THE UNI V E R S ITY OF MICHIGAN COLLEGE OF ENGINEERING Department of Nuclear Engineering Laboratory for Fluid Flow and Heat Transport Phenomena Technical Report No. 11 DETERMINATION OF CAVITATION CONDITIONS FROM DENSITY PROFILES OF MERCURY IN A VENTURI lan E. B. Lauchlan Frederick G. Hammitt Richard D. Ivany M. Joht Robinson Willy Smith ORA Project 03424 under contract with~ NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GRANT NO. NsG-39-60 WASHINGTON, D.C. administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR October 1963

ACKNOWLEDGMENT The electronic equipment was kindly furnished by the Department of Nuclear Engineering of The University of Michigan. ii

ABSTRACT The extent of the cavitation in mercury flowing in a transparent, Plexiglas venturi can be determined by measuring the decrease in the attenuation of a well collimated, Co60, gamma beam in passing through the venturi when voids resulting from cavitation are present. Experimental results for the axial fluid density profile are consistent with the visual appearance of the cavitating flow. iii

TABLE OF CONTENTS Page LIST OF ILLUSTRATIONS v I. INTRODUCTION 1 II. EQUIPMENT 2 III. EXPERIMENTIAL PROCEDURE Ao Calibration of Electronic Equipment 3 B. Axial Alignment 3 Co Test Runs 11 IV REDUCTION OF DATA 19 V. DISCUSSION OF RESULTS 27 A. Axial Density Profiles 27 Bo Central Jet Axial Density Profiles 28 C. Experimental Accuracy 29 VI. CONCLUSIONS 50 VIIo REFERENCES 32 VTII. APPENDIX 53 A. Degrees of Cavitation 33 B. Derivation of Relation Between Count-Rate and Density 33 Co Central Jet Axial Density Profile Determination 37 iv

LIST OF ILLUSTRATIONS Table Page I Pressure Settings for Mercury Cavitation Conditions 19 Figure 1. Sketch of overall loop layout. 4 2. Cross section of cavitating venturi test section showing locations of metal wear specimens and locations of the cavitation termination for various degrees of cavitation. 5 3. Block diagram of electronic equipment. 6 4. Photographs of densitometer positioned at venturi. 7 5. Schematic cross section of densitometer. 9 6. Determination of venturi centerline by densitometer method, assuming axial symmetry. 10 7. Count-rate vs. axial position for visible initiation at 34 ft./sec. throat velocity. 12 8. Count-rate vs. axial position for cavitation to nose at 34 ft./sec. throat velocity. 13 9. Count-rate vs. axial position for standard cavitation at 34 ft./sec. throat velocity. 14 10. Count-rate vs. axial position for cavitation to back at 34 ft./sec. throat velocity. 15 11. Count-rate vs. axial position for first mark cavitation at 34 ft./sec. throat velocity. 16 12. Count-rate vs. axial position for cavitation to nose at 48 ft./sec. throat velocity. 17 13. Count-rate vs. axial position for standard cavitation at 48 ft./sec. throat velocity. 18 v

LIST OF ILLUSTRATIONS (Concluded) Figure Page 14. NormaLized fluid density vs. axial position for visible initiation at 34 ft./sec. throat velocity. 20 15o Normalized fluid density and core void fraction vs. axial position for cavitation to nose at 34 fto/sec. throat velocity, 21 l6o Normalized fluid density and core void fraction vso axial position for standard cavitation at 34 fto/seCo throat veiocity0 22 17. Normalized fluid density vs. axial position for cavitation to back at 34 ft./sec. throat velocity. 23 18. Normalized fluid density and core void fraction vs, axial position for first mark cavitation at 34 fto/sec. throat velocity. 24 19o Normalized fluid density vs. axial position for cavitation to nose at 48 and 34 ft./sec. throat velocities. 25 20. Normalized fluid density vs. axial position for standard cavitation at 48 and 34 ft./sec. throat velocities. 26 21. Venturi cross-section as used in density calculations. 36 22. Void fraction contour schematic. 37 vi

Io INTRIT ION The present research investigation on cavitation-erosion damage in flowing systems has utilized transparent (Plexiglas) venturis into which damage specimens have been inserted, both with 2,3 water and room temperature mercury as the cavitating fluids The use of a transparent venturi has allowed the visual setting of the desired cavitation condition (as delineated by the location of the termination of the cavitation region - see Appendix for definition of various degrees of cavitation). An independent measure of the degree of cavitation has been afforded by the flow and pressure measurements, since the pressure drop across the venturi for a given flow is very sensitive to the extent of the cavitating region. However, it has also been found that the ratio of venturi (stagnation) pressure loss to throat kinetic pressure is a strong function of Reynolds Number and perhaps other variables, so that the pressure and flow measurements alone cannot be used, without an independent check, as an indication of degree of cavitation. As one of the next steps in the cavitation investigation, it is planned to conduct damage tests at somewhat elevated temperatures using mercury, and later molten lead or lead-bismuth alloy, as the cavitating fluids. Since this will probably necessitate a nontransparent (steel) venturi, it becomes necessary to develop a technique for obtaining an independent measurement of cavitation condition other than that derived from pressure and flow measurements, * This report summarizes a previous paper and also presents additional information O

-2so that the true meaning of these measurements can be ascertained. It is the purpose of this report to describe such a method, and the initial measurements which have been made, using room temperature mercury in a transparent venturi, The technique involves the measurement, by differential gamma-ray absorption, of mean density of the cavitating fLuid, in a plane through the centerline, as a function of axial position. It.was expected that, with such a density profile, it would be possible to delineate the approximate location of the termination of cavitation, and that this location would agree with that determined visuallyo As will be shown, this objective has been accomp:lished, so that effectively the axial density profile can be substituted for the visual indication in the determination of degree of cavitation, at least in those cases where there is substantial cavitation, ioe,, not initiation conditions New information relative to the form of the cavitating flow has also been obtained from these measurements in conjunction with the radial density contours previously measured o From a combination of these two sets of data, it is possible to compute the void fraction of the central (essentially liquid) portion of the flow, i oe. along the centerline, within the 10% void fraction contours previously5 obtained, and it is shown that this reaches a peak approximately at the visual cavitation termination point IIo EQUIPMENT The gamma-ray densitometer and the general technique have been previously described o For convenience the most significant portions will be summarized hereo Figure 1 is a schematic of the loop

-3used, and Figure 2 is a cross section of the cavitating venturi test sectiono During the experimental runs, two brass specimens were in place in the metal wear specimen holderso The electronic equipment and densitometer were of a similar type to that used previously o As before, as required by the 60 dense fluid, an energetic gamma source (Co ) was used. The use of a, single channel analyzer permitted the separation of the L.17 Mev peak from the entire pulse height spectrum, so that only the effect of a single energy photon need be considered in the calculations. Figure 3 is a block diagram of the essentials of the electronic equipment, and Figure 4 is photographs of the set-upo IIIo EXPERIENTAL PROCEDURE Ao Calibration of Electronic Equipment The electronic equipment was calibrated as previously discussed To improve stability of the equipment, it was operated for several days before the tests were made, so that it would be completely temperature stableo In addition, the tests were run during the late evening and early morning hours to avoid possible difficulties with power surges on the lineo Bo Axial Alignment The coll'imator-source assembly was securely mounted on a planing table capable of accurately controlled axial and transverse motion. The planing table was bolted to a welded steel stand which wa8s in turn securely bolted to the loop in the vicinity of the venturi, thereby permitting precise positioning of the collimator-source assembly with respect to the venturio The location of the center-line

176 + DRIVE PULLEY BEARING HOUSING -STUFFING BO THROTT.NG VALVE S T ( OFX/~~~~ LOCArING VALVEVENTURI TEST SECTION..~-.-l__ L ^ li IDIRECTION OF FLOW 61,. Io SUMP TANK MEASURING VENTRI ^-COOLER COOUNG WATER OUT, /I I COOLNG VTER IN THROTTLNG VALVE //7/7/7z~z7X5 11 TO STORAGE TANK -L ^ ^-STORAGE TANK (OUT OF LOCATION) TO /MAI/N LOO/P _ =DRAIN Figure 1. Sketch of overall loop layout.

~125~ — x3 STUD SPECIMEN HOLDER / VISIBLE INITIATION CA ro/AV ITM M 3 ~ 5..561'- - A-2 ~5773" —~ ~ —-C 1 ) SECTION A-A 14 578" 412"- ~- z AXIS 8-,o d1001 1.75~ Figure 2. Cross section of cavitating venturi test section showing locations of metal wear specimens and locations of the cavitation termination for various degrees of cavitation.

-6NoI (TI) PHOTOMULTIPLIER PREAMPLIFIER CRYSTAL TUBE H-V PULSE POWER SUPPLY GENERATOR NON-OVERLOADING LINEAR AMPLIFIER CATHODE RAY I ~ LOSCILLOSCOPE SINGLE-CHANNEL DIFFERENTIAL ANALYZER SCALER COUNT RATE TIMER METER 1257 Figure 3. Block diagram of electronic equipment.

Figure h. Photographs of densitometer positioned at venturi.

-8of the venturi relative to the collimator was determined by two independent procedures which were found to agree closelyo i) Optical Alignment Determination The top and bottom collimator were aligned by placing a light source in the scintillation tube holder, and then moving the bottom collimator so that a maximum intensity would pass through its slito The venturi assembly was then placed in position and rotated so that its flat outer surfaces were parallel to the surfaces of the collimatorso (This was accomplished by noting that the light would not be refracted when it passed through parallel surfaces)o The table was then moved in the transverse (x) direction (Figure 5)o The light was refracted in such a manner that it did not enter the slit of the bottom collimator unless it passed through the venturi centerlineo In this case the light was not refracted, since all interfaces were normal to the beam (Figure 5)> Thus, the centerline o of the venturi was establishedo ii) Densitometer Centerline Determination Measurement 60 The Go source was put in placeo The loop was filled with mercury, and a series of count-rate measurements were made at 0o05 inch transverse intervals across the venturio If axial symmetry is assumed, the centerline presumably coincides with the peak in the count-rate curve (Figure 6)o Since the results of these two independent methods were essentially the same, it is felt that the location of the true centerline of the venturi has been establishedo

-9PHOTOTUBE Noal (Tt) CRYSTAL LEAD SHIELD 3 ~ ~ ~'-COLLIMATOR VENTURI CROSS SECTION - ~I~ 3" 1I I a/- COLLIMATOR LEAD SHIELD COD~ SOURCE 5 D-MOVABLE TABLE DIRECTION OF MOVEMENT — ~ 1239 Figure 5. Schematic cross section of densitometer.

-10<: g 600~~3400 Id 200O Cf) Iz 100 0 C) -3.0 -2.0 -10 1.0.0 2.0 3.0 RADIAL POSITION FROM CENTERLINE (INCHES) 1258 Figure 6. Determination of venturi centerline by densitometer method, assuming axial symmetry.

Co Test Runs Experimental data were taken by moving the table along the z-axis, parallel to the venturi centerline, and taking readings at z = -0,250, 0000 0o250, 0412, 0o786, 1163, 1l500 and 10750 inches. (The throat exit plane of the venturi at the termination of the cylindrical portion, was established as the "zero"t for these axial measurements; the positive direction being down-stream) A. record was kept of all table motions to insure that the exact table position was known at all timeso Readings were made at all aforementioned positions for both cavitating (see Appendix) and non-cavitating conditions, Background counts were made with and without the pump running to insure that the pump motor was not affecting the detection equipment. Figures 7 through 13 show the experimental count-rates (corrected for background) for the cavitation conditions listed in Table I.

//VENTURI WALL I I I 2000 1 TEST SPECIMEN LI_ 16_00,_ VISUAL END OF CAVITATION 12001 1 I I T ~ ~ I z i Z RUN: 3 0 400o _ _ _ | FLUID: MERCURY O I I I VISIBLE INITIATION CAVITATION \ NON-CAVITATION i RU. 3 THROAT VELOCITY: 34 FTSEC. 1259 0 I _ _IIL INI _ _ _ -.25 0.25.50.75 1.00 1.25 150 1.75 200 AXIAL POSITION, INCHES Figure 7. Count-rate vs. axial position for visible initiation at 34 ft./sec. throat velocity.

IL ^I VENTURi WALL 20ooI 1600' ^ ^"-~ir^-4 ~r\ yTEST SPECIMEN AVIl ^0 R~^CAVITA TION I a: 1200 LL ~ ~ ~~^AA pnIiK ~* /^I~^^ I g 800 o-C~ 4oot~__ _ ~_I~ _ I I __.__ u 4. UO400f —zC RUN: 4 FLUID: ERFCURY\ 0 CAVITATION TO NOSE -.2 NON- CAVITATION ~6 O 251.5 J75 THROAT VELOCITY: 34 FT/SC.. AXIAL 1.025 150 POSITION, INCHES.75 Figure 8. Count-rate vs. axial posltion for carrtio n to ns2. at 34 ft./see. throat velocity.

VENTURI WALL TEST SPECIMEN 2"6000....... 1600 I I ~IVISUAL END OF CAVITATION - o \ 1200 i LllTHROAT VELOCITY: 34 FT/SEC. 1261 -.25 0.25.50.75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 9. Count-rate vs. axial position for standard cavitation at 34 ft./sec. throat velocity.

VENTURI WALL L _ 2000 ~~~ TEST SPECIMEN 16001 ~~ VISUAL END OF CAVITATION z 1200 0~~~~~~~~~~~ w,_________ _____ 800 (I) ________i____________ ___ z RUN: 6 3 400 FLUID: MERCURY Co o CAVITATION TO BACK r NON-CAVITATION THROAT VELOCITY: 34 FT/SEC. 1262 -.25 0.25.50 75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 10. Count-rate vs. axial position for cavitation to back at 34 ft./sec. throat velocity.

\I I-VENTURI WALL 2000 U)F^~ 1600 \ X V ITEST SPECIMEN 1600 I I D ^^ ~~ "VISUAL END OF CAVITATION ~ g o 1200~ ~~~, | U 1 LL) z RUN: 7 400_____FLUID: MERCURY o o FIRST MARK CAVITATION o NON- CAVITATION THROAT VELOCITY: 34 FT/SEC. 1263 0.25 50.75 1.00 1.25 1.50 1.75 2.00 2.25 AXIAL POSITION, INCHES Figure 11. Count-rate vs. axial position for first mark cavitation at 34 ft./sec. throat velocity.

\I \-VENTURI WALL i I 2000 ~ 0o i TEST SPECIMEN z 160VISUAL END OF CAVITATION 1200VLO: 48 I I —,,I a. 800.... z i RUN: 8 D^~~~~ o________L___ __ FLUID: MERCURY o 400 o,C o CAVITATION TO NOSE i, a NON- CAVITATION THROAT VELOCITY: 48 FT/SEC. 1264 _.25 0.25.50.75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 12. Count-rate vs. axial position for cavitation to nose at 48 ft./sec. throat velocity.

//VENTURI WALL 2000 TEST SPECIMEN D i 3 800 ~~- ~~~ W_ FLUID: MERCURY ~ _______ 400 l I o STANDARD CAVITATION i 0 N NON-CAVITATION \| THROAT VELOCITY: 48 FT/SEC. 1265 O0L I I _ r I'__ ____ -.25 0.25.50.75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 13. Count-rate vs. axial position for standard cavitation at 48 ft./sec. throat velocity. at 48 ft./sec. throat velocity.

-19TABLE I Pressure Settings For Mercury Cavitation Conditions Throat Venturi Venturi Venturi Cavo Velocity Inlet Pressure Outlet Pressue ressuessure Differential Condition ft./sec, PSI PSI PSI Visible 34 100 73 27 Cavitation to Nose 34 100 69 31 Standard Cavitation 34 100 64 36 Cavitation to Back 34 100 61 39 lst Mark Cavitation 34 100 50 50 Cavitation to Nose 48 225 163 62 Standard Cavitation 48 225 145 80 IV. REDUCTION OF DATA Figures 7 through 13 show the experimental count rates (corrected for background). Using these experimental points the corresponding density curves were calculated. These are shown in Figures 14 through 200 6 Adyanthaya has previously derived a relation between the count rate observed and the density, and this has been repeated in reference 5. That portion which applies to the present case is also summarized in Appendix Bo

VENTURI WALL - ------ - J- THROAT VELOCITY:34 FT/SEC. I \ VISUAL END OF CAVITATION TEST SPECIMEN 1.04 Z 1.00,:; 0 ~ (2 -20.2 0*.92 I.88 ~84.80 <: r.76 z.72 1266 -.25 0.25.50.75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 14. Normalized fluid density vs. axial position for visible initiation at 34 ft./sec. throat velocity.

FLUID: MERCURY \ \ \ ~~~~~CAVITATION TO NOSE VENTURI WALL THROAT VELOCITY: 34 FT/SEC. TEST SPECIMEN iVVISUAL END OF CAVITATION 1.04 1.00) ~ ^~ ~~ -A~-o ~~ g.92 ~> ~~~~ -88 I ___n_________>____________________________ Lu0.76 Ooz 1.72 ~___~8 1267 -.25 0.25.50.75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 15. Normalized fluid density and core void fraction vs. axial position for cavitation to nose at 54 ft./sec. throat velocity.

FLUID: MERCURY STANDARD CAVITATION VENTURI WALL Lo —J THROAT VELOCITY: 34 FT/SEC. SV VISUAL END OF CAVITATION 1.04.! 1.00_ a.96 EI.8815 I5J p.84 IO w Q 76 0 oposition for standard cavitation at o4 ft./sec. throat velocity. N.7280" r-^ 0.75 1.00 1.25 150 1.75 2.00 AXIAL POSITION, INCHES Figure 16. Normalized fluid density and core void fraction vs. axial position for standard cavitation at 34 ft./sec. throat velocity.

1.04 ~ ~ _ _ _ _ _ ~.96 Q *I FLUID — MERCURY a.9 ~:. ~,~ \~~~~, VENTURI LL -- THROAT VELOCITY:34/SE______ 1.00 i 88' N.80 1.76 <.72 0.72 t i| 1269 -.25 0.25.50.75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 17. Normalized fluid density vs. axial position for cavitation to back at 34 ft./sec. throat velocity.

~RUN: ~ faze\'i FLUID: MERCURY FIRST MARK CAVITATION VENTURI WALL THROAT VELOCITY:34 FT/SEC. TEST SPECIMEN VISUAL END OF CAVITATION 1.04 ^ 1.00)~^^ — ~~~~~~ 1 ~~~ ^ Z o.96 ( o. 92 &.88 I5.84 ~- T^ ^~~ ~~ l o ^.80 -^^ I - 5>.76 ~~- ~ 0 Cr 0^ z.72____0 1270 0.25.50 75 1.00 125 150 1.75 2.00 225 AXIAL POSITION, INCHES Figure 18. Normalized fluid density and core void fraction vs. axial position for first mark cavitation at 34 ft./sec. throat velocity.

FLUID: MERCURY CAVITATION TO NOSE VENTURI WALL o THROAT VELOCITY: 48 FT/SEC. irN VISUAL END OF CAVITATION 1- 1.024~.... A L P ON I, o.92' L I u...88.84 N.80 I <.76 o.72 Z I I 1271 -.25 0.25.50.75 1.00 1.25 1.50 1.75 2.00 AXIAL POSITION, INCHES Figure 19. Normalized fluid density vs. axial position for cavitation to nose at 48 and 34 ft./sec. throat velocities.

RUN:9 "^r~ i\~~ | | | ~FLUID: MERCURY ~~\ i~~~ \ STANDARD CAVITATION VENTURI WALL 7 —---- ------ - | oTHROAT VELOCITY: 48 FT/SEC. / iA " 1 __34 FT/SEC. TEST SPECIMEN *^.VISUAL END OF CAVITATION w.96 cr 1 oAXIAL POSITION, I oNCHES ti.88 ~~^~ ~~ - cavitation at 48 and ft/sec. throat velocities.80 1.76 ~ n, z 72 I{~~~~~~~ ~~~1272 -.25 0.25.50 75 1.00 1.25 150 175 2.00 AXIAL POSITION, INCHES Figure 20. Normalized fluid density vs. axial position for standard cavitation at 48 and 34 ft./sec. throat velocities.

-27Vo DISCUSSION OF RESULTS Ao Axial Density Profiles An examination of the density profiles (Figures 14 through 20) discloses the following results 1) Density profiles along the centerline of the venturi are generally sufficient to establish the cavitation conditions other than initiationo However, this method is not very suitable for determining the visible initiation condition, since the density changes in this mode are not sufficient, considering the statistical fluctuations of counting equipment 2) Figures 15, 16, 17, 18, and 20 show that the position of the cavitation as determined by the density correlates well with that of the visual settings, corresponding approximately to the start of the rise in the density profile. Since the precision of visual setting was only about + O1lO inches, all the figures cited fall within these limits0 3) Figures 19 and 20 show the effect of throat velocity on the axial density profileso In both cases, it is noted that the decrease in density in the cavitating region is less for the higher throat velocity, though the visual appearance is the sameo No theoretical explanation for this fact is yet apparent. However, a perhaps similar effect has been noted in water tests wherein the transparency of the cavitating region has been greater at higher * The high velocity profile for "Cavitation to Nose" a condition slightly in excess of initiation (Figure 19) shows uniform density. This may indicate a faulty setting of the cavitation condition, or other unknown errors in this particular run~

velocity for the same degree of cavitationo 4) The most consistent results were obtained at the lower throat velocity, perhaps partially due to the greater difficulty of maintaining steady-state during the run duration at the higher velocity, and to the increased mechanical vibrations of the system. Bo Central Jet Axial Density Profiles As previously mentioned, the axial density profiles already described apply to the mean density of fluid in a vertical plane containing the venturi centerline and extending entirely across the venturio The density of fluid comprising the central jet in the vicinity of the centerline is also of interest in providing further basic data on the nature of the flow. By comparison of the present data with those earlier derived from a radial and axial mapping of density profiles in a cavitating venturi of identical dimensions, it is possible to compute the mean density of the central fluid jet within a 10% void fraction contour (minimum measurable void fraction in previous experiment5) along the centerline~ Such a calculation supplies new basic data, as well as providing a check of consistency between; the present data and those of the earlier investigation5o The required relations are derived in the Appendix. The results, in those cases where direct comparisons could be made, are shown in Figures 15, 16, and 18o It is noted that where data are available, the maximum void fraction (minimum density) for the central core approximately coincides with the visual termination point, and hence the minimum density for the entire slice across the venturio Since the void fraction is generally less than

-295% and approaches 10% only in one case (Figure 16), it is apparent that the two investigations are consistent (reference 5 showed this region to possess less than 10% void fraction), and also that the central jet is indeed composed almost entirely of liquido Co Experimental Accuracy Several sources of error inherent in this experiment are: i) electronics of the system, ii) measurement technique iii) assumptions made in the analysis a) Electronic System Errors A variation in the gain of the non-overloading amplifier from its calibration would cause a change in the count-rate as would photomultiplier voltage variation The latter was minimized by using a highly stable high-voltage supply, and by attempting to keep the electronic components at a constant temperature throughout the experiment. A third possible source of electronic error is drifting of the photomultiplier output, as perhaps due to temperature changes, 7 causing a shift in the peak output of the scintillator, or by fatigue in the photomultiplier o This third source of error is small since the temperature was kept relatively constant and fatigue effects tend to be high current effects, which is not the present case, ioeo, if the anode current can be maintained below 0ol microamperes, fatigue changes are extremely small at room temperature, b) Errors in Measuring Technique Errors in the measurement technique due to positioning of the densitometer were extremely small, since the table could be moved to a specific position with an accuracy of + 0003 inches The

-30main source of error in the measuring technique resulted from the setting of the cavitation condition by a visual method. As mentioned earlier9 the accuracy in the visual setting was only + olO inches, and it was found difficult to improve the precision significantly by relying wholly upon pressure measurements. c) Assumptions of Analysis In the analysis' an "average" density was usedo In so doing it is assumed that the voids are small and randomly distributedO It is known, however, that certain non-random distributions, as vertical stratification for example, will give much higher count-rates for the same void fractiono However, it is believed on the basis of Fastax motion pictures that the bubbles are locally random in space-time distribution A further assumption, on which both this and the previous 5 investigation were based is that of axial-symmetryo It is believed that on a time-average basis, this is a good assumption though perhaps not at any given instanto VIo CONCLUSIONS The cavitation condition for the various degrees other than those approaching initiation may be determined in a non-transparent venturi by making a centerline axial density profile as here described. The position of cavitation t-ermination will approximately correspond to the point where the density profile gradient becomes positive. The method is not sufficiently sensitive (using the present equipment) to determine initiationo However, a higher count-rate would be desirable in general to reduce statistical fluctuations and

-31in particular to determine less developed cavitation conditions. Then the count-rate should be within the restriction (OI micrcamperes) presented by photo tube fatigue. The present data are consistent with those of a previous investigation and a comparison of these two sets of data allows a calculation of the void fraction in the region of the centerline. This is found to become maximum at the approximate axial location of minimum mean density across the venturio

-32VIIo REFERENCES l1 Lauchlan, Io Eo Bo, "Determination of Cavitation Conditions From Density Profiles", Final Report for Special Project in Course Mo E. 600, Mechanical Engineering Department, The University of Michigan, (June, 1963) 2o Hammitt, F. Go, "Observations on Cavitation Damage in a Flowing System", Trans ASME, Series D, Journal of Basic Engineering, Vol. 85, (1963), pp. 347-59. 3. Hammitt, Fo G., et alo, "Cavitation Damage in Mercury and Water in a Cavitating Venturi and Other Components," ORA Report No 03424-9-T, Nuclear Engineering Department, The University of Michigan, (Sept,, 1963). 4. Harmitt, Fo G., "Observations of Cavitation Scale and Thermodynamic Effects in Stationary and Rotating Components", Trans ASME, Series D, Journal of Basic Engineering, Volo 85, (1963). pp. 1-12. 5 Smith, W,, Atkinson, Go L., and Hammitt, Fo Go,'Void Fraction Measurements in a Cavitating Venturi", ORA Report No. 03424-7-T, Nuclear Engineering Department, The University of Michigan, (Sept., 1962); also as ASME Paper No. 63-AHGT-19, (Maro,, 1963), to be published Trans ASME, Journal of Basic Engineering. 6. Adyanthaya, B. Ao, "Mercury Void Fraction Measurements Using a Collimated Gamma Ray Beam", Term Paper in Course No E. 299, Nuclear Engineering Department, The University of Michigan, (June, 1961). 79 Cameron, J. F., et al., "Some Effects of Temperature on the Performance of Scintillation Counters", IAEA Nuclear Electronics. Volo 1, (1962)o 8. Cathey, L., "Fatigue in Photomultipliers", IRE NS-5, 109, (1958)

-33VIII. APPENDIX Ao Degrees of Cavitation The cavitation conditions used in this series of measurements and in previous measurements5 were defined as follows: "Visible Initiation" - that cavitation condition in which a continuous ring of cavitation is visible at throat discharge o "Cavitation to Nose" - cavitation terminates at the axial position corresponding to the location of the nose or upstream end of the test specimens (when they are inserted for cavitation damage studies)'Standard Gavitation" - cavitation terminates at the middle of of the damage specimenso "Cavitation to Back" - has its termination at the back or downstream end of the test specimeno "First Mark Cavitation" - has the termination 1-3/4 inches downstream of the throat exit. It may be noted that this is also downstream of the specimenso Bo Derivation of Relation Between Count-Rate and Density Figure 21 represents the cross-section of the venturi at any particular axial position zo Let R be the venturi radius, t the path length of the radiation within the area, and x the horizontal distance from the venturi center line to the collimator center lineo Also let no = number of photons/seco emitted by the source in such a direction that if they are unscattered) would pass through

-34the slit of area A of both collimators and strike the detector n (x) = Photons/seco passing unscattered through the entire test section, at a distance x, for any cavitation condition n2(x) = Photons/sec passing unscattered through the entire test section at a distance x, when there is no cavitation /f(x) =Average density of the vertical column of fluid, located at a distance x, and which has a cross section equal to the area A of the collimator slito h = Maximum vertical dimension of the test section, as shown in Figure 21. Then: n,(x) = n e (h-t) - (x)t n (x)- n e-o (h-t) e-t (2) where: = density of mercury = 221o977 gm/in3 /U = linear absorption coefficient for mercury for o117 Mev gamma radiation. = 2ol in / = /t = mass absorption coefficient for lo17 Mev gamma r iati on. = linear absorption coefficient of the Plexiglas for 1 17 Mev gamma radiation. Dividing (2) by (1) and taking the natural logarithm we get: in C =j0t[1P(x) fi n]-(x) =/p+t in n[(x)

-35In this series of tests x = 0, so we have: (0) = + n2in (0) With respect to equation (4) several things may be noted: In a cavitation region, n2<n; so the average density will be less than, the density of liquid mercury The relation is independent of the collimator opening, provided the source is monoenergetic, and the opening small enough so that the average density may be considered as a constant within the corresponding vertical mercury column. The number of photons per sec., n1 and n2, may be replaced by the actual count-rates since detector efficiences cancel in equation (4)

-360.030" COLLIMATOR 1Y I I 1273 Figure 21. Venturi cross-section as used in density calculations.

-37Co Central Jet Axial Density Profile Detemination Reference 5 presents void fraction contours for various cavitation conditions as sketched below:.% V \Void Fraction. \ _L\%- - 40% Void Fraction \ u\~ - \ ~ 30% Void Fraction \. — x \ ~. ~ ~ -~ C) 20% Void Fraction I 11 0% Void Fraction Figure 22o Void fraction coltour schnatic. Consider a vertical fluid coluimn of unit cross-sectional area, passing through the center line at any given axial position.o Divide this column into segments each extending between adjacent void fraction contours (Figure 22)o Then the total mass in such a fluid column is: (C) Aro Poa +Ar \ab - -- - - +r e ei,f (1) 0-a ~ ~ a-b e -f _b) I(2) (aThus lAr (l-voFoa - - + Are (lVF e, 0o0 0~25 0o50 0075 i O-.0 — Figure 22o Void fraction- cohtour schematic. Consider a vertical fluid column of unit cross-sectional rfo-a a-b In the right-hand side of eq (, all quantities are measured (2) -rf Thus ~~L ==n r -o -1V.F ar (1-V — (3) o-a e-f e3 rf except for V~Fio-a' which is stated to be less than 10%O The lefthand side is known from. the data of the present report.

-38Hence eq. (3) may be solved for V.F. and it is these o-a values which are plotted in Figures 15, 16, and 18. Appendix C Nomenclature: A^r. = Radial increment between radius r and r. over which lO i j the void fraction changes by about 10%. i = Average fluid density in the annular ring formed by r. and rj, or also the average density in the portion of the vertical column of unit cross section area between r. and r.. 1 J3 V]F.ij = Average void fraction in annular ring, between r. and rj. (Detailed calculations are filed under Project 03424, FGH calculations, 9/16/63.)