THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING VOID FRACTION MEASUREMENTS IN A CAVITATING VENTURI Willy Smith Gerald Lo Atkinson Frederick G. Hammitt September, 1962 IP- 581

PREFACE This work was performed as a term project in partial fulfillment of the requirements for the Master's Degree in the Nuclear Engineering Department of the University of Michigan by Mr. G. L. Atkinson, under the general supervision of Professor F. G. Hammitt. Direct supervision of the work was furnished by Mr. W. Smith, Research Assistant in the Nuclear Engineering Department. The cavitation facility itself was operated by Mr. M. J. Robinson, also Research Assistant in the Nuclear Engineering Department~ Financial support for the overall cavitation research project is provided under a grant from the NASA. Most of the electronic instrumentation for this particular experiment was kindly furnished by the Nuclear Engineering Department and the Phoenix Project of the University of Michigan. ii

TABLE OF CONTENTS Page PREFACE o. e..............................................e.o ii ABSTRACT.......................................... i. ii LIST F FIGURES.......... I INTR ODUCTION C ON.. i.. f n......................................... A. Motivati On for the In.estigatio......... 1 B. Review of Previous Werk.................. 2 II DESCRIPTION OF E4UIPMENT.......... o............ 4 A. Genetral.............................. B, Densitome+ o...,........... 4 C. Electronic E -ipmntl......................... 9 III EXPERIMENTAL PROED E.................... 12 IV REDUCTION OF THE DATAo.................. 44 V DISCUSSION OF RESE?LIS............................... 4.6 VI RECOMMENDATIONS O E E S................. 64 VII CONCLUSIONS... e s................................* o 67 BIBLIOGRAPHY............................................O e 68 APPE NIqD I(C ES APPENDIXC CALIBRATION OF ELECRON EQUPMENT.................. 69 B LINEAR ABSORPTION COEFFICIENT OF Hg FOR 1,17 Mev GAMMAS............................................, 79 C DERIVATION OF VOID FRACTION RELATIONS........... 8 D COMPUTER PROGRAM.................................... 97 ETABLES o....................iv. 105

LIST OF FIGURES Figure Page 1 Overall Loop Schematic.,,...,,.,,.,,,,,,..,,,~ 5 2 Cavitating Venturi Test Section..................... 6 3 Schematic of Densitometer..............o.......... 7 4 Photographs of Densitometer,,,,,.,................. 8 5 Block Diagram of Electronic Equipment............. 10 6 - 31 Experimental Count-Rate vs. Distance Curves.......... 15-40 32 Centerline Correction,, o o........................... 41 35 - 38 Void Fraction vs. Normalized Radius at Different Distances Z From Throat.,,o..... o................o. 48-53 59 - 42 Void Fraction vs. Radial Distance for Different Cavitation Conditionso,.......,....... o...,....... 54-57 43 Void Fraction Profiles,......,.,.................... 58-59 44 Comparison of Jet Diameters for Hot and Cold Water,., 61 45 Non-Dimensional Jet Diameter for Different Cavitation Conditionso.oo.....o......ooooooooooo oo...oooooo 62 APPENDICES Al Linearity of Linear Amplifier,,o..o...o,,,,,,,.o.o o.. 71 A2 Calibration of AE Dial,,,,,,,,,o o,,o,,,o,,..ooooO 73 A3 Differential Curves for Co60 and Cs137,,,,,, 000000 74 A4 Energy Calibration of SCA,,,...o,o....,,,,,.......oo,,. 75 A5 lo17 Mev Photopeak of Co60, o,,,,,,.,,, 76 Bl Mass Absorption Coefficient of Hg (LA-2237), o...,.. 81 B2 Mass Absorption Coefficient of Hg (Nucl, Engrgo Handbook, o).o o. o. O,.... o o oo.o o o o.,o o o 82 v

LIST OF FIGURES CONT'D Figure Page B3 Density of Hg as Function of Temperature,,,.......o 83 B4 Linear Absorption Coefficient of Hg (Data)oooo.....o o 84 Cl Venturi Cross-Section o,,,o............,oo,........ 89 C2 p(r) From p(x) ooo..................ooo.......ooo 92 Dl MAD Flow Charto.ooooo,,, o 0 o ooooo.. 102-103 D2 Flow Rate Calibration Curveo,,, o o oo,.o o ooooo 104 vi

I. INTRODUCTION A. Motivation for Investigation The present research investigation on cavitation-erosion damage in flowing systems has been concentrated on the examination of the phenomenon in geometrically similar venturi test sections. However, if the results are to be applied to other situations, it is necessary that detailed information on the two phase flow regimes in the venturi be obtained under different combinations of the applicable flow parameters. While this appears fairly straight-forward under the considerations of classical cavitation theory, in practice it has been found that there are substantial variations from such ideal theory 1,2, Thus it has been necessary to employ various special techniques to determine as far as possible the details of the flow pattern. So far these have included, in addition to measurements of static pressure, local velocity measurements 2' high-speed motion pictures of the flow 2,5 and local density (or void fraction) determination using gamma-ray densitometer techniques,,6 o The initial investigations using a gamma-ray densitometer were partially in the nature of feasibility investigations to discover whether or not useful information could be obtained. It was determined that it could, and, in fact useful preliminary data2 was obtained with water as the test fluid. However, it was apparent that greater precision in the technique would be most desirable. In addition it was desired to take measurements in mercury to compare with the initial water measurements as well as with future more precise water measurements. Thus it was -1

-2necessary to develop a precision densitometer for immediate use in mercury (or in other heavy fluids as molten lead), but with the possibility of later conversion, with a minimum of modification, to water. The development of such an instrument, and a discussion of the data obtained with mercury as the test fluid is the subject of the present report. B. Review of Previous Work Previous work under this research investigation 2,3,6,7)8 indicates the feasibility of the determination of the void fraction, or local density, occuring in a cavitating venturi by using a gamma-ray densitometer. However, after a critical evaluation of the technique used, it became evident that several errors had been introduced, and that a more refined procedure was not only possible but desirable. At the same time, the need of a computer program to reduce the experimental data to a more tractable form became obvious. The experimental equipment is essentially that used by Adyan8 thaya, who made preliminary void fraction measurements in cavitating mercury. The main difference between the present and Adyanthaya's investigation8 consists in a very careful calibration of the electronic equipment, in such a fashion that only the 1.17 Mev gammas of a Co6 source were counted. Background and statistical errors were reduced to a minimum within the practical limitations imposed by the need of restricting the counting times in order to keep the overall time required for the experiment to a feasible limit. *His work differed from that of Perez6 in that mercury rather than water was used. Also, a much better collimation and precision in the location of the measurement was obtained.

-3Another source of error in the previous experiments (particularly Perez's work6) was the lack of a proper location of the collimated gammaray beam with respect to the geometry of the cavitating venturio Some effort was devoted to avoid this difficulty, but as explained later in this report, the determination of the center-line of the venturi with reference to the collimated beam is of such importance that the accuracy obtained in the present experiment is still not entirely adequate. It is clear that the technique should be further improved in this direction. The design of the gamma ray densitometer using a collimated gamma-ray beam is discussed in Reference 7. The detector efficiency was determined to be between 18.5% and 63% depending upon the discriminator setting. This efficiency was computed on the basis of an average 1,25 Mev gamma energy from Co and a 2" by 21 NaI(Tl) scintillation crystal. The use of C6o was demanded by the strong attenuation of gammas in mer60 cury. The above calculations showed that a 20 millicurie Co source would be required to obtain statistically reliable observations of small void fractions in a reasonable counting time. It was shown that the standard deviation for a one minute counting time with the fluid cavitating sufficiently to cause a 2% void is much smaller than the difference between the non-cavitating condition count rate and cavitating condition count rate from which the void fraction is calculated. Therefore the 20 me source gives sufficient strength to determine reliably 2% void fractions with this densitometer using a one minute counting time. Reference 8 sets forth the general experimental and calculation procedures used in this report. The significant portions are summarized in the Appendices.

II. DESCRIPTION OF EQUIPMENT AC General The cavitation facility previously described 2, consists of a closed loop circuit powered by a centrifugal pump and including a cavitating venturi test section (Figure 1). Figure 2 shows the plexiglas venturi used to produce the cavitation field. The diffuser angle is approximately 6 degrees and the throat diameter is about 0.5 inches. In the same figure, the cavitation termination points for the different cavitation conditions mentioned in this report are indicatedo During the experiment, the stainless steel holders which are normally used to insert the metal test specimens were removed, and plexiglas fillers were inserted in their place to give continuity to the material density. B. Densitometer Reference 8 gives the details of the design of the collimator. However, the significant portions are summarized here for convenience. Figure 3 is a schematic diagram of the gamma-ray collimator and detector which respectively define a gamma beam and measure its attenuation upon passing through the venturi. Figure 4 shows two photographs of the densitometero The collimators have rectangular apertures, 0.030" by 0.200", accurately aligned. The longer aperture dimension is such that it is parallel to the direction of fluid flow within the venturi. The change in flow conditions in the axial direction over the length of the aperture;4

DRIVE PULLEY /BEARING HOUSING HEATER THROTTLING VALVE -TEST SECTION 32" 57" L ST UFFI GSTUFFING BOX SUMP TANK ~n MEASURING VENTURI THROTTLING VALVE ~~25 )1 i -~,I~~89 FiguCOOLING WATER IN COOLING WATER OUTFigure 1. Overall Loop Schematic.

IB x3 STUD AV TO NOSE WEAR SPECIMEN D,ABRD CAV TO BACK /-CAVTO IsTMK ---- 3.015 VISIBLE INITIATION - 3.013 -- 5.361"i B | ~ r. - 77535 —------ 1. l.lSECTION A-A 20 4 6.522c — ------------------— 1 — -14.578" —---.412"- Z AXIS 1.75" Figure 2. Cavitating Venturi Test Section.

-7PHOTOTUBE No1 (Te) CRYSTAL'L i XL-LEAD SHIELD 3l1 yI- CLI O LA COLLIMATOR 4S. X VENTURY CROSS SECTION f 3" / //-COLLIMATOR LEAD SHIELD CO6 SOURCE L MOVABLE TABLE DIRECTION OF MOVEMENT - Figure 3. Schematic of Densitometer.

- 8 - Figure 4. Photographs of Densitometer. Figure 4. Photographs of DIensitcmeter.

-9is not very rapid compared to the radial variations, and the 0.030" aperture is small enough to detect these variations as well as allow the passage of enough gammas to give statistical accuracy of about 1% with the 20 me Co60 source which was used. The whole assembly is mounted on a cross-compound index table so that the horizontal movement of the vertical gamma-ray beam in the radial and axial directions is possible to 0.001" accuracy. The detector and source were heavily shielded with lead bricks for personnel protection The source consisted of a 0.040" diameter piece of natural 59 cobalt wire (100% Co ), 0.252" long, encapsulated in a small aluminum holder 5/16" diameter by 2 inches long, sealing it permanently. It was irradiated in the Ford Nuclear Reactor at the University of Michigan. The aluminum holder also serves as means for attaching the source to the collimator assembly. C. Electronic Equipment The electronic equipment consisted of a sodium iodide thalliumactivated scintillation crystal detector, photomultiplier tube, highvoltage power supply, pre-amplifier, non-overloading amplifier, single channel differential analyzer, count-rate meter, scaler and cathode-ray oscilloscope. Figure 5 shows a block diagram of the units used, which are listed with manufacturers and serial numbers in Appendix A. The amplifier, although supposedly non-overloading, was easily overdriven during the calibration, and at times, upon moving the phototube. This, of course, would give spurious count rates which would

-10NoI(TI) PHOTOMULTIPLIER PREAMPLIFIER CRYSTAL TUBE, H-V I PULSE POWER SUPPLY GENERATOR NON-OVERLOADING LINEAR AMPLIFIER CATHODE RAY OSCILLOSCOPE SINGLE-CHANNEL DIFFERENTIAL ANALYZER: SCALER COUNT RATE ] TIMER METER Figure 5. Block Diagram of Electronic Equipment.

-11adversely affect the data taken. Continuous observation of the pulses on an oscilloscope eliminated such errors. The technique of observing only the 1.17-Mev gammas of Co60 in this experiment required an extensive calibration of the electronic equipment, especially the single channel analyzer. Details of the calibration procedure are given in Appendix A.

III. EXPERIMENTAL PROCEDURE The table that holds the collimator, Figure 3, was placed in an arbitrary position beneath the venturi in the mercury loop. Axial alignment was attempted by shining a light through the collimator apertures and observing the position of the beam as the micrometer was actuated to move the densitometer in a transverse direction. The table was then adjusted by hand until this light beam traced a path parallel to the sharp outer edge of the venturi test section. By repeating the procedure at the opposite edge, the center line of the venturi, at that particular axial position of the table, was determined. Moving the table axially, the position of the center line was completely fixed, and reference zeros were recorded on the micrometer densitometer positioners, both in the axial and transverse directions. A log was then kept of each micrometer adjustment which was necessary to keep track of the position of the collimator aperture relative to the venturi throughout the experiment. A constant and perplexing source of error was eliminated by this procedure. It must be noted that the arbitrary assignment of the zero positions relative to the venturi were "best guess" approximation by eyesight and that the actual venturi centerline was accurately determined by symmetry consideration once the data had been collected. The axial zero was placed as near as possible to the throat exit also by using a beam of light. Some time after completion of the experiment it was verified that this procedure of alignment using a light beam may lead to very -12

-13large errors due to the diffraction in the plexiglas, unless the beam is perfectly perpendicular to the upper surface of the venturi and opposite faces of the venturi are exactly parallel. For future experiments, provisions should be made for bolting or securing the table to the floor in some manner so that the axial alignment, once accurately determined, can be maintained and to ensure that the vibration of the cavitating system doesn't move the table during the test, which is a distinct possibility. Background counts were taken at the start of each day's runs and two or three times during the day. These counts were taken for ten minutes with the source in position on the shielded test table and the scintillation detector removed to a remote site from the test apparatus. 6o This procedure was mandatory, since the removal of the Co from the collimator could not be accomplished without a considerable dose exposure for the operators. Provision was made to shield the source in all directions to eliminate scattered radiation. Background corrections were made to the data in accordance with the closest time of background determination and test run. Table IX shows that generally these counts did not vary appreciably. Where there was considerable deviation, an average was taken, and applied to the data taken between the two background determinations. Test runs at a constant flow rate were made for different cavitation conditions and axial (z) positions from the throat as specified in Table X. Each axial position required a "no cavitation" run for comparison to the cavitation runs from which void fractions were calculated. The "no cavitation" runs could not be made with the fluid completely

-14stagnant because bubbles of gas collected at various positions in the test section. Hence, the pump was used to circulate the mercury at a low rate which eliminated the bubbles, but which could be considered definitely "non-cavitating" The experimental data were taken by advancing the table in the transverse (x) direction by increments of the aperature width, 0.030", in regions of relatively gradual change, and by 0.010" increments where the counts from point to point showed rapid change. Unfortunately, however, this was not done in the first experimental runs, and, as became apparent when reducing the data, introduced a rather large uncertainty in the region of the curves close to the walls. All possible loop parameters such as flow rate, room temperature, mercury temperature, cavitation conditions, pressures, as well as the settings of the electronic equipment and background count data were recorded, although they are not reproduced hereo Of special interest is the electronic equipment warming time. It was found that erratic results were obtained if this was less than about one hour, Consequently, the equipment was left on at all times, even overnight, with the exception of the voltage to the detector tubeo The experimental count rates, c, after background correction, b, are plotted in Figures 6 through 31 Each plot is for a certain cavitation condition at a particular axial distance z from the throat. Count rate was plotted versus x, the transverse distance with reference to the arbitrarily chosen zero (i.eo, approximate venturi centerline)o The curve was constructed and the assumed axial symmetry of the flow used to locate

-157000 l 6000 REF. l CO -0.3 -0.2 -0.1 iz 3 5000 - 0 K, TRUE WALL ---.255" I 4000 FI 3000 - 0.3 -0.2 -O.I 0 0.I 0.2 0.3 X, INCH Figure 6. Run N023, Zero Cavitation. Z = -0.25, R = 0.255, D = 1.0.

-167000 6000 REF. % -0.3 0.2 -0.1 5000 TRU 0 IJa i I ITRUE I WALL ---- R.255" - - 4000 3000 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 x, INCH Figure 7. Run N022, Visible Initiation Cavitation. Z = -0.25, H = 0.255, D = 2.5.

-170 7000 L 0 6000 REF.. I I I1 O -0.3 -0.2 -0.1 =E 5000 0 to IQ~~ ~TRUE C 3 II o | WAL --- R:0.255 4000 3000 X — -0.3 -0.2 -0.1 0 0.1 0.2 0.3 X, INCH Figure 8. Run N~21, First Mark Cavitation. Z = -0.25, R = 0.255, D = 2.5.

'O' = G' 0z' = H 0'0 = Z'uoTX'BQTA'O oaZ'6TN uH'6 a9nSuT HONI'X ~'0 Z'O I'0 0 0I'- Z'O- I'00 000 000 0 ------------- --------- I ---------- I 0 OOOb' 000 (0 I I;o' I -Z n.OS [ I'0- o'0- 1 c- 1 J3U'81 —- -- 0009 —. -_ _ —-... — - ~ O ~o.. - _ —--- OOo,000L ~0-8T

-19/, / 7000 0 6000 3000I REF. -0.3 -0.2 -0.1 OF() i^ \TRUE jL d 5000- --- WALL R — -R= 0.255 -- 4000 3000 0. -0.3 -0.2 -0.1 0 0.1 0.2 0.3 x, INCH Figure 10. Run N317, Visible Initiation Cavitation. Z = 0.00, R = 0.255, D = 2.5.

' (' =';'O =' 00' 0 = Z'uoT:,..TAso pi.rptr.S'[ToN umIE'*TT G.mST' HONI'x ~'0 8'0 0 0 I'o0-'o0 -- ~0 - 0 ^0 i 3000~ 00i 000 G9 — = 1: --—'I 1VM I,,.. ooo: 0009;% 0'oz~ I 0009 0 0

-217000 \. 6000 REF. ( | T 5000 TRUE o0 0<.0 WALL R-.255 4000 \0 1 3000 0 0 0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 X, INCH Figure 12. Run N~20, First Mark Cavitation. Z = 0.00, R = 0.255, D = 2.5.

-227000 REF.. 5000 0 8_ 0 -o.2 -o.1 / x, INCH Fiure 1. R N2, Zero R 0.268, D = 2.. I I,/ \ / 4000 0-0 \ / -0.3 -0.2 -0.1 0 0.1 0.2 0.3 x, INCH Figure 15. Run N~2, Zero Cavitation. Z = 0.25, R = 0.268, D = 2.0.

-23o o \\ 7000 6000 REF. q -0.3 -0.2 -0.1 TRUE CL ( i 5000 -i WALL -t ---— R = 0.268",D 0 4000 [REJECTED; BELOW THE NO CAVIT. - 1 CURVE) 3000 -0.3 -0.2 -0. I 0 0.1 0.2 0.3 X, INCH Figure 14. Run N~15, Standard Cavitation. Z = 0.25, R = 0.268, D = 2.5.

'*' = 9 = H = z'9soM 0o uoT.;;TAD IToM un *uH T a'i- g HONI'X ~0 0'0 10 0 10-' 0------ -- -— c0- -0 -—. 00-o / 0 0 9~ I / i / -- ---------— b —--- ooov.J^ ~ ~ _ l000\:a_0 /bI ic / -.=. -- -,,.99;~'0=y -\- -~-^. T VI; I'~10-; 0- ~0~ —---- ----- --------- ------ ~0009 0001.

-257000 _ T;00 6000 REF. c( -0.3 -0.2 -0.1 n h.TRUE *L s- 5000 WALL R —-- = 0.268 - - 4000 (REJECTED: MOST POINTS ON THIS CURVE ARE BELOW THE ZERO CAVITATION CURVE, RUN NO. 2, FIG. 13) 3000 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 X, INCH Figure 16. Run N~16, Visible Initiation Cavitation. Z = 0.25, R = 0.268, D = 2.5.

-26.,- \ \ 6000 REF.. -0.3 -0.2 -0.1 5000 TRUE - I z l. \ 0 4000 I WALL. R=.289" 3000 0/ ~/ 00 I\ ) 0 30 2000 -0.3 -0.2 -0.1 I 0 0.1 0.2 0.3 x,INCH Figure 17. Run N35, Zero Cavitation. Z - 0.625, R - 0.289, D - 1.0.

-277000 I2 iw 5000 - - _. --------- - _ _ TRUE WALL R: —.289 4000 Z~~~~~ I 0.3 -0.2 -0.1 0 0.1 0.2 0.3 Figure 18. Run N, Cavitation to Nose 0.289892. 4000 0/ x, INCH Figure 18. Run N04, Cavitation to Nose. Z = 0.625, R = 0.289, D = 2.5.

-287000 6000 REF. O. 30, 5000 1 i I Ix TRUEI.0 WALL: —.289 4000 ------ \ I I^/ 3 0 0 0 ---------— i —------- ------- - -- - 0.3 -0.2 -0.1 0 0.1 0.2 0.3 x, INCH Figure 19. Run N"6, Standard Cavitation. Z = 0.625, R = 0.289, D = 2.5.

-297000 \ 6000 REF.[ 5000 ma[I IWI I- -0. -0.2 -0.1 z - 0 ~0 l I TRUE 4000 I^ \ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~I 3000 CDv ~~~~~~/ / 2000 -0.3 -0.2 -0.1 0 0.1 0.2 03 X, INCH Figure 20. Run N~5, Visible Initiation Cavitation. Z = 0.625, R = 0.289, D = 2.5.

-30/ \ 7000 6000 6000 e —---------— COMP. WITH RUN REF. % -0.3 -0.2 - 0. Z I5000 U TRUE. 4000, --- ----— \i -REJECTED BY d\"COMP. WITH RUN NO. 10, /~ 3000, NP~~~~~~~~~ / / // -0.3 -0.2 -0.1 0 0.1 0.2 0.3 X, INCH Figure 21. Run N8, Zero Cavitation. Z ~ 0.786, R = 0.297, D = 1.0.

-5317000 0 6000 REF. 5000 --- -0. 3 -0.2 -0.2 -0.1 TRUE I I \I I ^ Z~~~~~~~~~~~~~~~I I 0 I I I I I I I 4000 \ /I WALL R 0.297" / 3000 / / 0 o- 0 2000 -0.3 -0.2 -0.I 0 0.1 0.2 0.3 X, INCH Figure 22. Run N07, Standard Cavitation. Z = 0.786, R = 0.297, D = 2,5.

-327000. 00 0 l 0 1 6000 REF. i -0.3 -0.2 -0.1 TRUE IC 5000 ZMISE I WALL- R:.297" 3D I.0 4000 0. 3000 -0.3 -0.2 -0.1I 0 0.1 0.2 X, INCH Figure 25. Run N~24, First Mark Cavitation. Z = 0.786, R = 0.297, D = 2.5.

-337000 0 REF. (. 6000 -0. -o0.2 -0.I (o 5000 - -------- -— TRUE Z Z 8 Lv 0 4000 R =.297 3000 0 0o _o o0 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 X, INCH Figure 24. Run Nl10, Visible Initiation Cavitation. Z = 0.786, R = 0.297, D = 2.5.

-346000 REF. 5000 -0.3 -0.2 -0.I TU) 1 Z TRUE t 4000 WALL R.297" / 3000 / 0 x, INCH Figure 25. Run N09, Cavitation to Nose. Z o0.786, 0.297, D 2.5.

3-56000 0 REF.. 5000 I I -0.3 -0.2 - 0.1, TRUE Fgr 26W uALL R --— R6=.317...-1 F.z z2 M4000 -- --- 3000 0 \0 2000 -0.3 -0.2 -0.1 0 0.1 0.2 X, INCH Figure 26. Run N~12, Zero Cavitation. Z = 1.163, R = 0.317, D = 1.0.

-566b~~~~ ~~REF. % 5000 - 0.3 -0.2 -0.1 TRUE G 4000 - LL -.317-~.0 gz \ 3000 -0.3 -0.2 -0.1 0 0.1 0.2 x, INCH Figure 27. Run Noll, Visible Initiation Cavitation. 1.163C, 0.317, D - 2.5.

-376000 5000 - REF. 40 -0.3 -0.2 -0. 1 O zI:j \ 7TRUE. 0 to 0 4000 --- =a- ~WA L ------- R =.317 3 I 3000 2000 -0.3 -0.2 -0.1 0 0.1 0.2 x, INCH Figure 28. Run N014, Standard Cavitation. Z - 1.163, R = 0.317, D = 2.5.

- 386000 0 5000 -0.3 -0.2 -0.1 TRUE e Z2 WALL R =.317 0 4000 I 3000 2000 -0.3 -0.2 -0.1 0 0.1 0.2 x, INCH Figure 29. Run N013, Cavitation to Nose. Z = 1.163, R " 0.317, D = 2.5.

-396000 0 |o I o o\ 3 00 0\ ol 5000 00 0 00 50 0 0 -------------- ^ ----------— REF.. -0.3 0.2 -0.1 Za IN0 Fgr 3WALL =n —------ R 0.317 —, 0\ 0 3000 — 0o 0 2000 - -0.3 -0.2 -0.1 0 0.1 0.2 X, INCH Figure 30. Run N025, First Mark Cavitation. Z - 1.165, R - 0.317, D - 2.5.

-40o. 1000 0 EXPERIMENTAL POINTS POINTS OBTAINED BY X SYMMETRY COLLIMATOR WIDTH COLLIMATOR I X WIDTH IT 9000 C -' I rTt I- -,, z 2r IT / REF 10 Ie, x IIC i I o WALL X. INCH Figure 51. Run N026, Venturi Filled With Air. Z = -0.25, R = 0.255.

-41RE. f -0.2 REF —-J TRUE 0 0.2 i0.2 | ~-RUN NO. I x 0.4 N o.6 RUN NO.6&k4 /-RUN NO. 7 & 8 0.8 THE CORRECTION WAS OBTAINED BY EVALUATING ALL THE EXPERIMENTAL CURVES. THE TRUE. RESULTED l~~~I ---- FROM CONSIDERATIONS OF SYMMETRY IN THE PARTICULAR CURVES INDICATED. 1.2 -.____. -0. I 0 0.1 0.2 Q3 0.4 X- AXIS Figure 32. Centerline Correction.

-42the true center line. These values of correction or deviation from the reference center line were plotted for the various axial positions in Figure 32 to give the true center line of flow compared to the arbitrary reference center line used to take the data. The true center line was finally added to Figures 6 through 31. It is observed that the standard deviation of a typical point on these curves represents a statistical error of less than 2%. Considerably more deviation than this was observed for points near or in the plastic walls of the venturi. This is considered to be due to the pitted condition of the wall surface, and the subsequent collection of a brownish oxidation material in the wall pores which radically changes the attenuation of gammas from point to point in this vicinity. Figure 31 shows a run made with the venturi containing only air and indicates a considerable deviation in the count rate at or near the walls, i.eo, of the order of three or four standard deviations. It is noted that the curve is symmetrical with respect to the true center line. The above irregularities could be reduced by the use of a new plexiglas test section which would not contain insert holes for wear testing. This would eliminate the possibility of a film of strongly attenuating material collecting on the boundaries of the wear inserts (Figure 2). The cavitation conditions labelled visible initiation, cavitation to nose, standard cavitation and first mark have been previously defined'3; however, the definitions are repeated here for convenience. Reference to Figure 2 will help to clarify the discussion.

543"Visible Initiation" is that cavitation condition in which a continuous ring of cavitation only is visible at throat discharge. For "Cavitation to Nose," the cavitation terminates at the axial position corresponding to the location of the nose of the test specimens (which actually were not present in this experiment) "Standard Cavitation" has its termination at the position of the middle of the damage specimens. "First Mark Cavitation" has the termination 1 3/4 inches downstream of the throat exit, and thus also downstream of the specimens. The above conditions are listed in increasing extent of the cavitating region. They can be reproduced quite accurately by reproducing venturi inlet and outlet pressures. Runs were made for each cavitation condition at several specified axial positions at a given flow-rate. For each run a traverse was made across the venturi using increments no greater than 0.030" and sometimes smaller. As will be shown later, with the assumption of axial flow symmetry, a single radial traverse is sufficient to delineate the mean density (or void fraction) as a function of radius.

IVo REDUCTION OF THE DATA After correction of background, the experimental count rates were plotted as function of distance in Figures 6 through 31o In the same figures, the correction of the center line position was performed, The count-rate values for the various cavitation conditions, Nl(x), were retabulated from these smoothed curves, and compared with the count rates, N2(x), from the corresponding non-cavitating curves, The use of smoothed curves, held at all times within the limits defined by the standard deviations of the experimental points, was desirable to produce consistent final results, The method for computing void fraction from the count-rate data has been previously given8, but it is repeated for convenience in Appendix Co The actual calculation was performed with the help of an IBM 709 computer using the program detailed in Appendix Do The final results are presented in Tables XI through XXVII, where F represents the void fraction in percentage and r the normalized radial distance with respect to the true center lineo Preliminary calculations were first performed taking a 0O030" increment between the points read from the smoothed curves, The first point was taken 0,015" inside the Hg to eliminate the possibility of a point involving partial attentuation in plastic and mercuryo If the void fractions, so calculated were obviously in error, such as gross nonsymmetry, the smoothed curves were modified, always within the limit of the statistical error,to obtain more reon reasonable resultso This was necessary in some -44

-45cases, since it was found that a small horizontal displacement resulted in a very large effect on the count-rate difference at a particular transverse position between the cavitating and non-cavitating conditions. This was particularly true in the neighborhood of the walls, where the count-rate drops steeply. When the computed void fraction versus normalized radius curve showed a fairly continuous nature, the count-rate curves were considered properly drawn (as they appear in Figures 6 to 30). At this point a more detailed machine calculation was made using increments of 0.010" between points. The results are shown in Tables XI to XXVII

V. DISCUSSION OF RESULTS A summary of the experimental runs is shown in Table X, and the reduced data, giving void fraction as a function of radius for the various cavitation conditions in Tables XI through XXVII. From the computed data the constant void fraction profiles for the various cavitation conditions are shown in Figure 43, which was constructed as a cross-plot from Figures 355 through 42 where the void fraction is shown as a function of distance from the centerline at various axial positions, and for the various cavitation conditions. The presentation of the data in the form of constant void fraction profiles is believed most useful for the present purpose, i.eO, a representation of the various flow regimes in terms of void fraction. The venturi outline between the throat discharge and the downstream end of the test specimens (actually not in place during these tests) is shown to scale with respect to the venturi center line in Figure 43 as well as the outline of the test specimens. Upon this diagram constant void fraction loci are superimposed for the different cavitation conditions covering the range from "Visible Initiation," where there is only a ring of vapor at the throat discharge, to "First Mark Cavitation" wherein the cavitation terminates visually downstream of the end of the test specimen (1.75 inches downstream of throat discharge and 0.56 inches downstream of the trailing end of the test specimen). An examination of the void fraction profiles discloses various significant results: -46

-471) The data presented in this fashion is quite smooth and consistent with the possible exception of the 10% line in the "Visible Initiation" condition, giving confidence in the accuracy of the results. 2) The region of relatively pure liquid (less than -10% void) is virtually a jet of uniform diameter downstream to the vicinity of cavitation termination. However, the diameter of this jet is substantially less than the throat diameter (a88%) for all the cavitation conditions. Thus even for "Visible Initiation" there is substantial vapor along the wall of the venturi, at least as far back as 0.25 inches into the throat and presumably further. This vapor film along the wall tends to obviate the often-made assumption that friction drop in such a throat is not a function of the cavitation condition. 3) In no case is there more than a few percent void caused by the overall cavitation field in the vicinity of the polished faces of the damage specimens. Hence it is surmised that the damage is probably mainly caused by local cavitation generated by the presence of the specimens themselves, and it appears from the damage tests that the greatest damage occurs in regions of relatively small void. *The precision of the data for void fractions less than 10% seems questionable from an examination of Figures 55 through 42. "*See Reference 9 for a detailed description of the test specimens and the venturi. ***It should be possible to verify this assumption in future water tests which are planned with a two-dimensional venturi.

-48100 80 8 os FIRST MARK z 60 0 II LL 40. 0 VISIBLE 0 X -----— II 0 20 40 60 80 100 NORMALIZED RADIUS % Figure 33. Void Fraction versus Normalized Radius. Z - -0.25, R = 0.255. Data from Computer Run N024.

-49100...... 80 80 Z 60 0 I —' XSTANDARD 0 4 04 o VISIBLE > x 20 20 FLiLFIRST MARKx X"T~" 0 20 40 60 80 100 NORMALIZED RADIUS % Figure 34. Void Fraction versus Normalized Radius. Z 0 0.00, R 0 0.255. Data from Computer Run N~25.

-50100 STANDARD 80 60 Z 0 IE,/ ~40....... 0! O[~~ ~NOSE 0 20 40 60 80 100 NORMALIZED RADIUS % Figure 35. Void Fraction versus Normalized Radius. Z = 0.25, R = 0.268 Data from Computer Run N~26.

-51100 I I I I INOSE U. o 40 VISIBLE\ 80 13 —-- STANDARD_0 20 40 60 80 100 NORMALIZED RADIUS % Figure 36. Void Fraction versus Normalized Radius. Z = 0.625, R = 0.289. Data from Computer Run N018.

-52100. 80 0-0I Z 60 0 l0{">O 1MIst MARK S4 40' I Z = 0.786, R = 0.297. Data from Computer Run N~27.

-55100,, / 1st MARK / NOSE 0 Z 60 0 VISIBLE IL 40 0 —~ Z = 1, 0, 3STANDARD 0 20 i -- 0 0 20 40 60 80 100 NORMALIZED RADIUS % Figure 38. Void Fraction versus Normalized Radius. Z = 1.163, R = 0.317. Data from Computer Run N~19.

-54100 80... 0 60 Z=- 0.25.1 Z 0.2 0.3 0.4 r DISTANCE FROM lb IN. Figure 39. Void Fraction versus Radial Distance for Visible Initiation Cavitation, u. 40 Z6-z.163 20' --- 0 I_____ _ I. _ I 0 0.1 0.2 0.3 0.4 r DISTANCE FROM ( IN. Figure 59. Void Fraction versus Radial Distance for Visible Initiation Cavitation.

-55100 80 Z 1.163 z 60 - 0 Z = 0. 625 0 Z 0.25 0 0.1 0.2 0.3 0.4 r DISTANCE FROM C, IN. Figure 40. Void Fraction versus Radial Distance for Cavitation to Nose.

-5600 Z = 0.25 60 Z 0 a F 4 V 2=0.786 U& ~ ~ fo.adrCviti Q I " 40 20 _________ Z:0.000 Z:1.163 0 0.1 0.2 0.3 0.4 r DISTANCE FROM I, IN. Figure 41. Void Fraction versus Radial Distance for Standard Cavitation.

-57100 Z: 1.163 Z = 0.786 80 60 z 60 0 Z= 0.000 20 0 0 0.1 0.2 0.3 0.4 r DISTANCE FROM i, IN. Figure 42. Void Fraction versus Radial Distance for Cavitation to First Mark.

-58z z 1.25 \ EST SPECIMEN F:20% OUTLINE | l I\F:20% F.oo300 - I F.40% " |\! I F 40 % 0.7501'u00% 7 0.50- I - \ I \\ 0.00 I I I END OF 0.2 -— CAVITATIONY I / I u VISIBLE NOSE Figure 43. Void. Fraction Profiles for Different Cavitation Conditions. Condi~tions.

-59z'1.75 END OF CAVITATION 1.50 z /-F 80 % 1.25 ^ Fz-20 % I I I F 20% I ^ \\ F':30% - - 1.000.75 F 50% I ENDOF F=40% CAVITATION — 0T^^^~Fi60 00 —- -------- ~'0.50 - - 1I'F=60% F 6 0 % -- 0.25 I I F=10% 0.00 0.00,,^~~~~~~~~~W II I /P~LL Y - ^ IWALL I I -^- -- -------------------- -0.25 r.3.2.1 o r.3.2.1 STANDARDO FIRST MARK Figure 43 (Concluded)

-6oHowever, it is certainly influenced by the overall cavitation field in that the local pressures are so influenced, and hence the collapse violence of the bubbles. The existence of such dependence has of course been demonstrated by the wear results.9 4) A direct comparison of void fraction profiles under the same cavitation condition between water and mercury is not at present possible, although runs similar to the mercury runs herein described are planned eventually for water. Water runs, using the present 2,5 venturi, were made previously with a non-collimated densitometer 2, from which average void fraction, rather than void fraction as a function of radius, was determined, at a given axial location. From this the diameter of a hypothesized jet of pure liquid centered about the venturi center line was calculated. This data is shown in Figure 20 of Reference 2 and reproduced here for convenience (Figure 44), Also shown in the same figure are jet diameter curves based on pitot tube, rather than densitometer, measurements. It is noted that the results are fairly similar at least for "First Mark Cavitation." Of interest in the present context is the gammaray densitometer curve for "First Mark Cavitation" with cold watero It is noted that in this case the diameter of the jet, if it were of pure liquid, is about 69% of the venturi diameter at the "First Mark" position. In the present tests with mercury, but under otherwise similar conditions, the locus of the 10% void fraction line is at about 63% of the diameter of this location, if it is assumed that a straight-line extrapolation in Figure 43 from the The possible reasons for the differences in results obtained from these independent measuring techniques were discussed previously.

1.I - - - 0.9 \^ 1^s 1Y XEHOT WATER DATA (160~F) 0.8 __ —.O.;.Z: 4_. -oCOLD WATER DATA(60 F) ____ ____ ____^ ____~ CHOTL WATER DATA(8160~F) Z 0.6 2 — 0.5 *'> H X 0.51 _ ____L __|__DDATA FROM PITOT LD WATER DATA (M80 F) I \' l 0.4 ZERO IST MARK 2IN.MARK 2 MARK 3RQMK CAVITATION CAVPOSITION OF OBSERVER FOR PITOT TUBE DATA 0.2 Figure 20. Comparison of Jet Diameters for Hot Water and Cold Water Runs* O.I DATAFROM TUBEMEAM* D = o.6 -- DATA FROM P ITOT TUBE MEASUREMENT (M HOD A) ZERO IST MARK2 N. MARK Radioactive M RDMARKements CAVITATION l....-t CAVITATION CONDITION Figure 20. Comparison of Jet Diameters for Hot Water and Cold Water Runs* * D = 0.603 For Pitot Tube Measurements D - 0.687 For Radioactive Measurements

24 2.2 2.0 0 o I0 2,,," -GCAVITATION TO T NO CAVITATION I.. 1.0L___I 0.8.0 A CAV ITATION I TO 08I9 ERVER \ ST MARKMARK- ---—.A —---- UaJ~ __ _DATA FROM PITOT TUBE I IN. o 0' MEASUREMENT z 0.2 ___D__ATA FROM RADIOACTIVE ___________________ SOURCE MEASUREMENT TAP NO. 0 E G H POSITION OF' OBSERVER DIFFUSER I ST, MARK NO. MARK P2 MARK 3RM MARK INLET Figure 45. Non-Dimensional Liquid Jet Diameter as a Function of Axial and Cavitation Condition, Cold Water Data, 1/2" Test Section.

-63zone of measurement is valid. Actually, as shown in Figure 45 (reproduced from Figure 7 of Reference 3 for convenience), the hypothesized pure liquid jet diameter tends to increase substantially as the region of cavitation termination is approached. Hence the straight-line extrapolation value of 63% mentioned above is probably too small. On the other hand, the diameter of a pure liquid jet would be somewhat smaller than one containing a fringe area of -10% void fraction, as well as some voids throughout. (An examination of the void fraction versus distance from center line plots of the present study, i.e., Figures 39 through 42, indicates the existence of perhaps 5% void even near the center line.) Considering all the above, the present mercury tests seem consistent with the past water tests within the precision of the available data. However, this is not sufficient to prove the absence of possibly significant differences between water and mercury with respect to void fraction location and value. Further information on this point must await more precise water tests which are planned for the future.

VI. RECOMMENDATIONS FOR FUTURE TESTS It is observed that all experimental count-rate vs. distance from center line curves are similar in the following aspect. They present an irregular pattern for positions of the collimator close to the venturi wall, drop suddenly when that distance increases, and level off for centralpositions of the collimator. The very rapid decrease of the count rates near the walls is of particular importance, since it is possible, within the standard deviation, to draw curves that satisfy the data and yet are significantly displaced horizontally from each other. Since the calculations are based on differences of values for a given ordinate of two of such curves, it is obvious that such horizontal displacement can become an important source of error. Moreover, in the present experiment, the possible uncertainty in the position of the center line of the venturi with reference to the table holding the collimator was about 30 mils. Using the computer program, an experimental calculation was performed by displacing the data of one of the curves by about half that amount. Results that were obtained were physically meaningless, while with a more suitable positioning of the curves the results of the computer were smooth and consistent. Fortunately, the correct position can be closely judged by symmetry considerations. Therefore, in future tests, it is recommended that the collimator, gamma source, and scintillation detector should be fixed in a permanent way to the floor or walls, in such a manner that the center line of the venturi will coincide as perfectly as possible with the zero-line -64

-65(or other known reference) of the table, and will not move or vibrate during the experiment. The required precise positioning is not easily obtained. However, the use of a beam of light is a possibility, provided that this beam is strictly normal to the free surface of the venturi, and that possible errors due to diffraction are eliminated. Calculations show the statistical errors to be of the order of 2 or 3%. It was observed, however, that sometimes two successive counts of 3 minutes would yield values differing in more than the standard deviation. This was particularly true near the walls, and can be perhaps explained by actual irregularities in the flow of the mercury, that do not average out in the counting intervals adopted. Hence, the counting times should be made as long as possible, to compensate for variations in the fluid flow. Of course, it is necessary that the nominal flow conditions (flow-rate and pressures) be maintained as nearly constant as possible during that period. It is believed that some of the difficulties encountered in reproducing the results near the walls, when part of the gamma beam was passing through the plexiglas only, were due to the roughness of the internal surface of the venturi, which had been in operation, at the time of the experiment, for many hundreds of hours, and was severely pitted at certain locations. This damaged condition of the internal surface could resultin local variations of the flow that wod not average out iner the counting interval.

-66Moreover, other obstructions to the gamma beam were present, such as the holders for the wear specimens, tap holes, etc. Thus, for new experiments, it would be desirable to use a new venturi in which specimen holders, taps, etc., had not yet been installed. Also, this would help in the accurate determination of the center line location.

VIIo CONCLUSIONS As described in this report, a method using a gamma-ray densitometer has been developed for obtaining precise measurements of local density (or void fraction) in an axially-symmetric cavitating flow wherein a dense test fluid such as mercury (or other heavy liquid metals) is used. The same technique can be adopted to light fluids as water or molten alkali metals; however, a source producing softer radiation than that used in the present investigation would be desirable. Such sources (promethium-tungstate for example) are available and have been previously used in the present cavitation work 23.'6,although a much less precise densitometer was used. Also significant information regarding the cavitation flow regime in a venturi has been obtained. This is summarized in Section V. Most significant from the viewpoint of the cavitation damage work is the observation that, for all degrees of cavitation used, there is only a very small void fraction (less than 10%) in the vicinity of the polished faces of the test specimens, excluding possible local cavitation caused by the test specimens themselves. -67

BIBLIOGRAPHY 1. Hammitt, Fo G., "Observation of Cavitation Scale and Thermodynamic Effects in Stationary and Rotating Components," ASME Paper No, 62Hyd-l, May 1962, (To be published in Trans. ASME Jour. Basic Engr ) 2, Hammitt, Fo Go, et al,, "Fluid-Dynamic Performance of a Cavitating Venturi, Part I," UMRI Technical Report NOo 03424-2-T, The University of Michigan, October 1960. 30 Hammitt, F. Go, et alo, "Observations and Measurements of Flow in a Cavitating Venturi," ORA Technical Report No. 03424-5-T, The University of Michigan, April 1962. 4o Hammitt, Fo G,, et al,, "Observations of Cavitation Scale and Thermodynamic Effects in Stationary and Rotating Components with Water and Mercury," ORA Technical Report No, 03424-6-T, The University of Michigan, September 1962, 5. Cramer, V. F,, et al,, "High Speed Motion Picture Studies of Flow in a Cavitating VenturiT," ORA Project No, 03424, Internal Report No 12, The University of Michigan, May 1962o 6, Perez, Simdn, "Cavitation Degree Measurements by Radioactive Attenuation," MoSo Thesis, Department of Nuclear Engineering, The University of Michigan, January 1960o 7, Ivany, R,, "Design of a Gamma-Ray Densitometer for Mercury or Molten Lead," ORA Project No, 03424, Internal Report No 5, The University of Michigan, March 1961o 80 Adyanthaya, B3 Ro, "Mercury Void Fraction Measurements Using a Collimated Gamma-Ray Beam," MoSo Thesis, Department of Nuclear Engineering, The University of Michigan' June 1961. 9. Hammitt, F. G,, et alo, "Cavitation Damage Tests with Water in a Cavitating Venturi," ORA Technical Report No. 03424-4-T, The University of Michigan, March 1962. 10o Etherington, Harold, editor, Nuclear Engineering Handbook, McGrawHill, 1958. 11, Hodgman, Charles D., Handbook of Physics and Chemistry, 33rdo Ed. Chemical Rubber Publishing Company, June 1951. 12, Storm, Eo, et al,, "Gamma-Ray Absorption Coefficients for Elements 1 through 100 Derived from the Theoretical Values of the National Bureau of Standards, LA-2237, 1957. -68

APPENDIX A CALIBRATION OF ELECTRONIC EQUIPMENT -69

CALIBRATION OF ELECTRONIC EQUIPMENT The single channel analyzer and associated equipment used in this experiment were extensively calibrated to ensure their proper operation. The single channel analyzer receives the pulses from the amplifier output. The pulse height region to be counted is selected (at a given amplifier setting) by using the E dial which has a range of 0-1000 arbitrary E dial units. The E dial is proportional to pulse height which is in turn proportional to the energy of the incident gamma. When the instrument is set on "Differential Count" the BE dial selects the energy increment above E over which the pulses will be counted. Hence, for a particular setting of the E and AE dials, only those pulses between E and E + AE are counted. All pulses below E and above E + AE are discriminated against and do not register a count. The range of the AE Dial is also 0-1000 units but the AE units are much smaller than the E dial units. The BE dial is calibrated in terms of E dial units, this value being referred to as window width.* The calibration of the electronic equipment requires the determination of the linearity of the linear amplifier, calibration of the E dial with energy, and the calibration of the bE dial in terms of E dial units at various E dial settings. A signal generator was used to put a 60 cycle square wave input into the linear amplifier and the output pulses were observed on a cathode *Window width: Opening of the BE dial in terms of E dial units. -70

5 _ _ I- 0 > 3 w 2 U) -J 0 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 AMPLIFIER GAIN Figure Al. Linearity of Linear Amplifier.

-72ray oscilloscope. Table I presents the data plotted in Figure Al which reveals that the amplifier is indeed linear. The BE dial was calibrated in percent window width at E dial settings of 300, 500, 700, and 900. This was done with the input of the signal generator. The percent window width was computed by, (E2 - E1) E dial units %0 w. w. = x 100. 1000 E dial units The data is presented in Table II and plotted in Figure A2o The plot reveals that the AE dial as a function of window width was non-linear but only to a moderate degree. The non-linearity was pronounced at the higher window widths. This did not introduce error into this experiment. This information was of importance since a precise window width at a particular E dial was required in the determination of the linear absorption coefficient of only the 1.17 Mev Co gamma in mercury and in the data taken to calculate void fractions. When the E dial position was yet to be determined, the experimenter was able to calibrate the AE dial for various E dial settings and pick the required value from the graph when the required E dial value was decided. This calibration gives an insight into the condition of the single channel analyzer. A very weak set of standard sources was used to determine roughly the photopeak positions of Co60 and Cs137 on the E dial. The differential spectrum data is presented in Table III and plotted in Figure A3. The position of the photopeaks was plotted versus E dial in Figure A4 which reveals the E dial is linear in energy. This, and the above calibrations, indicate that the single channel analyzer used was in good working condition.

1000 -— 5 800 E — 700 600 -- -----— 400- E = 0 - ------ 400 ~ E: 300 200 0 I 2 3 4 5 6 % WINDOW WIDTH Figure A2. Calibration of ZAE Dial. Data From Table II.

-742000 0.661 MEV. 1000 600 500'37 1.17 MEV. 500 -- CS +BKGND 400 1.33 MEV 300 200 z 40 o 30 s0 Co +BKGND 20 10 8 z 4 3 2 6 ----- --- -- - --- -- 60070 200 300 400 500 600 700 E DIAL UNITS Figure A5. Differential Curves of Co and Cs1. Data from Table III.

700 _ _ _ _ __ _ _ _ 60 Co 600 Co~~~~~~~~~~~~~~~~~~~~~~~oO 500 z 400 w l37 Cs 300 200 0.6 0.7 OB 0.9 1.0 1.1 1.2 1.3 Ey, MEV. Figure A4. Energy Calibration of SCA. Amplifier Gain: 2 x 56. Data from Figure A5.

-764200.. 4000 3800 3600 C ) 0I 3400 3200 3000 2800 2600 510 520 530 540 550 560 570 E- DIAL UNITS Figure A5. Precise Determination of Co60 1.17 Mev Photopeak. Data from Table IV.

-77Since only the 1.17 Mev Co60 photopeak was used in the linear absorption coefficient and void fraction determinations, a very precise determination of its E dial position was required. The 20 me Co60 source was placed in the collimator and the single channel analyzer was used with AE = 200 (-1% window) to obtain the differential spectrum exactly. A precise background determination was also made. Table IV presents the data plotted in Figure A5 which shows that the 1.17 Mev photopeak is at 545 E dial units. The Compton effect due to the 1.33 mev gamma can clearly be seen on the low energy side of the 1.17 Mev peak. Figure A5 indicates that an E dial of 530 with a LE dial corresponding to 30 E dial units would symmetrically include the peak and give enough counts to provide adequate statistics, i.e., about 1-2%. Thus, from Figure A2 a 3% window width at 530 E dial units required a AE dial setting of 490 units. These values were used throughout the rest of the experiment.

-78ELECTRONIC EQUIPMENT AND RADIOACTIVE SOURCES USED IN THIS EXPERIMENT MODEL AND NAME MANUFACTURER NUCo ENG. NOo SERIAL NO. 1) Scintillation Detector RCL 69 Model 11028 136 2) Super Stable High Atomic Instru- 108 Model 312 Voltage Supply ment Company 10972 3) Non-Overloading Baird Atomic 56 Model 215 Amplifier 528-N 4) Single Channel RCL 106 Model 2204 Analyzer 258 5) Scaler Baird Atomic 359 Model 1285 241 6) Pulse Generator Departmental 95 --- 7) Oscilloscope Type 592 Dual MA 2001 Type 502 Dual Beam (Mechan- Beam ical Engo) 767 8) Sources 1.) Co6- 10 - 20 mc 2.) New England Nuc. Corp. Set C-18.

APPENDIX B IINEAR ABSORPTION COEFFICIENT OF Hg FOR 1.17 Mev GAMMAS -79

LINEAR ABSORPTION COEFFICIENT OF Hg FOR 1.17 Mev GAMMAS A preliminary survey of the literature showed that there was some doubt as to the linear absorption coefficient of mercury for the 1.17 Mev gamma-ray, and that published values were based either on theoretical calculations or extrapolations of experimental results. Hence it seemed desirable to establish an experimental value of sufficient precision for the present investigation. Cross section data from Reference 12 were listed in Table V and plotted in Figure B1. An interpolation was made at an energy of 1.17 Mev to give a value of 0.822 cm-1 for the linear absorption coefficient for mercury. This value reflects only extrapolated calculations based on theoretical considerations of attenuation effects as a function of atomic number. Table VI gives the data taken from Reference 10 which is an experimental determination of i for mercury. Figure B2 was used to interpolate the above data to 1.17 Mev which gave A = 0.829 cm-. Since the density of mercury varies somewhat with temperature, data from Reference 11 (Table VII and Figure B3) was used. Since the temperature of the mercury in the loop during the tests was approximately 70 F, a value of 13.5435 gm/cm3 was selected. The maximum variation from this temperature is estimated to be about 5~F (during the non-cavitating runs when the mercury flow rate was reduced to a minimum). As noted in Figure B3 such a temperature variation corresponds to a density variation of about 0.05%, and is considered a negligible source of error. -80

-810 \ E 6 4 -..... -. 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 Ey, MEV. Figure B1. Mass Absorption Coefficient of Hg. (LA-2237, Ref. 12).

-8215 14 13 12 0 10 0.5 I 2 3 4 6 7 0. 5 1 2 32E MEV. Ey MEV. Figure B2. Mass Absorption Coefficient of Hg. (Nuclear Engrg. Handbook, Ref. 10)

- 83 - 13.5500 OP c O~1),F: 13-5435 13.5400 z I 13.5300 ----- 19 20 21 22 23 Oc Figure B35. Density of Mercury versus Temperature. (Handbook of Chem. and Physics, Ref. 11).

-84-.9.2 o I I I I I — MAIX. VALUE w N_ 4 ----- ^ —-MIN. VALUE - -J 0.0.05 X.04 0.10 20.30.40.50.60.70.80.90 1.0 1.1 1.2 1.3 MERCURY THICKNESS, INCH Figure B4. Linear Absorption Coefficient of Hg for Co60 1.17 Mev Gammas. (Experimental data).

-85As a simple but suitable experimental set up for the measurement of p, a glass beaker was used with a depth gauge attached to a metal cover platform to measure the depth of mercury within. This beaker was placed over the vertical collimator and three minute counts made with various mercury depths. With the proper E Dial and AE dial settings, using the 20 me Co6 source. The data is presented in Table VIII and the count rates corrected for background are normalized to the first measurement as "zero" thickness and plotted in Figure B4. The best straight line through the points was drawn. Considerable dispersion outside the statistical error of about + 0.009 (normalized value) exists in the points, due presumably to error in reading the depth gauge. The lowest two points can be neglected since their count is very nearly of background magnitude. The straight line drawn appears to fit the remaining points quite well. The linear absorption coefficient for mercury was then calculated from Figure B4, giving i = 0.827 cm-1 = 2.10 in-1. Figure B4 also shows lines drawn through the most divergent points to give the maximum error in j due to the dispersion of the points. These values are 0.869 cm~1 and 0.784 cm1l which give the maximum error in [ of + 4.2%. The value of 0.827 cm-1 is considered to be determined to much greater accuracy than these values, which are the maximum errors, i.e., total statistical and experimental errors. This experimental value agrees closely with the literature. Both of the results found in the literature are within 0.4% and their average is within 0.2% of the value obtained in this experiment. Therefore the experimental value,

-86p = 0.827 cm-1 (2.10 in-1) from the present tests is considered the most reasonable value to be used since it is based on direct measurements whereas the values reported in the literature are not.

APPENDIX C DERIVATION OF VOID FRACTION RELATIONS -87

DERIVATION OF VOID FRACTION RELATIONS The basic relations required to express the void fraction in terms of the observed count-rates were developed by Adyanthaya.8 The derivation will be reproduced here for convenience, since most of the intermediate equations are necessary for the computer program detailed in Appendix D. Figure C1 represents the cross-section of the venturi at any particular axial position z. Let R be the venturi radius, t the path length of the radiation within the flow area, and x the horizontal distance from the venturi center line to the collimator center line. Also let: no = number of photons/sec emitted by the source through the slit of area A of the collimator. nl(x) photons/sec passing through the entire test section, at a distance x, for any cavitation condition. n2(x) = photons/sec passing through the entire test section, at a distance x, when there is no cavitation (i.e., stagnant mercury). p(x) = average density of the vertical column of fluid, located at a distance x, and which has cross-section equal to the area A of the collimator slit. h = maximum transversal dimension of the test section, as shown in Figure C1. Then: -ip (h-t) - pp(x)t nl(x) = nO e 2(x) -p(h-t) - Bpt n2(x) = n0 e -88

-8960 CO GAMMA SOURCE -0.030" COLLI M ATOR 1t b Fiure C. Venturi Cross- n. Figure C1. Venturi Cross-Section.

-90where: p = density of mercury = 221.977 gm/in3 kL = linear absorption coefficient for Hg = 2.1 in = i/p = mass absorption coefficient yp = linear absorption coefficient of the plexiglas Dividing the above equations and rearranging: n2(x) In () = t[p(x) - p] or' n or: 1 n2(x) p(x) = p + t in nl(x But, from the geometry: t= 2 dR2 x2 thus: 1 _n2(x) p(x) = p + 2 R2 2 n x (c-l) 2D R2 _ x2i nl(x) This average density, corresponding to a column of height t and cross-section equal to the collimator aperture, is always less than the density p of the liquid mercury, since n2 < n1. Moreover, the procedure is independent of the collimator opening provided this is small enough so that the average density can be considered as constant within the corresponding column. Thus, the average density is a function of the distance x only, and the displacements of the collimator can be arbitrarily chosen. It is also worthwhile to notice at this point that the number of photons per second, n1 and n2, can be substituted by the actual counting rates, since the efficiency of the detector will cancel out in the equation above. A method has been found, then, to determine p(x) experimentally by measuring n1(x) and n2(x)o

-91One is interested, however, in obtaining the density as a function of the radial distance, r, rather than as a function of the transverse distance, x. For that purpose, two assumptions are made: (a) The flow within the cavitating venturi is axially symmetrical, i.e., the density at any value of r is a function of r only, p(r). (b) Between r and r +Azr, the density p(r) can be considered as constant, for small values of Ar. Naturally, the smaller Ar, the more accurate the calculations will be. Then, p(r) can be obtained from the values of p(x) as follows. Let A be the area of the opening of the opening of the collimator, and hence, the area over which p(x) is averaged. Thus: my /Y oP(Y) Ady p(y) dy p(x) -o Ady f dy But, from Figure Cl, _2 x2 r -X2 dr = dy sin @ = dy r or': or: r dr.^r- x2 and the above equation becomes: R r p(r)dr p(x) r=x r-x2 /R rdr r=x ~r2 x2 or: R -r p(r) dr p(x) 4R2 _ x2 = r (r) dr (C-2) r=x r - x2 which is an exact relation between p(x) and p(r).

-92I I I a.! j I I b. Figure C2. p(r) from p(x).

-93One observes then that at xl, x2, x,... the values nl(x) and n2(x) are known, from the experimental work, and that using Equation (C-l) the corresponding values of p(x) are readily calculated. The procedure is therefore to divide the flow section into different regions, as shown in Figure C2(b), where the different radii rl, r2,... correspond to the transverse distances xl, x2,..,. The outer radius of the first region is thus R, and the inner radius is xl. As per assumption (b), within this region the radial density is constant, and from Equation (C-2) one obtains: _ rdr rdr P(xl) R2) x2 = p(rl) =r p(rl) --- = P(rl)'R2 J1 x1 J r2 x2 x 2 1 - x2 or: p(rl) = p(xl) (C-3) For region 2, similarly: -R p(x2) ~R22 = A p(r)r dr = P'x2)4~ x 2 2 4r2 X2 2 1 (r)dr p(r) dr RP(r) j Y 2 X1 2 - X2 X(if rdr + p(rl rdr = p(r2) [r2 - x2 1 + P(r) [r2 _ 2 Thus: p(x) R2 x2 p(r2) Ix2 - x2 + p(rl)f R2- - Jx 77 (C-4)

-94Here, all values except p(r2) are known, which becomes now determined. The general expression for the n-th region can be written now as: p(xn) \R2 Xn = p(rn) nx2 - x + ~n-+ r1) [ _ + n + + P(rl)[ jx2 - x2 - x2 - X2 ] + + + P(r4 x x22 - 4 2 + P(rl) [ R2- X2 - x2 - X2 (C-5) where all values except p(rn) are known. Thus, from this expression, the value of p(rn) can be calculated. The repetitive nature of the calculations of p(r) make a highspeed digital computer a valuable tool for the reduction of the experimental data. As detailed in Appendix D, a program for an IBM 709 computer was prepared, and the values p(r) obtained. Once the values of p(r) are known, the void fraction, f, for a small fluid region (control volume) defined as: volume of voids Vv total volume V is easily calculated. Let: Vv = volume of mercury in vapor phase in control volume Vm = volume of mercury in liquid phase in control volume M = mass of mercury in control volume. Then: V = V + Vm ) mass of mercury _ M total volume Vm p _ mass of mercury _ M liquid volume Vm

-95and: p(r) _ Vm P V The void fraction is thus expressed: Vv Vm f - 1 — V V or finally: f = - p(r) (c-6) P where p is the density of the liquid mercury. The values computed following the above procedure are summarized in Tables XI through XXVII.

APPENDIX D COMPUTER PROGRAM -97

COMPUTER PROGRAM To facilitate the computation of the void fraction in terms of the radial distance r, a program for an IBM 709 digital computer was prepared. The program was written in the MAD language (Michigan Algorithm Decoder) currently used at the University of Michigan, and it is based on the equations developed in Appendix C. It was intended to make the program as general as possible. Thus, to facilitate future changes, the following three parameters were incomporated in the program as internal information on separate cards. (1) AX = width of vertical bands in which the flow area is divided. (2) p = density of fluid (gm/in3). (3) pi = linear absorption coefficient of fluid (in-1). It is observed that(l) will be changed according to the accuracy desired, and in fact, during the present experiment, the values AX = 0.030" and 0.010" were used, as explained in Section IV. The other two parameters depend essentially on the fluid under consideration, and for Ap, on the energy of the gamma rays emitted by the radioactive source. The input data are as follows: i) the axial distance from the throat of the venturi, Z ii) the radius of the venturi at distance Z. For this particular venturi, the radius R is given by the expression: R. 0495 Z + 0.255 in. (D-l) 9.217 iii) the number of regions in which the flow area is divided, M, obtained from the relation: -98

-99M = () (D-2) AX and taken to be an integer iv) Nl(I) = number of counts corresponding to the Ith vertical band (see Figure C2) in venturi cross-section, under cavitation conditions. v) N2(I) = number of counts corresponding to the Ith vertical band in venturi cross-section, when filled with stagnant fluid. Thus I is an integer varying between 1 and M. vi) D = a parameter, related to the flow condition of the fluid, which does not appear in the calculations.* During the first runs with the computer, the value AX = 0.030" was used, and, as indicated in Section IV, the first point was taken 0.015" inside the wall position to eliminate the possibility of a point involving partial attenuation in plastic. Then, the values of X(I) are given by the formula: X(I) = R(Z) - (2-1(D-3) 2 which was also used, for no particular reason, for the case AX = 0.010". The average fluid density corresponding to the Ith vertical band is given by: p(I) = p + P In N2(I) (D-4) 2 R2 - X(I)2 N1(I) which is identical to formula (C-l). It is desired to obtain the average density as a function of the radius, r. For that, formulas (C-3), (C-4) and (C-5) are used, after rewriting them in a slightly different form as follows: For I = 1: Pr(l) p(r1) = p(l) (D-5) *See Figure D2 for flow rate in GPM corresponding to values of D,

-100For I = 2: - x(2)2 R - x(2)2- X (2)2 -((2)2 Pr(2) P(r2) =p — x(2) - P(rl) XX(1)2 _ X (2)2 4X(1)2 _ X(2)2 (D-6) and, in general, for I = I: 4R2 - X(I)2 pr(I) = p(I) i 2 - x JX(I-1)2 - X(I)2 p R2 X(I)2 x 4X(1)2 - X()2 r 4X(I-1)2 - X(I)2 - P(2) NX(l)2 - X(I)2 - (X()2 (I)2 -r 4xX(I-1)2 - X(I)2 I generic p- (J) X(J-1)2 - X(I)2 - X()2 - X(I)2 term JX(I-1)2 _ X(I)2 2 < J < I-1 - (I-1) JX(I-2)2 - X(I) - X(J-1)2 - X(I)2 ( 4X(I-1)2 X(I)2 where, for example, one means: X(I-1)2 = [X(I-1)]2 s x2_1 Following the calculation of the radial densities pr(I), the void fractions in terms of r are obtained from the formula: F(I) = 1 - (I) (D-8) The output of the program was planned to provide not only the desired void fraction, but also the average density as a function of the radial distance, pr(I), and the average density as function of the transversal distance, p(I).

-101A flow chart of the MAD program is shown in Figure Dl where the numbers refer to the statement number in the program. A copy of the program, as obtained from the printer, is also included, where p is represented by the symbol RO, while Pr is indicated by ROR. $COMPILE MAD# EXECUTE DELTAX 0.'030~-'~ = —- 1 MU = 2.10 2 RO =221977 3- 3 START READ DATA ZPR#DtM N2(1)***N2(M) N1(1)..*N1(M) 4 -' -— T —---- ---- —. —' —------ tHA -G -... _.~ -q.........o 1...-M..'.._.__........ ——.-'.-..'' —--- X(I) = R - (2*I-1)*DELTAX/2- 6 BACK ROT I ) =RO-RO*ELOGo (N1 ( I ) /N2 I ) ) / (2e *MU*SQRT* ( R*R,-X( I)X ( i ) )- 7 ~ROR(1) = RO(1) 8 I = 2 9 NANCY AUX = RO(I)*SQRT.(R *R -X(I)*X(_ I ))/SQRT (X(I-1 )*X(I -1)- 10 iX(I)*X(I))-ROR(1)*(SQRTe(R * R -X(I)*X(I))-SQRT.(X(1)* 11 2X(l )-X(I)*X( I) ) )/SQRT. (X( I-1)*X( I-1)-X( I )*X( I)J 12 WHENEVER 1*'G2 13 THROUGH MARY. FOR J = 2, 1. J.G.I-1 14 Ta-ROR(J)*(SQRT,(X(J-1) *X(J1)-X()*X(I)) RT,(X(J)*X(J)- 15 1X(I)*X( I)))/SQRTI(XI-1)*X( I-1)-X(I)*X()) 16 MARY' - AUX = AUX + T ~..I17 ROR(I) = AUX 18 OTHERWISE 19 ROR(2) = AUX 20 END OF CONDITIONAL 21 WHENEVER IeLeM 22 — _ ______________ ---— _-_.-____ _______ ___ ___________ _.____________._..________.._________.._______________-__ I = I + 1 23 TRANSFER TO NANCY 24 OTHERW I SE 25 THROUGH JEAN FOR I =1,1. I.G.M 26 WHENEVER ROR(I) *GE. RO 27 F(I) 0 = 0 28 OTHERWISE 29 F(I) = 1. —ROR(I)/RO 30 JEAN ~~~ END OF CONDITIONAL 31._. END OF CONDITIONAL 32 INTEGER ItM#J 33 DIMENSION N1(30),N2(30), 1RO(30) ROR(30). X(30) F((O30) _NOR(30) _ _ 34 PRINT COMMENT $1VOID FRACTION MEASUREMENTS FOR MERCURY$ 35 PRINT COMMENT $-PARAMETERS$ _. 36 PRINT RESULTS DELTAX. MUt RO 37 PRINT COMMENT $OCAVITATION CONDITIONS 38 1 STANDARD AND NOSENEW DATA DEC 1961$ 39 PRINT RESULTS ZRD M — _ _ _ 40 PRINT COMMENT $-REDUCED DATA$ 41 PRINL RESULTS N l__JLN__M) N2(_N2(M 42 PRINT COMMENT $- COMPUTED VALUES$ 43 _ _ PRINT RESULTS RO(1) RO(M)!4_4 PRINT RESULTS X(1)..X(M), ROR(1).**ROR(M)) F(1)...F(M) 45 ---— _ —-----— J___ _I FkERfL_JQ_FiA E L_ _-_ _ -__ __.......46 END OF PROGRAM 47 ____AT_______________

-102(1),(2),(3) READ DATA AX, p, L X(I) = R (2 -x READ DATA - - ( (7)'> I > M J2 2 J=J+1_ __ (8 (10) AUX = p(I) - (1 —— 2 2 ) LX(I-l) -X(I) _- X(I) l (12) AUX = AUX + T 17) J 2 + 1 I(18) (I) = AUX 0) (22) ( I >M SEE NEXT PAGE Figure Dl. MAD Flow Chart.

-103SEE PREVIOUS PAGE I=I+ 1 _1 —-- R|(27) (28) Pr)> p F(I) 0 -(30) F(I) 1-^ (35) PRINT COMMENT (36) TITIE, ETC. ( 38 Nl(l).... Nl(M) (42) PRINT RESULTS (447) X(i).... X(M) (452) P2(1l)....p2(M) pp(l) *....p(M) F(1)....F(M) TRANSFER (46) TO START (47) FigurEND MAD Flow Chart Figure Dl. MAD Flow Chart (Continuntion).

-10480. 70 60 5 30 20 0! V. 9/ U 8 1I W 7 3 2 20 40 60 80 100 120 140 FLOW RATE, GPM Figure D2. Flow Rate Calibration Curve. (Metering Venturi).

APPENDIX E TABLES -105

TABLES I. LINEARITY OF LINEAR AMPLIFIER II. AE vs % WINDOW III. DIFFERENTIAL SPECTRUM FOR Co60 AND Cs137 IV. 1.17 Mev PHOTOPEAK OF Co60 V, o. IN Hg, DATA FROM LA-2237 VI. p. IN Hg, DATA FROM ETHERINGTON VII. Hg DENSITY AS A FUNCTION OF TEMPERATURE VIII. DATA FOR EXPERIMENTAL DETERMINATION OF p. IN Hg IX BACKGROUND INFORMATION X. SUMMARY OF EXPERIMENTAL RUNS XI THROUGH XXVII. REDUCED AND COMPUTED VALUES -106

-107TABLE I LINEARITY OF LINEAR AMPLIFIER Gain Pulse Height Volts Coarse Fine 2 36 0.30 4 36 0.60 8 36 1.10 16 36 2.20 32 36 4.30 63 36 5.8 See Figure Al

-108 - TABLE II CALIBRATION OF AE DIAL EDial Dial E2 E1 % Window 1000 915 867 4,8 900 600 917 885 3,2 200 918 911 0o7 1000 750 699 5o1 700 600 749 717 3o2 200 741 740 o 8 1000 5i6 462 5~4 500 6oo 516 480 356 200 516 506 lo0 1000 3.2 254 5.8 00oo 6oo 312 277 3o5 200 3.-53 3o3 150 See Figure A2

-109TABLE III PRELIMINARY DIFFERENTIAL SPECTRUM 60 137 Co Cs Dial c/m E Dial c/min E Dial c/min 1000 6 440 227 550 146 980 5 420 267 310 1072 960 6 400 249 290 450 940 - 380 230 270 185 700 6 360 241 300 1003 680 15 640 91 320 692 660 21 620 244 305 1175 640 78 600 242 620 225 580 126 600 232 560 139 580 87 550 267 560 167 540 410 540 381 530 339 520 245 520 261 500 154 510 193 i 480 173 570 92 46o 155 610 264 H.V. = -1000 volts AE = 200, Gain 2 x 36 See Figure A3

-110TABLE IV 6o PRECISE DET, OF Co 1.17 Mev PEAK t - -'- Net Co60 E Dial c/3 min Background c/3 min 560 3054 151 2903 + 31 555 3754 149 3605 + 35 550 4014 144 3870 + 36 545 4195 148 4047 + 37 540 18j 142 734o0 + 55 535 3621 146 3475 + 34 530 3407 139 3268 T 33 525 3299 124 3175 + 33 520 3038 131 2907 + 31 570 2698 155 2543 + 29 510 2691 105 2586 + 29 H. V == -1000, AE 200, Gain C-2 f-36 Differential count, scalar discriminator - 1.5. See Figure A5 TABLE V LINEAR ABSORPTION COEFFICIENT OF Hg FOR Co60 GAMMA-RAYS ENERGYo* E, Mev T KT ao + aI + ac T + KT + 0.80 2.50 x 10-2 5.930 x 102 8,48 x 10-2 lo00 1.70 x 10-2 5.248 x 10-2 6.41 x 10-2 1.50 0.81 x o0-2 Oo15 x 10-2 4.201 x 10-2 5 161 x 10-2 2.00 0.52 x 10-2 0o48 x 10-2 3.567 x 10-2 4.567 x 10-2 See Figure Blo All values are in cm2/gm Notation: T = photoelectric effect cross-section aa = Compton absorption cross-section cI = Compton scattering cross-section =c = Thompson cross-section KT = pair production cross-section * Reference 12: LA-22537 "Gamma-Ray Absorption Coefficients for Elements 1 through 100 Derived from the Theoretical Values of the National Bureau of Standards," 1957.

-111TABLE VI i IN Hg. DATA FROM NUCLEAR ENGINEERING HANDBOOK10 Energy - Mev p/p - cm2/gm. - cm o 5 0.147 1.993 1.0 oo0692 0.939 2o0 0.0451 o.611 3.0 o.0411 0.557 6,0 0.o441 o.598 *. values computed using P70oF = 15.5435 gm/cm3. See Figure B2 TABLE VII MERCURY DENSITY AS A FUNCTION OF TEMPERATURE* Temp - ~C p - gm/cm3 0 1355955 19 13.5487 20 13o5462 21 13o5438 22 13o5413 25 1355389 * Data from Handbook of Chemistry and Physics1 See Figure B3

-112TABLE VIII ABSORPTION OF 1.17 Mev y IN Hg Hg Total Hg Background Net Co60 Normalized Height-in Ah-in Ah-in Height, in c/3 min c/1 min c/3 min Rate 2 7/64 0 0 0 8931 153 8472 1.0 2 41/ 5/128.0391.0391 8457 172 7941.937 1 62/64 13/128.1018.1409 7211 171 6698.790 1 56/64 6/64.0937.2346 5935 173 5416.640 l 51/64 5/64.0782.3128 5147 171 4634.547 1 46/64 5/64.0782.3910 4335 169 3828.452 1 39/64 7/64.1095.5005 3467 167 2963.350 1 35/64 4/64.0625.5630 2966 173 2453.289 1 21/64 14/64.2190.7820 2286 172 1770.209 1 14/64 7/64.1095.8915 2012 165 1517.179 1 6/64 8/64.1205 1.0120 1626 188 1062.126 1 6/64.0937 1.1057 1313 186 755.089 52/64 12/64.1875 1.2932 912 168 4o8.o48 H. V. = -1000, AE = 490, Gain 2 x 36, E Dial = 530 Differential Count. See Figure B4

-113TABLE IX BACKGROUND INFORMATION Counting Counting Standar Date Time No. Counts Time Rate Deviation Dec. 21 9:00 330 10 33 CPM +1.81 CPM Dec. 21 14:10 426 10 42.6 CPM +2.06 " Dec. 21 16:09 329 10 32.9 CPM +1.81 Dec. 21 20:30 296 10 29.6 CPM +1.71 Dec. 22 8:30 383 10 38.3 CPM +1.95 Dec. 22 13:10 376 10 37.6 CPM +1.93 Dec. 26 8:30 289 10 28.9 CPM +1.69 Dec. 26 13:20 438 10 43.8 CPM +2.09 Dec. 26 19:10 446 10 44.6 CPM +2.11 Dec. 27 8:25 363 10 36.3 CPM +1.90 Dec. 27 13:55 301 10 30.1 CPM +1.73 Deco 27 20:30 342 10 34.2 CPM +1.84 Dec. 28 14:00 411 10 41.1 CPM +2.02 Background corrections will be performed as follows: Dec. 21 runs: use background closest to actual run time Dec. 22 runs: as above: 115 counts/3 min Dec. 26 runs: morning: use closest background determination; afternoon and evening, use: 438 + 446 = 44.2 CPM 20 363 + 301 + 342 Dec. 27 runs: use average value: 30 = 33.5 CPM Dec. 28 runs: 41.1 CPM or 123 counts/3 min.

-114TABLE X VOID FRACTION RUNS December, 1961 Cavitation Condition Run N~ Z, inch R, inch First mark 21 -0o250 0o255 20 0 000 j 0255 24 1 O O786 0.297 25 1.163 5 05339 -- 1.750 0,349 _- 2.250 0.376; 2.750 0.402 --------------- _^....... —~ —~- - t — r^. —.~..^ Visible i 22 -0250 0 255 17 0.000 0.255 16 0.250 0268 5 0 625 0.289 10 0,786 0 o 297 11 1.163 05317 Nose 1 0,250 0,268 4 0,625 0o289 9 0,786 0.297 13 t 1163. 0.317 Standard 18 0 o 000 0,255 15 0,250 0.268 6 0o625 0,289 7 0.786 0.297 14 1o163 0,317 No cavitation 26 -0,250 air only (one run for 23 -0250 0,255 each Z value) 19 0O000 0.0255 2 0,250 0.268 3 0o625 0o289 8 Oo786 0 297 12 1 ol63 0o317 — o 1o375 055339 — ~ 1o750 o349 - - 2o250 0o376 __ - 2o750 0.402 Remarks: Total N~ of scheduled runs, o532 Actually performedo.......... 26

-115TABLE XI Cavitation Condition: Visible Axial Position: Z = - 0,250 R = 0,255 in, Reduced Data Computed Values r (in)........ N2 N1 F% r% o250 5600 71.80 98,04.240 4975 6200 47,46 94,12 o230 4375 5325 26,94 90,20.220 41.50 4825 7~79 86,27.210 4000 4505 0,30 82,35 o 200 3885 4265 0 78.43 o190 3770 4065 O 74,51.180 3675 3875 O 70~59.170 3580 3725 0 66.67.160 3490 3590 0 6274 o.150 3410 3480 0 58,82 o40 3335 53390 0 54.90.10 3260 3315 0 50o98 o120 3190 3250 47006 ol10 3115 5185 43514.o100 3050 31.30 0 3922.090 3005 308o 0 35529 o080 2965 3 040 31o37 0070 2925 3005 0 27,45 o060 j 2905 2975 2353 0050 2885 2950 19.61 o 40 2870 2930 15.69.030 2855 2910 0 11.76.020 2850 2895 O 7084.01.0 2845 2885 3.92 o 000 2845 288 0 1.46 __ _ _ ___ __ j __.___ __.__....

-116TABLE XII Cavitation Condition: lsto mark Axial Position: Z = - 0250 R = 0255 ino Reduced Data Computed Values r (in) N2 N1 F% r% o250 5600 7100 98o04 o240 4975 6350 57~03 94o12 230 435 5575 5 39080 90o20 o220 4150 4800 0 86o27 o210 4000 4440 0 82o35 200 3885 41g90 78043 190 3770 4015 0 74.51 1o80 3675 3880 0 70o59.170 3580 3760 0 66.67 1 o60 3490 3640 0 62.74.1 50 3410 3550 0 58.82 1 o40 3335 3455 0 54,90. o13 20 26 3365 0 50~98 i o120 3190 3280 0 47 o,6..1o0 53115 3210 0 43 14.100 3050 3135 0 39o22.090 3005 3070 0 35529 o080 2965 3005 0 31537 0 70 2925 2945 0 27.45.o6o 2905 2905 0 25353.050 2885 2865 0 19o61 o040 2870 2830 0 15 69.030 2855 2805 0 1176.020 2850 2790 0 7.84 o010 2845 2775 0 3593 o000 2845 2770 0 1,46._.,..,,......, __. — __

-117TABLE XIII Cavitation Conditions: Visible Axial Position: Z = 0.000 R = 0.255 in. Reduced Data Computed Values r (in )............ N2 N1,250 6550 7050 4.86 98.04.240 5725 6250 21o79 94,12.230 4975 5500 19o32 90.20.220 4485 5025 19o33 86.27 o210 4100 4575 13563 82,35.200 3835 4285 12.64 78.43 1o90 3615 4035 10,93 74-51.180 3430 3825 9,84 70~59.170 3280 3600 2.98 66.67.160 3145 3415 0o68 62,74 o150 3060 3285 58,82 o140 2985 i 3195 0 54,90 o130 2930 3125 50.98.120 2885 3060 0 47.06 o110 2845 3010 0 43514 i i i o100 2825 2965 0 39 22.090 2790 2925 0 3529 o080 2765 2895 o 315o37 o070 2750 265 0 27.45 o060 2735 28400 23,53.050 2720 1 2820 0 19 61 o040 2710 2805 0 15.69 ~030 2705 2785 0 11,76,020 2700 2770 7, 84 010 2700 2760 0 392 000 2700 2750 1.46 I____________ s__________i ______ ______________ _______________

-118TABLE XIV Cavitation Conditions: Standard Axial Position: Z = 0.000 R = 0.255 in. Reduced Data Computed Values r (in) N2 N1 F| r.250 6550 7065 35586 98.04.240 5725 6300 24.27 94,12.230 4975 5450 14.91 90.20.220 4485 4875 9.48 86.27.210 4100 4535 15,32 82.35.200 3835 4230 11 00 78o43 1o90 3615 3975 8 75 74,51.180 3430 3770 8.29 70.59.170 3280 3565 3'o43 66.67.160 3145 400o 2.69 62.74.150 3060 3275 0 58.82.140 2985 3175 0 54.90.130 2930 3100 0 50.98.120 2885 3035 0 47.06.110 2845 2990 O 43.14.100 2825 2940 0 39.22.090 2790 2910 0 35529.o80 2765 2875 0 31-37.070 2750 2845 0 27.45.o60 8735 2820 0 23.53.050 2720 2805 0 19.61.040 2710 2790 0 15.69.030 2705 2780 0 11o76.020 2700 2775 O 7.84.010 2700 2775 0 3592.000 2700 2775 0 146 c. _ ______________2775.I. 0.

-119TABLE XV Cavitation Conditions: lsto mark Axial Position: Z = 0.000 R - 0,255 in. Reduced Data Computed Values r (in) ----.... N2 N1 F% r%.250 6550 6875 22,95 98.04.240 5725 6325 28.60 94.12.230 4975 5650 27.85 90.20.220 4485 5050 16.92 86,27.210 4100 4540 8.58 82.35.200 3835 4200 5.33 78.43.190 3615 3985 9.19 74.51,180 3430 3800 10,30 70~59.170 3280 3635 9.18 66.67.16o 53145 3510 1 1142 62,74; 150 3060 3405 8553 58,82 140 2985 3315 7o42 54,90 o130 2930 3245 6,22 50~98.120 2885 3175 3557 47 06.110 2845 3120 30o6 43014 o100 2825 3070 0 39.22 o090 2790 3025 0o41 35o29 o080 1 2765 2990 0,22 31 37 0070 2750 2960 0 27.45 o060 i 2735 2930 0 23553.050 I 2720 2900 0 19,61 o040 2710 2880 0 15069.030 2705 2865 0 11.76.020 2700 2850 0 7.84.010 2700 2835 0 3592 o000 2700 2835 0 1,46._ __..-. _.___...__________

-120TABLE XVI Cavitation Conditions: Nose Axial Position: Z =0,250 R = 0.268 in. Reduced Data Computed Values r (in) -__N2 N2 N F% r%.265 58oo00 6225 32.68 98.15.255 5525 5925 27.,85 94.40.245 4850 56oo00 50.91 90.67.2533 4450 5275 51.05 86.94.223 4175 4975 25.29 85.21.2135 5965 4640 14.47 79,48.205 5800 j 4525 4.57 i 75.75.195 5665 4075 0 72.01.1875 5225 586o 0 68.28.1775 53415 5710 0 64,55.165 53310 575 0 60.82.1575 5215 5465 0 57.09.145 5125 53385 35.01 537556.1335 5040 53305 4.44 49.65.125 2965 5275 5.55 45,90.115 2905 5170 4.8o: 42.16.105 2850 5115 5.335 58.45.095 2810 5065 3.76 54.70.0875 2770 5015 2,81 750.97.075 2740 2980 2.85 27.24.065 2710 2975 0.49 I 25.51.055 2690go 2900 0 19.78.045 2675 2870 0 16.o04.0533 2655 2850 0 12.51.025 2645 2875 0 8.58.015 2640 2820 0 4.85.005 2640 2815 0 1.12

-121TABLE XVII Cavitation Conditions: Standard Axial Position: Z = 0.250 R = 0,268 in, Reduced Data Computed Values r (in)._ _ N2 N1 % r%.263 5800 7175 98 31 98.13.253 5325 6860 61,28 94.40.243 4850 6050 31.14 90.67.233 4450 5275 9.69 86.94.223 4175 4800oo 294 83.21 i.213 7 5965 4465 0.09 79.48 o 203 13800 4175 0 75.75.193 3665 3950 0 72.01.183 3525 3770 0 68.28 I.177 3 3 415 3615 0 64.55.163 7 3310 3485 0 60.82.153 3215 3270 0 57.09.143 3125 3245 0 53.36.133 35040 3125 0 49.63.123 2965 3025 0 45.90.113 2905 2960 0 42.16.103 2850 2900 0 38.43.093 2810 2850 0 3470.083 277281 0 3 0.97.073 2740 2780 0 27.24.063 2710 j2755 0 23.51.053 2690 2735 0 19.78.043 2675 2715 0 16.o04.033 i 2655 2705 0 12.31.023 2645 2700 0 8.58; 013 2640 2690 0 4,85.003 2640 269 0 1.12

-122TABLE XVIII Cavitation Conditions: Visible Axial Position: Z = 0,625 R = 0.289 in, Reduced Data Computed Values r (in ).................. N2 N1 F_..% r_ %.284 4250 4225 0 98.27.274 3800 3850 4.77 94.81.264 3540 3600 3.88 91.35.254 3370 3450 4.89 87.89.244 3240 3350 6.82 84.43.234 3100 3250 9.61 80.97.224 2990 3160 9.66 77.51.214 2885 3070 9.80 74.05 o 204 2795 3000 10,90 70.59.194 2715 2925 10,00 67.13.184 2635 2860 11.22 63.67.174 2575 2800 9 90 60.21.164 2515 2745 10.14 56.75.154 2465 2695 9.50 53.29.144 2415 26510o.o8 49.83.134 2375 2610 9.52 46317.124 2340 2570 8.32 42.91.114 2305 2540 954 39045.104 2270 2510 10.30 35597.094 2245 2490 10o76 32.53.084 2225 2470 1004 29007.074 2205 2455 11.02 25.61.064 2185 2440 11 81 22.15.054 2180 2425 7.84 18.69.044 2170 2415 8.66 15.22.034 2165 2410 8,74 11.76.024 2160 2405 8,81 8.30.014 2155 2400 8,92 4.84.004 2155 2400 8.77 1.38

-123TABLE XIX Cavitation Conditions: Nose Axial Position: Z = 0,625 R = 0,289 in, Reduced Data Computed Values r (in) _. N2 N1 F^ rO,284 4250 48oo00 5413 98,27 o274 3800 4425 36,07 94,81,264 3540 4125 24072 91o35.254 3370 3875 15o31 87,89,244 3240 3675 9o70 84,43,234 3100 3505 9029 80,97,224 2900 3365 779 77o51 o214 2885 3225 5~75 74,05 o204 2795 3110 4,94 70o59.194 2715 300 3514 67o13 o184 2635 2915 487 63067 ol74 2575 280 248 60o21 1o64 2515 2765 376 56,75.154 2465 2705 3531 53529 o144 2415 2650 3 77 49083 ol34 2375 2610 4,63 46537,124 2340 2570 4.18 42,91 o114 2305 2540 5087 39045 o104 2270 2515 7~99 35597 o094 2245 2490 7~24 i 32,53 o084 2225 2470 7o01 29,07,074 2205 2455 8,22 25.61 o064 2185 2440 9,16 22,15.054 2180 240 6,75 18,69 o044 2170 2420 7,11 15,22 o034 2165 2415 7o06 11,76 o024 2160 2410 7,09 80 o014 2155 2405 7,20 4,84 o0o4 2155 2405 7004 1,38

-124TABLE XX Cavitation Conditions: Standard Axial Position: Z = 0.625 R = 0.289 in. Reduced Data Computed Values r (in) N N —-1N2 N1 F% r.284 4250 5225 91.87 98.27.274 3800 4625 41.47 94.81.264 3540 4200 21.63 91.35.254 3370 3915 12.54 87.89.244 3240 3705 7~99 84.43.234 3100 3520 7.17 80.97.224 2990 3370 5.64 77.51.214 2885 3235 4.98 74.05.204 2795 3125 4.92 70.59.194 2715 3030 4.94 67.13.184 2635 2945 6.00 63.67.174 2575 2865 4.13 60.21.164 2515 2800 5.07 56.75.154 2465 2740 4.50 55.29.144 2415 2695 6.52 49.83.134 2375 2655 6.72 46.37.124 2340 2620 6.93 42.91.114 2305 2595 9.08 39.45.104 2270 2570 10.63 35597.094 2245 2550 10.70 32.53.084 2225 2530 9.92 29.07.074 j 2205 2520 12,08 25.61.o065 2185 2505 12.44 22,15.054 2180 2495 9.76 18.69.044 2170 2485 10.00 15.22.034 2165 2480 9.85 11.76.024 1260 2475 9.82 8.30.014 2155 2470 9.92 4.84.004 2155 2470 9.70 1.58

-125TABLE XXI Cavitation Conditions: Visible and Nose Axial Position: Z = 0o7 R = 0,297 in, Reduced Data Computed Values r (in) _______ N2 N1 F.282 4050 4050 0 94.95.252 3370 3370 0 84.85.222 3010 3010 0 74 75 o192 2760 2760 0 64.65.162 2590 2590 0 5455.132 2490 2490 0 44.44.102 2415 2415 0 34534.072 2370 2370 0 24,24.042 2335 2335 0 14,14.012 2325 2324 0 4,04

-126TABLE XXII Cavitation Conditions: Standard Axial Position: Z = 0.786 R = 0.297 in, Reduced Data Computed Values r (in) | N | —|.. N2 N1 F% r%.292 4600 4880 25.92 98532.282 4050 4750 44.14 94.95.272 3750 4160 9o80 91,58.262 3540 3910 9.45 88,22.252 3370 3725 9,52 84,85.242 3215 3540 7.54 81,48.232 3105 3385 4.05 78.11,222 3010 3245 1.22 74~75.212 2915 3120 0,41 71.38.202 2835 5010 0 68,01 192 2760 2910 0 64.65.182 2690 2810 61,28 I o172 2640 2730 0 57991.162 2590 2675 0 5455.152 2550 2620 0 511.8.142 2515 2565 0 47o81,132 2490 2535 0 44.44.122 2460 2495 0 41,08.112 2435 2465 0 37071.102 2415 2440 0 34,34.092 2395 2420 0 0.98.082 2380 2400 0 27.61.072 2370 2380 0 24.24.062 2355 2365 0 20,86 o052 2340 2350 0 17.51 o042 2335 1 2335 0 l4,14.032 2330 2330 0 t 10,77,022 2325 2320 0 7.41.012 2325 i 2315 0 1 4,04.002 2520 2510 0 0,67 ___ _ _ I __ - ___t ___ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-127TABLE XXIII Cavitation Conditions: 1st. mark Axial Position: Z = 0786 R = 0.297 in, Reduced Data Computed Values r (in)..... -___ N2 N1 F rF 2i ii I _ o292 4600 98.32.282 4050 94.95 o272 3750 91.58.262 3540 6900 88.22.252 3370 6480 75 72 84.85,242 3215 5855 48.37 81.48.232 1 3105 5275 25.53 78.11,222 3010 4655 0.12 74.75.212 2915 4230 0 71538.202 2835 3990 0 68.01.192 2760 3795 0 64.65 o182 2690 350 60 61.28.172 2640 3550 0 57.91 o162 2590 1 3465 1050 54,55.152 2550 3385.lol0 51o18,142 2515 3320 1,55 57081.132 2490 3265 0.94 44.44.122 2460 3215 1.87 41o08 o112 2435 3165 10o4 37 71 o102 2415 3125 0,82 34534 092 2395 3085 0o29 30,98 o082 2380 3050 0 27~ 61.072 2370 i 020 0 24.24.062 2355 2995 0 20.86 0o52 2340 i 2975 0o41 17.51.042 2335 2955 0 14.14 ~032 2330? 2940 0 10.77 o022 2325 2930 0 7.41 12 2325 2920 O 4,04 o002 2320 1 2915 0 0.67 X _............. ~~~~~~~~~~~~

-128TABLE XXIV Cavitation Conditions: Visible Axial Position: Z = 1o163 R - 0,317 in Reduced Data Computed Values r (in) N2 N1 F~ 312 3050 5500 35545 98~42 302 2900 5025 5014 95 27 o292 2790 2840 0 92,11,282 2710 2720 0 88o96 272 2640 2645 0 185080 o262 2585 2585 0 82,65 o252 1 2530 i2530 79~50,242 2485 2485 O 76534 o232 2440 2440 0 75319 o222 2400 2400 0 70,03 o212 2370 2370 0 66,88 202 2330 2330 O 63072 1o92 2305 2305 0 60,57,182 2275 2275 0 57o41 o72 2250 2250 0 54,26 o162 2225 2225 0 51o10 o152 2205 2205 0 47~95,142 2185 2185 O 44,79 ol32 2165 2165 O 41,64 o122 2150 2150 0 38,49 oll2 2140 2140 35o33 o102 2130 2130 0 32o18,092 2120 2120 0 29,02 o082 2110 211.0 0 25 87.072 2100 2100 0 22~71 o062 2095 20950 1 19056.052 0 2090 20. 16o40 o042 2085 2085 0 13525 ~032 2085 2085 O i0o09 o022 2085 2085 0 6,94

-129TABLE XXV Cavitation Conditions: Nose Axial Position: Z = 1.163 R = 03.17 ino Reduced Data Computed Values r (in) -... N2 N1 F r% 312 3050 3525 61,45 98,42 o302 2900 3320 26,98 95o27.292 2790 3150 15.25 92.11.282 2710 3035 10,87 88.96.272 2640 2955 10.23 85080.262 2585 2885 8.60 82.65.252 2530 2825 8.53 79050.242 2485 2780 8~72 76534.232 2440 2730 8,12 73o19 o222 2400 2680 6,98 70.03 I.212 2370 2645 6,72 66.88 202 2330 2610 8.00 63572.192 2305 2575 6.26 60.57.182 2275 2545 6.86 57.41.172 2250 2520 7002 54.26.162 2225 2495 7o13 51.10 o152 2205 2470 6.26 47.95.142 2185 2450 6.64 44.79.132 2165 2430 6.81 41.64.122 2150 2415 6.83 38.49.112 2140 2400 5073 35533.102 2130 2390 6.12 32.18.092 2120 2380 6.27 29.02.082 2110 2375 7.58 25.87.072 2100 2365 7.21 22.71.062 2095 2360 6.98 19.56.052 2090 2355 6.90 16.40.042 2085 2350 6,89 13 25.032 2085 2350 6.69 10o09.022 2085 2350 6.60 694

-150TABLE XXVI Cavitation Conditions: Standard Axial Position- Z = 1,165 R = 0517 in. Reduced Data Computed Values r (in) 2N N1.312 5050 5225 25,00 98.42 3,502 2900 5075 12,06 95,27,292 2790 2965 928 92~11,292 2710 2885 7953 88~96. 272 2640o 2820 7.74 85.80,262 2585 2755 580 82,65 o252 2550 2700 5,87 79,50.242 2485 2655 5,71 i 76,54,252 2440 2610 560 i 75,19.222 2400 i 2570 5.48 70053 | 212 2570 2555 4,6 6 66,88 202 255330 2500 5.64 65,72.192 2505 2465 3.576 6o,57 | 182 2275 2440 i 510 5741.l72 2250 2410 i 4,08 I 5426.162 2225 2585 4,57 51,0.152 2205 4 2565 4,42 4795,142 2185 2545 4,47 44,79.132 2165 255330 549 41,64.122 2150 2510 J 4,o05 58.49,112 214o 2295 3518 i 553355.102 2150 2285 365 52,18 o092 2120 2275.5,82 29,02,o82 2110 I 2265 5o95 25.87,072 2100 * 2255 4,01 22,71,o62 2095 2250 3598 19o56.052 2090 1 2245 3.598 16,40,o42 2085 2240 4,01 15,25,052 2085 2255o 1,96 I 1o,09,022 2085 2250 555 I 6,94

-131TABLE XXVII Cavitation Conditions: lsto mark Axial Position: Z = 1.163 R = 0o317 in, Reduced Data Computed Values r (in) |i i "N2 N1 F% r%.312 3050 98.42.302 2900 95027.292 2790 5975 92,11.282 2710 5925 88 96,272 2640 5780 84,57 85.80.262 2585 5675 75.53 82,65.252 2530 5485 64.23 79.50.242 2485 5175 47.16 76534.232 2440 4775 27087 73519 o 222 2400 4375 10,66 70~30 212 2370 4000 0 66.88.202 2330 364o 0 63072.192 2305 3515 o 60,57.182 2275 3420 0 57041 ol72 2250 3360 0 54,26 t I.162 1 2225 3300 0.24 51010.152 2205 3255 1.93 47595.142 2185 3215 337 44 79.132 2165 3175 407 41,64 o122 2150 3145 1 4.77 38049.112 2140 3125 j 5.51 35533.102 1230 3100 5.05 32.18.092 2120 075 4.66 29.02.082 2110 3065 7~00 25.87.072 2100 3045 6.34 22,71.o062 2095 3025 441 19.56.052 2090 3015 5.27 16.40.042 2085 3005 5.45 13525.032 2085 j 2995 27 10o09 o 022 2085 2990 35.00 6,94 I

UNIVERSITY OF MICHIGAN Il3 901 03ll 2l 4l 3 9015 03525 1472