run No.3 Water 64 3 1 3.9 4.4 3.0 54~F 2 4.2 4.5 3.4 3 4.6 5.0 3.9 Water 97 3 1 2.6 2.6 2.4 540F 2 3.4 2.9 2.9 3 4.9 4.3 3.3 Water 200 3 1 4.0 3.9 3.5 75~F 2 5.5 5.2 5.2 3 11.7 7.1 6.2 "Dry" 23 3 1 3.5 4.7 3.6 Mercury 2 9.2 11.0 10.0 75~F 3 15.1 16.0 15.2 "Dry" 34 3 1 5.3 7.0 6.5 Mercury 2 11.5 17.5 13.8 88~F 3 19.1 29.3 25.5 "Dry" 46 3 1 12.1 9.1 8.7 Mercury 2 9.4 9.8 8.2 120~F 3 14.7 16.3 16.6 "Wet" 23 3 1 9.7 11.1 9.7 Mercury 2 15.5 15.8 15.4 75~F 3 21.6 22.1 21.5 "Wet" 34 3 1 3.3 3.1 3.0 Mercury 2 11.4 12.2 11.0 88~F 3 31.1 31.3 29.3 "Wet" 46 3 1 8.3 3.5 4.8 Mercury 2 20.6 16.0 15.0 115~F 3 58.8 30.5 51.8 "Dry" 34 2 1 1.7 1.7 Mercury (180~) 2 4.9 1.7 78~F 3 9.5 5.3

51 )= ss, 64 FT/SEC, 50-100 HRS. AVG. MERCURY, 2-SPECIMEN VENTURI Er= CbZr, 48-34 FT/SEC AVG. MERCURY, 2-SPECIMEN VENTURI ~= SS, 34 FT/SEC, 87 HRS. MERCURY, 2-SPECIMEN VENTURI SS, 34 FT/SEC, 50-100 HRS. AVG. MERCURY, 2-SPECIMEN VENTURI 1.2 r= cu+cz, 200 FT/SEC, 50-100 HRS. AVG. WATER, 3-SPECIMEN VENTURI *= SS, 64 FT/SEC, 51 HRS. WATER, 2-SPECIMEN VENTURI I= SS, 64 FT/SEC, 3.5 HRS., WATER, 2-SPECIMEN VENTURI 1.1 Operating point for present investigation I. 0.8 E4i 04 0.7 / 0 z i 0., z. / 0.25 0,2 0.1 0) 1445 ZERO SONIC VISIBLE NOSE STANDARD BACK IST MARK DEGREE OF CAVITATION Fig. 27. —(MDP/MDPmax) versus cavitation condition for various materials in mercury and water.

52 conditions in water and mercury, the corresponding visual flow patterns are not identical. Detailed visual descriptions and cross-correlations between water and mercury are given in Appendix A. The pressure profile examination of the effects of one, two, and three specimen insertion geometry has been made. Figures 28, 29, and 30 show the results for water at three velocities and "standard cavitation." A corresponding examination was made, Figures 31 through 34, in mercury at two velocities and two cavitation conditions, "visible initiation" and "standard cavitation." The latter condition in both cases was selected for the damage correlation with mechanical properties, presented later. In general, it is observed that the magnitude of the pressures on the test specimen surface is increased as the number of test specimens is increased for a given velocity and cavitation condition, It has 37 been previously observed that the maximum damage occurs with a lessdeveloped cavitation condition for mercury than for water (Figure 27) An examination of the pressure profile plots shows that the pressure gradient on the test specimen surface is very similar when a comparison is made between mercury at 34 feet per second, "standard cavitation," and water at 97 feet per second, "cavitation to nose." Similarly, "standard cavitation" in water compares closely to "cavitation to back" in mercury in the velocity range used and with the same number of test specimens. However, an examination of the actual pressures above vapor pressure, as listed in Table 1, shows that the magnitude of the pressures are quite a bit higher in mercury. Also, it is evident from

1.4 1.2 IN 0L C,) W 0.6 p' co. Test w W ~~~~~~~~~~~~~~~~pecimenI N 0.4 V) ~ ~ ~ ~ ~ n- Throat I Throat I 1/ 0~~~ Standard, 3 Specimens, 6455fps ~Z I c ii I I I ~~~~~J IIE]Same, 2 Specimens ~0.2'~~/ / \ I A Same, I Specimen l ~~~~~~ ~~~a,, OE WALL TAP " SPECIMEN TAP 0 ~, 1446 0 1.0 02.0 3.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 28. —Normalized pressure profile for velocity of 64.5 ft./ sec. for "standard cavitation" in water with one, two and three specimens.

1.4,.2 C\q a0.8 m A Co o0O.6 N -~lSpecimen - 0.4 Cr -4 -a:~~~~~~~~~~ Throat / OStandard, 3 Specimens, 96.43fps Z | I 1/' EISame, 2 Specimens ~~0.2 2' 1 I ~~~~~~~~~~i i Some, I Specimen I WALL TAP "'L..... /... b.... IIU SPECIMEN TAP,_, ~1447 0 1.0 2.0 3.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 29. —Normalized pressure profile for velocity of 96.4 ft./ sec. for "standard cavitation" in water with one, two and three specimens.

1.4 1.2 W 0.6 ecimen' l co L _z *EN cF 0.6 reft a.: Thro at se' 0 Standord,3 Specimens, 199.46 fps t z;II 0Same,2 Specimens 0.2 ASame, ISpecimen.I 0: ~3 WALL TAP.... I z U SPECIMEN TAP 0 _________ _ A1448 0 1.0 2.0 ~) 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 30. —Normalized pressure profile for velocity of 199.5 ft./ sec. for "standard cavitation" in water with one, two and three specimens.

0*. 1.4i __ i1.2 i(n ~~eSpecimen?,\7 G o 0.6 t Test 0O.4 sec.fr"visblentiati'0 Visib"e,3 Specimens, 22.93 ps o A Some, I Specimens 02~ 0.4 El WALL TAP _ _ ESPECIMEN TAP 1449 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 31. —Normalized pressure profile for velocity of 22.9 ft./ sec. for "visible initiation"in "dry" mercury with one, two and three specimens

1.4 _ _ _ _ 1.2 0~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~10 e\,, ~~~~~~~O.8 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~O ClV~ ~ ~ ~ ~ ~ ~ ~~~~I) lSpecimen1 C,, a- 0.6 w 0.4 / I ~F~_T I _I n SSme, I Specimen _~~N4 SPECIMEN TAP < 0.4,Xtf- I' 1450 Fig. 32. —Normalized pressure profi Visble for velocitymens, 33of 33.1 ft./ps sec. for "visible initiation" in "dry" mercury with one., two and three specimens Z'OE]Same, 2Specimens _____ I ~A Same, ISpecimen ~':". ~'~J"/;",, lli o WALL TAP'~'~':'~'':"'..:......7* SPECIMEN TAP 0 0_ _ _ _ 1.0_2.0 __. DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 32. —Normalized pressure profile for velocity of 33.1 ft.! sec. for "visible initiation" in "dry" mercury with one, two and three specimens.

1.4 1.2 01.0 C,) o0. o 00~~~~~~~~~~~~~~~~~~~~~~~~~0 LJ 0.8 SR, 3S2 Test qYCL -I Aam, impecimenim U) 04 sec fo "sandrd avthatio"i dr"mruyihoe Stwoandad3 three ies,2 0 0s m CI ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~, PCME A 0t0. a~ ~~~ec or"sadadcaiatio" n"dy mrur wt oe toand threeecmns 293p 1, O Samespecimens.n

1.4 1.2:3 W 0.8 C) Co o 0.6 ~c3)~~~ _._1J~~~ ~ ~Test ilo 0ISpecimenr-' I 0.4 oa T.hroat 0 OStandard,3 Specimens, 33.14fps 0 t z |0 Same, 2 Specimens 0.21 —- / / | II A a W Same, I Specimen 0 WALL TAP "o.................'.....-...-.~, —— 1452 0 1.0 2.0 3.0 4.0 DISTANCE OF TAP FROM VENTURI THROAT ENTRANCE (inches) Fig. 34. —Normalized pressure profile for velocity of 33.1 ft./ sec. for "standard cavitation" in "dry" mercury with one, two and three specimens.

60 Table 1 that the actual pressure above vapor pressure gradient on the surface for the mercury, two specimen symmetrical arrangement at 34 feet per second is almost identical to that for the water three specimen symmetrical arrangement at 200 feet per second. Still, the damage obtained in mercury on most materials is about the same as that obtained in water, thus, with regard to the above statements, indicating a similar cavitating situation in mercury. Previous work done to measure the extent of the cavitation regime with test specimens in the venturi via void fraction techniques has shown that the apparent visual termination of the cavitation cloud on the test specimen surface does coincide with the point of maximum fluid void. However, a closer examination of the appropriate data, Figure 35 (reproduced from the above reference), shows that there is a fair amount of void present in the mercury out to the end of the specimen for "standard cavitation" in mercury, where the visual termination is at the center. This tends to confirm the earlier statements as to the existence of bubbles above the specimen surface over the downstream half of the surface. B. High-Speed Photography of Cavitation Regime 1. General In a highly transient phenomenon such as cavitating flow of the type under examination, it is impossible to observe any detail at normal visual speeds. In addition, for complicated flow situations, such as this test-specimen and venturi combination, no reasonably complete

VENTURI WALL THROAT VELOCITY: 34 FT/SEC. >- 1.04 0 / II - 1.00 1 1 W.96 -A.88 15, 88r 15: uL c3.80hotveoiyo 4f.84c5 <w~~~~~~~~~~ ~w 1268 -.25 0.25.50.75 1.00 1.25 150 1.75 2.00 AXIAL POSITION, INCHES Fig. 35. —Normalized fluid density and core void fraction vs. centerline axial position for "standard cavitation" in mercury at a throat velocity of 34 ft./sec.

62 theoretical treatment is currently possible. Thus, high-speed photography becomes a very useful technique for detailed understanding of the flow patterns. The goal thereof is to observe the flow regime at normal visual speeds, including hopefully the collapse of cavitation bubbles and the corresponding surface damage. Due to the very transient nature of this phenomenon and the obtainable equipment, however, this has not been fully possible. 2. Motivation Many theoretical treatments and theories have been advanced concerning the pressures and forces produced by the collapsing cavitation bubbles. Also, it has been postulated that a spectrum of bubbles exist, and that this is related to the size spectrum of the pits produced on 40 the damaged surface. It was hoped to be able to photograph the flow and visually determine the size spectrum of bubbles that came into contact with the test specimen surface. This spectrum of bubbles could then be related to the spectrum of pits that are observed or the damage specimens. Due to its opacity, mercury seems to offer an especially good opportunity for such a study. The photographic technique, however, was attempted both in water and mercury, and as expected, it proved difficult to obtain suitable information in the water system. In the mercury system, howe-er, the technique worked well. The specimen surface to mercury interface was clearly observed, and the only bubbles that appear on the film are those in direct contact, in some period of their life history, with che test specimen surface. It was riot possible to record the number acnd size

63 spectrum of the bubbles in contact with the surface, for the particular experimental set-up considered. However, some indication as to the size and number ranges were obtained. It is not meant to imply that necessarily only those bubbles in direct contact with the surface are responsible for the damage. In fact, the observations have not shown this to be the case, as is discussed later. Two of the more prominent hypotheses regarding the bubble implosion and the resulting surface damage are: (1) the spherically symmet2 ric collapse model leading to the imposition of shock waves on the surface, either during the initial collapse, or more probably, according 41,42,43 to recent theoretical studies, during a subsequent rebound, and (2) the liquid jet impact model where the bubble collapses in a nonspherical-symmetric manner such that a jet of fluid pierces the bubble 17 in the later stages of collapse, impacting on the surface. Both 17,18,42 19 experimental and theoretical evidence now indicate that such a collapse model does in fact occur, although perhaps not in all cases. 41,42,43 Recent theoretical studies indicate that the bubbles must be very close to the surface if the forces produced are to be of a damaging magnitude, and then only rebounds would be damaging. 3. Qualitative Observations The high-speed movies of the mercury cavitation cloud indicate that the local cavitation induced by the specimens themselves is of *This is assuming that the center of collapse is stationary during collapse, whereas actually the bubble would, 19,44,45 at least to some extent, migrate toward the surface during collapse. In addition, the close proximity of the surface would obviously prevent a symmetrical collapse.

64 primary importance with respect to the damage received. This has become apparent in the water venturi tests where the complete cavitation cloud 40 can be observed, but until now was only a postulation for the mercury tests. A cavitation region appears to initiate on the nose of the test specimen and extend downstream along the specimen to a point determined by the back pressure at venturi outlet. The visual termination has been fixed at the axial center of the test specimen for this portion of the study ("standard cavitation"). A more or less stationary "void" is attached to the nose of the specimen from which individual bubbles detach and are swept downstream with the fluid, The high-speed motion picture observations have shown an oscillation in the apparent ending point of the cloud. However, no fixed frequency has been found. The attachment of a cavity at the nose of the specimen, and the subsequent detachment of bubbles from it, has been verified by the electrode specimen tests described later. Typical sequential photographs from the high-speed motion pictures for the two-specimen symmetrical venturi arrangement are presented in Figures 36, 37, 38 and 39. It is observed that the cavitation cloud consists of two separate wakes trailing downstream along the surface near either edge and also a wake along either radial side of the specimen. Only the -very edge of this cloud is visible in the photographs, i.e., the side nearest the wall of the venturi, as the rest is obscured by the opaque mercury. The pattern of pitting damage on the test specimens matches the observed cavitation cloud pattern in that the heaviest concentration of pitting lies on the polished surface along the edges

65 cavitat io n." E...: ro.::.:i::: Reel #19, for two specimen symmetrical arrangement, "standard~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:i::i:-: cavitation."-;;~ %

66......... Fow Direction`'%. | -.... X!!,::',...: __ Fig. 37. —Typical sequence of pictures of cavitating flow on specimen surface in mercury at 34 ft./sec., exposure time per frame = 26 microseconds, time between frames = 79 microseconds (12,700 pps), Reel #19, for two specimen symmetrical arrangement, "standard cavitation."

67 _i _ i!~.... iliii~' II~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iiiii~'i-n::::I l:::i~l __:::::::::ii:_iiii;: i _1~~~~~~~~~~~~~~19:::::::::.iiiii:::::::::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~iii1i;!?::!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:............. ii!I1!I........... rid ~~~~~~~~~~~~~~~~~~~d Fig. 38. —Typical sequence of frames of cavitating flow on specimen surface in mercury at 34 ft./sec., exposure time per frame= 25 microseconds, time between frames = 76 microseconds (13,200 DDS). ~~ ~ ~ ~...;~;:~:~:::::" ~:;i;i ~... 10 i;::...... i:!!iiiiii ~~~~~~~~~~~~~~~~~~~~~~~~~~~ Fig. 38. —Typical sequence of frames of cavitating flow on 25 microseconds, time between frames = 76 microseconds (13,200 pps), Reel #19, for two specimen symmetrical arrangement, "standard cavitation."

68 Flow Dtrettion lomputational _auritania9F_:..:::,:-1 Fig. 39. —Typical sequence of frames of cavitating flow on specimen surface in mercury at 34 ft./sec., exposure time per frame = 25 microseconds, time between frames = 74 microseconds (13,450 pps), Reel #19, for two specimen symmetrical arrangement, "standard cavitation."

69 and on the sides perpendicular to this. (See Figures 57 and 58.) Figure 40, for the same flow conditions as Figures 36 through 39, with the exception that only one test specimen was in place in the venturi, shows a more uniform cloud on the surface and relatively more bubbles on the surface. In several bubble sequences from this Figure, bubbles along the side of the specimen (actually in the corner formed by the side of the specimen and the venturi wall) appear to transform from an oblong to a spherical shape during collapse (Figure 40, frames 7 to 12 and 15 to 27). This observation appears inconsistent with the nonspherical collapse model already discussed. However, the depth of view in the photographs is not clear and the influence of the corner is uncertain. In all bubble sequences observed on the surface, the bubbles retain their circular form during collapse to as small a diameter as can be observed, but to what smaller radius they remain hemispherical cannot be ascertained. A relatively stationary void at the nose of the specimen is indicated, and is confirmed by the electrode specimen tests discussed later. The existence of more bubbles and a steeper pressure gradient on the surface (Figure 34) for this condition than for the two specimen case, indicates that it should be a more damaging condition, although this has not yet been verified. Figure 41 shows the flow condition for the three specimen symmetrical arrangement in water at a throat velocity of 97 feet per second for "standard cavitation." In this case "back-lighting" was used to silhouette the cloud, which is possible for a transparent fluid. There

70 6i Fig. 40. —Typical sequence of frames of cavitating flow on specimen surface in mercury at 34 ft./sec., exposure time per frame = 30 microseconds, time between frames = 90.5 microseconds (11,100 pps), Reel #2, for single specimen arrangement, "standard cavitation."

I13l~n7 i 3 19 Ow irec ~on _ _.ll_ 14: = 20.?:.? 15 21 166 22 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.....!...:,'::)i~ ~ ~ ~ ~ ~ ~ ~ ~ ~ a..sS~~: 17 23:. PPBa:::~::::::::::...:........ 1824 -;"~""'~ I'I aa~- 2k2 1694(cont'd 1) Fig. 40. —(Continued)

72 25 1~,~ ~:i~,,~:_.3.....1 iFlow Direct %cn ion.I 26 2 77_ 33 283 34 35 30 36 30:11694(cont' d 2) Fig. 40. —(Continued)

73 12 1695 Fig. 41. —Typical sequence of frames of cavitating flow on specimen surface in water at 97 ft./sec., exposure time per frame = 1.2 microseconds, time between frames = 160 microseconds (16,250 pps), Reel #223, three specimen symmetrical arrangement, "standard cavitat ion."

74 are two wakes along the edge of the polished surface, as in the mercury case, extending downstream from the nose. There are also heavy cavitation wake formations along the radial sides of the specimen. Of particular interest is the appearance of cavitation bubbles beyond the surface (i.e., further into the fluid) in frames 8 through 11. Since the focal plane of the camera was adjusted to the fluid-specimen interface, and since the depth of focus with this lens system is very shallow, it can be concluded that these bubbles are removed from the surface a distance of about 1/16 to 1/8 of an inch. The small bubbles that are evident near the ends of the surface wakes are on the surface, but no bubbles are noted on the downstream portion of the surface. Typical damage patterns for this flow condition (Figures 63, 65, e.g., presented later) show that the pitting distribution is heaviest on that portion of the surface where no bubbles were observed. The following conclusions can be made with reference to the above observations: 1. Since no bubbles are observed on the surface in the downstream area for an observation time of about 0.1 seconds, it can be assumed that the time interval between bubbles is at least 0.1 seconds. Since the pitting rate in this area has been estab-2 3 lished as 0.3 x 10 pits per second (i.e., "' 10 pits in 100 hours), Figure 91, the ratio between bubbles and pits could be 3 as large as 3 x 10:1. This would be in agreement with the 4 54 ratio of 10:1 as reported by Plesset recently for an ultrasonic test.

75 2. Since no bubbles appear on the surface during this observation time of 0.1 seconds, but one group was observed in the background, perhaps these are the damaging ones which are drawn toward the surface during collapse as has been suggested on a 19,44,45 theoretical basis recently. All of the aforementioned photographs of the flow have been taken through the transparent specimen-holder apparatus. However, with water, it was possible to photograph the flow from the side, through the venturi wall. The field of view was enlarged to include the complete vertical height of the venturi and the throat exit. Figure 42 shows this view in the water system for the same flow conditions as Figure 41. The detail is not optimum, but still bubbles can be observed near the throat exit, which disappear into the overall cloud in the venturi further downstream. The significance of the cavitation induced by the specimens themselves is made evident in these pictures. The side wakes are clearly shown, in addition to individual bubbles in the immediate wake behind the specimens. The elapsed time between frames is too large in all of these pictures, due to equipment limitations, to allow the following of individual bubbles at the higher velocities. 4. Quantitative Observations From the high-speed photographs in the mercury system a number distribution of bubbles versus axial position on the specimen has been estimated on the basis of about one hundred frames (Figure 43), as well as the maximum and minimum bubble diameters observed on the surface. The upstream one-third of the specimen appears to be under an almost

76 Flow Direction'.5 t.......... 1696 Fig. 42. —Typical sequence of frames of cavitating flow from side in water at 97 ft./sec., exposure time per frame = 1.2 microseconds, time between frames = 181 microseconds (5,500 pps), Reel #226, three specimen symmetrical arrangement, "standard cavitation."

77 Flow Dir ct. ion 6 1696(cont'd 1) Fig. 42. -- (Continued) at";;CEDFig.':'i __-(oniud

78 Flow Direction 13 O S ki.. 5# u f:0 ____ 1696(cont'd 2) Fig. 42. —(Continued)

* 6 C x Essentially a continuous void observed in this area. o 4 z a0~ t| \ ~~~Flow Direction|, z Tail 2 z 1698 0 0.25 0.50 0.75 DISTANCE ON POLISHED SURFACE - INCHES FROM NOSE Fig. 43. —Bubble number distribution vs. axial position on test specimen surface in mercury at 34 ft./sec., for two specimen symmetrical arrangement, "standard cavitation," Reel #19.

80 continuous void, as confirmed by the electrode specimen tests discussed later. Downstream of the void region the number density of bubbles decreases very rapidly. However, the actual numbers of bubbles per second is very large with respect to the numbers of pits per second which 5 occurred, being larger by a factor of about rV 10 at the center of the specimen and -v 10 near its tail, discussed in greater detail later. The observed bubbles ranged between -v 30 and nV 5 mils diameter, the lower cut-off being due primarily to the limited resolution of the photographs. Also, due to the limited framing rate of the available equipment, it is not possible to determine the relation between a given bubble observation and the stage in its life history, at which it has been observed. Hence, one can only say that bubbles with a maximum diameter of at least 30 mils exist adjacent to the specimen and in very large numbers compared to the number of pits, most of which were less than 0.1 mil diameter. It is thus clear that to photograph a pit being formed in this type of system where the event is not triggered (as with spark-induced bubbles) would require extreme good fortune in sampling the very small applicable portion of the total time, and also very large photographic magnification and resolution. The limitations of photographic technology are such that this goal does not appear presently attainable. For typical mercury samples (Figure 57 and 58), numerous small pits are observed on the upstream portions of the specimen and relatively smaller numbers of larger pits on the downstream portion, where the pressure is higher. This pitting distribution and its relation to the measured fluid pressures is discussed in greater detail later.

81 However, since, in general, a larger bubble requires a longer time to collapse, it will penetrate further downstream before collapsing, and as 42,e.g. analyses show, there will then be larger pressures imposed by it on adjacent structures. This hypothesized pattern of events is fully substantiated by the observed pitting patterns. In general, the high-speed photographs show very few bubbles on the downstream portions of the specimen polished surface where the maximum numbers of large pits are observed, and very little damage, if any, is observed on the upstream portions of the surface where the relatively stationary void is attached, however, the static pressure is close to vapor pressure, and hence does not provide the required driving force for a violent collapse in the void region. The existence of a large ratio between observed numbers of bubbles and resulting pits on surfaces exposed to cavitation regimes, as experienced here and elsewhere, is thought to be an area of basic interest to the overall understanding of the cavitation phenomenon. In this particular investigation it has been observed that this enormous ratio increases with distance in an upstream direction where the mean static pressures on the surface are lower. Considering the presently most likely mechanism of damage as being the unsymmetrical collapse of a bubble with a resultant fluid jet of high velocity at the end of collapse impinging on the surface, this large ratio can be explained. It 42 was observed in our own venturi tests that the resultant fluid jet is formed in a direction parallel to the fluid streamlines which, in the case of the venturi, is also normal to the pressure gradient. To cause

82 damage to a surface oriented parallel to the fluid streamline, as in the present case, it is necessary that the bubble be reoriented during collapse so that the resultant jet is directed towards the surface. Conceivably this could be somehow accomplished by the influence of the adjacent wall. However, in the present case, this reorientation might also be provided by the cavity oscillation as it moves upstream on the specimen surface. When the cavity retreats upstream, a nonspherical bubble sufficiently close to the surface might be tipped by the drag forces on its side nearest the specimen surface, so that the resultant fluid jet would be directed towards the surface. Consequently, only those bubbles that are located at the precise distance from the wall and are at the proper point of collapse at the moment the oscillation occurs, would be able to damage the surface. From another viewpoint, the bubble must be at the proper distance from the surface, so that it will migrate towards the wall during collapse and be at the-proper distance from the wall for the fluid jet to be effective, when it is formed, and the bubble reoriented as discussed above, as suggested by Benjamin and 19 Ellis. This clearly would be a very selective process and could indeed explain the large ratio of bubbles to pits formed. This rather complicated process seems capable of providing the required forces for damage, as opposed to the spherical collapse, and in addition explains the anomaly of the bubble to pit ratio. Conceivably a pit so formed would have unique characteristics indicating its method of formation. In general, for those specimens traced in the direction of flow for the mercury system, a raised rim is

83 present around the crater, which is sometimes uniform and more often than not higher on the downstream side. This is consistent with the proposed mechanism as one would expect the reorientation to be incomplete at times, so that the resultant jet would be tipped towards the downstream end of the specimen. Detailed examinations of the damage from the water facility (Figures 85 and 88 e.g.) in general indicate an elongated pit in the flow direction, with a predominant ridge on the downstream end and rather uniform ridges at both sides. This can also be explained by the above damage hypothesis. In this case, the velocity is much higher and consequently the reorientation of the resultant jet twards the surface could not be expected to be as complete, thus giving rise to jets oriented generally towards the surface, but predominantly tipped downstream. That the velocity can be an important factor in the degree of reorientation of the jet is shown in Figure 44, where typical photomicrographs of the damage on the high heat treat copper nickel alloy at a duration of 1 hour are compared at three different velocities. Very little damage is evident at the lowest velocity of 64 feet/ second, but the damage present consists of small pits that are essentially round. In the next highest velocity of 97 feet/second the damage is somewhat triangular in shape with the base on the upstream side, as if the force were applied to the surface at about a 45~ angle in the direction of flow. At the highest velocity of 200 feet/second the pits are in the form of elongated grooves, noted in all the examinations of damage at this velocity, indicating a force aligned at a smaller angle to the surface and in the direction of flowo Consequently, this would

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85 tend to explain the difference in the basic damage appearance between the water and mercury tests as the velocities were 200 and 34 feet per second, respectively. It has often been observed that trailing vortices from pump impeller vanes, for instance, are much more damaging to the surfaces on which they impinge than to the initiating vane. This important observation can be explained nicely in light of the above hypothesis. In this case, the bubbles are already moving toward the surface rather than parallel to it as in the venturi, so there may be no requirement for bubble reorientation to the surface. Those bubbles that collapse in close proximity to the surface then need only be at the proper distance from the surface. On the other hand, the initiating surface compares closely to the present specimens. Thus reorientation is required, resulting in fewer damaging bubble collapses. C. Specimen-Fluid Contact Measurements During Cavitation 1. General-Motivation During the analysis of the high-speed photographs taken of the mercury flow, it was noted that the fluid seemed to lift clear of the specimen at the nose or initiation point and to recontact the surface at some point downstream on the surface. This seemed to indicate that, for the more advanced cavitation conditions such as "standard" to which the present study applies, there was a continuous void attached to the nose of the test specimen, and consequently, as was actually observed and expected, no damage was observed in this region. Thus the electrode specimen equipment described earlier was developed and used to explore

86 the relationship between the various degrees of cavitation and velocities, and the duration and amount of contact between the mercury and the specimen surface versus axial position. Since there were trace amounts of water in the mercury, some question arose as to whether water might preferentially wet the surface, and thus prevent good contact. Simple static tests in a beaker showed that there was no problem in this regard. 2. Data Reduction and Analysis After determining optimum oscilloscope settings, the vertical sensitivity was set at 2 volts/cm and the sweep rate at 200 milliseconds/cm, and the magnifier at normal (lx). Then a second photo of the same condition was taken with the magnifier at 5x so that one-fifth of the trace was obtained at a sweep rate of 4 milliseconds/cm which has the effect of spreading out one-fifth of the trace to the full screen and "magnifies" the breaks in the circuit. For each photo the camera shutter was opened and a single sweep initiated via the scope manual single sweep switch and then the shutter closed. Thus there was no possibility of obtaining an overlap of the trace. Normally, for each cavitation condition and velocity used, four photographs were obtained: (1) comparing the first probe to the middle probe at ix, (2) comparing the first probe to the middle probe at 5x, (3) comparing the first probe to the last probe at ix, and (4) comparing the first probe to the last probe at 5x. In all photos the upper beam denotes an open or closed circuit on the first probe and the lower denotes an open or closed circuit on the other probe, eiter the e middle or last. Figure 45 shows representative oscilloscope traces of the data.

Photo No. 8, Zero Cavitation, Sweep: 20 ms/cm Photo No. 27, Std. Cavitation, Sweep: 20 ms/cm Mag. XI, 34 ft/sec, Stainless Steel Venturi, Mag. X1, 34 ft/sec, Stainless Steel Venturi Upper traces:Probe 1(100/),Lower:Probe 2(100%) Upper traces:Probe 1(20/),Lower:Probe 2(91/5 1642 Photo No. 10, Vis. Cavitation,Sweep:20 ms/cm, Photo No. 12, Cavitation to BackSweep:20 ms/cm M-ag. X5, 34 ft/sec, Stainless Steel Ventu' Mag., X51 34 ft/sec, Stainless Stee'l Venturi, Upper traces:Probe l(45%),Lower-.Probe 2(1b0%*) Upper traces:Probe 1(8%),Lower:Probe 2(28%) Fig. 45. —Typical oscilloscope traces of signal from electrode specimen.

88 Photo number 8 was taken at zero cavitation, with full voltage (closed circuit) on all probes in order to make sure that all photographs taken later were observed in the proper orientation. Thus, in all photos, a line on the upper trace of one particular beam indicates a closed circuit, i.e, mercury in contact with the surface, while a line on the lower trace of the beam indicates an open circuit, i.e, no mercury contact with the surface at that probe position. From the traces, the percentage of time the mercury spends in contact with the surface can be determined versus axial position on the specimen. All of this data is tabulated from 59 photographs, in Table 2. Representative photographs only are included in Figure 45. The measurements taken with the electrode test specimen confirm the fact, as presumed from the high-speed movies, that the mercury actually does lift clear of the test specimen surface at the nose and rejoins it at some point downstream. At intermediate points between, the mercury comes in and out of contact with the specimen surface. No fixed frequency of the motion was noted. In Figure 46, the percentage of time the mercury is in contact with the surface as a function of axial position is compared in mercury for various cavitation conditions at two velocities. Two specimens were placed in the venturi at an orientation of 180~. The curves which show some time out of contact show most at probe position 1, with an increase of in-contact time in the downstream direction. The same trend, an increase of in-contact time in the downstream direction, is indicated as the cavitation condition is decreased at constant velocity and as the

89 TABLE 2 PERCENT OF TIME MERCURY IS IN CONTACT WITH SURFACE Photo Cav. Cond. Vel. Sweep Rate % of Time Hg in-Contact No. "Degree" fps ms/cm Mag. Probe 1 Probe 2 Probe 3 9 Visible 34 20 5 100 100 10 " h " 45 100 24 1" if o 100 100 25 it" " " 100 100 avg. VISIBLE 34 20 5 86 100 100* 1 Standard 34 20 1 80 100 2 11 " " " 16 90 3 " " " 5 100 100 4 t " " " 100 100 5 it " " It 24 90 6 " " " " 90 100 7 It I" 5 100 100 19 " " 3 76 20 " " 70 100 21 " " " rr 48 100 22 " " " II 68 100 23 WI II 5 100 26 " " " 1 47 98 27 "r " I It 20 91 28 it" " I I " 16 100 29 it ",,,, 4 100 avg. STANDARD 34 20 1/5 49.5 94 100 12 Back 34 20 5 8 28 13 if " " " 10 54 14 ti it iI fr 36 50 15 if I II If 5 50 16 it if if it 20 42 17 it WI li 1I 4 86 18 if if if 7 80 avg. BACK 34 20 5 9 39 67.5 8 ZERO 34 20 1 100 100* 100 38 Visible 22 20 1 100 100 39 " " " 100 100 avg. VISIBLE 22 20 1 100 100 100* 30 Standard 22 20 1 100 100 31 it if if It 88 100 32 It if I,, 100 100 33 i" It i 70 100 avg. STANDARD 22 20 1 89.5 100 100

90 TABLE 2 —Continued Photo Cav. Cond. Vel. Sweep Rate % of Time Hg in-Contact No. "Degree" fps ms/cm Mag. Probe 1 Probe 2 Probe 3 34 Back 22 20 1 3 57 35 "I "i It 5 7 59 36 if" " " 1 51 94 37 if" " " 5 8 92 avg. BACK 22 20 1/5 17.3 58 93 Note: Above values are for two specimens in stainless steel venturi. Following values are for one specimen in stainless steel venturi. 49 Visible 22 20 1 84 100 50 " " " 5 100 100 51 it if i" 1 100 100 avg. VISIBLE 22 20 1/5 94.7 100 100 45 Standard 22 20 1 74 100 46 "l if i" 5 62 100 47 It il f l 1 95 100 48 " " " 5 100 100 avg. STANDARD 22 20 1/5 82.8 100 100 40 Back 22 20 1 0 71 41 ff if t" 5 0 69 42 " " " 1 2 85 43 if" " " 5 5 100 44 " " " 5 0 97 avg. BACK 22 20 1/ 5 1.4 70 94 52 Standard 34 20 1 26 94 53 it" " " 5 8 90 54 it " " 1 10 100 55 " " I" 5 5 100 avg. STANDARD 34 20 1/5 12.3 92 100 56 Back 34 20 1 15 84 57 " " " 5 23 75 58 " " " 1 1 2 100 59 I" " " 5 23 100 avg. BACK 34 20 1/5 18.3 79.5 100 *Extrapolated, no data.

ZERO CAVITATION 10 IVISIBLE INITIATION STANDARD CAVITATION VISIBLE INITIATION 44 V80 60 z STANDARD CAVITATION. 1-4 40 u UUPSTREAM DOWNSTREAM ENDNOSE DNSTAM END, TAIL H 20 I _ _ _ __ _ _ _ z CAVITATION TO BACK 0 ~= 22 ft/sec PL4 CAVITATION TO BACK = 34 ft/sec 1638 0.000 0.375 0.750 AXIAL POSITION ON SPECIMEN SURFACE ------ (INCHES) Fig. 46.- Percent contact time of mercury to surface vs. axial position on surface for various cavitation conditions in mercury at two velocities for the two specimen symmetrical arrangement in the SS venturi.

92 velocity is decreased at constant cavitation condition. The same type of data is shown in Figure 47 for the case of one specimen in the venturi. Again, it is evident that the percentage in-contact time at any probe position decreases as the cavitation condition is increased. The same trend is shown for velocity and axial position as was for the two specimen case. Comparing Figures 46 and 47, the rate of increase of incontact time with axial position is greater for the one specimen case than for the two specimen case. Figures 48 and 49 show the data replotted for constant cavitation condition, with a comparison of one specimen versus two specimens at two velocities. Figure 48 is for standard cavitation and shows that in the one specimen case the mercury is out of contact for a larger percentage of the time at the upstream end of the specimen, and the in-contact time increases to about the same value at the downstream end as compared to the two specimen case. This results in a larger rate of increase of in-contact time versus axial distance on the test specimen surface for the one specimen as opposed to the two specimen case. This holds true for both of the velocities investigated. The same general trends are shown in Figure 49 for visible initiation at 22 feet/second and cavitation to back at 22 feet/second. The only exception is for cavitation to back at 34 feet/second, where the one specimen case shows more time in-contact than the two, although still showing a larger rate of increase of in-contact time with axial position. This one exception is probably due to the visible setting of the cavitation termination point being farther downstream than it should have been for the two specimen case. Since the cavitation was

ZERO CAVITATION 100 VISIBLE INITIATION STANDARD CAVITATION 04 80 M~~~~~~ E-4 U:: 60 z 0 z'- I / >4 40 0d UPSTREAM DOWNSTREAM END,NOSE END, TAIL W~~~~~~~~~~ F-4 20 z CAVITATION TO BACK STANDARD CAVITATION El = 22 ft/sec STANDARD4 V ITATION~ D = 34 ft/sec AVITATION TO BACK _ 1639 0.000 0.375 0.750 AXIAL POSITION ON SPECIMEN SURFACE ----— (INCHES) Fig. 47. —Percent contact time of mercury to surface vs. axial position on surface for various cavitation conditions in mercury at two velocities for the one specimen arrangement in the SS venturi.

100' STANDARD, 22 FT/SEC STANDARD, 22 FT/SECr 80 c3: H~~~~ EQ 60 _ Hz Q0 v / 0 Z.STANDARD,34 FT/SEC /'-4C, __ __ >- 40 I_/ UPSTREAM DFWNSTREAM END, NOS E END, TAIL I 20 1/ ----- z U STANDARD,34 FT/SE0 = 1 Specimen Venturi Fig. 48. —Percent contact time of mercury to surface vs. axial pos ition on surface for "standard cavitat ion" in mercury at two velocities comparing one specimen vs. twVenturio. 1640 0.000 0.375075 AXIAL POSITION ON SPECIMEN SURFACE -....(INCHES) Fig. 48. —Percent contact time of mercury to surface vs. axial position on surface for "standard avtto" in mercury at two velocities comparing one specimen vs. two.

100 VISIBLE, 22 FT/SEC VISIBLE, 22 FT/SEC VISIBLE, 34 FT/SEC 44 80 C,, H'z 60 z 0 z C,) 40 40 UPSTREAM DOWNSTREAM u ~~~~END, NOSE END, TAIL C.,/ z 20 BACK, 34 FT/SEC H- BACK, 22 FT/SEC W BACK, 22 FT/SECzI/ 0= 1 Specimen Venturi / = 2 Specimen Venturi C14 BACK, 34 FT/SEC BACK, 22 FT/SEC 1641 0 0.000 0,375 0.750 AXIAL POSITION ON SPECIMEN SURFACE ------ (INCHES) Fig. 49. —Percent contact time of mercury to surface vs. axial position on surface for various cavitation conditions in mercury at two velocities comparing one specimen vs. two.

96 adjusted visually and the downstream end of the cavitation cloud was set at the downstream end of the specimen in this case (visibility beyond this point being limited by venturi opaqueness), it is conceivable that some overshoot could have occurred. If the whole curve were shifted upwards in accordance with a correction for overshoot of the cloud termination point until the probe 3 values matched, then there would be no discrepancy in the trends. 3. Discussion This technique provides an independent means of determining quantitatively the extent of the cavitating void in the venturi on local obstructions such as the cavitation damage test specimens. It could be used in any type of two phase system where the fluid phase has an electrical conductivity appreciably higher than the gaseous phase for determining fluid-surface contact time or amount. The data indicates, as expected, that more voids appear on the surface as the degree of cavitation is increased. A somewhat surprising fact is that the average contact time of fluid to surface never falls below about 50% even when the specimen is completely immersed in a highly turbulent, cavitating flow regime. This fact could be of importance for various direct conversion MHD concepts. The electrical current path for such a system might well be made through a region of substantial void, thus avoiding the necessity of completely separating the fluid and vapor phases. Comparing the voids measured by the electrode specimen technique, with the pressure profile data taken earlier, it is observed that for "visible initiation" the mean static pressures on the surface at the

97 same three axial locations are well above vapor pressure, while the mercury loses contact with the surface at 34 feet per second (Figure 46), about 10-15% of the time at the upstream position. For "standard cavitation," the pressure on the surface at the center position is well above vapor pressure, while the mercury loses contact with the surface only a small portion of the time. It should be pointed out that the pressures are time mean values while the contact time technique can show instantaneous fluctuations. For "cavitation to back," the pressure profile measurements show that the entire surface is under a very low pressure slightly above vapor pressure, while the contact time as recorded in this investigation still averages about 50%, ranging from 15% at the upstream position to about 80% at the downstream position. From the observed damage patterns on the specimens for these conditions, it appears that the pitting occurs in a region where the mercury has a contact time approaching 100%, and where the pressures are considerably above vapor pressure. The same statements apply for the visible initiation data for only one specimen in both cases. The standard cavitation, one specimen, 34 feet per second data shows essentially vapor pressure existing at the first two probe positions and a higher pressure at the third, while the mercury contact data shows about 15%, 80% and 100%, respectively. This also tends to confirm that the most intense damage occurs in regions of essentially 100% contact and high pressure, as the damaged surfaces from this condition show very heavy damage on the rear one-third of the specimen. (See Figures 57 through 61.)

98 If it had been shown that very little contact existed between the mercury and test specimen surface in the zones of heavy damage, then the assumption that damage was primarily caused by an impingement effect would be somewhat strengthened. However, since the data indicates approximately 100% contact with the surface in the damage region, there is still the possibility of both the central jet impingement model and the shock wave model. The major conclusions that can be drawn from this phase of the investigation are: 1. The technique described for measuring the mercury to surface contact time is feasible and could be applied to many other twophase and/or two component fluid flow regimes. 2. The mercury to surface contact time decreases as the degree or amount of cavitation on the surface is increased. 3. The mercury to surface contact time decreases as the number of specimens is decreased from 2 to 1. 4. The most intense cavitation damage occurs on a region of the test specimen surface where the mercury is in contact with the surface essentially 100% of the time. 5. The mercury contact time increases with distance from the specimen leading edge, but does not increase at the same rate as the increase of pressure along the surface in the axial direction. 6. The mercury contact time averages about 50% even when the entire surface is completely immersed in a highly turbulent cavitating flow regime.

CHAPTER IV CAVITATION TEST SPECIMEN DATA ANALYSIS A. General The normal procedure that each test specimen is subjected to has already been described in an earlier section. In this section are presented the details of the test specimen preparation and mechanical properties measurements needed as correlation data for the subsequent data correlation. B. Mechanical Property Measurements As previously mentioned, it is necessary to determine the exact mechanical properties for the materials tested. This requires that mechanical property and cavitation specimens be made from the same stock, thus exhibiting the same heat treat and cold work properties. Table 3 is a listing of the measured mechanical properties to be used in correlating the damage data. All but a few of these items have been measured in this laboratory from the same stock as the specimens. In this table are listed two values for strain energy to failure, i.e., "engineering strain energy" which is based on the "approximate" or engineering stress-strain curve and is equal to the area under this curve, and "true strain energy," which is based on the true stressstrain curve, which takes into account necking of the specimen, 99

TABLE 3 MECHANICAL PROPERTIES OF TEST SPECIMEN MATERIALS Engr. True True Hard- % Tensile Yield Strain Strain Brkng. ness Elastic % Red. Material Strength Strength Energy Energy Stress (BHN) Modulus Elong. Area 304 SS 95,200 44,000 44,800 74,500 172,800 133.5 28x106 54.4 50.9 1008 CS 50,000 30,000 15,500 23,000 55,200 91.5 28x106 40.0 71.0 Tenelon 131,800 82,000 54,500 94,800 220,900 218.0 28x106 44.2 46.6 Cb-lZr Annealed 29,300 14,600 6,000 25,000 30,000 115.0 12x10 42.5 92.8 Cb-lZr C-Wrked 56,000 52,500 2,900 10,000 80,000 124.0 12x10 6.0 84.0 Ta-1OW 80,900 72,800 16,800 91,300 117,100 163.0 29x106 21.0 63.3 Ta-8W-2Hf 89,300 80,400 20,800 96,000 135,600 175.0 29x106 22.0 59.6 Mo-1/2Ti 94,700 89,600 15,000 83,000 120,000 216.0 37x106 30.7 54.7 1100-0 Aluminum 14,300 10,500 7,500 52,000 35,600 23.0 10x10 36.3 89.3 2024-T351 Aluminum 70,300 56,000 14,400 36,000 102,500 120.0 10x106 21.3 35.1 6061-T651 Aluminum 45,000 41,000 10,300 40,800 86,800 95.0 10x106 19.0 48.1 Copper-Zinc As Rec'd. 93,900 82,000 4,700 55,400 137,000 168.0 16x10 5.3 40.7 Copper-Zinc 6 (L.H.Trt) 47,600 20,000 28,600 57,000 119,500 65.0 16x10 62.6 60.9 Copper-Zinc (H.H.Trt) 40,400 11,000 15,300 33,000 79,500 29.0 16x106 58.9 51.7

TABLE 3 —Continued Engr. True True Hard- % Tensile Yield Strain Strain Brkng. ness Elastic % Red. Material Strength Strength Energy Energy Stress (BHN) Modulus Elong. Area CopperNickel 1 (As Rec'd.) 87,300 77,000 6,100 13,200 87,400 162.0 22x106 4.5 15.4 CopperNickel 1 (L.H.Trt) 57,900 20,000 3,100 36,200 85,900 76.0 22x10 34.9 43.5 CopperNickel 1 (H.H.Trt) 53,300 18,000 16,300 21,800 70,500 56.0 22x106 34.4 34.4 Copper OFHC (As Rec'd.) 53,400 49,500 3,100 11,800 85,600 104.0 17x10 6.2 19.8 Copper OFHC (L.H.Trt) 31,500 9,500 13,900 26,900 54,300 66.0 17x106 51.3 48.5 Copper OFHC (H.H.Trt) 30,700 5,000 6,100 11,800 43,200 15.0 17x106 32.5 33.2 Nickel 1 (As Rec'd.) 93,100 82,000 3,200 8,300 99,100 173.0 30x10 3.9 10.2 Nickel 1 (L.H.Trt) 50,500 13,000 18,300 48,300 92,700 55.0 30x106 43.8 51.6 Nickel (H.H.Trt) 48,700 7,000 16,100 40,500 79,500 45.0 30x106 41.8 49.7

102 reduction in area after plastic deformation begins and the resulting higher values for the true breaking stress and strain. If it is assumed that the volume of the necked section remains constant, then for non39 uniform strain: t =- n i =n (V/A)/(V/Ao) In Ao 1 A o which can be written for a circular cross section as: Et =2 In do d Similarly, the exact definition for the true stress, based on the actual area A rather than the original area Ao must be used to take into account the necking phenomena: = P/A The rest of the values listed in Table 3 are rather commonly reported values and need no further explanatory remarks. Typical grain structure photomicrographs and chemical compositions are already listed 39 elsewhere. C. Specimen Preparation The test specimens are milled from sheet stock and then the 0.060" x 0.750" surface to be exposed to the cavitation regime is metallographically polished. Figures 50 to 56 show typical roughness profiles of the surfaces before exposure to cavitation and serve as

103?......~i:i::::::: L:(~ir~~::.:i:i'i-':ii ~:::~~~~~~~~~~~~~~~~~~~~~~~:.....0~~ ~':.1 i,:: i: 0O 1"'.:~..........''.....:.: ~::~X V 0 X; -::::::::::i::Ei::::946S:..:: t < @ t > S Q E. ~?:;:::::::!?::......... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... < ~pe:n............31... - t: O'.!!i?~~:i'.. i.:ii.1,: i.lf:::::::i;: surfaco;~ve>> charactristic Aof spe~cime Nos. 39-1 (100 cabo s tee) 13 ~dio2 <X~-Fs Tn i ils i sp-stel) iii~% 4:: ii;. i i! ~:ii.. iiii _ 12 _ t::~~!,!iiii,:. f 0' S 0t.::i!i i _i Fig. 50. —Photomicrographs and proficorder traces of original surface characteristics of specimen Nos. 39-1 (1008 carbon steel), 13-F (Tenelon), and 188-3 (304 stainless steel).

104 X'' ~'?...................................................................:7............:.::.:.......... /:~':?:'..-,.:;:: i/ Specimen No. 10-A'Teie:.,'Q~,.:,::;_.l —-:: ~: --- - - ----------------- ~ ~ ~ ~ ~ ~ ~ ~ -~ —-~~............ S pe c imen 10. - i....~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......,":~~~~~~~~~~~~~~~~~~~~ tii'................................................ i..............'"::: ":........................... ~..........-..........::.:.:.:.~' ~...........'.:'......:,........................::.................:..I-, —,","..:.:.............\.\.......:::: ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........... c........... Specimen No. 9 E H....................'i:~~~~~~~~~~~~~~:: htni(ranhqsn rfnrp fnp fnlg-q

105..ii j ~00 ii Oi:i: ['ia:: i::':: ii;i: I::~:: ~I!>/i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ii i:~:::: i:~g ()!i:~!:70 i:~ i:> i i:~i~i /rl ~":I /-, t.i?; / I.......... 0 jill~~~~~~~~~~~~~~~ ~ ~~~~~~ ~~ iii: iiii/Jl:::~ii~iiiil/i:ri,:........... S eC I~n ubr --.........: ~~~~~~~~~~~~~~~~~~~~~~~~~...........?..........................................:?~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:,..........?:: / i.................................?::~~~~~~~> <:~:........................:::..:...::.:::~'~:! i:~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.........................................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.:i!:..................... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..?...................... r I`::e~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~::..v:?::.......... ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:..................... —........... ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~~~y:/.........................................:Spe.c~imen: N:.=...b, 1::4:2.:~~ ~ ~ ~~~:ume 1:54.~2 — $ I:: ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~:.................:...................................:::.::.........::::::::::::::::::::::::: surface chaatrit of secie Ns 23-2 (1 0- Almnum,7(202-T35 Auinm,142(01T5 Auinum)

106 00 I~~~~~:I"~:".s_;...........:~: -..................... i "'?.........:'........................ i~1........................... 5"':,'/ ~....... _.... __-._..............................................................................?~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~........ eca-men_.i'?3 ---- ~. ~x~~:::................................................................................... ~,.........................................................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............ S,~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ C " -............. c imen o 1~~~~~~~~~~~~~~~ ~. 4 I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: ~~~~~~~~~~~~~~~~~~~~...............................!............................!................:..............................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.............. i{i....................................'. i i: i S............................'rri~:.T 5 I - -- "p-" e9. i ii~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......:f~~~~~~~~~ ~~~~..............~ i..... ~::~ iC:i' P ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:....:;..._.,__1~........,,;,,._-l....l:.,.:: j j. ~~~~~~~~lr5~14 61 Fig. 53. —Photomicrographs and proficorder traces of original surface characteristics of specimen Nos. 34-cz (as rec'd brass), 104-cz (low heat tr. brass), 258-cz (hi. he. trt. brass).

107 X-03 A.................... E_............................. EZP a...:....... 0: F, 0 i~~~ ~ i-~:c,~-~~-;: x!~~;- ~::Xi~ ~...oo' - ~':.:.'.:~x x..I;..;.......;......:.:...~;~.~.....;.......:.................................. Z.:k:~:. ~........'Si'"...;iO'"!,.!O!-. i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!": ~,:. S~pe cLinen N o. t'- cu i:~: S p e c i m e n N o, z- - c u.........................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;~..................................::.........~ MP -IROCORDER,:........ A.ii'i: $.....:;~~~~~~-;;~. ~- 1 ~~ t~................ i~~~~~~~~~~~~~~~~~~~t: ii; i. ~ ~ ~.:,:::~~::,~.....................~............:.............' 8~~~~~~~~~~~ i ~~~~~~~~~~~~~'I'1 ~i::............. i'j ii.'...........S'""i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~p'e":i!C imen....NO'........2'21'"'"C":i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~n:il!i' i~~~~~~~...................11 1 I...............................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i.:..~............................................................~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~!.::............... ~::::::::.::............':.........~-*-...........'.;...................... ~!~...........................................................:'i~ ~'!~:'~::!~:::: ~::':!; i:.~i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i~............~....... Fig. 54. —Photomicrographs and proficorder traces of orig2inal ~~~~~~~~~ ~I148-c u ~:~ (lo hr. tr.copper, 221 —:-cu (h-i. hr. rt. cpper)

108.001~~~~~X................ X:z i::I: X: ~ i~ N E`...:.:.... ~...:.. (.]....:}:i:..i2:X.:.....::......;.:........ ".......................:......'....~[....~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... ~~~~~~~~~~~~~~~[......... Spoecimen k~ 6C~~~~~~C::i Fig. 55.. —Photomicrographs and proficorder traces of original..:" ~............................................................:,,?........................... $ pec imet N'o. 6 9- cn surface characteristics of specimen Nos. 69-cn (as rec'd copper-nickel), 149-cn and 223-cn (low and high heat trt. copper-nickel)

109 */00 1 P R TOFF.- CT................................................................i-r:::...;....:...._. ~,..,.;.......,.l,,:.,,....:...~._ ~~;~-~~~~~;-:~~:~:;~-~~-i —i...................................T.....:..:.i.................................................::,~..1.'...........?'''::,~"~ i'x..!i:::~ii;:: [..'Z.~o:'~ o,.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.................!: ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...........: i...........................'..........................................................-.-..- i................................................................................................. S-Dec imen No. 175n i 164 f~~~~~~~~~~~~~~~~~~.f i~~~~~~~~~~~~~~~~~~~~~~69':!?~':::~'eno.1~-Jii~.......... ch:'~: ",:'S'"'p e'C imen No............. icel) 9(low ht~~~~~~~~~~~~~~~~~~~~"0..........i"'!?") 17-' " n.......... h. r.! nikl...............~:

110 reference surfaces for the detailed proficorder measurements after damage, discussed later. D. Typical Damage to Specimens in Mercury Facility Full surface photomicrographs of specimens representing all the materials tested were taken at a magnification of 40X to determine the pitting distribution for comparison with the high-speed motion pictures. Typical photomicrographs for several materials are included (Figures 57 through 61), illustrating the general pitting pattern on the polished (labeled in Figure 6-a) surface after exposure to "standard cavitation" in mercury in the two-specimen symmetrical (180~ separation) stainless steel venturi for which the damage correlation was made. The polished surface is only about one-eighth of the total wetted area of the specimen so that the weight loss derives from an area eight times larger than this. However, the other surfaces are not as suitable to photographic studies or metallographic polishing, and hence surface traces have been limited to the polished surface. Figure 57 for Cb-lZr shows the typical damage pattern for this case at three stages in the damage runs. The larger pits and the more intensely damaged area is on the rear fourth of the specimen where the high-speed photographs and electrode specimen investigations indicated essentially a pure fluid environment on the surface. In the limited time samples taken there was no indication of vapor or bubbles in contact with this portion of the surface. However, from an extrapolation of the data from the motion pictures (Figure 43), it would be estimated that there were still on the order of 10 times

.....................................................................................................................................................................................................................I........................................................................................................................................................................................................................................................................................................................................................................... I............"."...."..,.................................................................................................................... -........... I.........................................I..................................................................................................................................................................................................................................................................................................................................................................................................................... M.,..........................................................................................................................................................................................................................................................................................................................................................................................................................I................................................................................................::.:................................................................................................................................................................................................................................................................................................................................................................................................. I..................................................................................................................... ----------------- --------------------- MEE --------------................................................. --- --.......... ---------- ---- - ----- ------------------- - ----.......................................................................................................................................................................................................................................................I....................I................... I..................................................................................................................................................................................................... -......................................................................................................................................................................................................................................................... I..,..,.."......,...........,.,...,...'I......................................................................................................................................................................-................................................... 1..1....................................................................................................... - 11.1.............................................................................................................................................................................................. ----------------------------- - - ------- Flow Direction Fig. 57. —Full surface photom'crographs of the pollshe4 I 2. mercury cava.Itation damage test of (a) spec. No - 10-Cb-lZr at 0 (c) 3-Cb-lZr at.150 hours.

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........................................... --- --------.................................................................................. X -:-::;:-:-:-::-:..::............................................................................................I...................I................................................................................................................................................................................................... -------------------------------................................................................................... ---- - ----- -- --- -- - - - - -------.......................... ----------................ -------------------............................................................................................. ----------.................................................................................................................................................................................................................................................................................................................................................................. Flow Direction ( 59. —F-,;Il surface photo=' a -pi s o f the Icrogr a 2. Itation damage test of (a) 177-3, 304SS at Ohours, mercury cave

(194 --------------- - - ---------- - -------------...... -............... -----------...................................- ------- - --------.............. --- - - ----------------------.'Flow E)"irectiorn, tb) Fig. 60 — Full urface p,' oto=icrographs of -he polished I g S -'tatio-z't damage test of spec. No. 8-B, Ta-8W-2Hf, (a) mercury cav2.

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116 as many bubbles adjacent to the surface in this region as there are pits. The row of smaller pits along each side of the polished surface is typical. This is in the region where a cavitating wake of small bubbles was observed on the surface (Figures 36 to 39)~ It has been 48 previously noted in many cavitating tests in turbomachinery and rotat49 ing disks, for example, that flows involving considerable vorticity, as this "wake" from the cor'ner of the specimen are much more damaging than translatory flows. This is confirmed by the present observation since the wake, even though it exists in a low pressure region, does create considerable damage. Figures 58, 59, and 60, typical for carbon steel, stainless steel, and Ta-8W-2Hf, respectively, also show the same pattern. These photomicrographs are for a duration for which the damage consists of individual pits, i.e., prior to significant overlapping, so that the formation of individual pits and craters could be investigated. 40 As pointed out in an earlier paper from this laboratory the evidence is very strong that these are single-event failures, randomly located. Their shape and appearance does not change with additional exposure until overlapping becomes predominant. Pure nickel in three different heat treats were also tested in the mercury facility. Figure 61 shows the resultant damage. The visible appearance and the fact that these specimens exhibited large weight gains after exposure, comparable to the weight loss exhibited after baking under vacuum, indicate that corrosion was closely coupled with mechanical cavitation damage for this material in mercury~ Since this

117 is not the case for the other materials, it is not reasonable to include the Hg-nickel data in the mechanical properties correlations to be considered later. E. Typical Damage to Specimens in Water Facility While some full-surface photomicrographs have been taken of the water-facility specimens, generally smaller areas in regions of probable maximum damage, have been photographed at larger magnification. This reduced photographic coverage was necessitated by the very large numbers of test specimens used in the water test program. Figures 62 and 63 show the propagation of damage on the polished surface for tenelon and Cb-lZr respectively, up to a duration of 100 hours, Figure 64 shows the respective damage at 100 hours on the three heats of nickel, and Figure 65 the 100 hour condition of stainless steel, Mo-1/2Ti, and the coppernickel alloy in the "as received" condition. Individual photomicrographs of the pitting damage in both mercury and water are presented in the next section at much larger magnification, along with the proficorder trace data, and comments regarding the individual pits will be reserved to that section. F. Comparison of Damage Pattern to Pressure Profiles Referring to Table 1, the suppression pressures (i.e., pressure above vapor pressure) are tabulated for the conditions corresponding to the photomicrographs previously described for mercury and water. It is noted that the actual suppression pressure gradient is almost identical

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...................... ------------------------------- -- - --------------------------------------------------------------------------------------- - - ------------ - ----------............ X............ X........................................ I X.:.......................... a.................... a.................. a X:................................................................ d............. a............... da............................ x:%xx: X................d: M i;.................................................................... ---- ------ - --- - - - ------------------------------............ -............................................................................... A.'Cyclical:, X x:in dividuals......... X:................................................................. aided..........:.fg-.......... X.................................................... -r low Jilrection F Jt ZIS 01. 2-4. 63. alkali S=Zace P' otomicrograpn. he pollishecL water cavitation dammage test of spec. No. 2-Cb-12r at (a) 0 hoti

17 - W.... V............ 1-Z................................ tx........................... -------------........... M......................................................................................................... -gi...................... ----------------------------------------- ------ ------...........R............ Flow DI' reeltion t S 64. —',Rull surface paoto=1crograD.111S Oz.,e .ec water cavitation damage test olA_ spec. No. (a-) 10-ru at luv nouz 170-n..;.i. at 100 hours,

.............. ----------- ---------------------................ -- - --------------------- - -- - - ----- -----------................ ----- - - ------ WPM......... It Rk,.................................. - - -------- ------------------------ ----------- -------................ iow M-I-ection' Fig. 65. —Full surface photomicrographs of the polishe water cavitation damage test of spec. No. (a) 139-3, 304 SS, at 100 hou,-rs.

122 for the three specimen symmetrical arrangement in water at 200 ft./sec., and for the two specimen symmetrical arrangement in mercury at 34 ft./ sec. However, the gradient for the two specimen unsymmetrical arrangement in mercury for the same flow conditions is much steeper, as shown earlier by the pressure profile figures, and later in Table 5, and the actual pressures on the downstream portion of the specimen thus are higher. This latter case has been found earlier to be considerably more damaging than the symmetrical arrangement as used herein, indicating that minor flow geometry changes can result in major changes in damage rate. Although the pressure distribution on the specimen surface is similar for the two symmetrical arrangements in water and mercury, it is not possible with the present state of knowledge to draw any conclu2,42 sions concerning the expected damage. Theoretical analyses show that the same collapse velocities would result if the driving head were the same, i.e., (P-pv)/p, neglecting for the moment the relatively minor affects of vicosity, compressibility, surface tension, etc. Hence, for these conditions, the collapse velocities for water should be greater by roughly a factor of 3.5 (proportional to square root of density ratio). In addition, for the same collapse velocities and equally compressible fluids, the force exerted on the adjacent structure would be proportional to the density ratio, being a factor of 13.6 "This is an approximately valid comparison for water and mercury, since the sonic velocities are about the same in the two fluids, and hence, for equal collapse velocities, Mach Numbers would be the same.

123 greater for mercury. Thus, with this simple approach, one would expect forces applied to specimens in the mercury system to be about 3.5 times as great as in the water system under these conditions. What this would mean in terms of volume loss to the specimens is not easily determinable. Actual across the board comparisons of damage on five materials tested in both systems for the specified conditions shows the damage in mercury to be slightly less than that in water (Table 4). This does not evidently agree with the simple theoretical approach presented above, indicating that a much more complicated situation exists. In the water venturi the visible cavitation cloud extends to the rear of the specimen for this condition, while in mercury it ends at the center of the specimen. The difference in appearance are at least partially due to the slightly different geometries (2 versus 3 specimens), and the fact that only the boundary layer is observed in the opaque mercury. These two conditions with their similar pressure gradients are the most damaging respectively in the two systems (Figure 27). Comparable data exists for water at two lower velocities, and these are also presented in Table 4, where the comparison is made to mercury. There is a small velocity effect in the water system, showing a damage increase by a factor of about 1.75 with a range in velocity of about 3, i.e., 65 ft./sec. to 200 ft./seco This is in agreement with earlier results 40 from this laboratory which indicated very little effect of velocity on damage in this system for this cavitation condition. It was reported in this earlier work that there was a factor of about 100 greater damage produced in mercury than in water. Th4is observation was based on a

124 TABLE 4 COMPARISON OF MERCURY AND WATER DATA Hg Damage MDP(mils) H20 Damage MDP(mils) H20 Damage at 50 Hrs. (34 fps) at 50 Hrs. (200 fps) /Hg Damage Material 2-spec. 3-spec. Ratio Stainless - -2 Steel 0.277x10 (6)* 0.527x10 (27) 1.90 Ta-lOW 0.17x10 (2) O.lllx10 (3) 0.65 Ta-8W-2Hf 0.847x10 (2) 0.762x10 (3) 0.90 Cb-lZr 0.179x10 (2) 0.203x10 (3) 1.13 Mo-1/2Ti 0.210x10 (2) 0.997x10 (6) 4.75 Tenelon (USS) 0.186x10- (2) 0.220x10-2 (6) 1.18 Overall Average 1.75 Hg Damage H20 Damage Material (34 fps) (97 fps) Ratio Stainless Steel 0.277x10-2(6) 0.377x102l (3) 1.35 Hg Damage H20 Damage Material (34 fps) (65 fps) Ratio Stainless -2 -2 Steel 0.277x10 (6) 0.277x10 (6) 1.00'Numbers in brackets after damage value indicate number of test specimens for which damage value is averaged.

125 different test specimen arrangement than currently used for the mercury tests. The two-specimen unsymmetrical arrangement was used for these tests, and in addition the mercury contained trace amounts of water. Evidence exists that the "wet" mercury is somewhat more damaging than 50 "dry" mercury. The current investigation was conducted in dry mercury for a two-specimen symmetrical arrangement. The wet mercury two-specimen unsymmetrical arrangement was analyzed in terms of the pressures on the specimen surface during the current investigation, and the comparison made with the current arrangement. The results are shown in Table 5, where it is observed that the suppression pressure (pressure above vapor) axial gradient is very much steeper for the earlier system. This indicates that more damage would be expected since the available head for bubble collapse is much higher, particularly at the rear of the specimen, thus giving rise to more energetic bubble collapses. In addition, a crosswise pitting pattern was observed, indicating local cavitation as the flow crossed the specimen edge, due presumably to the nonsymmetrical arrangement. Thus, for this system, bubbles are carried into the high pressure region and very violent collapses afforded. This does not occur in the symmetrical arrangement because if the pressure is raised to the same levels, no bubbles are present on the damaged face. The present comparison does not mean that identical degrees of cavitation with the same velocities in identical systems, in one case using water and in another mercury, would produce approximately the

126 TABLE 5 ACTUAL PRESSURE ABOVE VAPOR PRESSURE ON TEST SPECIMEN SURFACE FOR STANDARD CAVITATION IN MERCURY FOR TWO SPECIMEN SYMMETRICAL VERSUS UNSYMMETRICAL ARRANGEMENTS Pressure above vapor Velocity No. of Spec. pressure Fluid ft./sec. Specs. Tap No. Run No.1 Run No.2 Run No.3 "Dry" Mercury 34 2 1 1.7 1.7 75~F (symm.) 2 4.9 1.7 3 9.5 5.3 "Wet" Mercury 34 2 1 2.2 2.1 2.0 75~F (unsymm.) 2 12.3 16.8 19.3 3 41.3 39.8 40.8 same damage, but merely that in this particular case, about the same suppression pressures between water and mercury on the polished surface, but with a considerably greater velocity in water, have produced about the same damage. Since the pressures are not known on the sides of the specimen (which provide about 88% of the exposed area), and since the geometries in the water and mercury venturis are not identical (3 versus 2 test specimens), the present data cannot be regarded as a generalized comparison between water and mercury damaging capabilities anymore, in 40 retrospect, than the previous tests which indicated a factor of about 100 between mercury and water. Unfortunately, the physical limitations of the systems are such that a direct experimental comparison cannot be made. Eventually, however, such data should be provided by the vibratory facility tests also being conducted in this laboratory. Ideally,

127 if the cavitation condition, velocity, geometry, and suppression head are identical between the two systems then, assuming that the compressibilities of the two fluids are also similar, the forces exerted on adjacent solids should be proportional to the density ratio (13.5), so that the damage from mercury should be much greater. At the present, there is no real evidence to contradict this expectation. However, it is quite evident at this point that seemingly minor changes in flow geometry can have important effects on damage. G. Detailed Examinations of Damage 1. Mercury Specimens Typical areas from the heavily pitted regions of each material were traced with a precision profilometer ("Linear Proficorder"), at a horizontal sensitivity of 1000:1 and at a vertical sensitivity of 50,000:1. For each specimen several crosswise and longitudinal (in the direction of flow) traces were made at intervals of about 0.5 mils. Due to the extreme sensitivity used, very precise leveling of the surface was required if the trace curve were to remain on scale. This was accomplished by a built-in adjustment on the machine, and the specimen was incremented by a micrometer table adjustment made especially for this purpose. After tracing, the specimens were examined with a metallographic microscope at 500X and photomicrographs taken of the area *Micrometrical Division, The Bendix Corporation, Ann Arbor, Michigan.

128 traced. The trace marks left by the diamond-tipped stylus were visible, with the use of oblique lighting techniques, very clearly in some cases though not so in others, depending on the hardness of the material. The edge of the specimen is a good reference point, clearly indicated by the dropping of the stylus, which facilitates the location of a particular pit on the photomicrograph. Also, it was possible to visually observe where the stylus had passed through a pit (by the trace mark) with reference to the pit centerline. Figure 66 shows the procedure in complete detail for matching the traces with the corresponding photomicrographs. In general, it was not necessary to photograph the entire length of the traced area, as only those areas of interest could be located. This was accomplished by a micrometer adjustment on the metallograph by which the specimen could be indexed by.001 inch increments. Thus, once the end of the proficorder trace was located (the end where it dropped off the edge), it was only necessary to index back along the trace by the amount measured from the end of the trace to the pit from the proficorder trace. Due to the size of the pits examined, the sensitivities used and the random location of the pits, roughly ten to twenty feet of chart paper were required per successful pit trace. Figure 66 shows six transverse traces, spaced apart by either 0.5 or 1.0 mils, and covering almost the full width of the specimen for carbon steel tested in mercury. Since the stylus had to be started on the surface, the full width of the specimen is not covered by the traces. The corresponding photomicrograph is at slightly smaller magnification than the trace, so that the arrows are necessary to indicate the correspondence

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131 between pit and pit trace. However, in the following figures in this section, each of which cover only about 8 mils in length, the correspondence between pit and trace is obvious since there is only a very small difference in magnification and the width of the area covered is small. Figure 67 shows the areas on the polished surface covered by the proficorder traces. To compare pit sizes and shapes between materials it was necessary to trace all specimens in corresponding areas so that regions which had been exposed to the same cavitation flow regime would be compared. Figures 68 through 81 are photomicrographs ( /-J 500X), with the corresponding proficorder traces for the mercury specimens. A careful inspection of all of these figures indicates that generally the individual pits are very symmetrical and are surrounded by raised rims, i.e., they are "craters." No preferred orientation has been observed for the raised rim formation, i.e., it occurs on all sides, upstream and downstream, as often as not. In Figure 69, e.g., the surface area around the individual pits clearly is raised into the form of a rim, as would be expected from a central load in excess of the yield strength of the material. This type of pit formation, presumably due by its symmetry to a single bubble implosion, is very prominent in this investigation in mercury, although sometimes obscured by the damage in adjacent areas. In only one case (Figure 77) was a fatigue-type failure observed, i.e., grossly nonsymmetrical failure, presumably due to many blows of reduced violence. The "fatigue pit" (trace #1) is triangular in shape and has a raised lip on the downstream

132 Nose Numbered Side Flow Direction Axial traces taken in this area and direction Transverse traces taken in this area and direction Tail 1697 Fig. 67. —Schematic of polished surface showing areas covered by transverse and longitudinal traces.

133 Trace #3 Tra c e #3a Trace __* 11 IS 1111e D irection11 i ~,~:.............;..... Trace #1 4 5 A 1 i(VHE1 3 Trace #3o s 1 2 t':1' lj..lJ.::. ~.: \1675 Trace #4 Fig. 68. —Photomicrograph and corresponding proficorder traces of surface of specimen 11-F (Tenelon), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

134 Trace Direction, Flow Direction,0079" Fig. 69. —Photomicrograph and corresponding proficorder traces of surface of specimen 22-SS (304 stainless steel), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

135 IZO~~~~~~~~~~ PART1 > 23-SS 07.0 1PRKQQ1-:.E% I~~~~~~~ I Trace B~-~~~;:~;~ ~~;~.i~-\; ~~~~ ~~- ~~~~-~;-.-~;~; —~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-~- -~:;~;~~;;~:-~;i~~ ~.~~~~~~~~~~~~~~~~~~~~~~~~~~~............................ I''~' Trace Direction..................................; ~ ~~~~~~~~~- I ~ — ~~I —- —; i..... ON Fig. 70.- Photomicrograph and corresponding proficorder traces of surface of specimen 23-SS (stainless steel), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per seonnd.

136' 0001.....................: 5 Flow Direction — s —Trace Direction s -— u t r-q 1, it —qJ-in " nItf- - -11- -4- - -—'- - -' / f.. -:; e.::,!.::!.: v...;' > e Fig. 71. —Photomicrograph and corresponding proficorder traces of surface of specimen 4-Cb-lZr, after 50 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

137 \ \ a~~~~ i JTrace.1 i~~~~ \..:................................. "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.,.. -.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~...........:: i:. ~::'..................'low:,Direction....... ——. t Ii i ~~~~~~~~~.. -.".~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~-~-~~~~~~~~~~~~~~~~~~~~~~~~~~~~-~- ~ —~~i.....~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..............001~1 9....:;............................. 679............................;.~~.;. Fig. 72. —Photomicrograph and corresponding proficorder traces of surface of specimen 10-Cb-lZr, after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

138 ra-e #T................................... r;'e #1/..,..... it;.... Q,, X.,0., iVS....:'....,..,,...,'.,, F'ow Direction -';::. Trace Directiion -,,: _ --...........................! - n1680 Fig. 73. —Photomicrograph and corresponding proficorder traces of surface of specimen 10-Cb-lZr, after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

139.........'": S Trace #3.,.. Fow DIr ion.!i i.... -?::......Trace:5 _ " 168..??5 /'.:.::' Fig. 74. —Photomicrograph and corresponding proficorder traces caittin in mecr atatra eoiyo 4fe e eod j: Tr.e it3 i,o r; - ---.......c~t;~ cln. 1681. Fig. 74. —Photomicrograph and corresponding proficorder traces of surface of specimen 10-Cb-lZr, after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

140 ~~~~~~~~~~~~~~~~~~::.................................................,,!::: i:::::::.; ~~~~5:::' * *~~ ~ ~~~~~~ ~~ ~ ~ ~~ ~~~~~~~~.;........... i........................... V i.! 1682 Fig. 75. —Photomicrograph and corresponding proficorder traces of surface of specimen 9-A (Ta-1OW), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

141 9-A- L L7 ~ 00OO 79| I" i:..... ~~~:'' __.......:.....,... Tace #31 ard.. cvitt i. m r at a th tvec of 4 fe..............t p.....r i:!:;::.. "-.:: i:' i!'.............:.,.....'i'' S1683 Fig. 76. —Photomicrograph and corresponding proficorder traces of surface of specimen 9-A (Ta-1OW), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

142 -i~~ ~ X................ ~~;...~.```...~.......- - --— ~ ~x -.- q-~- ~~- -i~I~-~-~.I V~~-"~ —-~~~~~~~~~~~~~~~~~~-i 5 r i -:... -........ -...:::.......~~~~~~~~~~~~~~~~~~~~~~....................... ITrae #.... ~ ~~~~~~~~~~!:164........... Fig. 77;.;-Photomicrograph andcorresponding proficorder traces T urace -A r ard cavitation" in mercury at a throat velocity of134fr T. i-a C ef "i'Tr~~3ce -~~5~~.i.:ii......:.......... Fig. 77.-Photomicrograph and corresponding proficorder tae of surface of specimen 9-A (Ta-lOW), after 10 hours exposure to "sad ard cavitation" in mercury at a throat velocity of 34 feet per second.

143 Flow Direction Trace Direction.006" Photromicrograph of Cavitated Surface of Specimen Number 8-B as Described Below. xr~ 5/pna: X: F:. —- — i: i ~~ ~ V7/65 x!/ 8-B X 001 V.....................:I...........i.......:1........;.....:;...:,,,a,:.;,:. ~',,.ii::~..:,~:':':i::.::i:.~.:'.i:~::C:::~i: i:> iii.:.:i:. 1685 Fig. 78. —Photomicrograph and corresponding proficorder traces of surface of specimen 8-B (Ta-8W-2Hf), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

144 *' 5:.,;. ~i-''*'*.9!!?:'!i~, <;5v* *:..z ~'' iiiiN -..................0..:.......... 3-s X.~~~~~~~002.: *::::::.........-.-....... 5; >.............. Tr.ace'..#I::: /. @::?:-::........................:::,'.,.... lI............................................ Trace,,,,,5i,.:::5:......::........... J:~,':': > $i:V i:~~'':: 5 i': ~ ~ ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......:: ~ ~ ~~:'...::Trace'' - 2 ":'~ Flow~~~~~~~~~~~~~ Direction0 TraTe #...... - l 2:,,:E:; O~~~~~~~~~~~~~~~~~~~~~ Trace Deio /A Fig. 79. —Photomicrograph and corresponding proficorderI: traces of surface of specimen 8-B (Ta-8W-2Hf), after 10 hours exposure to It -::::: -'::'':::......:I "''' t ~ ~~~ ~ ~~~~~~~~~ ~:::. Fig 79-Poomcorp an corepndn proficre tracesD 11 of surface os p c mn8- ( T 8W2 f,atr1 0 hor exosr to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

145 Flow Direc t ion Trace Direct ion!C. 00791. I.': j'.'.. S..........; Ait:"9i X i...........'.. i........... *...........'..:..1.....''..'.;;'-~ 1687 Fig. 80. —Photomicrograph and corresponding proficorder traces of surface of specimen 8-B (Ta-8W-2Hf), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

146 Trace Direction and Flow Direction ~~~~~~~~ I ion~~~...................:~....-:....-.:.:.. —r:::: —:::::.:::..... _:......-.:::.::..:-:.:-.......~.......::::::::......~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~.......:.......~::::,,,~,............~.:::: —:....~~~ ~~~~~ ~~~~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~................ 911 1l1.111 ll~llllilll~-..113*Ilil........: I.... i.0079" ""~.........-..: -.s ~......::..-.~:. ~:::~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~......:::/:'C~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~':::E 9o~~~~~~~~~~~~~~~~~~'A- trace 21:::. il::.:':;,i: /:;:..........~.................................:j;:. i~ ~......,}:::......~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... ~ ~i:: l /:;.................. ~::.::,:.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............ ii~~~~i::1688 Fig. 81. —Photomicrograph and corresponding proficorder traces of surface of specimen 24-E (Mo-1/2Ti), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

147 side. This is believed to indicate a surface failure produced by fatigue action, which has loosened a slab, conceivably along grain boundaries, and subsequently the slab was torn away by the flowing mercury, leaving a raised lip on the downstream side. This type of failure was previously observed and described in tests conducted several years 40 ago in this laboratory. This fatigue type of failure has been observed only rarely for the mercury specimens. In many instances, Figure 76, e.g., the damage has the form of very shallow craters, as 24 perhaps first discussed by Knapp, for aluminum, and is thought to be the result of a single blow from a bubble collapse, which was not sufficiently strong enough to cause material removal. On the other hand, the other craters, which appear dark in the center and show a greater depth to diameter ratio on the traces, are thought to be the result of a single blow which was strong enough to cause material removal. 46 In an earlier investigation, where a few proficorder traces of this type were compared with microsections through the traced pits, it appeared that material was actually removed from such pits (contrary to 24 Knapp's guess), in that the volume of the depression exceeded that of the raised rim. However, the margin of error for such measurements was considerable. Since, on many specimens, this is essentially the only type of damage observed, and a measurable weight loss exists, it is further substantiated that material removal occurs in this type of damage. As already mentioned, this type of damage appears to result from a single blow to the surface, since the size and shape of these pits does not change with additional exposure, while numerous other pits appear in

148 adjacent areas. In the present study it has been observed that many times smaller pits will appear on the rim of larger ones, and even within the larger ones (Figures 69, 73, 75, 77, etc.). It is thus ver40 ified, as also previously reported, that the formation of pits in the initial stages of cavitation damage is a locally random process, and that gross material removal from cavitation damage, at least in the present mercury tests, is the result of many superimposed individual craters of this single blow type. The transition of this type of pitting to the gross damage often fcund in prototype equipment can be seen in Figures 78, 79, 80, and 81, where the craters are so close together that even at 500X, the distinction of individual pits is hard to make. To the unaided eye, this type of damage looks like a fog on the polished surface. Figure 82, typical of the nickel specimens, illustrates the interplay between mechanical cavitation damage and the associated chemical attack, which may be enhanced by cavitation. The shape of the damaged areas is about the same as the mechanical damage areas of the specimens already discussed, where there was very little, if any, chemical attack. The individual pits of the nickel are very much deeper than those previously discussed. However, there is no visible attack on the surface, other than in those areas where it was indicated by the previously discussed specimens that cavitation damage would be expected. Thus it appears that the chemical attack is accelerated by the mechanical pounding due to cavitation, and the amount of damage is greatly increased by the combined action of these interconnected phle;rcmena.

149 ow'Direction 5race: / 5 Trace Direction...............: a ii I X AW ( f,01639 Fig. 82. —Photomicrograph and corresponding proficorder traces of surface of specimen 13-ni (as rec'd nickel), after 10 hours exposure to "standard cavitation" in mercury at a throat velocity of 34 feet per second.

150 That the combined damage from corrosion and cavitation is considerably greater than the summation which would be caused by the two mechanisms 53 working separately was clearly demonstrated by Plesset in a vibratory facility. This general phenomenon appears to be very similar to stress corrosion as encountered in many fields. The depth to diameter ratios for all of the proficorder observations for which the tracer tip passed through the center of the pit are listed in Table 6. These ratios do not depend very substantially on type of material, being of the order 0.015 to 0.06 for most materials, and ranging as high as 0.09 for one particular material, Mo-1/2Tio This lack of strong dependence on the material may be reasonable in that the variation of mechanical properties between the materials tested in mercury is not excessive. Presumably, if a very weak material could be included (or one weakened by a high temperature environment), the depth to diameter ratio would be markedly larger. This has been observed in fact in high temperature cavitation tests with potassium on stainless 48 steel and in certain particle or droplet impact tests where the depth 51 to diameter ratio increases with impact velocity. The larger depth to diameter ratios for nickel are presumed due to the combined cavitationcorrosion effects previously mentioned. It is again noted that the pits on the nickel are roughly of the same diameter as those on the other materials, indicating enhancement of corrosion in the area where craters were formed. The number distribution of pits versus pit diameter was also examined on two materials tested in mercury, stainless steel and carbon

151 TABLE 6 DEPTH TO DIAMETER RATIO FOR MERCURY CAVITATION PITS Pit Diameter Pit Depth Depth/ Material (mils) (mils) Diameter Tenelon (USS) 0.3 0.009 0.03 0.5 0.010 0.02 0.4 0.012 0.03 0.3 0.006 0.02 0.4 0.007 0.018 Average 0.024 304 SS 1.8 0.035 0.02 1.0 0.012 0.012 1.0 0.027 0.027 1.5 0.034 0.023 1.0 0.025 0.025 Average = 0.021 Cb-lZr (10) 0.8 0.037 0.046 1.5 0.035 0.023 0.5 0.017 0.034 Average = 0.034 Cb-lZr (4) 0.8 0.027 0.034 0.7 0.030 0.043 1.5 0.050 0.044 Average 0.040 Ta-lOW (9-A) 0.3 0.018 0.06 0.6 0.027 0.045 0.8 0.015 0.02 0.25 0.007 0.003 1.0 0.009 0.009 0.3 0.008 0.027 0.6 0.015 0.025 0.8 0.013 0.017 1.2 0.037 0.03 0.5 0.019 0.038 Average = 0.027

152 TABLE 6 —Continued Pit Diameter Pit Depth Depth/ Material (mils) (mils) Diameter Ta-8W-2Hf (8-B) 1.0 0.032 0.032 0.4 0.017 0.043 0.2 0.012 0.06 0.4 0.023 0.058 0.5 0.025 0.05 Average = 0.049 Mo-1/2Ti (24-E) 0.3 0.010 0.093 0.25 0.006 0.024 Average = 0.055 As Rec'd Nickel 0.5 0.115 0.23 (13-ni) 0.3 0.085 0.28 0.25 0.075 0.15 0.3 0.090 0.30 Average 0.22

153 steel, in considerable detail. Figures 83 and 84 show the results of this study, made at 500X. The maximum number density lies in the size range of 0.025 to 0.25 mils. As already indicated, the diameter of bubbles in contact with the surface ranged from -v 5 to -' 30 mils, showing that the pits are about 10 times as small as the bubbles. It is thus indicated, as expected theoretically, that the bubbles collapse to very small sizes before the damage is produced, or that the central jet produced from a nonsymmetrical collapse covers a very small area compared with the initial bubble size. 2. Water Facility Damage Specimens The general areas traced by the proficorder for the following specimens tested in the water facility and the general procedure followed is the same as that listed in the previous section for the mercury facility. However, one additional difficulty was encountered in the course of the specimen examination, in that the tracemarks of the stylus tip were not visible on most materials. Thus it is not possible to obtain photomicrographs of the exact areas traced in most cases. Typical photomicrographs at' — 500X and typical proficorder traces are presented of the damage in water for comparison to those for mercury. The difficulty in locating the tracemarks on the surface of the water specimens is believed due to the following: The surfaces may be harder due either to additional coldworking of the surface layers in water by the cavitation which takes the form of larger numbers of less energetic bubbles so that the surface layer is more resistant to marking

2500 2000 Z = Stecimen Number 173-3,(304 SS), Tail Section 1500 0 F-4 ~-4 1000 04 500 0 _ _ _ _ _ _ _ J _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~~~~~~~~~~~1700 0 0 0.1 0.2 0. 3 0.4 0. 5 PIT DIAMETER- D - (mil~s) Fig. 83. —Pit size density vs. pit diameter for stainless steel tested at "standard cavitation" in mercury at 34 ft./sec.

2500 2000'/I Ol l 1 = Snecimen Number 37-1, (1008 CS), Middle Section IY 0 2/ 1 l v= Specimen Number 37-1, (1008 CS), Tail Section H 1500 H 500 0 0.1 o.2 0.3 0.4 0.5 PIT DIAMETER D- (mils) Fig. 84. —Pit size density vs. pit diameter for carbon steel tested in mercury at "standard cavitation" at 34 ft./sec.

156 by the stylus (evidence of such an increase in surface hardness has been observed in this laboratory). Also, in general, the pits are more numerous and the surface correspondingly more roughened, making location of the traces more difficult. In mercury, individual pits are more predominant in a rather flat surface. Figures 85 through 90 are photomicrographs and proficorder traces of typical damage areas on several materials from the water facility. As mentioned earlier, the damage consists of pits which are elongated in the direction of flow on almost all of the materials. Also, in general, there is a predominant lip on the downstream side of the pit, due presumably to the application of a force slanted in the downstream direction. In addition, it was observed (Fig. 88, e.g.) that transverse traces exhibit no preferential location of the rim, i.e., the transverse traces show predominantly that a rim is present either on both sides of the pit or on one side or the other in essentially equal numbers, thus eliminating the possibility that the rim indications are cue to peculiarities of the tracing mechanism. These observations are consistent with the earlier discussed damage mechanism consisting of an unsymmetrical bubble collapse with the formation of a jet, oriented by the flow into a partially downstream direction. The depth to diameter ratio for the water cavitation pits has also been tabulated from the proficorder trace data, although it was not possible to determine whether the stylus had passed through the pit centerline or not, due to reasons presented earlier. Howavever, enough pits have been examined to give a good statistical indication of the

157 ~~~~~~~~~~~~~~~~~..............:........ 1716 Flow Direction — Trpce Direction-........... ~..........?~~~~~~~~~~~~~~~~~~~~~~~~i::: i~ /"::,:/:~: ~~~~~~~~~~~~~~ ~ ~~~~~~~~~...............:..............?:.001 \J Fg 85 Tpcl htmcorp and.~~~~~~~~~~~~~: typical a:xilpofc......!.::~:;. i - i. " i~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ tation1~~~~~~~~:' (a noeae'b)ti ra i"~~~~~~~~~~~:. ~: ~ i! ~;ii~....~.~~ ~;~I i ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:..:. ~~~~~~~~~~~~::.~`':~~:~~: ~.:.~:,~,......,,.....:. —yia................................... —a axa_..fior traces of cavitated surface of specimen~~~~~'o.'193(0 S fe 0 Faig." 85-Tyal phtmogrps and, b typicl axap r forder

158 Flow Direction Om m..'xx,~ ~ ~ ~~~~~~~~f.-.1 -:,~~~~~~~~~~:I:.: -,.:':':':~:l-:Wll?:~j::':',;:i:'':'::::'::::':!"-,.:: 1. 1,::,... I —,: - *:::.1:':.".. ".:-:~iii,;::: i- i~~i i ~ii~~'~.ii:i;::~:::-(:~~:-:-:..::I:::~:j:l:-(j.....i,~~~~~~~~~~.:i —-,:]..:i~i ii'';li:'' j:.",. -.1,:: i::::i::.::ii. ii-, -..j ii' -'':".'':':1:..:: 1-:ili:.::~~m,,: i "'-::: ii;~,~:::' Vi`:L~'*.....,p:,:,:- _~.l;.r: I..:: ~:: ~ ~::::.:::::.::.::lix:: 7,::I ~ ~ii.. -- ". "... 1 1-. -.. 1.1::... -:::i Wi-:W " k i'i::,i::::.:::':::iI:"i~i,;:~: —,:~i i;:''"I:::.::':.:.I ii~i,':.:..li.': i''.~ "I I'll",:: 1 A ll -, - I... i~c::::::i... ~'::!:::i::i;:i'i::''':':I:(.!::,': ii:::i... I:':i:,-11: 1....-.:::...I.... P ". I...... I...,.':i.. -: Ii~::::i'i.:::....:..::!:i: i~.:: -,.l..-,~''..-..... I.':::'. I. "..', I:::'::::.x.,::,iiI'''.il:::::ic::`I:-.::_: i::~:i: l..::''"' —.'::::::i:::O::.::~i:~ iii i,ii:ii::i2:: -'-".:::::",,, I..::::- I~~~~~~:Ii~i —:::: 1~.1. I., 1,,:,:::i~.~!:!,i: iiii:i;`! —:~ i::- iii::, i::::~:::::::.::]::::: ]:::.:: Ii " I. -1.- v: I::i.::i.:-::iti.:ii: ii;sl:i-,-,j..xx,::.~;il:iiw:x i:::r "::.:::- *': cii:"'''::::':,, "i:::':~ —-- -I I~i ~:_i:l:x:!- %::::;:;':: -. ". I -::: -.::-,:::::::,.'_.I -11-X..:,.,i.....-,1...:j.I....''. —, —..'.....,. -I.: -:::X..-:,::%:q....::~~:::i;,~:..'..Il:, 1,.....I.:: 111,...I I I 1. 1.11 I I I,. I::i,.:l',i':- ~: ~ ~l,.,-i-,:::;:::: i -,.:,1..:.-:..". ~~~...::! -~~~~~~~~~~~~~~~~~~ I-l-'..''...I~~~~~~~~~~~~~~~~~~~~~~-:. -::: l:i'.::':.:l":...:,:. 11: 11.1:,.-. -.-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,:.::-:::: -:v:...: 1:~.-.' ~.:.:.". j".::::::,: -:,-,... -::, -.-,.1 ~, -1-... I:1,,...I -:..:x:.:..... -!.:::::, _:::..,: I - I. I,..V I:,~Y:ri'',,,;:: i x. -:,:::.. -,. -.`....:,:I-:I - 4:.,:i:mi-:;::::!W:.1.... 1...., I."'."'"...l'.....,,....:: I. 1 1: I:- 1 W -,.:i,.. I I - - - -. I z. ": _..'.I..''.::.:c:::_::.:':.:.. ] -. -, " 1- - -.-.. -, 1.,'..,. ~~,-.'-.,::.~~:"::-.:~... ~ ~ ~ 1. 1- -::: v -::A::,::':i*i' 1,I:.11, - 1 I:..::.::A::.:;:. -. - 1, I.-.,:-. 1:.- -:,.,,P:].:-1- - -11... ---- 1 I,,:::...- -::: I 11.1-II.''I-: —.:,:::::ii::: "l'....,.,..".,..~~~~:~~~~~~~:~~~:~:~:]::..,:'I 1:." -::-:::: I -, 1, - -, v -1- 1.1.1, 1.1-1. I.'...:_ _.'' ~ ~ ~ ~ ~ ~ ~~~~~~ I.. 1.:-::~~~: 1. 11,", -.11~:i::: I., --:-:::,, 11 -—,..-,,,I.I..-l.... -XI. --,:~:.-. I1.1....,. -x. -,:. ~::~: - -:. -..- -:. I I.:: Ie.~"~.".,~.,.~'.."'..',, -.- 1-: I...-1.,,"'l i::..,.,-.. ~., - I -,...''., -.,.-I l ". - -.1 1.. -, -- ~. ~ 1- -.. m -l,-. - -, i.1.1'.,....!.::::!.-. —-.- -: —: I m —:l,.-, — - 1..:::.:..: II-II..: 1..1.-,ll.,.',....lI:1."..-I 1. 11.. 1.' —:I 1. i i. - W, - -.'.".1 1 - -......:::: - 1-1.1,~:::-:::i ]: ~ ~:~-~:.,xv I:::::. 1-.. 1.:: - - %:::i:: -....,... - w,,', I. 1. 1. -,: -::: -;.,. i,: BI I,. I I -,., 0:,. W,~. % - I.::: -::. _ _.:,: -. 1 ~~~;.:.., 1.- 11.1 I I1...~~~~~~~~~~~~~~~~~~~~~~~~~~~-.....::X.,..-I....- 1' —.. I.,.11. - ]... ~~~~~~~~~I~~i... -...... -:1-1.".. -.:-:.::~ ~ ~~ ~ ~~~~~~~~~~~~~~~~.11,-...ii ~:..'..'.., - -~ 1 1 -.._:. I'' 1 - l.. - 1. - - 1.,1, 14 - - Ij'i. 1.-,1.. 11 I -. - -:. 1,..- -:...'::: 1.:::.1::..,: -:::\:1 11. 1 1I,'...... - -:d.F:] i]ifm::x':,~,:,.::.,:., ~: -..,.:. l:-.. I...I.'..,".. -. 1 1 1 -.::: - *., I 1 - - I. I I...,:: I 11:1..,", ~ ~.,~:.~s,. ~. -... I'';.. I...,1. ~ ~,m:,,".-,,-...l... I... I.-...::: - -.'. W -'. -I.1 1 11- - - I. -1in w ater at::::'- o... I,.1- vv.-. II... I.....-l.-l-,d,"!:-,.on.1

159'i,::'........::: ":i....".... i:'..i ~ s: -":';' -: t;'s:'sh..... \: Flow Direction- Trnce Direction.-.-s..-.::: ~....'................ ~~~~~~~~~~~~~~~~~~~~~ *YN~~~~~~~~~~~~~~.: /?:'~.:!,;i...a.... ~\ }:; t'<.,>^s f i: " 4 E #.. i I,, J`.:~.. ~...... ~...... /'~ ~ ~:.' 2 forw "sadardavttion" (a) nos Tarea (b tilrea.:o::: v.. i\:: -:::::' -i -.: F-. b: —'.:; W bsS';'.:. F; f~~~~~~iw:, X; t L Y 0 17S'5~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~: Fig 8.-Tpclpooirgah an tyia axa prf ode trace ofcvttdsraeo pcmnN.2C-. Clmim1 Zicnim afe 0 or nwtra hotvlct f20f.sc for~~I "sadr aiaio"()ns ra,()ti ra

160 I t = -4 C)4 aj Q)~~~~~~C "4k ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~~~~~~~~~~~~~C "0: "t~ m ~o N4 4-4 o)C ) *~~~~~~~~~~~*<~~~~~~~~~~~~~~..... Q. CdU co w N4 CO47~~~~ ~ ~~~~~~ o -:: ~~~?ce'~~~ ~ " ~ -Iri j Q~~~~~~~~~~() CJ"Z.~ ~ I 0 0 10 00 u Q.,C) C4 41 p CQI) coE ~ (r N 0J.,::..-_ i:::::I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~i~ ~ ~ ~ ~ ~ ~ ~~ ii i i:- ti~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... COO Ii rl~~~~~~~~~~r C)-H U)4- 44.......... co C) -W'...,.f k ~~~~~~~~u i:, i', c: N~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ )r r~~~ CdC[)N cU k ~~~~~~~~~~~~~~~~~~~~~~~~~~~d cw~......... dc Ii b iIc04 "0 4iC) Cl IT" 0 N, $4 C 4 0 -vB~~~~~~~'- i I>..-...'~~~~~~~~~:i~~~i::iii~~~~~~~iii-'iilI:::i:;~~~~~~~~~~~~~-ii~~~~li::iji*:i iii i i: i: g B a o a,~~~~~~~~~~~~~~~~........... ~4-4 C4 d ~ ~ ~ 4JC'v-I aC) a) ~,;r N.........N.. ~~~~~~~~~~~~~~~~~~~~~'- C) i t 4 I 1~ ~;i0 r -en ~9~~:::ii::i'44 ~ ~:::::::~:i~ii:::i (NI~~~~~~i::o~

,Vale I-Fuj (q) cBalV aSOU (V~),,uo-T~jU-jTAP3 plVPuU~,, -101 3~s/'3 00g Zo JO IOIaA 3IoRxq3 e IV:~9ez U1 sanoq 00T aaq[e (iataiu -jaddoo p,oaa su) uo-8'oN uawioads Jo aoeucns pqeITAvo lo saouil aapiooijoad Ie!Xx TpoidKl pue sqdeajo ao-ood ijoodaoT -"69'~-c.~ G IL 1~~ r~ 12'lb'!!! i. i i!1!. i......'I.........!!! III II I I I I~~~~~~~~~~~~~~~~~~.......'...........~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~..... C) Z)aD - Z c lii 5...:i -i ~:::= Nei;i 11:t i~~~~~~~~~~ ~~~~::i:.::::ii ~i:::: I 1:::':~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~' TOW~~~~~~~~~~~~~~ XEZ ~ ~ ~ ~ ~~:: P00 e~nu*~~-~~ ~Oiii....... "i: iiii iiiii i Ill~~~~~~~lliN ~ IIIIIIII I II I I.........................~~~~~~~bii:::::.i.~.....~o;~.{>.;~d~eoea~ ~ ~~-e~'~.G ~o~ ~~~~~~~~~~~~~~:~~~~~~~~~~~~~~~~~~~~~~-t"~~~~~~~~........ ~~~~~~~~. ~~~~~~~I'['

162 Flow Dire tion Trace )irct ion —* t-' I Trae D irection'iji' I~aI I I/..'"........ traces of cavitated surface of specimen No. 85-ni (low ht. trt. nickel) after 100 hours in water at a throat velocity of 200 ft./sec. for "standard cavitation.'"

163 actual situation. The general range of values for this ratio (Table 7) compares quite closely with the mercury data presented earlier. Maximum and minimum values are 0,.06 and 0.01 respectively.- It is indicated in general that pits in the weaker materials show a greater depth to diameter ratio from similar blows, as stated in the discussion of the mercury data. The measured diameter data (taken as the length of depression from the proficorder trace) could be misleading, considering the elongated shape of the pits, since the direction of trace compared to the orientation of the pit is not precisely known in most cases. A detailed pit size distribution was made for stainless steel tested in water and is presented in Figure 91, where it is observed that the majority of pits on this material are in the size range below 0.1 mils, with no apparent lower limit. Thus, in addition to the overall volume loss being about the same for this particular combination of conditions in mercury and water, the individual pit sizes are also about the same and are distributed in similar size ranges. This would seem to indicate that the same type of bubble collapses are present in these two fluids, and that cavitation damage in general is not dependent on type of fluid other than as the choice of fluid results in different fluid dynamic situations during bubble collapse (assuming chemical effects are negligible). Such a change in fluid dynamic regimes would be expected in the present case between mercury and water under identical flow situations where, for instance, the suppression pressures present for bubble collapse would be higher in mercury if the same velocity were maintained due to the density difference, and the damage in mercury would presumably be greater.

164 TABLE 7 DEPTH TO DIAMETER RATIO FOR WATER CAVITATION PITS Pit Diameter Pit Depth Depth/ Material (mils) (mils) Diameter 304 SS 0.3 0.007 0.023 (139-3) 0.5 0.007 0.014 0.2 0.003 0.015 0.2 0.002 0.010 0.3 0.018 0.060 0.1 0.003 0.030 0.2 0.004 0.020 0.1 0.002 0.020 0.2 0.004 0.020 0.4 0.010 0.025 0.2 0.008 0.040 0.1 0.005 0.050 0.2 0.004 0.020 0.2 0.003 0.015 0.1 0.003 0.030 0.1 0.004 0.040 0.6 0.018 0.030 Average = 0.027 Cb-lZr (2) 0.4 0.011 0.028 0.4 0.007 0.018 0.2 0.008 0.040 0.3 0.009 0.030 0.5 0.007 0.014 0.3 0.010 0.033 0.5 0.022 0.044 0.4 0.017 0.043 0.2 0.010 0.050 0.2 0.009 0.045 0.3 0.013 0.043 0.2 0.006 0.030 0.3 0.010 0.033 Average - 0.035

165 TABLE 7 — Continued Pi't Diameter Pit Depth Depth/ Material: (mils) (mils) Diameter Tenelon (USS) 0.2 0.005 0.025 (l-F) 0.2 0.005 0.025 0.1 0.003 0.030 0.3 0.007 0.023 0.2 0.005 0.025 0.1 0.003 0.030 0.3 0.008 0.027 0.25 0.006 0.024 0.2 0.005 0.025 0.2 0.003 0.015 0.2 0.003 0.015 0.1 0.002 0.020 0.2 0.002 0.020 0.25 0.003 0.012 0.4 0.008 0.020 0.4 0.018 0.045 Average 0.022 Copper-Nickel 0.2 0.018 0.090 (As Rec'd.) 0.3 0.015 0.050 (8-cn) 0.2 0.005 0.025 0.3 0.008 0.027 0.5 0.008 0.016 0.4 0.008 0.020 0.2 0.006 0.030 0.6 0.022 0.037 0.4 0.024 0.060 0.5 0.015 0.030 0.3 0.010 0.033 0.4 0.022 0.055 0.2 0.011 0.055 0.4 0.010 0.025 0.4 0.018 0.045 0.4 0.012 0.030 Average = 0.039

166 TABLE 7 —Continued Pit Diameter Pit Depth Depth/ Material (mils) (mils) Diameter Nickel 1.2 0.019 0.016 (L. Ht. Trt.) 0.7 0.015 0.021 (85-ni) 0.5 0.012 0.024 1.8 0.037 0.021 0.3 0.007 0.023 0.4 0.007 0.018 1.0 0.024 0.024 0.8 0.016 0.020 1.0 0.042 0.042 1.2 0.018 0.015 Average = 0.022

2500' 2000 Z M; v E ] = Specimen Number 139-3,(304 SS), Middle Section = Secimen Number 139-3,(304)SS), Tail Section 1500 0.5 0 0.1 0.2 o.3 0.4 0.5 PIT DIAMETER- D- (mils) Fig. 91. —Pit size distribution for stainless steel tested in water at 200 ft./sec. for "standard cavitation."

168 If one considers the unsymmetrical bubble collapse and resultant fluid jet as the major damage mechanism, as it is observed in this investigation, then it should be possible to draw some confirming conclusions from analogous droplet impact tests. An examination of several pertinent reports from this type of study reveals that in general the type of damage sustained due to droplet impact forces is quite similar to the damage observed in this investigation. In particular, damage consisting of individual pits with raised rims are reported by Engel51 where the fluid and material used were mercury and copper respectively. It was noted that the craters produced in this case are dependent on the size of droplet and the velocity of impact. It is also noted that the depth to diameter ratio, scaled fromn figures presented, is 0.60, 0.286 and 0.083 for velocities of 2445, 1200 and 695 feet per second~ The lowest of these is comparable to the range of values observed in the present investigation, indicating an impact velocity of - 600 feet per second for the cavitaticn craters. It is apparent that the larger depth to diameter ratios reported for the mercury inmpact pits result for the larger droplet velocities, which are presumably larger than occurring in the cavitation case. It is encouraging to note that the ratio decreases with decreasing droplet velocity, indicating that it is not unrealistic to expect, with jets from bubbles of the size observead, that this shallower cavitation damage is indeed the result of this hypothesized mechanism, but with jet velocities lower than used in the impact tests. Cavitation pits in stainless steel from high temperature potassium have 48 been reported which have thLe same shape as the higher va.scity impact 51 pits reported above, further confirmLig the hypothesized mechanism of impact in the cavitation case.

CHAPTER V CAVITATION DAMAGE DATA CORRELATIONS A. Mercury Damage Data Analysis Versus Mechanical Properties 1. General To obtain a better understanding of the damage mechanisms, it is useful to attempt to correlate the damage data with the mechanical properties of the test materials. Unfortunately, only the data from the present tests can be used appropriately, since systematic tests wherein the presently required material mechanical properties have been measured do not as yet exist in the literature. The use of nominal handbook values for standard materials listed in previous investigations has been found far too inaccurate to be useful. 47 A digital computer program which was available, consisting of a relatively sophisticated least mean square fit regression analysis incorporating simple learning techniques, was employed for the data correlation. The general description and unique operational features of the program are described in Appendix D. Ten applicable properties of the test materials and/or fluids were selected either because previous investigators had attempted correlations with respect to them, or because they were involved in hypothesized damage mechanisms. These 169

170 independent variables were utilized in the program with ten allowed exponents, ~1, +2, ~1/2, ~3, ~1/3. The selected variables are listed in Table 8, and their precise definitions are found in Chapter II. 2. Single Property Correlations The first analysis of the damage data was performed with respect to each property individually to determine the relative importance of each alone with respect to the observed cavitation damage. The ten variables considered, along with the best predicting equation generated by the program for each variable and the corresponding coefficient of determination and standard error, which indicate the degree of correlation and the degree of fit or data scatter around the mean respectively, obtained between the best fit curve and the data, are listed in Table 8-A. No good single property correlation of the mercury data is obtained. However, true breaking stress exhibits the best fit. The rest of the variables are listed in order of significance of the fit obtained with the da-a. ITn the following tabulations of this type, no predicting equation will be listed if the coefficient of determination values are less than 0.5, as a value of 0.95 or better is indicative of a good correlation, and a predicting equation for anything less than 0.5 would be misleading. 3. Multiple Property Correlation Next, the relation between the damage data and a combination of all ten variables, raised to the ten above-mentioned exponents, was examined. The resultant best predicting equation is shown in Table 8-B. The data correlates best with a combination of true breaking stress and

TABLE 8 A. TERM BY TERM ANALYSIS OF HG CAVITATION DAMAGE DATA VS. MECHANICAL PROPERTIES Property* Correlating Equation F Level Std. Error Coef D. -12 2 1. True Breaking Stress MDP = 0,025 - 0.63x10 (TBS) 12.90 0.008 0.85 2. Engineering Strain -6 Energy MDP = 0.028 - 0.54x10 (ESE) 10.60 0.009 0.83 -l 1/2 3. Percent Elongation MDP = 0,029 - 0.24x10 (7E1.) 9.20 0.009 0.82 4. True Strain Energy MDP 0.008 + 0.24x1012 (TSE)-3 8.00 0 009 0.80 -6 5. Tensile Strength MDP - 0.034 - 0.25x10 (TS) 5.80 0.01 0'.77 6. Percent Reduction -6 Area MDP = 0.022 - 0.11x10 (T7RA) 2.86 0.011 0.70 5 -3 7. Brinell Hardness MDP = 0.007 + 0.10xl05(BHN) 2.60 0.012 0.69 8. Yield Strength MDP = 0.009 + 0.17x10 3(YS) 0.415 0.013 0.604 9. Elastic Modulus MDP = 0.013 + 0.85x10 (E) 0.11 0.013 0.59 10. Acoustic Impedance MDP = 0.024 - 0.64x10 (AcI) 0.21 0.013 0.59 *Precise definitions of properties given in Chapter II.

172 TABLE 8 B. BEST CORRELATION WITH ALL TEN PROPERTIES CONSIDERED MDP = - 0.064 + 0.34x102 (TBS)1/2 - 0.17x109(TS)-2 + 0.74xl08(TBS)-2 Coefficient of Determination - 0.994 Standard Error 0=.00188 Maximum Absolute Deviation = 0.0034 Maximum Percent Deviation - 44.56%

173 tensile strength. This is a reasonable result. The type of damage observed on these materials, i.e., crater-type pitting, indicates that cavitation damage resistance would likely be a function of the ultimate strength of the material and a property associated with the plastic flow of the material at stresses above the proportional limit, as e.g., true breaking stress. The degree of fit of the data to this predicting equation is shown in Figure 92, which also serves as an illustrative example of the degree of fit and amount of data scatter indicated by particular values of the coefficient of determination and the standard error as reported later. B. Water Damage Data Analysis Versus Mechanical Properties 1. General The procedure already described for mercury was followed in the analysis of the water damage data. In addition to the full data analysis, since many more materials were tested in water than in mercury, an analysis was also performed using only those data for which comparable mercury data existed. Next, the remaining data was treated alone. Thus a direct comparison between water and mercury effects are afforded using precisely the same test materials for each fluid. In these two particular systems, and at the chosen test conditions, the water and mercury damage is very similar, as already mentioned, both in amount and type. The carbon steel water cavitation damage data has been deleted from this analysis since significant corrosion effects exist in water for this material.

0.04 z 0'-4 E-4 CY z 0.03'-4 o ___ ____ __ __ ____ ___ _ ____ ____ Predicting Equation: 4.0 MDP = -0.064 + 0.34x10 2(TBSY~k W 7 -0.~~~~~17x10 (T5Y2 + 0.74x108(TBSY-: Coefficient or Determination = 0.994 Standard Error = 0.0019 0.01 17151 p.00 0.00 0.01 0.02 0.03 0.04 0.05 MDP DATA POINTS (OBSERVED) Fig. 92. —Comparisons of predicted values of MDP from the prediction equation listed to the actual values observed in mercury for all materials tested.

175 2. Single Property Correlations The relative importance of each mechanical property considering the full set of water data was examined as with mercury. They are listed in Table 9-A, in their relative order of significance. The best fit is obtained with the acoustic impedance ratio between material and fluid. However, nearly as good a fit is obtained with elastic modulus, indicating that this term which appears in the definition of the acoustic impedance (see Appendix D) may be of primary importance as compared to the other terms in the acoustic impedance ratio. A set of single property correlations (Table 9-B) for the water data on materials also tested in mercury shows that again a very good fit is obtained with elastic modulus and also with percent reduction of area, although the fit with acoustic impedance for these materials is quite poor, as it was in mercury. The analysis of the remainder of the water data (i.e., those materials tested in water only —Table 9-C) shows that the correlation with elastic modulus and acoustic impedance again is very good. However, there is no reasonably good correlation with any other single property. 3. Multiple Property Correlations The excellent fit of the acoustic impedance parameter was overriding in the multiple property analysis, and in view of the close comparison of this parameter to the elastic modulus, it was decided to *Chosen as a coupling parameter between fluid and material, and related to the ratio of reflected to transmitted energy as liquid shock waves or jets impinge on the solid.

TABLE 9-A SINGLE VARIABLE CORRELATIONS FOR FULL SET OF WATER DATA EXCEPT CARBON STEEL Rank Property* Correlating Equation Std.Err. Coef.D. 1 Acoustic 3 -1/3 Impedance MDP = 0.095+4.75(AcImp) -0.239(AcImp) 0.107 0.970 2 Elastic Modulus MDP = -31.23+0.639x1022(E) -0.134x1017(E)- 0.117 0966 3 Percent Elongation MDP = 0010 + 0.173x10 (E%1) 0.411 0.542 4 Tensile Strength MDP = 0.070 + 0.673x1013(TS) 0.428 0.503 5 True Breaking Stress 0.551 0.179 Percent Reduction Area (No more correlating equations listed 6 Percent Reduction Area 0.562 0. 145 7 Engineering Strain since the data does not show Energy 0.564 0.138 sufficient correlation.) 8 Brinell Hardness 0.565 0.135 9 True Strain Energy 0.569 0.123 10 Yield Strength 0.573 0.110 *Ibid., Table 8.

TABLE 9-B SINGLE VARIABLE CORRELATIONS FOR WATER DATA SUBSET OF MATERIALS AS USED IN MERCURY Rank Property* Correlating Equation Std.Err. Coef.D. 1 Elastic Modulus MDP = 0.0536+O.lO5xlO -22 (E) 3_.357xl015 (E)2 0.0016 0.998 2 Percent Reduction MDP = -1.72-0.109x10 (RA) -2+0.864x10 I(RA) -1 0.010 0.946 Area +0.172x10O (7.2 -10 2 -15 3 3 Yield Strength MDP 0.054-0.616x10 (YS) +0.714x10 (YS) 0.020 0.765 4 Engineering Stress MDP -0.146-0.275x10 11(ESE) -3 Energy +0.249x10 (ESE) 0.023 0.692 5 Brinell Hardness 0.028 0.497 6 True Breaking Stress (No more correlating equations listed 0.030 7 Percent Elongation since the data does not show 0.033 0.321 8 Acoustic sufficient correlation.) Impedance 0.033 0.300 9 Tensile Strength 0.034 0.275 10 True Strain Energy 0.034 0.255 *Ibid., Table 8.

TABLE 9-C SINGLE VARIABLE CORRELATIONS FOR WATER DATA SUBSET OF MATERIALS AS TESTED IN WATER ONLY Rank Property* Correlating Equation Std.Err. Coef.D. 1 Elastic Modulus MDP 56.63+0.476x lo23(E3o 690xl016(E) -2 -l 1/2-21 (E3.5 97 -0.106x10 (E) 2+.273x10 (E) 0.156 2 Acoustic Impedance MDP = -0.119+0.248x101Aclmp) 0.149 0.970 3 Percent Elongation MDP = 0.0105 + O.167x10 -2(7X) 0.562 0.547 4 Tensile Strength MDP = 0.131 + 0.656x10 13(TS)-3 0.577 5 True Breaking Stress 0.683 0.330 (No-more correlation equations listed 6 True Strain Energy 0.719 0.258 7 Engineering Strain since the data does not show Energy 0.743 0.208 8 Percent Reduction sufficient correlation.) Area 0.747 0.200 9 Yield Strength 0.761 0.169 10 Brinell Hardness 0.763 0.165 *Ibid., Table 8.

179 examine the correlation with only the other nine variables, all of which are actual mechanical properties of the specimens, not involving fluid properties. Considering the full set of water data, the resulting best fit predicting equation is: MDP; -27.75 + 0,563x1022 (E)-3 - 0.118xlO17(E)-2 + 0.885x109(E) -1 +0.316x10-6 (E) + 0.186x10 9(Ts)2 _ 0.849xlO2(TBS)1/2 where Standard Error 0.0547 Coef. Determination 0.993 Maximum Absolute Deviation 0.176 Maximum Absolute % Deviation 1111.9 A correlation was also determined for the two subsets of water data, i.e., those for which comparable mercury data existed, and those remaining. The best correlation for the former is: MDP = 0.887x10 23(E) 3- 0.274x105(E) + O o70xlO (TSE) where Coefficient of Determination 0.9993 Standard Error 0.00108 Maximum Absolute Deviation 0.00276 Maximum Absolute %7 Deviation 105.7 The other subset of water data, consisting of those materials tested only in water, produces the following predicting equation:

180 MDP = 0.273 + 0.239x01(AcImp)3 - 0.104xl07(TBS)-2 13 -3 4 -1/2 + 0.217x103 (TS) - 0.169x10 (E) where Coefficient of Determination = 0.9949 Standard Error 0.0651 Maximum Absolute Deviation - 0.1735 Maximum Absolute % Deviation 604.3 C. Discussion and Conclusions It was found that no good correlation existed between any single mechanical property and cavitation damage in the mercury tests. In the water tests the elastic modulus did correlate very well with the observed damage. The resultant multiterm predicting equation also is dominated by terms involving the elastic modulus, and shows that MDP decreases as E increases. This correlation with E may indicate that the damaging mechanism is very local in nature. Thus a material capable of substantial deflection under load without permanent deformation would not be damaged. This suggests the possible influence of a rigidity parameter, in addition to E alone, as the ratio of yield strength to elastic modulus which is the maximum possible nonpermanent deformation for the material. However, a check of this parameter as a single correlating parameter produced a coefficient of determination of only 0.18 for the full water data set and 0.69 for the mercury data set. However, the local nature of the damaging mechanism is consistent with the already discussed hypothesized damage mechanism wherein a central jet

181 along the axis of symmetry of a nonspherical collapsing bubble impinges upon the surface to be damaged, in that the penetrating range of such a microjet at full strength is very small. E did not appear in the multiterm predicting equation for mercury, perhaps because it does not vary significantly between the materials tested in mercury, and also perhaps because the data used for E for the refractory alloys may not be sufficiently precise to allow a good correlation with E, if it did exist, over the narrow range of variation available. In the full set and one of the subsets of water data, a good correlation was obtained with acoustic impedance ratio, showing that as this increased, damage also increased. This is consistent with the variation of damage with elastic modulus, since E appears in the denominator of the acoustic impedance ratio. For a given material, the predicting equation for acoustic impedance indicates that damage should be greater with mercury than water, other things being equal, which is probably the case. However, it does not explain the qualitative obser40 vation previously made in these tests that plexiglas is relatively resistant to damage in water (as compared with the metals), but comparatively nonresistant in mercury. In any case, it is indicated that further understanding might be achieved by tests in which elastic modulus and acoustic impedance were varied singly over large ranges. This could be a key approach for future investigations after the present study. Since no good physical explanation of the apparent correlation with elastic modulus can be advanced at present, and since the amount

182 of variation in this parameter is relatively small as compared to the other variables, the data was further analyzed with neither acoustic impedance or elastic modulus allowed as a variable. In this case, a best fit curve was generated as follows: MDP 2.706 - 0.189x10/ (TS) / + 0.209x10 (TS) / - 0.116x103(YS)-/2 where Coefficient of Determination 0.560 (i.e., essentially no meaningful degree of correlation) Standard Error 0.415 Maximum Absolute Deviation 0.145 Maximum Absolute % Deviation = 10,698.9% It is thus not possible to correlate the water data with any function of the other eight variables when elastic modulus and acoustic impedance were dissallowed. This could indicate that some mechanical property not yet considered is significant. As an example, properties difficult to include quantitatively as ability to be cold worked, or corrodibility may be important. From a consideration of the types of damage observed it was 26 anticipated, in connection with the present study, that two or more properties in combination would be required to predict the damage, and that these would include a strength and an energy property. As already mentioned, the mercury damage data correlates well as a function of tensile strength and true breaking stress. This is consistent with the argument presented above, since true breaking stress involves strength and ductility, and hence, is related to failure energy.

183 The subset of water data for materials not tested in mercury includes the weaker materials for which, in some cases, three heat treats were utilized. For many of these materials the tensile strength increases as the strain energy is decreased, according to the different heat treatments, although the steels and refractory alloys, tested both in mercury and water, behave in the opposite manner. The material subset not tested in mercury was chosen partially to allow a selection between the strength and energy property effects. As it results, the best fit equation for these materials includes, in relative order of importance: acoustic impedance, true breaking stress, tensile strength, and elastic modulus. Again, the correlation was possible only with a combination of strength and energy properties, as true breaking stress and tensile strength, which were also involved in the mercury correlation. However, the surprisingly predominant effect of elastic modulus and acoustic impedance is still not clearly understood. The full set of water data correlated similarly as a function of elastic modulus, tensile strength and true breaking stress, although in this case accustic impedance did not appear. Several conclusions can be stated as a result of the foregoing analysis: 1. No single mechanical property correlates well with the mercury damage data. However, elastic modulus correlates well with both water subsets and with the full set, and acoustic impedance with the full set and one of the subsets. Acoustic impedance does not correlate for that subset of materials for which strain energy Increased as strength increased.

184 2. Fairly good correlations are possible for a combination of tensile strength and true breaking stress in mercury, and of tensile strength, true breaking stress and elastic modulus in water. 3. The correlation is best in both fluids for those materials that have the highest strength properties. An examination of the standard errors for the predicted results shows that there is more scatter in the data for the weaker materials. Since these are more susceptible to handling damage, it is conceived that errors introduced in this fashion may be significant. 4. The absence of certain mechanical properties in the correlations is significant, i.e., yield strength (which is generally proportional to fatigue limit) does not occur, further substantiating the conclusion that single-blow craters, rather than multi-blow fatigue failures, are predominant in these tests. Hardness also does not appear, although in general increasing hardness indicates increasing cavitation damage resistance. Apparently the numerical hardness values within a given range and the various hardness scales are not sufficiently rationally related. 5. Since cavitation-induced loading is of a highly transient nature, it is not surprising that some difficulty is encountered when attempting to correlate cavitation damage with the semistatically determined mechanical properties. However, in

185 general, suitable dynamically measured property values are very difficult to obtain. Nevertheless, investigations such as the present one can assist in the selection of properties for which dynamic values might be obtained in a future investigation.

186 CHAPTER VI CONCLUSIONS Many detailed conclusions have been drawn throughout the body of the report; however, the major conclusions from the overall investigation are summarized below. A. Pressure Profiles The measurements of pressures on the test specimen surfaces have shown that in general the venturi wall pressure profile measurements can be adequately assumed to represent the pressure profile along the venturi and on the test specimens. A very much larger axial pressure gradient has been measured on the test specimen surface for an unsymmetrical two-specimen arrangement than for a symmetrical two-specimen arrangement in the same venturi in mercury and for the same apparent termination of the cavitation cloud. This observation tends to explain the larger amount of damage, observed in earlier tests in this laboratory using this equipment, than was obtained in the present series. It has been observed that similar pressures above vapor in water and mercury on the test specimen surfaces result in similar quantities of damage, as might be expected. However, the velocities to

187 produce these pressures were of course far different and, as it happens, the system specimen geometry differed to some extent. Very approximate theoretical treatments indicate that more damage should occur in the mercury system, under identical velocity and geometry conditions; this is not contradicted in the present case. Minor geometrical changes can apparently result in major changes in local flow parameters affecting bubble collapse during B. High-Speed Motion Pictures In the mercury system, it has been observed from the high-speed 3 4 pictures that there exist on the order of 10 to 10 bubbles adjacent to the specimen surface per pit formed, and similar observations have been 52 made by other investigators using other test systems. Thus a damaging bubble collapse must involve a highly selective process separating the very large number of nondamaging bubbles from the very few which produce damage. It has further been observed in the mercury that some bubbles detach from the relatively steady-state void at the nose of the specimen, travel along the corner formed by the test specimen radial sides and the venturi wall, and transform from a nonsymmetrical to a circular shape as they collapse at a slight distance from the test specimen. Since the bubbles observed in mercury must be in contact with the viewing surface, only their contact area can be viewed, and it is not possible to determine their behavior in the dimension normal to the viewing surface. All bubbles that were observed to collapse on the polished

188 surface of the test specimen were observed to retain a circular shape during collapse to as small a diameter as was visually observable. However, the technique of observation did not allow a determination of the retention of symmetry to critically small diameters where nonsymmetries might conceivably occur. In the water tests, no bubbles were observed to contact the polished surface in the area of maximum damage during the short time sample available (less than 1/20 second per 100 foot roll of Fastax film). However, an estimate of the probable numbers of bubbles in the area, by extrapolating from regions where bubbles were observed, confirms the large bubble to pit ratio observed in the mercury tests. C. Specimen-Fluid Contact Measurements The unique technique employed to observe the amount and location of contact between the specimen surface and the fluid in the mercury system confirmed the observations from the motion picture analysis that there exists very little, if any, contact between the fluid and specimen near the nose where the motion pictures indicated essentially a continuous void. Also, this technique indicated almost continuous contact between the specimen and fluid at the tail of the specimen where the motion pictures indicated very few bubbles in contact with the surface. D. Typical and Detailed Analysis of Damage to Specimens It was found that the type of damage inflicted was very similar in the two different fluid systems. The damage appeared as craters

189 with raised rims, as have also been observed in many droplet and particle impact tests by other investigators. Due to the symmetry of the craters, and the fact that they do not change in any way if exposed to 40 further cavitation, it must be concluded that the damage is the result of single blows. A rim predominantly on the downstream side of the craters was observed in the present series of water tests as it had been 40 in a previous study in this laboratory. The nonsymmetrical location of the rim lends support to the unsymmetrical bubble collapse with resultant fluid jet damage hypothesis, as opposed to the shock wave impingement hypothesis. The similarity in amount and type of damage due to two different fluids leads to the conclusion that the effect on damage from different fluids, chemical effects excluded, stems from the different flow regime which may be afforded, and the resultant driving pressures for bubble collapse. The size range of pits (predominantly less than 0.1 mils diameter), compared to the observed bubble sizes, confirms the belief that damage is produced in the very final stage of bubble collapse which is, of course, the most difficult portion to observe, Comparison of the depth to diameter ratios for the two fluids 51 with those from impact type tests leads to the conclusion that the damage is produced by an impact mechanism in the later stages of bubble collapse, and that probable velocities of impact in mercury are on the order of 600 ft./sec. Assuming the "water hammer equation" to give a first approximation to pressure exerted by an impacting drop on a solid surface, then since the velocity of sound in water and mercury is about

190 the same, a water velocity necessary to create the same force would be scaled up in proportion, i.e., about 8000 ft./sec. 54 A recent article from water jet impact tests with velocities in the 2500 to 3500 ft./sec. range reports damage of an almost identical type to that observed in the present investigation. The profiles of 54 pits reported are strikingly similar to those presented herein which fact lends very strong support to the unsymmetrical bubble collapse with a resultant fluid jet damage hypothesis being the contributing factor in the cavitation damage case as subscribed to in this investigation. E. Damage Data Versus Mechanical Property Correlations The analysis of the mercury damage data showed that it was not possible to correlate the observed damage with any single mechanical property. In the water damage data analysis, it was found that either elastic modulus or acoustic impedance correlated well with the full set of materials. A fairly good correlation was found in terms of a function of tensile strength and true breaking stress in mercury, and as a function of tensile strength, true breaking stress and elastic modulus in water. Accelerated corrosion effects were noted for three nickel alloys in mercury and for carbon steel in water, attributed to the interplay of mechanical forces applied to the surfaces from the cavitating flow regime and ordinary corrosive action. The fit of the acoustic impedance parameter in two of the three water data sets, and elastic modulus in three, indicates that further studies where these two parameters were singly varied over larger ranges would be rewarding in determining whether such a correlation exists over a larger range of different materials.

APPENDIX A DEFINITION OF CAVITATION CONDITIONS The degree of cavitation as defined in the overall damage investigations in this laboratory and in this particular investigation differ between mercury and water. In the mercury venturi, where only two specimens are used, cavitation initiates at the throat outlet for all velocities used thus far, and the degree of cavitation applied to the mercury tests describes the extent of the cavitation cloud starting at the throat outlet and extending downstream to the point indicated, ioe., "cavitation to nose" is self explanatory. However, in the case of water, where three specimens are used, thus presenting more blockage to the venturi, the cavitation cloud initiates on the nose of the specimens and extends downstream to some point arbitrarily labeled by the degree of cavitation terminology. The first visible manifestation of cavitation occurs on the nose of the test specimen, and thus the term "visible initiation" was applied in this case. Then, succeeding degrees of more fully developed cavitation followed the old progression, regardless of the termination point on the specimen. The following are the definitions of the degrees of cavitation as used in this investigation: Mercury Visible Initiation - continuous ring of cavitation at the throat outlet, about 1/8" longo 191

192 Cavitation to Nose - cavitation cloud extends from throat outlet to termination at the nose of the specimen. Standard Cavitation - cavitation cloud extends from throat outlet to termination at the middle of the specimen. Cavitation to Back - cavitation cloud extends from throat outlet to termination at the rear of the specimen. Water Visible Initiation - cavitation cloud extends from nose of specimen to a point downstream on specimen about 1/8" long. Cavitation to Nose - cavitation cloud extends from nose of specimen to termination at the middle of the specimen. Standard Cavitation - cavitation cloud extends from nose of specimen to termination at the rear of the specimen. From the pressure profile data in this report, the correspondence between water and mercury from a standpoint of degree of cavitation is as follows: Mercury Condition corresponds to Water Condition (2 spec.) (3 spec.) Cavitation to Nose -- Visible Initiation Standard Cavitation -- Cavitation to Nose Cavitation to Back -- Standard Cavitation This would result in the pressure gradients on the surfaces and the termination points on the surfaces being approximately the same for corresponding conditions from water to mercury.

APPENDIX B COMPUTER ANALYSIS OF PRESSURE PROFILE DATA The computer program used to reduce the raw pressure data taken during the venturi pressure profile portion of this examination is listed below. The program is based on earlier work in this laboratory, 40 35 another thesis investigation currently under way, and several modifications incorporated for the present investigation. A typical set of pressures and the resulting computer output is also presented below. 193

194 $COMPILE MAD,EXFCtUTE,I/O DUMPPRINT OBJECT,P.UNCH OBJECT R R PRFSSURF PROFILF DATA REDUCTION PRGGRAN! MJR THESIS R INTEGER CONDNRD,NPT,NRS,RPM,FL, I,J,K,L,M,N,DEATUTALkEP-AT, 1SHTNO,PFC CORR, TPC],TP" 2 REPEAT = 1 V'S X ( )=-2.00,0O.100,1.226,2.271,2.9'79,2. 784,..166,3.354, 1 3. 166,..5409,4.1 t,6.000 RCGIN READ DTA TOTAL REGIN1 FEX = 1 START READ FORMAT INI1,CON[D,,PFC'HR,HCNRD.NPTNR.SgTEMPgINiCHGPM, 1FL.RPMSHTNODT V'$ IN1 = $213.2F8.4,313,3F7.3, I3,I5,I8,F7.4*$ PRINT FORMAT HEAD V'S HEAD =$1H1,550,33HPRESSURE PROFILE R!JNS, MJR THESIS*$ W'R FL.=. 1 PRINT FORMtAT LIQl V'S LIO1 = $lHO,S1O,19HTEST FLUID IS WATER*$ O'E PRINT FORMAT LIQ2 V',S I..02 = $1.HO),S1O,21HTEST FLUID IS MERCURY*$ TRANSFFR TO CON(COND) CON(1 ) PRINT FORMAT ZFRO V'S ZERO = $]HOSO10,38HCAVITATION CONDITION = ZERO CAVITATION i*$ TRANSFFR TO SPN(SPFC) CON(2) PRINT FORMAT VIS V'S VIS = $1HO9S10,41HCAVITATION CONDITION = VISIBLE INITIATI 1. ON*$ TRANSFFR TO qPN(SPEC) CON(3) PRINT FORMAT NOSEF V'S NOSF = $HO,.S10,41HCAVITATION CONDITION = CAVITATION TO N I OSF*% TRANSFFR TO s.PN(.SPFC) CON(4) PRINT FORMAT STD V'S STD = $1HO,S1O,42HCAVITATION CONDITICN = STANDARD CAVITAT 1 ION*$ TRANSFFR TO SPN(SPEC) CON(5) PRINT FORMAT BACK V'S BACK=$1HOS10,41HCAVITATION CONDITION = CAVITATIuN TO B/C 1K*$ TRANSFFR TO.PN(SPEC) SPN( ) PRINT FORMAT lNF V'.S ONF = %1 H0,SlO,42HNUMRER OF TEST SPELC I NiNS iN VENTURI = 10ONF*$ TRAN!FFR TO INFO SPN( 2 ) PRINT FORMAT TWO V'S TWO = $1HO,S1O,42HNtJMHER OF TEST SPFCIiFiNS IN VENTURI = I TWO*$ TRANSFFR TO TNFO SPN(3) PRINT FORMAT TRE V'S TRF = $1HOS10O,44HNUMbER OF TEST SPEClCi,ENS IN VENTURI = 1 THREF*$ INFO PRINT FORMAT CONDSTEMP,H HHC, INCHPiGPRRPirtSHTNO( V'. CONIDS=$1HO,514,22HTFMPFhRATURF = F7*3,2h h/1H,S14 ],22HPAROMFTRTC PRESSURF = F8.4,8H MMA HG./1H,S] 492HHFIGCHT C,.ORRFCTION = F8.4,1OH,MM FLIJID)/I r 1' 722 HFLOw RATF

195 = F7.,14H IN. FLUID ()R F7.3,4H (iPM/1H,514,22HPUMP SPF FO 4 = I5,4H RPM/IH,S14,26HORIGINA[ DATA ON SHEET NO.I8 5*$ Vl ( 2 ) = NPT V2(2) = NPT PRINT FORMAT TAPS V'S TAPS = $1HO,525, 4HV-INS4,4HP-OO,5393HP-OS4t3HP-1lS4,3HS 1-l,S493HP-2,S4,3H%-2,S4, 3HS-39$4 93HP-39S493HP-4iS493HP-59S39 2 5HV-OUJT*$ RFAD FORMAT TN?,PTD( 11)...PTD(NPD9NPT) V'S IN? = $(6F7.2/6F7.2)*$ PRINT FORMAT OPTD1 V'S OPTDI = $1HO,S43926HORIGINAL PRtSSUtF- lAP uATA-$ PRINT FORMAT OPTD2,PTD(1,1)...PTD(NRD,NPT) V'S OPVD2 = $1HO,S23912F7.2/(S24912F7.2)*$ AT = 3.1416*(DT.P.2.0)/576.0 Hk = 0.002228/AT W'R FL F.. 1 TRANSFER TO BETA1A O'F TRANSFFR TO FETA2 F'L sETAlA DEN = 1.0409*62.3'689/TEMP.P.O.01089 W'R TEMP *.[ F. 11 3. LNVP = 2.303 + O.03175*(TENlP - 50.0) O'E LNVP = 4.290 + 0.0261*(TtEMP - 113.U) E'L VAP = FXP.(LNVP)*(14.7/760.) TRANSFFR TO GAMMA,-ETA2 DEN = (13.5708-0.001-448*(TEMP-50.) )*62.3689 WHFNFVFR TFMP.L F. 158. VAP = OC. TRANSFFR TO GAMMA OR WHFNFVFR TFMlP.G. 1.58. TRANSFFR TO FRROR 1 FNID OF CONDITIONAL GA MMd A PC = h3*(14.7/760 ) + HC*DE`N/1728. VT = GPM*R KE = (VT.P.2.)/64.4 THROUJGH DCLTA, FOR I=1,1,,I.G.oNR THROIUGH DFLTA, FOR J=1,1,J.G.NPT NPSH( I J) = (PTD( I,J) + PC - VAP)*144.*1l./)EN i) FI.. TA NRMPR( T,J) = NP.SH( (I J)/KF PRINT FRMA4T I NFO0 V'S, INF02=$1HO,S32,36HTHF UNCORRECTED NORvlALIZD PRESSURES*$ PRINT FORMAT OUIT 2, NRMPR( 1 1 ) NMPR(NRDNPT) V'S OLJT2 =$1HO,2 3,1 2F7.4/ (,24, 1 F 7 4 )*$ PRINT FORMAT OLJT., VT V'S OUT 3=$1HO, c1. 4,18HTHROAT VELOCITY = 7. 2 7H FT/SEC*$ READ FORMAT IN39CORRTPC1,TPC2,LTH1-LTH2,;liULT V'S I N =$ (3 T 5, F 7.4)*$ W'R CORR.E. 2 T' ZETA O'F PRINT FORMAT INF02A V'S INFO2A=$1H0,S14,43riNO CkR-"'CTluNS i'iAL)L TU I,,'iALIZLE PkES ] St)JR F*t T' O THFTA

196 F' L Z A r'I Z t.i 1 lA r()R!=]i i.9 * R L)ELP(N) = (' Sit (. " )J - NmiP (N ) / L /i 1 CALNPKi:.(,) = A t.' i-(,3) - (ut L(N )' L T h'1 *,!L T) LET' A rA i (N) = Ni PR(,z ) - CNALNPR(N) T H ZEIAAFO< J=31,1J..Nr<, T'H ZETA2, FOR 1= TIPC1,1i I.GTPC2.T A 2 R 1NI?:'R ( J P I) = iNi-PFR ( J ) I- A ACTOR ( J) rlTA P,. T I NFO3 V' S I\NFO:=$I 1 -,F,3 a 4 nTh1TE CiORREC TED NORkiAL I ZED Pik,.%SsUtlSE.*$ P T OU'r 2,N\iRM: ( I 1 1 ) ~ l * NR1PR (NRf),NPT) Thij TA THROCGH THFITA2 FOR I=1,1, I.GeNPT SU'l (I. E X I ) = 0.0 ihROUGH THET lI, FOR J= I1 J.G.*NRf) T H [Al SUM( )uEXI = SUM(DEX9I) + NRMPR(J,1 T r-tr. TAVGNP(EXI ) = SJUM ( Ut' X I ) / NR. LUSC ( EX) = AVGNP(DEX,1) - AVGNP ( X NPT) I'OT. F[riRC)OG IOTA], FOR.= 1,1,, i., R.. i... -: THRCUGH IOTAl, FOR L=1, 9,I.O.NPT DEVNP ( iL) = NRMPR (r,, L) - AVGNP( DEX L ) TOTAl1 SCDFV(ML) = D'VNP(iMlgL) *P.2. THRPOIi, IC, T3, FOR 1,1, I ~1G. NPT -;i iF.'O(.cXI ) = n... X 0 THROtlGH IOTa 2, F-OR Ji'-1,].,J.G.NRD T OTA2 S. UMsJM0( )EX, I = SLJUMS D EX, ). +, S0lE VA i J) VAR( = UEXI, SI)U/Q(RD X, -" STP, FV( DEX, I I VA R( DEX, I )..Q. 50 O;' ^ IOTA3, COVAR(DEX.I) = - (.AbS.STDDTEV( _EX 1I)- ) *OO. ) (. ADOS.AVVRiPEH (Wt,. Xi )J ) KAPPA,PRINT FORMAT INFQ-04 V' S IN`JFO4=$1HO,S42, 32hTHIE AVERAGi_ P;NO1i6AL:IZI4.; iK SSURtS-x PRINT FORMAT OUT4, AVGNP(E) ))i.X..AVdN t(LX, NPT) V' OUl 4=$1HO, -(.23,2F7, 4) )$. * +$ PR T INT FORMAT OtiT4A, t.OlS-C( f:-'.X,) V' T OC 4Al$I-, HO?,:14,:'"H"1tl:t LO(',S ~ COr, r' 1 4i' APPA 1 PR I N T (,.,/LT.4I;.,} -'" V's t,, 3 Ht VAi I N 5 I' h,.:/L.[', 1, - r U., PRIN6T -0';.',. f'., WN L;'-, I' L:\A I I I Pk INT 0,R- Ti,,Wr& r - LJt,'t A! eo I V4Ja ( i~v t L'i,A'., \/; * tR,\ti I -*'.',.'~ d P.INJ T F'1.r,a t ", i Iy I FO 4 ]; 2 -t /t?%4 lfi'Ur k uh, 1 A, 1(A I (i' 1,.'., i * - -, f,..'' v u I TVft;I'I; jf~t 1,11"'";5~s~ 9 I I L.',, A V N I X' 1-'''' -I -:.. r v,,,~ Fa,!(-I H A 1 L.' ic,' i L. F iAS,, I KIT P F ir, P t','i i: tV jR W N-1 F 1 N I 4 N V i T 4 L,, ) RR-t * 1 P, I ()THVI'.- 4

197 TRANSFFR TO PI END OF CONDITIONAL PI THROUGH PI2, FOR I=1,1,I.G.NPT SUMAVG(I) = 0.0 THROUGH P11, FOR J=11,J.G.NRS PI1 SUMAVG(I) = SUMAVG(I) + AVGNP(JI) MEAVG(I) = SUMAVG(I)/NRS PI2 Y(I) = MFAVG(I) THROUGH PI3, FOR L=1i1,L.G.NRS THROUGH PI3, FOR,vl=1,1,M.G.NPT DEVME(L,M) = AVGNP(LM) - MEAVG(M) PI3 SQDMF(L,) = DFVMF(LM).P.2. THROUGH PI5, FOR J=1,1,J.G.NPT SUSU91E(J) = 0.0 THROUGH PI4, FOR I=1,1,I.G.NRS PI4 SQSUME(J) = SQSUME(J) + SUDME(I,J) VARM(J) = SQSUME(J)/NRS STDEM(J) = VARM(J).P.O.5 P I 5 COVRM(J) = (.ABS.STDEi;(J)-1OO.)/(.A5S.iKEAVG(J)) PRINT FORMAT HEAD RHO PRINT FORMAT INF08, NRS V'S INF08=$1HOS]4,16HMEAN VALUES FOR I3,48HSETS AT SAME FLOW 1, RPM, AND CAVITATION CONDITION*$ PRINT FORMAT INFO9,GPMPRPM V'S INFO9=$1HO5S14,12HFLOW RATE = F7.3,4H GPM/1H,S14,13HPUMP 1 SPEFD = I5,4H RPM*$ TRANSFER TO RH(COND) Rhi(l) PRINT FORMAT ZERO TRANSFFR TO SP(SPEC) RH(2) PRINT FORMAT VIS TRANSFFR TO SP(SPFC) RH(3) PRINT FORMAT NOSE TRANSFFR TO SP(SPFC) RH(4) PRINT FORMAT STD TRANSFFR TO SP(SPEC) RH(5) PRINT FORMAT BACK TRANSFER TO SP(SPEC) SP(1) PRINT FORMAT ONE TRANSFFR TO AGN SP(2) PRINT FORMAT TWO TRANSFFR TO AGN SP(3) PRINT FORMAT TRE AGN PRINT FORMAT OUT3,VT PRINT FORMAT TAPS PRINT FORMAT INF04 PRINT FORMAT OUT9, MEAVG(1)...MEAVG(NPT) V'S OUT 9 =$ I HO, (S23, 1 2F 7.4) *$ PRINT FORMAT INFO5 PRINT FORM'AT OUT 10 VARM( 1 )...VARM(NPT) V'S OUT10=$] HO(S23,12F7.4)*$ PRINT FORMAT INFO6 PRINT FORMAT OUT119 STDEM(1)...STDEivi(NPT) V'S OUT 11=$1HO ( 523, 12F 7.4 )*$ PRINT FORMAT INFO07 PRINT FORMAT OUT129 COVRM(1)...COVRM(NPT) V'S OU112=$1H0( (S23 12F 7.2 )*$ TAU MECAV = MFAVG(1) THROUGH TAU1, FOR J=29,iJ.G.NPT WHFNFVFR MEAVG(J).LF. MECAV

198 MI-('A =.i[- AV (J) Tul1 Ni. (r CONiU)ITIONAL PRINT i-oR'~A' OUT 13.,'4r V'5 UUI i.)-$1HC,..14,92ri-t-l Mir-AN CiAv TAi'iN,JUi4, - ro.4't',i< INT1 -d)SA r' i I -LF V ~ i L L. -b 1iH1,S (U)34hlPkiL'LtCJi<- hL r i L t P LuTS, S;v;J, ITrt:-.* Lt r C ii A - Pt_) r ]. ( NSCALE,, A,, f )I V' S N,( ALr = 1 0 o3o. 3 FX ( I I- ( 1, ( I Mi,o.O OO -2 0,). 6U,-u. 40) F-((!J -r ).'1 ()1', (.)$, X ( 1 ) Y ( 1 ),N PT ) X t C U [ - F) 4. ( 4 4, O R i) ) V'sb')=i;=$ AVERAGE NOR.'ALIZUE PrESSUk PIRINT r-ORVAT HCATTO?, V' r HITM = $1H, S 1 1, 1HV S 2 5, 1HP,S1, 1 1P,S14, 1H, S6, 1i1 P, S1 12H 1s,53,3HS P,S, 11 P,SZ, 1HV/ 1H,S I, ii HP/ i, n rS1 rn H iS'TIN9LL 2 OF TAP FR()M VFNTURI ENTRANCE --- (INCricLS) A-N I)I M ENF I ()N Y ( 1 6) X( 1) IMAGF (1000) OMEGA WHFNiVFIR RFPFAI.L. TOTAL RFPFAT = RFP:AT + 1 IRANSFFR T}O FEGIN1 OTHERWI; I F TRAN,.SFFR TO H F GIN FND) OF CONDI TIONAL TRANS F PR TO) T TAR 1'' RRCR PRINT OP MAT FRRI 1 VECTOR VALUEi: Ei R k 1n I,Su,~,21rTLi';FEl ATi9UFL Lii Ei'A_ L L A L. L SL TRANSFFR TO PEGIN DIMENSION PTD( 16'), i ),NH Di 6 j I RMP( l;v ) R 16) Vi ) LJL LP( ij 1CALNLPR( 10),,FAC- F ( i J ), uVN- (0 0 ) V,,L V;, (i - i u,V i ), 2SUvlSQ (96,V Z) Ak ii(bu,V 2), IjuLFv(_V'uV2 ),COVAN(t(V, A'),t A'vNt, ), 3lU MAVG(G ( 16),6' A VG( i 6 9 L, Ivl if' (o () 9 V V ) 9,ft,,.;'L (Gug2 ) 6Sw.' S' L) ( io ) 9'+4 V A R M ( 16 ),STb.9 l( 1 ),\Ov, T i ) % Ll) L V ( j 9 V 1 ) t L US S( 1 0) VFCTOR VA. UF \V = 2, I, VECTOP VA -UF F?V = FNDF) -)F PROC RAMNA

PRESSURE PROFILE RUNS, MJR THESIS TEST FLUID IS MERCURY CAVITATION CCNDITION = STANDARD CAVITATION NUMBER CF TEST SPECIMENS IN VENTURI = THREE TEMPERATURE = 88.000 F BAROMETRIC PRESSURE = 735.6000 IN. HG. HEIGHT CORRECTION =.0000 IN. FLUID FLCW RATE = 2.500 IN. FLUID OR 21.100 GPM PUMP SPEED 1490 RPM ORIGINAL CATA ON SHEET NO. 198350 V-IN P-CO P-O P-i S-1 P-2 S-2 S-3 P-3 P-4 P-5 V-OUT ORIGINAL PRESSURE TAP CATA 112.00 -3.95 -5.95 -8.95 -9.00CO 4.25 -2.75 4.80 -8.60 29.OC 45.50 76.00 THE UNCORRECTED NORMALIZED PRESSURES 1.2646.1030.0829.0529.0524.1851.1150.1906.0564.4331.5984.9'39 THROAT VELOCITY = 33.14 FT/SEC NO CORRECTIONS MADE TO NORMALIZED PRESSURES THE AVERAGE NORMALIZED PRESSURES 1.2646.1030.0829.0529.0524.1851.1150.19C6.0564.4331.5984.9339 THE LOSS COEFFICIENT =.3606 THE VARIANCES IN NORMALIZED PRESSURES ~CCOC.0000.OCOO.0000.COCO.0000.0CCO 0.'.."O00.C&Q.0. THE STANDARD DEVIATIONS.CCOC.CCOO.0000.OCCO.OOCO.0000.C000. CCO.OC30.OCO 0.O03C.. THE COEFFICIENTS OF VARIATION.%0.00.00.00.00.00.0.30.3) THE CAVITATION NUMBER =.0524

PRESSURE PROFILE RUNS, MJR THESIS TEST FLUID IS MERCURY CAVITATION CCNDITION = STANDARD CAVITATION NUMBER OF TEST SPECIMENS IN VENTURI = THREE TEMPERATURE = 88.CCO F BAROMETRIC PRESSURE = 735.3000 IN. HG. HEIGHT CCRRECTION =.0000 IN. FLUID FLOW RATE = 2.500 IN. FLUID OR 21.100 GPM PUMP SPEED = 1492 RPM ORIGINAL CATA ON SHEET NO. 19835C V-IN P-00 P-0 P-1 S-1 P-2 S-2 S-3 P-3 P-4 P-5 V-nUT ORIGINAL PRESSURE TAP DATA 112.GC -2.95 -4.75 -8.65 -7.30 3.30 3.20 15.00.5C 31.50 47. 5 77.CC THE UNCORRECTED NORMALIZED PRESSURES 1.2645.1129.0949.0558.0693.1755.1745.2927.1475.4580.6183.9139 0 THROAT VELCCITY = 33.14 FT/SEC NO CORRECTIONS FADE TO NORMALIZED PRESSURES THE AVERAGE NORMALIZEC PRESSURES 1.2645.1129.G949.0558.0693.1755.1745.2927.1475.4580.6183.9139 THE LOSS COEFFICIENT =.3506 THE VARIANCES IN NORMALIZED PRESSURES.CCCO.O000.OCO0.0000.COCO.O 0.0. 0000.00 000..OC.0 0C.IOCO THE STANDARD DEVIATIONS.CCOO.C000.0000.0000.00CO.COCO.0300 000C.0000. 0C30. C300. o. COC THE COEFFICIENTS OF VARIATION.CC.00.00.00.00.CO.00.00CO.0C.C00.CC.03 THE CAVITATION NUMBER =.0558

PRESSURE PROFILE RUNS, MJR THESIS TEST FLUID IS MERCURY CAVITATION CCNOITION = STANDARD CAVITATION NUMBER OF TEST SPECIMENS IN VENTURI = THREE TEMPERATURE = 88.000 F BAROMETRIC PRESSURE = 737.3000 IN. HG. HEIGI-T CORRECTION =.COOO IN. FLUIC FLOW RATE = 2.500 IN. FLUID OR 21.10 iOC GPM PUMP SPEED = 1496 RPM ORIGINAL DATA ON SHEET NO. 198353 V-IN P-00 P-0 P-1 S-1 P-2 S-2 S-3 P-3 P-4 P-5 V-OUT ORIGINAL PRESSURE TAP OATA 112.V0 -2.95 -5.05 -8.80 -7.80 4.05 -.50 11.20 -3.95 30.50 47.0C 76.00 THE UNCORRECTED NORMALIZED PRESSURES 1.2649.1133.0923.0547.0647.1834.1379.2551.1033.4484.6137.9C42 THROAT VELOCITY = 33.14 FT/SEC NO CORRECTIONS MADE TO NORMALIZED PRESSURES THE AVERAGE NORPALIZEC PRESSURES 1.2649.1133.0923.0547.0647.1834.1379.2551.1033.4484.6137.9-42 TFE LOSS COEFFICIENT =.3606 THE VARIANCES IN NORMALILED PRESSURES.CCJC.0000.C000.0000.OCCO.000GO.000.000C.0000.CCOO.0CCC.v' C' THE STANDARC DEVIATION..O0Oc.CCO0000.oo.COCO.000C.0CO.0300..000 C. D o 000.0.C 02?: -C THE COEFFICIENTS OF VARIATION.O0.0L.OC.00.CO G0C.00.CC.00.C.O.O.. THE CAVITATICN NUMBER =.0547

PRESSURE PROFILE RUNS, MJR THESIS MEAN VALUES FOR 3SETS AT SAME FLOW, RPM, AND CAVITATION CONDITION FLOW RATE = 21.100 GPM PUMP SPEED = 1496 RPM CAVITATION CCNDITION = STANDARD CAVITATION NUMBER OF TEST SPECIMENS IN VENTURI = THREE THROAT VELOCITY = 33.14 FT/SEC V-IN P-OO0 P-O P-1 S-i P-2 S-2 S-3 P-3 P-4 P-5 V-OUT THE AVERAGE NORMALIZEC PRESSURES 1.2646.1097.0900.0545.0621.1814.1425.2461.1024.4465.61e1.9I 73 THE VARIANCES IN NORMALIZED PRESSURES.0000.OCOO.0000.0000.0001.CCCOO.G06.0018.0014.0001.0001.OC30 THE STANDARD DEVIATIONS.CC02.0048.0051.0012.0072.0042.0245.0422.0372.0103.0085.0046 THE COEFFICIENTS OF VARIATION.o1 4.36 5.70 2.23 11.53 2.30 17.22 17.13 36.33 2.30 1.40.51 THE MEAN CAVITATION NUMBER =.0545

PRESSURE PROFILE PLOTS, MJR~ THESIS 1.600 -- - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - - - - - - -- - — ~- - -- - - - - - 1 I0 I — - - - -- - - - - -I — - - -- - - - - -- - - - - -- - - - - -I — - - -- - - - - -- - - - - - A~~~ v~~~ E~~~ R~~~ A 0.80 I I — - - - -- - - - - -- - - - - -- - - - - -I — - - -- - - - - -I — - - -- - - - - -I — - - - G~~~ E~~~~~~~~~~ N~~~ 1.0 ~~+~~~ R~~~ D ~ ~IIIIII A V EIIIIII R A 0.0 00 -- - - -- - - - -- - - - -- - - - -- - - -- - - - -- - - - --- - - -- - - -- - - - -- - - - -- - - - GR EIIIIII I' I ~~~~~~~ISTNEO A RMV I INRAC IINIHES

APPENDIX C COMPUTER ANAL-LSIS OF CAVITATION DAMAGE DATA The computer program used to compute the mean depth of penetration, both from the pit court data and the weight loss measurements, is listed on the following pages, Included also is a page of typical output showing the numbers calculated, etc. 204

205 $CO(lP I LF:'A,r),f- XFUC.T T,F ),P, 3 P!H C J4 JFC T R P R ()A-GRA A R REVISFI) AS OF PER 23, 19b. Z=Z RFAD FDATA FLUID PR I NT F()RMAT TAP, LF PRINT FnPMAT TITIFT FLUID J=O K =]:;TART RFAD FO3R!MAT RFMTMATL_,NOVFl_ CAV DnPR = 0 AMDPR = 0 MDP2 = 0 AMDP? = 0 H? = 0 I=0 AGAIN REAf) DATA HRS,N1, N2,N3,N4,AWL WHeNroVeR 7,:, PRINT COM,'FFNT $0 NEXT SAtMP ll DATA W'.!FRF OFRTAINED IN THF OLDr WATFR LOOP$ J = J + 1 OR WHFNFVPR Z.F.4 PRINT COMMENT sO NEXT SAP 1LE DATA WFRl- ORTAINE!) IN DRY MERCURY $ J = J + ]. 7 = 2 FND OF C O.! I TI T I ONAL WI-IFNV F \ J.F. 5': = Y + 1 PR T NT FORPMAT PAOR, K PRIN T FO(RMAT TITI. F, FLU!.ITD J = n END OF rCON!D IT I jON 4HFNFEVFR HRS.L.O, TRANSFER TC START WHFNFV'R I.FO. FL-AG = HRS N 10=N 1? N, 0 = N 3 N40=N4 I=1 E'N' nF'ONDITT 1ONU. ml = C N1" = 0 N'3 = r n! 3 = U) N4 = 0 OTHER W SF 1 = N! -." 10 N? = N 2-N? 0 N 3 =N 3-! 30 N 4 = N 4 - 4 0 0 N4+=N4-NO40 FND OF CO'IIT T OAL WHFNF-V'L-R MATI.F,.$..SS$,OR.,MATI. E.SC S$ rO = -7.= I OR WHC'NFVmR'MATl-..F$PLK-X$ P) = 1.23

206 OR WHENFVFR MATL.F.$CBZR$ RO = 8.72 OR WHFNFVFR MATL. F.$AL$ RO = 2.77 OR WHENEVFR MATL.E.$CZ$ RO = 8.61.6 OR WHENFVFR MATL.F.$A$.OR.MATL.F.$B$ RO = 17.655 OR WHFNRIVRR MATL. F. $CUS RO = 9.0248 OR WHFNEVFR MATL.F.$CN$ RO = 9.040 OR WHENEVFR MATL.F. $NI$ RO = 8.973 OR WHENEVFR MATL.E.$SS1$ RO = 7.994 OR WHENEVFR MATL.E.$F$ RO = 7.810 OR WHENFVFR MATL.F.$D$ RO = 9.832 OR WHENEVFR MATL.F.$G$ RO = 4.52 OR WHENEVFR MATL.F.FE$ -RO = ].0.215 END OF CONDITIONAL AUX1 =.5216*N1+6.0363*N2+71.1547*N3+334.4513*N4 KO = 7.346E-3 KP = 1.172 KS = 3.601 WLPS = 1.642F-8*RO*KO*KP*P.3*AUX1 WL = KS * WLPS APS = 3.72E4 AT = 3.362F5 MDPPS = KO * KP.P.3 * AUX1 /APS MDP = KO * KP.P.' * KS *AUX1/AT AUX2 =.6480*N] + 3.1525*N2 + 16.4799*N3 + 46.6233 * N4 PDAPS = 25.*3.14159 * KP.P.2 *AUX2/APS PDA = 25.*3.1 4159*KP.P.2 *KS *AUX2/AT AMDP = AWL/(AT * 1.642E-8 * RO) WHFNFVFR WL. E O APDA = 0 OTHERWI SF APDA = PDA * AWL / WL FND OF CONDITIONAL. WHFNFVFR HRS.F.O MDPR = 0 AMDPR = 0 MDP2 = 0 AMDP2 = 0 H2 = 0 OTHERWISF H1 = H2 MDP1 = MDP2 AMDPI = AMDP2 H2 = HRS MDP2 = MDP AMDP2 = AMDP MDPR = (MDP2 - MDP1)/(H2-H1) AMDPR = (AMDP2 -AMDP1)/(H2-H1)

207 FND OF CONDITIONAl WHFNFVFR HRS.Go-F —LAG WHFNFVFR Z.F.1 PRINT FORMAT PFMT1 HRSN1.gN2,I?N3, N4,MLDPPDA.M DPR,AMDPAPDA, 1 AMDPR,AWL OR WHFNFVFR 7.F.O PRINT FORMAT PFM T,HRS,N 1,N2,N 3 N4,MDP,PDA MDPR OR WHFNFVFR 7.F.2 PRINT FORMAT PFMT2,HRS, AMDP, AMDPRgAWL END OF COND I T IONAL OTHFR W I SF PRINT FORMAT PFMTgMATL,NO.VEL,CAVHRSN1,N2,N3,N4MDPPDA, 1 MDPRAMDP.APDAAMDPRAWL FND OF CONDITIONAL J=J+1 WHFNFVFR J.F.25 K=K+1 PRINT FORMAT PAGE,K PRINT FORMAT. TITLF, FLUID J=O END OF CONDITIONAL TRANSFFR TO AGAIN FORMAT VARIARLE Z INTEGER MATLNON1 9N2N39N4,JKI,ZFLUID. CAV R R FORMAT VALUES R VECTOR VALUES TABLE=$1H.] S63,8HTABLF *$ VECTOR VALUES TITLE=$1H OS50,30HCAV I T AT I ON DAMAGE DATA IN 1 9C6//.c10 10'3H WL = WEIGHT LOSS9 MOP = MEAN DEPTH OF 2PENETRATION, PDA = PERCFNT DAMAGED AREA, R = RATF ///S9 31919HTHROAT CAV. HOURS PIT COUNT DATA ---- CALCULATED 4VALUS - ACTUAL (OR MEASURED) VALUES 5 /129HMATL NO. VFL-FPS COND RU.N N1 N2 N3 N4 MDP-MIL 65 PDA-PERCENT MDPR-MILS/HR MOP-MILS PDA-PERCENT MDPR-MILS 7/HR WL-GRAMS *$ VECTOR VALUES PAGF=$1H1,S63,o5HPAGE 9I2*$ VECTOR VALUES RFMT=$C4,5S6,I33,S7,EF5*1S5,CS4*$ VECTOR VALUES PFMT=$1HOC4, I3,2,F5.1 S2 C4+S1 F5.1 S1 I4. lSl, I3,52,I2,S1.I 2.93, PE1.3,S2, 1PE1O.3,S2, 1PElO3.S2, 1PE103I 2,S2,1PF10.3,gS2,1PE10.3,S2,1PE10.3*$ VECTOR VALUES PFMT1=$1HOS21* F5.1,S] *IZ4 151,13,S2,I2,12,S1lI2,S3,1PF1O.3,S2,1PF10.3,52,1PF10.3,52,j1PE10.3 2,52,1PR1O.",S211PF1 F.3,52,lRPilfn.*$ VECTOR VALUES PFIMT2 = $1HOS521lF5.1 55H ---- PIT COUNT 1ING WAS NOT POSSIBLE ----,1PElO.'3,S14. 1PF1C 2.352,1PF1 0.*$ END OF PROGRAM

CAVITATION DAMAGE DATA IN WATER WI, WEIGHT LOSS, MOP = MEAN DEPTH OF PENETRATION, PDA = PERCENT DAMAGED AREA, R = RATE THROAT CAy. HOURS PIT COUNT DATA -- CALCULATED VALUES -- ACTUAL (OR MEASURED) VALUES~ —MAIl NO. YEL-FPS COND RUN Ni N2 N3 N4 MDP-MILS PDA-PERCENT MDPR-MILS/HR MDP-MILS PDA-PERCENT MDPR-MILS/HR WI-GRAM Cu 84 20C.'.i STND.0 0 0 0 0.C 0GE 00.,OCCE CO.COOE 00.COOE (0 LCOOE 00.LOOE CO.OCGE 0 1. n 51 8 0 0 9.486E-06 6.733E-0.2 9.486E-06 3.212E-03 2.279E 01 3.212E-03 1.60CE-0 4.0 53 36 1 3 1.671E-Q4~ 3.515E-01 5.255E- 5 5.219E-03 1.098E 01 6.691E-04 2.60GE-0 10.0C 1 2' 54 2 6 3.214E-C4 6.479E-Cl 2.572E-05 9.635E-C3 1.942E 01 7.360E-04 4.800E-0 20.0 161 50 3 3 2.03CE-%04 5.214E-Cl -1.184E —05 1.285E-02 3.300E 01 3.212E-04 6.400E-0 — ___ ~~~~~~~~~~30-.0 293 64 7.4 3.008E-0-4 8..013.E-101 9.7-84E-06_. 1.8qt06E-QZ2_ 48.B1ZE 01 5.219E-04 9.OOOE-4 4C.C 643 124 11 9 6.177E-04 1.627E CC 3.169E-Q5 2.328E-02 6.135E 01 5.219E-G4 1. 16CE-3 50.0 -- PIT COUNTING WAS NOT POSSIBLE -- 2. 509E-02 l.806E-04 1.250E-0 75,Q — P1T CO~TNWSNOT POSSIBLE -- _ 3. 352E-02 3.372E-04 1.670E-0 100o.0 C- PIT COUNTING WAS NOT POSSI-BtE — 5.600E-C2 8.992E-04 2.790f-0 C.W.-A57 200.0 STND.C 0% 0 (3 0.OCCE C0.OOQE 00.OOOE CC0 CCCE 00.OOOE 00.0OOE 00.OOOE 0 _________ ~~~~~~~ ~~~~44 6 Ma78E-!5 -71k 8Ez4 -~Q 5__12 E -Q i!3E00 3.412E-03. 1. 700E-0 4.0 107 30 4 2,158-4 373-1 2763E-C5 6.423E-03 1.590E 01 1.004E-03 320-0 10.0 193 59 11 7 4.535E-04 9.460E-01 5.046E-05 1. 285E-0Z 2.679E 01 l.C71E-03 6.400E-0 __________ 20,0 242 56 11 6 ~~~~~~~~~~~~4.121E-C4 9.179E-01L-4 2E:Q6.465E-C2 3.263E 01 1.806E-04 7.300E04 ___ ~~~~~~~~30.0 381 67 1 2 7 4.811E-04 1.135E 00 6.897E-C6 l. 827E-02 4.309E 01 3.613E-04 9.100E-0 --- ~~~~~~~~~~~40,0 1521 160 14 13 8.997E-04 2.689E CO 4.186E-05 2.IC8E-02 6.298E 01 2.810E-04 1.050E-0 ________ P~~~~~~~~~~~~~~~~~I TCOUNTING WAS NOT POSSIBLE -- 2. 148E-02 4*014E-05 1.OTOE-3 75.f. ---- PIT COUNTING WAS NOT POSSIBLE -- 3.593E-02 5.781E-04. 1.790E-0 100.0 ---- PIT COUNTING WAS NOT POSSIBLE -- 7.025E-C2 1.373E-03 3.50CE-0 Cu15BZO0 ~T.O O 0 0 QQ 0E00 _.0OCE 00.000E 00 _OCCE 00.OOOE 00 _.000E 00.OOOE_0 1.0 0 0 I 1 ~5.138E-05 7.292E-02 5ol38E-05 3o2l2E-03 4.558E 00 3.212E-03 1.600E-0 4.0 0 1 5 4 -2.153E-04 3.143E-o1 5.o464E-05 5.419E-03 7.913E 00 7.36(oE-04 2.700E-4 ________ I~~~~~~~~~~~flT2I~~~~ 6 3o291E-04A 6oZ29E-QL 1.897E-05 9.835E-C3 lo856E 01 7o360E-04 4.900E-0 20.0 179 31 5 4 — -2,500E-C4 5,577E-01- -7o903E-06_ -5o821E-0.3 1.298E 01 -4.014E-04 2.900E-0

APPENDIX D COMPUTER REGRESSION ANALYSIS OF DAMAGE DATA VERSUS MECHANICAL PROPERTIES Due to the length and complexity of the regression program it is not reproduced in detail here as it appears in the original reference. 4 However, it is desirable to describe in general the characteristics and unique operational features of the program in order to better understand the predictions resulting from the use of it with respect to the damage data. The program is in essence a least mean square fit regression analysis. It is capable of handling 59 independent variables, one dependent variable, 36 terms per variable, i.e., 36 powers per independent variable, and third order interactions of terms, i.e., a term of this latter type would be X(l) aX(2) X(3). Due to the tremendous number of possible terms available if the program is utilized to full capacity, it has incorporated into it a process of learning. The program selects a subset of up to 59 terms for,a single pass out of the possible large number of terms generated for the entire number of variables considered to their different powers and interaction orders, e.g., for 8 variables, 10 terms per variable, there are 80 possible terms to analyze. However, if second order interactions are permitted, the total number of possible

210 time to examine all possible terms in this manner. The simple learning technique incorporated in this program consists of a weighting of the terms in the matrix, such that the probability of selecting terms of the type that have been selected in a previous pass as good fits are increased, and vice versa, for the terms of a type that have not been shown to have a good fit in a previous pass. Thus, the program is able to converge more rapidly on a statistically good fit of the observed data points with a function of the independent variables that were presented to'it. The regression analysis is terminated when either of three criterion are satisfied: (1) The probability of inserting another term or removing a term from the current predicting equation is such that the chance of getting a bad term in or of taking a good term out is greater than the control value specified, (2) the total number of possible terms is exhausted and there are none left to insert, (3) the total number of trial passes specified is exceeded. The sequence of analysis events occurs as follows: The program reads in the specified control information and data sets, sets up a labeling system for the total possible number of terms, and then randomly picks out a subse't of up to 59 of these for the first pass. It then computes individual correlation coefficients for each term with respect to the observed data values listed. The term with the highest correlation coefficient is selected to be entered into the equatLon and the least mean squares analysis is used to generate the coefficients for an equation of the following form:

211 and the statistical informat~ion regarding the fit of this equation to the data is computed.- The program then computes an importance factor for the test of the terms not in the equation with regard to how each will best account for the deviations between the actual data and the predicted values. The best term in this respect is entered into the equation if the test for the probability of insertion and deletion error is passed. If not, the regression is terminated. This process is continued until the best fit predicting equation possible with the first subset of terms is achieved. This completes a standard trial. Then, still working with the same subset of terms, a random trial is performed. The above process is repeated through the entering of the first term. The second term in this case is chosen randomly from the remaining terms of the subset with respect to the'importance factors, This process is continued as for the standard trial until the regression is terminated for one of the three reasons mentioned previously. Several random trials are possible per pass, and in some cases result in a better predicting equation than the standard trial due to the combination of several terms that did not have as high of importance factors being better than another single term with the highest importance factor as selected in the standard trial. At this point, the learning technique is employed by increasing the probability of picking terms of the type that got into the equation in the last pass and decreasing the probability of picking those types of terms that did not get in. The terms that are in the equation from the last pass are entered in the subset for the next pass and a random

212 process of selection, with respect to the changed probabilities of term selection, is employed to select enough other terms from the total possible to fill out the subset to its normal value. Another pass as described above is then initiated and carried out. At the end of the prescribed number of passes, the best trial of the best pass is indicated and the statistics of degree of fit to the data are generated and printed out along with the predicted equation. A typical pass and set of trials for this pass are included for the data and control parameters as used in this investigation for clarification of the above statements. Control parameters used for following pass: Prescribed Coefficient of Determination =0.97 Prescribed Standard Error of Y -0.00 Probability of insertion error 0.01 Probability of deletion error -0.01 Number of independent variables = 10 Number of terms per variable - 10 Interaction order I Number of terms per pass.- 40 Thus the total possible terms'is 100. TYPICAL PASS FOR MERCURY REGRESSION ANALYSIS In the following program, the mechanical properties were read in as follows, i.e., as dependent variables: X(l) =Tensile Strength

213 X(3) =Engineering Strain Energy X(4M Elastic Modulus X(5) Brinell Hardness ((E/f )1/2) X(6) Acoustic Impedance.- fluid (f(/1 )l2)material (Density x Sonic Velocit)fluid (Density x Sonic Velocity) mteia X(7) = True Breaking Stress X(8) = True Strain Energy X(9) =% Elongation X(lO) =% Reduction of Area X(ll) MDP (Independent Variable)

- FIRST 0ROE-R ITliTERACTICJ - HG AVERAGEn nDATA W/1n'JICKEL POSSIPLE rE,..;S= 1 00 STARTER PRn'G! Al PROBLEM NO. 5 RAW DATA OBSERVAT ION'tO). 29 W-IGHT = 1.00000 X( 1) =.9520000E O1 X( 2) =.3700000E 01 X( 3) =.44300002 01 X( 4) =. _00,0 OE 02 X( 5) =.1250000E 03 X( 6) =.43200OE 01 X( 7) =.1723000F 02 X( 3) =.740);00E 01 X( 9) =.544000CC 02 X( 10) =.5090000E 02 X( 11) = 2430000E-02 X( OBSERVATION'4r). 30) W:-IHT =.COO)0O X( 1) =.9520000)3 01 X( 2) =.3700000E 01 X( 3) =.44F30000E 01 X( 4) =.2_P00)OOE 02 X( 5) =.13250005 03 X( 0) =.4320GCOE 01 X( 7) =.1i720005 02 X( 8) =.7+450000E 01 X( 9) = 544C00C- 02 X( 1) =.5090C00OE 02 X(11) =.1850000E-02 X( OBSERVATION 13. 31. - tHT = 1.000 XI 1) =.95220)o%^- JI )( 2) =.3700000E 01 XI 3) =.4410000E 01 X( 4) =.29'0000OE 02 Xi 5) =.132500E 03 X( ) =.432OOOOE 01l X( 7) =.17283000E 02 X( 3) =.7450000E 01 X( 9).54403000r 02 X( I0) = 50909OOE 02 XI 11) =.4040000E-02 X( OBSERVATION Nl. ) 32 w:~ I;H T 1. 0J000 X( 1) -.5000J'2JO0; 01 X( 2) =.3000COE 01 X( 3) =.1550000E 01 X( 4) =.20003OE 02 XI 5) = X ) =.39100 12 XI 7 ) =. O7 5520000 01 X0 8) =000 01 X( 9)=.-40CCO iOE,2 X( 10) =.710.0000E 02 Xl 11) =.3900000'-01 X( OBSERVATION NO. 33 WEI rT 1.00000 XI 1) =.444iJ00u 01 X( ) =.34000005 01 Xt 3) =.1550000E 01 X( 4) =.2q00(U0E 02 XC 5) =.7)CO3OC2 02 X( 6) =.4320000E 01 X ( 7) =.552G0000 01 X( 3) =..300000)E 01 X( 9) =.40C00C E 02 X( 10) =.7100000E 02 X( 11) =.1973000E-01 X OBSERVATION f.l. 34 0'0:I7HT = 1.C')0() X( 1) =.003))'J' 01 Xt 2) =.7280-F, 000 01 X( 3) =.])680000E 01 X( 4) =.2900300E 02 X( 5) = 1.63000 E 03 X( S) =.'340C00E 01 X( 7) =.1171000E 02 X( 9) =.9i13000)E 01 X( 9) =.2iOO - 02 X( 10) =.633CCOOE 02 X( 11) =.1709000E-01 X( nBSERVATIONI v). 35 f I HIT = 1.OCOOO X( 1) =.8933C))'- 01 X( 2) =.8040000. 01 X( 3) =.2030000F 01 X( 4) =.'9000000 02 X( 5) =.175; X0C 6 03 X( 6) =.1334C0OE 02 X( 7) =.1356000E 02 XI 9) =.9600000 t 01 X( 9) =.22C,) FlC 02 K 10) =.5q6CCOOE 02 X( 11) =.8470000-02 X( OBSERVATION NO. 35 WfI Ii.T = 1.00000

Xl 1) =.2930000- 01 X( 2) =.1400000E 01 X( 3) =.6000000i 00 X( 4) =.i?O)UOfE 02 X( 5) =.115COOCE 03 X( 6) =.6280C00OE 01 X( 7) =.300(000[ 01 X( 3) =.500('.)0E 01 XC 9) =.425000CE 02 X( 10) =.9280000E 02 X( 11) =.17.77000E-01 X( OBSERVATION'NO. 40 WEIGHT = 1.C)O000 X( 1)=.9470000E 01 X( 2) =.8960000E 01 X( 3) =.15000OUE 01 X( 4) =.710, (02 02 X( 5) =.216C0000 03 X( 6) =.3270000CE 01 X( 7) =.1200000r 02 X( ) =. 0u' X( 9)=.307GOUJO 02 X( 10) =.5470000E 02 X( 11) =.2102E00E-01 X OBSERVATION NO. 41 WEIGHT = 1. 00000 X( 1) =.1375000E 02 X( 2) =.83200000E 01 X 3) =.54000E 1 X( 4) =. CuO O X( 5) =.21BC0OOE 03 X( 6) =.4320000E 01 X( 7) =.2209000' 02 X( 5) =. 49- CrJ'-JE 01 X( 9) =.4420000- 02 X( 10) =.46600oOE 02 X( 11) =.1860000E-02 Y( IS Vt

216 EDITOR PRO5GRAI:PRORLFM NOI. 5 SC! rION PASS- \in. NO. OF I',]DEPENFEF4T VAR~IARL'ES = NO. OF TRIA-L TEENVS = 4 0 TRIAL TERN DEFNIIOS f2 PA~SS 00o. 2 TERM( 1) = 1.0v(, CoNSTVANT TL-VtA. TERM( 2)= INlTE7RACTIOjN OF- ItER 1 WHERE THE- COMPONENl~TS ARE DEFINED TO "E - COMPON'ENlT( I) = X( 7) TERM( 3) = IhTRI`ACTIcVI (IF ORD,'ER 1, WHERF 1HZ- COMPOINEINTS ARE D)EFINED TO PE -- TERM ( 4 ) = I'\!T P:iA",,T I ON OIF ORDeR 1, W HERE T HEF COMPONENTS ARE DEFINED TrO PECOnM.PONEN'4T ( 1 ) = X C 7)* P. 3~.000 W) f TERM( 5 ) = I NTERACT I O:lrI -1t ORDnER' 1, w HERE,1 T HY CrMPDNFNITS ARE [)EFIN!ED TO Pi E CWOlPOnENTC 1) = X( ).P..0 0 j TERM( 6) INIT:-R)CT I!'! JF-f OD f7R 1, WHE-lRE TH- COmPONE'_NTS AREDElE TO DE CotAP9OAiENTC 1) = X( D) *P -2. 0000 __ TERM( 7) = INlTERQACTIO)JN fl_ 0RDR I, W H ERE T HE_ COM11PON ENfT S A RE- DE F INED TOf F E COMPONE\N'TC 1) I C2 P.33 33 3 TERM( 8) I NTR: 4AC TI C N OF C URE I WHERE THErl COMPONIENTS ARE DE:FINED TO EcnOPo\,EN\TC 1,) = XC( 5) TERM( 9) = PI ",T R CT Ix OF,, ORDER-Pi~f): 1, WHERE THE COmPOrNEN'\TS ARE DEFINED TO R ECOMPONENI`T 1) = XC 9).P -2.C0 0 03 TERM IO) = NTRCTONO ORDIER.1 W HEP TOH COmpONENTS ARF DEFINED TO P FECMAPCI\NEN T( I)=X.P. 5 0(0) T ER M(I 1) INIT[RACTIrDJ OlF ORD1ER 1, wiH-RE THE-`9M400H14_ITS ARE DEFINIED TO E - CnOMPONENITC 1) = XC L).P. 3.200 TERM(1 2) INTERMCION OF- ORDER 1,'WHERE T11E- COMPONENJ_-',TS ARE DEFINED, Tn CCnOjlNPONrTC i) = <( 10).P.500C TERM(13) = INTE-RACTITNJ OF ORDER 1,v W Hr'RL THE - N CM IN T SAR )INDTFECOm PON ENT( 1)I XC4.P.3 3 3 33 TERM(14) = INT7ERACTIOn, OF vORDE:R 1, WHE-RE THE- cOm2ONEN;l~TS ARE DFINlED TO t3 -- COMPO'N~~rET( 1) = XC 4).P. -. O(i) r,1 TERM(1 5) = INTERACTI(N F ODE 1, NHER-E THE COMPONENTS ARE DEFINED Tl RE - C OIMPONIEN.lT ( 1) =X 4).P 2, OOO 0 TE (16) = A ITER-XA C T ION OlF OD ER 1,I W HEE R TH I. COrMAP ON F\ T S AR E D EF I NED TO D — E C OMPO N FNlT C 1) X 9) *P * -3 J J3~ TERMC17) = INTEIRACTION O F RO E R 1t, WHERE_ THE COM-P."'lJENITS ARE DEc-FINEDr TOl OF COC1MP (ANCN 4TC 1 I) = XC 0 ) P. 2.GI0 0003_

217 TERM( 18) = TNTE-R~CTIO'J1 OF ODR 1, ~HC-RF THE1 Cfl~1PONE-NTS ARE FIV Ti 1 - COM P0N N T ( 1) X(I 3).P -1. 00 J TERMC 19) = INTE-RACT10ID rOF'11RDER 1, WHE-RE — THE cO~mPONEN~-'TS AR EINLI) Tf) -' COMP9ONENT( I) X( 4) *P.50030 TERMC20) = IN1Tr-RACTIOn, 9 F O RDE)R 1, 1WHERE THE C0MhPt)1U-\1LTS AR~E )EFIO'ED TO) RFC OM PO NE N1TC 1. = XC 1).P. -2.0 0 0 TERM(21) =INTE-RACTION OF O~nRDE,WEETECMCET R EUDT? COMP)NENT( 1) = X((10) WHRTHCMr4TSAErFI.DTIQ7 TER.MC22) = PITIERACTI(N o F OnrDER It WHqRE THE COMi-P0OJENTS A-RE DEFINEDU TOl 8 rCOMPONENT ( I. X ( 3) *P. -C0 TERM(23)= I' TERACTION nF ORDER 1, WH7P'E THE compwNE"TS ARE D)EFINEJD TO RE CDMPOIEIJFT( 1) = X(ID).P. 2.00000 TERM(24) = I NT ER ACT IO9N OF ORrDE-R 1WHE-RE= THIE- CIOhPONENTS ARE DEFINFD TO fE -- C OM PON EN4T( I) XC( 4).P. -3 3 3333 TERMC25) = INTERACTIO~N OF ORDER 1, WHE-RE THE COM-PONE NTS ARE DEFINED TO RE - COMPONENT( 1) = X( 3).P. -3.a 0 00 TERM(26) = INT7ERACTION O F R DE R 1I WH-RF THE- COMPO)NENTS ARE [)FFIINEF-D TO ElF - COMPONENTC 1) X( 7).P. -, 50000 TERM( 27) IN\JrERACT ION OF ORD 0E:R 1, WHE:R E THE,- COM1'iPOfN EAT S AR E 1)F F INEI TOF B E COMP0ONENT( 1) X= X1O).2..0009)0 TE. (2 8) I \NTER A'C TION O 4 lF OlRDL)E R 1,1 RHERE T HE COMPONENSM )F Dro FE - COMPONENT( 1)= XC 5) P2. -3.0f0 03 TERM(29) IN4TERACTIO'N OF ORDER 1, WHERE THC- COrMPONE4NTS A~IP DFFI`4ED TO P~ F COMPONENTC 1) =UX 5).P. -50013 TERM(30) = INTERACTION- OlF UORDE)R 1,9 WHERF THE- CO-MPONENTS ARE DFFINJED TO RE -- COM P OE' —'NTC 1) I XC 7).P. -1.COO') o TERM(31) INTtERACTION IF- ORIDCR 1, WHERE THE COMPON-ENITS ARE 1)WEFI:\I E DTOLIEP — COMPONENT( 1) = XC 8)*2 -2.~OJ T ER M (3 2) INTERACTION O F fIR oE-R. 1,P WHE-RE TH OPNNSAEDFNDT ECOMPONENT( I) = XC 5) P0. 3.00330t TERM(33)= INTE7RACTIONI OF 0RDE-R 1, WHERE THE- COMPONENTS ARE DEF FINE FD TO0 FE C 0PIPON1E N1TC I. XC 5) 0P 500001 TERM( 34)= INTE-RACT IOi IF OrlDER 1,v WIERE THrE COM13OtJEO~ITS ARE IDE F INED TO- RE - COilMPON E'T( I) C5.P -2.0r3) U ). TERM(35) =INTE-RACTIU1 O)F O)RDE'R 1, WHE-rE THE: CO1MPOnEN —TS ARE D0E FI NED T EC OM PON E\TC 1) I XC 9) P0.5000) TERM(36) = IJNTE-RACTION i-1F ORDER 1. WPHERE THEr- CntAPONEN-'TS ARE n!,-F IN'EDTO RE FCOMP9NE`'T( 1) XC 5) P.I -C 0 )J~ TERM(37) INTERACTION OF, RE R 1,WHRE THE cnmCDOrNETS ARE D F I N1 TO _COMPfONENTJ( I1) = XC 7).P. - 2.C )O,)J

218 TE4M ( 8) I \I7AT U Y! i)r fR I),EL v,, 7 HTF TI i:,n, flP njl'NLT S A,~ kE r F)I 41D ri T Q - Cf M PCVITE:,JT(I) XI 7) P~ -3.C%)r, T E RM (9) I AT ~ AC, TI RN fIr FR~P 1 R1WHP. F 1 HZ, fmpflNENJTS U EP FLI NED To KE - C ni POG"Ei T (1 =Xl).P.iQ0 T ER M 14 0) I ".IT R ACT IA(N A)FU F)RIE 1 WHERZ THI n~ COpoWNIS AREE DE FI NE'-D Tn AC EICA(iM PA1-'YENI ( 1 ol2 P2.. ECCi,) TERM(41) = Xlii), nFPFr"AE'!T VARIA6L-.

STEPWISE REGRESSION PROBLEM'NO. 5 t OF DAA SETS = 10 NO. OF TERN CHiOICES = 4) PROBAPILITY OF 1) ERqrl IN EATEIRIN TERM = 1.COCO 0/0 2) ERq'OR I' DEL. ETING rERM = 1.0000 0/0 WEIGHTED DEGR-EES C-O FF E_-IDI,; = 10.00 PASS NO. 2 STANJDARI) TRIAL. STANDARO ER.ROR OF Y =.194522433F-01 STEP NO. 1 TERM ENTERED 1 F LEVEL =. OOOOOO0E 00 STANDARD ERROR OF Y.126781249E-01 COEFF OF DETFRMINATION.58037710E. 00 MULTIPLE CORLTN Cl-FF =.761824846E 00 -ONSTANT TERi =.00000COOOE 00 TERM NO. COEFFICIENT STD FRR OF COEFF F LEVEL TERM- 1.1. 33359993E-01.400917511E-02 -.968164429E 01 PREDICTED RESULTS VERSUS DATA POINTS OBS. NO. PREDICTIONS DATA DEVIATIONS Y - SIGMA Y Y + SIGMA POINTS (OATA - Y) PERCEfNT 29.65787439E-03.13335999E-01.26014124E-01.24300000F-02 -.10905999E-01 -448.807 30.65787439E-~).13335999E-01.26014124E-01.18500000E-02 -.1148599qE-01 -620.865 31.65787439E-0J.133359)9E-01.26014124E-01.40400000E-02 -.92959993E-02 -230.099 32.65787439 —03.13335999E-01.26014124E-01.39000000E-01.25664000E-01 6:-. 805 33. 65787439E-03.13335999F-01. 26014124E-01.19730000E-0 1.63940004E-02 32.403 34.65787439E-03.13335999E-01.26014124E-01.17090300EC-01.37540006E-02 21.966 35.65737439E-U-3.13335999E-01. 260141241-01.84699999E-02 -.48659994E-02 -57.450 36.657,87439_E —3.,13335999F-01.26014124E-01.17370000E-01.45340005E-U2 25.372 40.65787439gE-03.13335999E-01.26014124E-01.21020000E-O 1.76840005E-02 36.556 41.65737439E-03.13335999E-01.26014124E-01.18600000E-02 -.11475999E-01 -616.989 MAXIMUM S3SOLUTE DEVIATIC'. =.2566400E-Oi,(SEE n0S. NO. 32, LINE NO. 4) MAXIMUM ABSOLUIF EC..EPRC.''T rEV IATIN.._ 62.0.8,.5., (SEE OBS. NO. 30, LINF NO. 2) STEP NO. 2 TERM EN-TEPR ED 2 F LEVEL =.129055079C 02 TANDARD ERROR r- y =.803735927E-02 -tOEFF OF DET9ERK'IrITIn, =,.5.434799_E..0 _ MULTIPLE Cr)iLT"I CO-FF =.923273958F 00 CONSTA',T TER'i =.0 )u000000E 00

TF2E 1lq. CIEFrFIC I-,T ST9'-!0 OF 5nEFF F LEV-L TERM2- 1 0.-1. 4 2 1)4 )4 7-02 -. 3' 5i 57b 02 TERM- 2 1 54292099E —?2.-2 3494713E-03 -. i 1061 3639F 02 Pq<F)IC TFr OES JLTS VE SUS D\TA Pn INTS OBS. NO. P' EDIC r[[1s D AT! _ V I T I r',J S y - SI Y y + S I GA4 Pr)I\ITS (DAA - Y PE.' 1IT 29 -.203952'0, -uv'.59978 3'UI7:-01.2430.J000. -02 -I3. 7 7837E — 4:. R' 30 -.20395206E-L, 5997887- 02. i4035190E-01. i85000OE-) -.$141t8 7E- )- -2?4. 07 31 -.203-5206-_-j, 59)9783q7r_ 0.14351 9, %-O1.4I4 OODG+u00E-o' -. 19578r, 7E-O? -4o.46i 32.161)5299E-!.2414222 42E —1.3 O'3 0)3 7E-1.3'9)0D0u00 0 -Oi.14,7'342E- 1 3 Q.,33.16105299E-0Oi.2414265E-01.3iu6 -17E-01.1973300007-0i -.44I26085E-rjL -'.( 34.65545813E-0?.14591941-0O1. 629 ~ F OOE-0(i.1709000.0-01.24930bs3E —0' 14.617 35. 37001673E-02. 11737527F-01. 1)774836E —i. 3469)9999-0 -. 2675 27E- ) -37. 7736. 19993474E-)1.2803083 4 -01. 350601 93E-01. 17870000-01 -. 101 6034E-01 -56.;S 40.6 1071325f-02. 14144492)-01. 2 13151 E-01.21020000C-0 1. 6,' 7505) 305- 02 5. 70o 41 -.94609971-02) -. 14236378E-02.6 137 15E-0.18600000F-02.32P3637PE-() 17 *.4 MAXIMUM ABSOLUTE DEVIATIOI =.1495734F-01,(SEE ORS. NO. 32, LIJE NO. 4) MAXIMUM A3BSnL(JTE PERCEENT D,-VIATION = 224.237 (SE- nlS. NI. 30, LINE NO. 2) REGRESSION TERMINATED AFTER 2 ST:ES. DIAGONAL ELEMENTS VAR. NO. VALUE 1.547893651E 01 2.547893651E 01 3.670395739E-02 4.753390677 —01 5.310583644 —02 6.564924158E-02 0 7.218209295E-01 8.575747900E-01 9. 372760940E 00 10.132635543E-01 11.173221907E 00 12.133868573E-02 13.5489151 11E-02 14.354802053E O0 15.955615543E-01 16.568901233E 00 17.1144U5777E 00 18.840869285E-01 19.112671576E-01 20.2016707P5. 00 21.6917146001-02 22.116608379- 00 23.402577464E-01 24.791389525E-02 25.542865485E 00 26.1448411035-01 27.108746253E 00 28.287460446E 00 29.1482762825-01 30.818887427E-01 31.162732925E 00

3 1) VV)j~ 32. 317~!0J )- 9 3 3 I 5 4, 01; 2 1>?v,^ i 34 1 7 1 45 9 4 3') 35.22L66o' 7-6- 1'U 3f6, 4e l2I'23-01 37.29174 )75 rO 38. 44735 0 4R 0 3 9.4 634 r25 2 0 1 40.49864,)5%3-01 POSTULAT E) CRITE' I STaNDaRD ERROR OF Y =.CC'))COo7 O0 COEFF OF DETER'I'~,1iATI9l =.97C0000)E 00 FITTED CURVE PR'PPERTI'-S STANDARD ERROR Oc Y =.8,3 373o9E-02 COEFF OF!)FTERMINATI'lJ =.8524349E 0o PASS NO. 2 WILL,C EXACUTED 2 TIM'S, USI,4,' R;AD:l0 SELlCTIL(J"R.SS NU,'OER 2:. -\',l OU TR I AL iIq10, R! STANDaRD XR',OR,OF Y =.F184522433- )1 I —I STEP NO. I TERM, ENT ER EIJ l F LEVEL =.GC')COODCCOOE O0 STANDA?,D ERROR OF Y =. i2o7i1249E-01 COEFF OF r)ETE-. t1I"IAT' rl =.58037710E 0O0 MULTIPLE CORLTN CO-FF.761824(~451 O CONSTANT TE;RM =. 0000300>0E nO TERM O10. CO'EFFICIENT STf ) ERR OF C EFF F Li-VEL TERM- 1.133359'9 93 —01.400917:511 u-02 -.:96,164429c- 01 PRF-DIC TD RESULTS VERSUS uATA POuI'TS OBS. NO. PRE-DICTIONS DATA T;FVI;TIr:T S Y - SltMA Y Y + SIG MA PnI1T.S (r)ATA - Y) PYF'I'IT 29.657874398-O?. 133359'-i)l.2 r14124-01. 24300000) -' -. F10905 999E-I1 -4. 9,-; 7 30.6578743E-03-Q3. 33%sO 9E-01 -. 6014i24E-4'. 1854()0:0)F-J2 -. 4 4; 5999- [- -',.'1, - 5 31.657-7439=-03. 13 J3599 -) 9E-1.' 4)14124-()1.40400000F-0" -9 092'59993C-' -2C. 4) 9 32.6578749E'' ~-()-i.390nOOO.f-() 9.2O+(aOf_-4l(9-0 9'5.'=^ -i 33.637P74 9-. i, 339 99 —1.2 3 3 9 2 4-1 t) 1 ~ 973,i.4F-j o 39 g t40,'W ~-'3'./ )' 34.657 74 99:-0 -. 7 35 39:-'_, *' -0 14124-)I. 1 7'O) C 0 0 0.37540,JU'3[ —. 2, 35..5 787&3'-3.133 993- J-.2C j 414-1. 4 4599999-U -.4, 9994- -7.4 36.6570j74'3 )[-O,.1333 99 - 1 I 1 4 -.).'77 )0()0 —,)..4 40 " ) - (., _ 40.6 37 74:39E- 3. 3. )1'- 4 I4-).2 1 J -.)i.7 0A, E- 7-.5 41.65787411L-0".1l 3 9 E9-')!.:)1414- )1.1R )0:-) _ -i 99-N1 -(i]. 7"9

MAXIMUM ABSOLUTE OEVIATI\nN =.2566400E-01,(SEE n0S. No. 32, LINE NKO. 4) MAXIMUM ABSOLUTE PERCE`IT 11-VIATInN = 620.955,(SEE nFS. NO. 30, LINE NO. 2) P NO. 2 fERM ENTERED 26 F LEVEL =.459425967- 02 STANDARD ERROR OF Y =. 132853172E-01 COEFF OF DETERMINATIC" =.758337393E 00 MULTIPLE CORLT'4 COEFF =.870825700E 00 CONSTANT TERM =. OOO0OOu0OOE 00 TERM NO. ClF-FFICIENT STO ERR OF COEFF F LEVEL TERM- 1 -.8077071301E-02.99737031-02 -.561232217E 00 TERM- 26.635723443E-01.293216225.-01 -.441839866- 01 PREDICTED RESULTS VERSUS DATA POINTS 08S. NO. PREDICTIO IS DATA DEVIATI9rIS Y - SIM4A Y Y + SIGMA POINTS (DATA - Y) PERC_-tT 29 -.23412124E-02.79443048.-02.18229822E-O1._ 24300000E-02 -.551430)48E-02 -225.92 30 -.23412124E-92.7944304SE-02.18229822E-01.18500000E-02 -.60943O4RE-02 -329.422 31 -.2 3412124E-U2.79443048E-02.1?229822E-01.40400000E-02 -.39043u48E-02 -9. o41 32.99790417E-02.20264359E-01.30550076E-01.39000000F-01.18735441E-01 4. t)a 33.99790417E-02.20264559E-01.30550076E-01.19730000E-01 i -.53455913E-03 - 2. 7) 9 34.10982609E-02.11383778E-01.21669295E-01.170900008-01.57062'19E-02 3.39 35 -.27746253 —03.10003055C-01.20293572E-01..84699999E-02 -. 15330548E-056 -1. 159 36.20079530E-01.30365047E-01.40650564E-01.17870000E-01 -.1249504PE-0l - 69.9;40.861750336-03.11147267E-01.21432785E-01.210200008-01.98727323E-i)2 46.9o 6 41 -.4191700RE-02.60938163P-02.16379333E-01.13600000E-02 -.42338163E-02 -227.625 MAXIMUM ABSOLUTE DEVIATIO' =.18735446-01,(SEE O'RS. NO. 32, LINE NO. 4) ~....._.____.__............ MAXIMUM ABSOLUTE PERC'ENT DEVIATION = 329.422,{SEF ORS. NO. 30, LINE NO-. 21) STEP NO. 3 TERM ENTERED 20 F LEVEL =.190802384E 02 STANDARD ERROR r: Y =.377533772E-02 _ COEFF OF DETERMINrATION =.972035036E 0O MULTIPLE CORLTN COEFF =.9859437278 00 CONSTANT TERM =.000000CGOOE 00 TERM NO. CIEFFICIENT STD ERR OF COEFF F LEVEL TERM- 1 -.o213R3607E-01.877700008E-02 -.417682342E 02 TERM- 20 -.974804571E 0(.12906344,E 00 -.382854979E 02 TERM- 26.3121378015 00.377944969E-01 -.568400346E 02 PREDICTED RESULTS VERSUS DATA POINTS OBS. NO. PkEDICTIONS DATA D)EVIATIONS Y - SI'MA Y Y + SIGMA POI'NTS (DOATA - Y) PEiRCEENNT 29 -.477951:36E-03.32978& 9r-02.70737235E-J2.24300000E-02 -.857885388E-03 -35.715 30 -.47795186E-03.32973859P-02.70737235E-02.19590000 -02 -.14478859E-02 -78.2o 4 31 -.47795186E- 3.329733 59E-02.70737235 —02.404000008-02.74211409E-03 1~.369 32.31948239E-0i.357241266-01.39499963E-01.39000000E-01.32758741E-02 >3. 40) 33.22 564784 E- i.263436211-01.30116459E-01.19730000E-01 -.66106217E-02 -33. 35 34.11934763 —0l!.15710b0,)1E-1.19486438E-01.17090000E-01.13793993E-0? 8.f)71 35.78807566 E-0.116563)45-01.15432432E-01. 84699999E-02 -.31865945E-02 -37. 622 36.12395257t-01. 16174095E-01.19949932 E-01.17870000E-01.16959051 -02 9.490

40.144375872-0l.182134?5E-0i.21999262E-)I.21020000-01.28065750E-02 13.352 41 -.41289626E-0 -. 35312492F-,)3.3/42,7129E-,)2. 8.600000F:-02.22131249E-02 1IA.931 MAXIMUM.IStLUTE E-VIATI'D4 =.66lU022E- }2,( SF O!]S. iO). 33, LINE NO. 5) MsXIMUM A3SSLUTE P=RC- NT [)DLVITICl: 1?.V 9,(SI'IIS.,10. 41, LINE ND. 10) STEP NO. 4 TERM ENTERED 37 F LEVEL =. 03 O 0) 0E 09 STANDARD ERqR OF Y =.1 88477',), E-0' COEFF OF DETER1MINAT I') =. 994203761 — J) MULTIPLE CORLTN COn.FF =.970U)771 — O C) CONSTA. T TERV = 000000 )C) C O TE!-'>)'PD. C FFIC IEJT STn',RR nF COFFF F LE-VEL TERM- -.b 4' 135 9 329T -01.4t4049479-0-(2 -. 16959145 1 3 TERM- 20 -.i7 1 5, 721E 01 2U297 33IE 0 -.57151 2 4!3 92 TERM- 26 * 344i75375F 00 ~2'.4i3424' -0l -.231293l9 7E 03 TERM- 37. 749 t87 ~r 09.i71504cD9iF J) -.152641907- 02 P rEF) I C T RESULTS VERSUS DTEA PrI ITS OBS.,'0. PFF)ICTIY NS DATA EVITIqTtS Y - SIGMA Y Y + SIGMA P0 Ir'.TS (P, ATA - Y) P,' 29.354765123 -3.23 9j321-.4 1 2 430)E-9 2 4 000, F-u.F I 4079 2E- 3 7.,330.35476123 03.223953.41i24300-( - 4 824 -I-) 23 15'- 0: OOE - 3 L-'.u0-0 31.35474123E-0. 2239321-..zi243, 9 9-09.-+040000f)-O'.-0.2 14l.-4, 7 ) 32.36433703 _-0. 33144 —01.l 2344-.39)0 004-")1.- 4 4 E -;3',2,' C 74 -, 33.18,)31842E- 1.13915613- 11.8 1Ui374E: I. 7i7300 0b — - _ ii,~ -v -. 3U, I' 34.1333771ZE-Ji.l 9) 3- -l.17 77. -U.170900C)[-0.1 975!.-0;' 7'7 35.1CJ0O5704E-(0)'.~ 1 9.1, 7 — 01. 377L 4.7 -'1 F.1 bF46 ) 9999 F-i)" 3 -.4 D 7'4? - 36.16u:2 635SF-,1.17')774(,.I-,1:19?621 77E- -1 17D70000E-U -. i )740, 41iE-' -. - 40. 1 -)4 J 7,,2 2E-) I. Sl. 76 t9 3 1 E- )1.2102 000 7-u 1 - 2 71 0!7-. l -I.2 >7 9 1 - 41 -. 33052427-,J 3 * 1.55414~ 0-'.333'9i7'-~-U * i73600000T-0- * 3) 5' "TYE-5' iE ~' MAXIMUM ArSfILUTr- tV')VIATID'-J =.D42;:475' —,,(SEF O, S. ^'. 35, LI'IL' fl. 7) MAXIMUM ABS.35fLUET PECt-.'T i)'VI TI:,': I4. 3D, (SFr PS. ",D. 31, LINE Nfl. 3) POSTULATED C<I Tr:I A STANDARD ERR.> OF y =.CCC-'JOCC' 0') COEFF OF D9 TE2',I',ATIrl'!.- 7 C0 (GE 0) FITTED CU.V'-,.g-) PFTITi STANDARD:9pFItrj - Y =.1', 4 177 —,) COEFF OF )EFI.!'I2',TIH; =.;4~0)>95 C'D BEST. PREV'l lJ$ FIT'. CtT',v-' T1-TIT STANDARD FY',t) r, Y =.y.,,7,S -5' COEFFICIC-,T 7;.. T r'''I,,'TI:.,; 34: 4.

STANDARD TPIAL P': J!-CT - I! F \VO"'F Ti- CIJ!,', T'1 L. PASS NUO"lER, "', T!2 I \L:lt;J,`;3, K STAND4RD [ -:R30.)C Y =.!.;52 433-_-01 STEP NIO. 1 TERM ENTFRE 1 F LEVEL =.C0 30)0)D 00 0D STANIARD'- FRI; ( F Y =.1 36-7 I-)149g- i COEFF OF nETFR TI,&,AT)l!':. 5qj37 710l0 C1 O MULTIPLE CGLT\'' - =.7,,4-E4E,)jJ CONSTANT T —< =. CCCE'DOCeO(). 00 TER M N.0 CFFFICIIFI 5T STI) FRR. OF CFEFFr F LE V.L TERM- 1.1 9-f'99:) —C(.~d0917511E —02 -.'6'164429E 01 I' I-C D n 9 -F SUlJLTS VE' StUS DA1TA P3Ir TS OBS. NO. PR I ICTIONIS DAT [) FV I ATI J'S Y -SI,6A Y Y + SI',,11 P11I\21S (DATA - Y) P- I CI-:HT 29.6570_7439E-0 ~ l 3i399c- 1. 6 3 901 4 EL-:J-. 124300U1(:-'J2 -. 4 1 )9E-01 423J- 4-:. ~'J 7 30.65T71)-). 13sk9,r_.-.260J14iAJ'+E-01. iXC. 3J00000rt)-0,: -. 1 14,f55" 9EJ-')i -\K2 )..A65 31.657 74 39E-) 03 333'999 — O 2)2014i 4E-O24. 434I))C,) 030 1- -. 929599' 2- -' 4,). 9) 0) 3 1.6 -5 7 R 7 43 9,' - 3 1 3 339 3 —014124 E 1 4 J'1) ) 0 0) F'J - -J 9 * 9 t'-t) i9 9 2 3 32.5578 74392- 33. 3 99)E-"!.3 Z6J4124E-0!.3900000E-:D'l S.2 E-! 33.6578743AF —'J5.1333599)9':-)1. 0114 i 24E-J1.1973000u 0 —— 0 i.63 )40')4E-O 3. 4 1% 34.65737'37 53-) -'3.13' 5,99 -01 2"014124 0E- 1790 000-O. 754006-u L. 9' 35.63 9. l -9_. 7 ) 7 4 9 ). 1 3 3 ) 9. 1 2041 2+E 1 4 9999 9 99 4-: -. 9. 2. 4;L - 36.65757439-03.13335999E-l).260141!24-).1787000OE-O.45 240005E-O 2. 572 40.657 7439_E-03.13335)99 —;1.26014124E-01.'21) 2000 JC-1.763400(5E-02 36.55$ 41. 657q7439E-',3.1333 59)9 01.26014124E-01. 600000-02 -. 1 1 475992-01 -61 t 2 -9' - MAXIMUM ABSOLUTE )_VIATIq'] =.2566, t 1,,) I(S- OPS. NO. 32, LINE,0. 4) MAXIMUM ARSOLUT"- PE30:ENT OVI\ TI N 6 29.,SEE FO S. NO. 30, LINE NO. 2) STEP NO. 2 TERM ENT!ERED 31 F LEVEL =.00 C000JOO: JE0 STANDARD Rr Kljr< OF Y =.941521563E-") COEFF 9F DET'._RMII'JTIO' =.7T750)33:3-7E O0) MULTIPLE CFrLT",J C::-F: =.3)303J457E CO CONSTANT TERk =.00030000)E 0') TERM NC. Ci.FF IC Ir T ST' -R, O(F 2C0rFF F LEV-L TERM- 1.6450)1236E-02.0 3962'6F7F- A)2 -.234959931E O1 TERM- 31.107475b410F 30.30793? 613F-01 -.64j34l0979E 01 P,'EI C TD',ESULTS Vr'-RSUS ST. PI INTS OBS. NO. PR-D I CT I [IS nATA I)EVI [IONS Y - SIGMA Y Y + SIGMA POINFS (D3ATA - Y) PRC T

29 -.1lO27879fDF-3. 8387'3370F-02 * 179002553E1-1.24 3')iU006-u-.5737-2 24. 30 -.102787360 —)2.8387337G1-0.17E'02553F-01 15O1Z0i-o?371-2 ->:'.31 -.1.02787361-D7.938733701 —02- 315251i 44O0Z3.37 1- -17.36) 3 2.173525913E-01.26767814E-01l.3 q 3,'310j- )1I 3000jP~j 33.17352598E 30.26767814P-01.3-318313(3E01.1'.9 7 3 0000' 0-7'- 7' )) I 4 4[E-J 34 -.16749509E ()-.77402 64 RE-02.1715504306 01. 17 09 000) -l I'-4)73 2E-?',)4> 7 T4 35 -.17981O95F P2.76 17106 1 E1-02.17.D3232,2 6. R4690i999F- J * De-L, *9169E-A I 3 3 6.1423 19)32 31E-'.23647139F-,1.3 306 2 3. 18405)0 —I -P5771, 73 40 -.l4041l169E-02.801102371-702".1742624'7-0 1.110)2 0 000 -ul 130039l71E:Il i&W 41 -.17683987F 0L.7b468169c>02(.17062033 E30 1.13600007 ~ 7't Q A'- 9' ii MAXIMUM 4BSnLUTE nlFVIATIO"'J 1 3 00 89 7E -0, I SEF 9 S. 0J'- 4 LINE- A()*'4 MAXIMUM ABSOLUTE PERC -:NIT O7VLATION 353.37.) (SF-;- O1S. NO0 30 L~lE NJO* STEP NO. 3 TERM REMOVED 31 F LEVEL =. ocoocOOOE 0(3 STANDARD ER.RnR OF Y=. 146394'376E-01 COEFF OF DETERNINATI(TA. 5803771)21 0) MULTIPLE CORLTN CO0rFF=.76182qa46E 00 CONSTANT TERNi C000010007 00 TERM JO 0. COEFFICIE-lNT STO ERR, OF CIIEF-F F L 7VEVIL TERM- 1 * 133359;993t1 —01.462939657r1-02 -.691546030E 01 PlfSE O I TE R ESUL TS V E'RS US 0D1T P lI T S OBS. NO. PREDICTIONS OAT4 D FV I T I S V SNI GMY Y + SIGMA Pr0INTS (0414A - Y) P FFCR5P ET 29 -.1 30343F03R 3' * 1333 59991- 01 * 27975437E-01 2 430 0 03E F U -.l1)9i)59991 01 -4,tl-. 87 30 -. 1303438> o-?0.133359")91-01O.27975437E-01.185'(0Clk00 -J-. 11485999E1J 01 6'20.0 31 -.13034,38> E02 *13.335999E-01.27975437E-01.4040330L' 0 -.97959993 09), 3? -.130343 A> u2 * 133359991E-01.279754371-01.3900'000O.?5-400 i30 33 -.13U343%3E 0.13335~99c-01.27973-4377-01.1973,'Ju 00-.3394 000 4 F- 32 40 34 -.13034383E-:D.1 33 3 59 E1-0(1.27975437E-01l 17 0q00)01 -0 3L500I I 966- 35 -.13334-383F-0?.133359199>01.27975437E-Jl1 ~ 4 64~99 99 Ej2.4 39 659)94 E- 74,50 3 6 -1 3U03 4 3833E- 02.133359)991-0l.27975437E-01.17370300F) -0.45340001 37 40 -.130343831l-0-.133359991-01.27975437E-01. 21) ~0 )0 0 r-3 1.7 0 4000> E~ - 4 1 -1 303 4 3 833E1-Aj.133 3 59 991E-01).279754371-0l.1 ~8 61;) 0 E- -.1i'5"I 9 3 MAXIMUM ABSOLUTE OEVIATInO4.2566400F-01,ISEET OOS. NO. 32, LINE 10). 4) MAXIMUM ABSOLUTE PERCENT L)7AVIATION 620.83,5,ISEE OBS. NO. 30, LI'E- NO. 2I STEP NO. 4 TERM REMOVED I F LEVEL =.000000001o 00 STANDARD ERROR OF Y. 2t75623210E-01 COEFF OF DOE T E R1I NA TIO f=1.745058060E-09 —.,ULT1IPLE C-OKLTN14COGFF = 6 8i3 i6 7A~E CONSTANT TERM =.0OOOOOCCOOfI 00 TERM NO. COEFFICIENT STO 18'?R OF CGFFF F LCIVCL TULATED CRITERIA STANDARD ERROR OF Y.010,000001 00 COEFF OF DETERMINATIfO1 = 97C0000E 00

226 FITTE17 CtjkvF P2DprI- LT I-S STANDARD 1kRf)'IF Y = 7~ 15,"21- ) cnOEFF OF OFTF-u'L ~ATIiT'; = *7 4t5 (5`IJ- G bL:ST PREVLI'JS ~-VTTD_) CIW~VC PROfPER<TIES STANDAR<D ERO nF Y.1893~4771E-.o2 COEFFIC~rNITOF DT1L\IJ=.99411)382O CURRE~IT TRIAL -~FJ`aCT~7D IrFAfV F RikNOCv4 TRIA\L 0U. 1 POSTULATED CRITLa,~v STANDARD ERRM) FWY *CJ)))Y0 COFFF OF D ET i1I',JA T~ I.7 CO O 00 FITTEn tr ~ c'f_ F'VE ~P'TLI 7 STANDARD -R~ rF Y.i47I.) COEFF OF r,)c-TFkPIINATIIIN = 9942b33 7) FITTEO CUJQViI M~EETS 0~YCqO`F. iF F ~R ~T9iCRITE~~FpN, C -RENT PASS IS THr- F S OCAR. PASS Nqum1BJ, 3, BEC),UN P'VrIj~IL fl*L 5 TOTAL PASSES AL~j'rJ-r,.

MAD EXTERNAL FUNCTIOI STATEMENTS FOR PREDICTING EQUATION PRODUCED BY LAST REGRESSION STEP $ COMPILE MAD PUNCH OBJECT $ PRINT OBJECT EXTERNAL FUNCTION(XI,X 2,X 3,X 4,X 5,X 6,X 7,X 8,X 9,XLO) ENTRY TO HG;M)P. INTEGER I DIMENSION T( 4) T( 1) = -.64135933E-01 T( 2) = -.i7155672E O0 T( 2) =Tt 2) * X 1.P. (-2) T(3) =.34417588E C) T( 3).=..T( 3) *. ABS. X 7.P. ( -.500000) T( 4) =.74914379E 00 T( 4) = T( 4) * X 7.P. (-2) T(O) = 0. THROUGH SlIM, F(.]) I = 1, 1, I.G. 4 SUM T(O) = T(O) + T(I) FiJNCTION R-TURNJ T(0) END OF FUNCTIOnPROBLEM NO. 5... N'O-MAL TERMINATION *** ALL INPUT DATA HAVE SEEN PROCESSE0. AT LOCATIONI 10220

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