'.T'HE'UNIVEPRSIT:'' OF MIL C' HIG CAN IND.'US'TRY PR.OGHRAI M T OF',THE COLLEGE O E IrI lN'EERIN OBSERVATI ON OF CAVITATI ON SCiALE ANID:THERMODYNAMlIC'EFECTiS IN S ATI ONAR'. AND F3OTATSING COMVPONlENTS Freder:ick G.o Hanmmi.tt J lune 1.961. IP- 5.17

ACKNOWLEDGEMENTS The major share of data reduction and preparation for this paper was carried out by, or under the supervision of, Vo Fo Cramer and Po To Chuo The test instrumentation was largely conceived and installed by Co Lo Wakamo, assisted by Jo SchmidtO The tests were supervised and conducted by Vo Fo Cramer, assisted by M, Jo Robinson. Other major contributions to the program were made by To A, Sheehan, A. Travers, and E, Rupkeo All are or were research personnel of the office of Sponsored Research of the University of Michigano Financial support for the project was provided by the NASA. ii

TABLE OF CONTENTS Page ACKNOWLEDGEMENTS... oo o 0 00 00,00000o0oooooooooooooooooooo00oooo ii. LIST OF1 FIG TRES.......................O OQO...........OOOO OOOOO i NOMENCLAT RE o o o o o o o o. o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o I INTRODUCTION.......o...................................oo 1. II OBSERVATIONS ON A STATIONARY COMPONENT (VENTURI)......... 1. Ao Description of Component and Cavitation Conditions...o 1 B. Scale and Thermodynamic Effects for Different Degrees of Cavitation,,,.............o o o o 2.o Scale Effects at Different Degrees of Cavitation......................................... 3 2. Thermodynamic Effects.......O.. o o O o O 10 III OBSERVATIONS ON A ROTATING COMPONENT (CENTRIFUGAL PUMP IMPELLER).................................. o 18 Ao Description of Component and Cavitation Condition..... 1.8 B. Pump Test Results..,,,,.,........,.......... 1.9 IV DISCUSSION OF RESULTS....................................0 0 23 Ao Theoretical Considerations...... o....................... 25 1. Thermodynamic Effects.......................... 26 2. Reyn.olds' Number Effects.....................O O. 27 35 Velocity Weber Number, and Time Effects........... 29 V CONCLUSIONS..,...,,,,,.......,...,.......,..... 30 VI BIBLIOGRAP.............o o o o o o o o o o o o o............. 32 iii

LIST OF FIGURES Figure Page 1. Cavitation Number vs. Throat Reynolds Number in a Cavitating Venturi for Sonic Initiation,...e......... 4 2 Cavitation Number vs. Throat Reynolds' Number in a Cavitating Venturi for Visible Initiation............ 5 3 Cavitation Number vs. Throat Reynolds' Number in a Cavitating Venturi for Cavitation to First Mark........ 6 4 Cavitation Number vs. Throat Reynolds' Number in a Cavitating Venturi for Cavitation to Second Mark....... 7 5 Cavitation Number vso Throat Velocity in a Cavitating Venturi for Visible Initiation..................... 8 6 Cavitation Number vs, Throat Velocity in a Cavitating Venturi for Cavitation to Second Mark........ o.. 9 7 Loss Coefficient vso Throat Reynolds' Number in a Cavitating Venturi for Visible Initiation.o...o...... 11 8 Loss Coefficient vs. Throat Reynolds' Number in a Cavitating Venturi for Cavitation to First Mark......... 12 9 Loss Coefficient vso Throat Reynolds' Number in a Cavitating Venturi for Cavitation to Second Marko....... 15 10 Loss Coefficient vs. Throat Velocity in a Cavitating Venturi for Visible Initiation.....o..,,... o o o o..... 14 11 Loss Coefficient vso Throat Velocity in a Cavitating Venturi for Cavitation to First Marko............o...o 15 12 Loss Coefficient vs. Throat Velocity in a Cavitating Venturi for Cavitation to Second Mark................... 16 13 Thoma Cavitation Parameter vso Normalized Reynolds Number........ o o o o.......... o o o o...................... o o o o 20 14 Thoma Cavitation Parameter vso Normalized Pump Speed... 21 15 Suction Specific Speed vso Normalized Pump Speed........ 22 iv

NOMENCLATURE p absolute static pressure Pv vapor pressure gc mass to force conversion factor v fluid velocity Vt fluid velocity in throat p mean fluid density Pmin - Pv cc cavitation number min -P Pvt /2gc Pin - Pout CL venturi loss coefficient = - pvt2/2gc NPSH oT Thoma cavitation parameter aHp AlH pump head rise in non-cavitating condition RPM -~ GPM S suction specific speed =RPM - GP (NPSH3)5 4 NPSH net positive suction head = Pv at impeller inlet referred P to elevation of impeller centerline and assuming mean velocity equal to pipe velocity. v

I. INTRODUCTION It has become increasingly evident of late that significant departures from idealized cavitation similarity relations, as for example the concept of the Thoma cavitation parameter or suction specific speed, exist. These are of importance in that they can easily invalidate model tests both with respect to fluid-dynamic performance and, certainly, cavitation damage if they are not fully understood. It is the purpose of this paper to present some new data regarding variation from idealized relations of cavitating performance for both stationary and rotating components, and to attempt to rationalize these variations as far as present theoretical knowledge will permito II. OBSERVATIONS ON A STATIONARY COMPONENT (VENTURI) Ao Description of Component and Cavitation Conditions Cavitation performance tests using water as the test fluid have been run on two geometrically similar venturi plexiglass test sections of 1/2 and 1/4 inch nominal throat diameter. Each has a cylindrical throat of length equal to about four diameters, followed by a diffuser which tapers on a straight-line 6~ included angle out to the nominal 1-1/2" pipe diameter. The nozzle taper to the throat entrance is also a straightline 6~ included angle, with a well-rounded entrance from the pipe diametero Detailed drawings are shown in Reference lo Several cavitation conditions were defined for these venturis: 1) Sonic Initiation: first appearance (or disappearance*) of audible soundo * No cavitation hysteresis was observed in these tests between disappearance and appearance of cavitationo Perhaps this is due to the fast recirculation of water and absence of a settling tanko -1

-22) Visible Initiation- first appearance (or disappearance*) of complete visible ring of cavitationo 3) First Mark Cavitation: cavitation cloud appearing to end at "first mark," ioeo, one inch downstream from end of cylindrical throat portion in small venturi; geometrically similar location in large venturio 4) Second Mark Cavitation: analogous to aboveo Variation in the cavitation condition for a given throat velocity and fluid temperature is achieved by adjustment of upstream and downstream valves. In addition, throat velocity for a given cavitation condition can be varied in this closed loop facility from about 55 to 95 feet/second, and fluid temperature from about 60~F to 160~F with the plexiglass venturiso The facility, designed for liquid metal tests, is described in detail in Reference 1, Gas content can be controlled between approximately 30% of saturation and slightly supersaturatedo It was found in initial tests that within this range gas content was not a significant variableo This observation is also reported by Kermeen et al (2) For the venturi and pump tests the water was generally settled over a period of several hours to at least remove gross entrained air, and. had total gas content of the order of 2/3 of saturation at room temperature and one atmosphereo B Scale and Thermodynamic Effects for Different Degrees of Cavitation For the purposes of this paper, and as partially substantiated by its results, it is assumed that deviations from the idealized relations * See footnote, page lo

-3can be grouped into "scale effects" encountered with changes in velocity or dimensions, and "thermodynamic effects" from changes in the thermodynamic properties of the fluid as brought about by a temperature change.3) 1. Scale Effects at Different Degrees of Cavitation Previous papers have considered scale effects as related to the cavitation number for either the first appearance or the final disappearance of cavitation.(2 4) This paper presents new data relating to cavitation initiation (or disappearance*) and also data for.various degrees of well-developed cavitationo In all cases a significant scale effect has been observed such that the cavitation number (defined with respect to the minimum static pressure existing in the venturi, and the throat velocity) decreases with increasing throat Reynolds' number, approaching the theoretical value of zero and becoming negative at high Reynolds' numbero The well-defined trend with Reynolds' number is striking in that the tests comprise a range of about 2:1 in throat diameter, viscosity, and velocity, (Figures 1, 2, 3, and 4 — Revised from Reference 1) Figures 5 and 6 show the same data in two typical cases plotted against throat velocity rather than Reynolds' numbero It is noted that there is a clear differentiation according to venturi size so that two separate curves are requiredo The figures show the approximate standard deviation of the data computed on the basis of repetitive runs for typical points. It is noted that this is sufficiently small so that the trends shown are meaningful, and also that the scatter of points around the curves shown is far beyond * See footnote, page l,

.26 __ LARGE (1/2") FLUID SMALL (1/4") _________24 I _ __I I I I I ITEST SECTION CONDITION TEST SECTION 0 AERATED C W AERATED COLD WATER.22 -_________________ ___ __ _ __ DEGASSED jE DEGASSED A AERATED jv W AERATED.20 I (=000404) STANDARD DEVIATION.I8 ____________________ ___ _____________TO SCALE b~.16:D.12 z.10- 0- - a___ — v A (3 \ 0 i04 2 3 4 5 6 7 8 9 105 2 3 4 5 6 7 8 9 106 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret Figure 1. Cavitation Number vs. Throat Reynolds. Number in a Cavitating Venturi for Sonic Initiation..04 -.02 104 2 3 4 5 6 7 8 9 iOs 2 3 4 5 6 7 8 9 iE s REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret Figure 1. Cavitation Number vs. Throat Reynolds'. Number in a Cavitating Venturi for Sonic Initiation.

~~~~.2 ~4 -Lr - |;~~ LARGE (/2") FLUID SMALL (1/4") TEST SECTION CONDITION TEST SECTION.22 0 AERATED 0 AERATED COLD WATER 20. _____ ___ * DEGASSED C LDEGASSED.20' A AERATED _v AERATE & HOA DEGASSED W SE.18 ~18 (0.0014) STANDARD DEVIATION I(= 0.00141) TO SCALE.i6 b.14 o-.12 i i2-.10 z.08 - 0_ _ I,.. — - - __ -.04 -,... Il1^ s. V 104 2 3 4 5 6 7 8 9 iO5 2 3 4 5 6 7 8 9 -O6 0 -.2I_ * A. -.04 ___ O4 2 3 4 5 6 7 8 9 2 3 4 5 6 7 89 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret Figure 2. Cavitation Number vs. Throat Reynolds' Number in a Cavitating Venturi for Visible Initiation.

.24 - - ___ LARGE (I/2") FLUID SMALL(1/4") TEST SECTION CONDITION TEST SECTION.22 2 AERATED WAAERATED COLD WATER * DEGASSED _ _ _ DEGASSED.20.. A AERATED AERATED A DEGASSED ___ DEGASSED.18 S0TANDARD DEVIATION (= 0.00 ) TOO SMALL TO ILLUSTRATE.16 b.14 W.12 z.10 z 0.08.06 U.04 __v __ __ -.02 -.04 104 2 3 4 5 6 7 8 9 105 2 3 4 5 6 7 8 9106 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret Figure 3. Cavitation Number vs. Throat Reynolds' Number in a Cavitating Venturi for Cavitation to First Mark.

.24.r T LARGE (/2") FLUID SMALL (1/4") T________________________ ____TEST SECTION CONDITION TEST SECTION o AERATED 0 AERATED ___20_______ * DEGASSED COLD WAR DEGASSED A AERATED H V AERATED A DEGASSED WA DEGASSED NO REPETITIVE STANDARD DEVIATION _1 6___ RUNS NOT CALCULABLE.16_ ------ bo U-j O.12 z z I ------------ --- -- -- ------------ -- ---- z.08.04.04 ---.00 -[-'-_' -'-'- ---- ---------- -- --- -- __ _ —----------- -- 10 2 3 4 5 6 7 8 910 2 3 4 5 6 7 8 9 1 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret Figure 4. Cavitation Number vs. Throat Reynolds' Number in a Cavitating Venturi for Cavitation to Second Mark.

.30 LARGE (1/2") FLUID SMALL (i/4") TEST SECTION CONDITION TEST SECTION.26 3 0 AERATED AERATED 0 DEGASSED W DEGASSED A AERATED T WATER V AERATED.22 ----------------------- ---------- A DEGASSED V DEGASSED STANDARD DEVIATION 01x ( = 00141) |TO SCALE 18 bo:.14 U I D I z I.0 ------- _O_ —- _ _ _ _ _ — _ _|.0 -- ___,06 _ r______ _______________.00 -----—' —--------— SMALL TEST SECTION.0o2 —------.00 ____T -TEST SECT ON HO aO COLD -.04 40 45 50 55 60 65 70 75 80 85 90 95 VELOCITY AT THROAT, FPS Figure 5. Cavitation Number vs. Throat Velocity in a Cavitating Venturi for Visible Initiation.

.12...... LARGE (/2") FLUID SMALL (1/4") TEST SECTION CONDITION TEST SECTION'10 -0 AERATED CE AERATED. DEGASSED COLD ATEEGASSED A AERATED V AERATED HOT WATER.08 A DEG-SSE- A DEGASSED DEGAS NO — b —---.06... —-- i ---------- I R UNO STANDARD DEVIATION RUNS -.06 LU Z.04 Z SMALL TEST SECTION O -— \ HOT a COLD WATER - H-.02 I I\ I I 0\ Q |/ —,LARGE TEST SECTION.00 - - - - - - - -/ HOT a COLD WATER I _ _ XI- - --------------- -- ---------------------- -------— __ -- -.02 _ --- -.04........ 40 45 50 55 60 65 70 75 80 85 90 95 VELOCITY AT THROAT, FPS Figure 6. Cavitation Number vs. Throat Velocity in a Cavitating Venturi for Cavitation to Second Mark.

-10experimental error for both velocity and Reynolds1 number plotso Hence, it appears likely that other parameters are significant. What these may be and how they enter cannot be specified without a better understanding of the bubble growth and nucleation process. However, some further indications of the interrelations do existo 2, Thermodynamic Effects Examination of Figures 1 through 6 discloses no thermodynamic effects per se in that both hot and cold water points, for cavitation number, are equally correlated by a single curveo However, a fluid-dynamic parameter other than cavitation number which might be considered to characterize the cavitating flow in a venturi is the loss coefficient; i.e,, the ratio between overall pressure loss across the venturi to pressure differential between inlet and minimum pressure pointo Since it is much more sensitive to degree of cavitation than is the cavitation number, it might be taken as a more sensitive indication of significant correlating parameters. Figures 7 through 9 (revised from Reference 1) show this parameter plotted against Reynolds' number, using data from the tests previously described, for the various cavitation conditions. The same data is replotted against velocity in Figures 10 through 120 For the loss coefficient vs. Reynolds' number plots (Figures 7 through 9) the following significant points are evident: 1) For visible initiation (or sonic initiation which is not included since it is nearly identical) there is no differentiation between hot and cold points or between points from the

~70 LARGE (1/2") FLUID SMALL (1/4') __ TEST SECTION CONDITION TEST SECTION o AERATED 0 AERATED * DEGASSED C DEGASSED.60 4.... A AERATED V AERATED A DEGASSED W R DEGASSED STANDARD DEVIATION.(500.0053) ________ _TO SCALE.50 _ _ I..______.50 3 Iw.40 b- -!a. ___ LUJ 0 00.20 __________.10 _ 4 6 10 2 3 4 5 6 7 8 910 2 3 4 5 6 7 8 9 1 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret Figure 7. Loss Coefficient vs. Throat Reynolds' Number in a Cavitating Venturi for Visible Initiation.

.70 Z 40 ___- -__^ 0,30< 0 U ^^ A 0 0 LL 30 c) I _____ ___________ _ _c |TEST SECTION CONDITION TEST SECTION 0 AERATED 0 AERATED ____ 0____________;* DEGASSED OLD DEGASSED.10 A AERATED v AERATED A DEGASSED vHOT ATER DEGASSED I (=00175) STANDARD DEVIATION 4*_________ _______ -__ — _i - _ __ __TO SCALE 10 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 0 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret Figure 8. Loss Coefficient vs. Throat Reynolds' Number in a Cavitating Venturi for Cavitation to First Mark.

1.10 LARGE (1/2") FLUID SMALL (1/41) TEST SECTION CONDITION TEST SECTION O AERATED tr AERATED 0 DEGASSED C DEGASED rA DEGASSED I DEGASSED DEGSSE i.400 NO~.RENOD _TV TA EV AEIRATED |.0 RUNSNOTCAL ---------— ____ —---— Caitain V o C LE/n bL /. 0/.50 7LL —— __ —-- __ 140 2 3 4 5678910 2 3 4 5 6 7 89 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS Re Figure 9. Loss Coefficient vs. Throat Reynfolds' Number in a Cavitating Venturi for Cavitation to Second Mark.

LARGE (1/2") FLUID SMALL (1/4").45 TEST SECTION CONDITION TEST SECTION 0 AERATED C AERATED * DEGASSED C * DEGASSED.40 A AED HOT WATE VAERATED -A DEGASSED v DEGASSED.35 -------- El _ —-- _ —-- ----- ----— S(0.0053) TANDARD DEVIATION I I (=l 0.0053) l TO SCALE.30 -------- -SMALL TEST SECTION --'L " U \HOT a COLD WATER LU _ _ _ _ _ _ _ __ — ^'"'^ - - - - - ----- i r^ """"" -y " - - - - _ ^, _ __-_ __ —- --------- 0).25 | 4 -tt C== == = e < - -—...H 0 — 30 0 / l / -.20 LARGE TEST SECTION LARGE TEST SECTION -------------------- HOT WATER — COLD WATER —-.15 ----------.10 _ _ 40 45 50 55 60 65 70 75 80 85 90 95 VELOCITY AT THROAT, FPS Figure 10. Loss Coefficient vs. Throat Velocity in a Cavitating Venturi for Visible Initiation.

LARGE (1/2") FLUID SMALL (1/4') TEST SECTION CONDITION TEST SECTION.80 --------------------------- 0 AERATED 0 AERATED 0 DEGASSED COLD WATER U DEGASSED A AERATED V AERATED.70 A DEGASSED V DEGASSED 0. ) --— STANDARD DEVIATION bI I (: 0.0175) ~~~b~~~~ l ) g g 1 I * ) | ~~~~~~~TO SCALE -.60..... (n._0 0 _ | \___ 1 1 C L W _ Z / --'-SMALL TEST SECTION J E H-oQT - -COLD WATER- -- ----- LE.50 01.40 t 0. -~ LARGE TEST SECTION -J' / / COLD WATER ~~~-0 LARGE TEST SECTION.30 -- [- - HOT WATER.2 0 --------- I I _ —.10._. _ 1 _ _ 40 45 50 55 60 65 70 75 80 85 90 95 VELOCITY AT THROAT, FPS Figure 11. Loss Coefficient vs. Throat Velocity in a Cavitating Venturi for Cavitation to First Mark.

1.00 LARGE TEST SECTION.70 --- - HOT a COLD WATEF R -_ —*Z.l~~~ \l~~ ^~'m~ iT —SMALL TEST SECTION.4 --------------- \i —-— DEGASSED-| COLD WATER | —-DEGAS — D - - - - --------------- ^ ^ ^ ^ - ^ ^ —---------------------------- -------------.50.LARGE (1/2") FLUID SMALL (1/4') TEST SECTION CONDITION TEST SECTION SMALL TEST SECTION.40 HOT WATER 50 AERATED 0 AERATED 0 DEGASSED COLD WATER * DEGASSED A AERATED HOT WATER V AERATED.30 A DEGASSED V DEGASSED NO REPETITIVE STANDARD DEVIATION RUNS NOT CALCULABLE 20 _________ 40 45 50 55 60 65 70 75 80 85 90 95 VELOCITY AT THROAT, FPS Figure 12. Loss Coefficient vs. Throat Velocity in a Cavitating Venturi for Cavitation to Second Mark.

-17large and small venturio The data correlate fairly well in terms of Reynolds' numbero This is not surprising since the degree of cavitation is too small to affect the overall flow pattern very significantlyo 2) For substantial cavitation (first and second mark) Reynolds' number does not correlate all the points; rather, the cold and hot water points are separatedo 3) The loss coefficient for cold water is higher than for hot water where a differentiation is possibleo The direction of the differential is as predicted from consideration of the thermodynamic parameters, as first suggested by Stahl and Stepanoff (3) 4) For first and second mark cavitation, the loss coefficient increases significantly with Reynolds' number, and the rate of increase accelerates for higher Reynolds7 numberso Examination of the standard deviations shown on the figures indicates that the trends mentioned are significant. When loss coefficient is plotted against throat velocity (Figures 10, 11, and 12) separate curves must be used for throat diameter and temperature of fluid, even for initiation conditions (Figure 10)o Thus it is apparent that Reynolds' number at least partially accounts for changes in diameter and temperature as well as velocityo The situation is complicated for the more developed cavitation conditions (Figures 11 and 12), since it was shown in the Reynolds' number curves (Figures 8 and 9) that thermodynamic effects in themselves were important. Hence in the velocity plots, there is a temperature effect both

thermodynamically and through Reynolds number~ The direction of curve separation indicated by each of these effects is the sameo It is noted that in all cases the loss coefficient for cold water is greater than for hot at a given velocity as would be expected.(3) The loss coefficients for developed cavitation generally increase with velocity as well as with Reynolds' number~ III. OBSERVATIONS ON A ROTATING COMPONENT (CENTRIFUGAL PUMP IMPELLER) Ao Description of Component and Cavitation Condition Cavitation performance effects have also been observed on a single-stage sump-type centrifugal pump used to power the cavitation loop of specific speed equal to 740 in GPM units (manufactured by the Berkeley Pump Coo) In this system(l) pump cavitation can only be obtained by reducing the sump pressure to near vacuum, balancing vacuum pump capacity against stuffing-box leakage. The rather large scatter of the data is probably a result of the required test procedure, even though high-response-rate pressure transducers were usedo A long-radius elbow immediately upstream of the pump suction is partially responsible for the low suction specific speed values. In addition, the pump was designed for high-temperature liquid metal performance rather than good cavitation behavior. The data points presented (with one exception) are the result of several repetitive runs (varying from 2 to 6). In each case the standard deviation was calculated and an average value computed. As noted,

-19data of sufficient precision to be statistically meaningful has been obtained (Figures 13 14, and 15). The onset of cavitation is defined as sufficient cavitation to cause a decrease of 5o in the pump head at a fixed speed and system resistanceo It is considered that this small. amount of cavitation is probably more nearly similar to the visible initiation condition in the venturi than any other, and hence comparisons are made with this condition. B, Pump Test Results Pump speed is varied in the pump test runs over a range of about 17; flow (ioe., ratio of actual to design flow) over a range of 1.3; and fluid temperature over the range from about 90~F to 160 ~F Tests were run at three distinct speeds, presented in the figures as ratios of actual to design speed, two flow ratios, and three temperatures (including the extremes of the range above) The resulting Thoma cavitation parameters are presented in Figures 13 and 14 plotted against normalized Reynolds' number and normal. ized pump speed respectivelyo The figures discloseo 1) The data can be correlated reasonably well either in terms of Reynoldsv number or pump speed, i eo,, velocityo 2) The data divides naturally according to the flow ratios, i oe the Thoma parameter for the higher flow ratio (somewhat above design flow) is higher than for the lower (close to design flow), for the same N/No or Re/Reo o

-soTHOMA CAVITATION PARAMETER VS. NORMALIZED REYNOLDS' NUMBER.26.24.22 A 0.18 1 — Q/Q =12 1_ _,2.16.14 I-.12.10 Q/Qo=.93.08 TEMP FLOW.06 -- 0 HOT 0 MEDIUM Q/Q =1.2.04 A COLD 0 HOT j STANDARD DEVIATION (TO SCALE).02 -- MEDIUM Q/Q=.93 V COLD 0 I - 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 Re/ Reo Figure 13. Thoma Cavitation Parameter vs. Normalized Reynolds' Number.

-21THOMA CAVITATION PARAMETER VS. NORMALIZED PUMP SPEED.26 ~-. -.24 \.22.18.20 -- -- -- -- --- - - ~ Q/Qo 1.2~- -- --.16.14.12 Q/Q0 =.93.10.08 TEMP FLOW 0.06 0 HOT 1 _ 0 MEDIUM O Q/Q,=1.2.04 A- COLD J I.0l HOT Q/Q.93 STANDARD DEVIATION (TO SCALE).02 O MEDIUM Q/Q =.93 ~ -- - V COLD J 0I II I — 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 N/No Figure 14. Thoma Cavitation Parameter vs. Normalized Pump Speed.

-22SUCTION SPECIFIC SPEED VS. NORMALIZED PUMP SPEED 5000 4000 "el __W m- / TEMP FLOW 0 HOT 1000 A^ COLD A HOT T STANDARD DEVIATION (TO SCALE) - MEDIUM Q/Q =.93 - V COLD 0 I_ I_ I_ 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 i.6 1.8 2.0 2.2 N/No Figure 15. Suction Specific Speed vs. Normalized Pump Speed.

-23 3) There is no significant separation within the precision of the data as plotted against either velocity or Reynolds' number. In the case of velocity curves there is no substantial separation of the points; hence there must be such separation in the case of Reynolds' number, as Figure 13 shows. However, it is not in the direction anticipated from a consideration of the thermodynamic parameters (3) The indicated separation of the curves is small as expected from consideration of the venturi results since the pump cavitation condition corresponds only to initiation. Thus, only a single curve is warranted within the precision of the datao 4) There is a substantial decrease in Thoma cavitation parameter as the Reynolds' number or velocity is increased (30-50% for a speed increase of 75%)o The data from Figure 14 are replotted in Figure 15 in terms of suction specific speed whic:h varies over almost a 2,1 range, from about 2500 to 4500. The direction of variation and the relation between high and low flow curves of course follows from. the previous curveso IV. DISCUSSION OF RESULTS Since the cavitation condition in the venturi tests is based on visual extent of cavitation, and that in the pump on proportionate head loss, a direct comparison of results is not necessarily meaningful., However, the following points of similarity- exist between the results from

-24the venturi and those from the centrifugal pump (Figures 1, 2, 3, 4, 14, 15) 1) In both cases, there is a substantial decrease in cavitation number (or Thoma parameter) as either velocity or Reynolds' number is increased., 2) In both cases for the cavitation number curves, for conditions of initiation, no significant thermodynamic effects are indicated 3) In both cases, for the cavitation n:umber curves, the data can be correlated to some extent in terms of either Reynolds number or velocity, although the velocity plots for the venturi can. be conveniently divided in terms of temperature and sizeo The Reynolds numnber correlation is very much better for the venturi and appears to take care of the size variation between the different venturis as well as the temperature variation to some extent o The velocity correlation, however., is somewahat better for the pump, where there is no size variation. Other points of major significance are, 4) In the case of the venturi. substantial scale effects exist for well-developed as well as initial cavitation. No data for equally well-developed cavitation with the pump as compared through proportionate head losses is available, but it is presumed that the ventur.i results would qualitatively appl.y 5) The scale effects for the venturi apply to both cavitation nuimber and to loss coefficient (see also Figures 7^ 8, 99

10, 11, 12)o However, the latter is much more sensitive to degree of cavitation than the former. 6) A substantial thermodynamic effect, in the anticipated direction,(3) is found for the loss coefficient, but only for well-developed cavitation. Ao Theoretical Considerations Fairly clear-cut arguments can be advanced to explain a dependence of cavitation number or loss coefficient on ReynoldsT number and on the thermodynamic parameters, and also, perhaps to a lesser extent, on other parameters. A summarization of the arguments follows, If it is considered that cavitation bubbles originate in the boundary layer(4) and also that local under-pressures in the fluid are a function of degree of turbulence, it is not surprising that Reynolds' number should, to some extent at least, correlate cavitation datao Other possible parameters(5) include Froude number, Mach number, Weber number, and Peclet number (ieo.,'thermodynamic effects")~ Also, the influences of absolute time and pressure on. tlhe microscopic nucleation process may be significant in themselveso Of these, the author believes it most likely, within the range of parameters of the present; tests, that Weber number and "'thermodynamic effectss are of greatest importance, aside from Reynolds' number, A variation of cavitation number with Reynolds1 number has, in fact, recently been derived by Oshima(6) by considering only inertial, pressure, and surface tension effectso However, the predicted variation is in the opposite direction to that observed in the present testso

-26 1L Thermodynamic Effects In the pump tests, the cavitation conditions are defined as those producing a pump head reduction of 50o As suggested by Stahl and Stepanof(377) and Jacobs, (89) tentatively this can be taken to mean a given vapor volume within the pumpo Again, as originally suggested by Stahl and Stepanof (?7) and Jacobs(899) and discussed and corroborated by Salemann,(10) considerably greater local head depression for hot than for cold water, at least under equilibrium conditions, is required to abstract the sensible heat from the surrounding liquid for production of the requisite vaporo If, as previously discussed by the present author,(ll) the applicable parameter is defined as the equilibrium ratio of vapor volume formed to liqu.id volume per unit head depression, it is found to vary by a factor of about 5 over the temperature range of the present tests In other -words, under equilibrium conditions, a head depression, 5 —fold increased over the cold water tests, is required to produce the same proportionate head reduction in the hot water tests. It is apparent that this is not quantitatively meaningful in the present case, since the head depression for the cold water tests is of the order of 4 feet9 and does not differ greatly for the hot water testso Qualitatively, however, the trend characterized in the current literature as "thermodynamic effects' has been shown to exist by the test results of Stahl and Stepanoff(-'7) Jacobs 9) and Salemann,(10) as well as the present data for the loss coefficient of the venturi with wel.ldeveloped cavitation. In most of these tests it has also been shown that a quantitative prediction from the equilibrium considerations is not meaningfulo

-27The fact that no thermodynamic effects were found for the pump or venturi cavitation number is in apparent agreement with the results listed by Stepanoff(7) and Salemann. (10) The vapor pressure values for the present tests are far below those which they considered, and extrapolation of their data indicates that the thermodynamic effect would not be appreciable in the present. tests Jacobs, tests were with cryogenic fluids for which the equ.librium vapor/liquid volume ratio is so much different from the present tests that no comparison ca:n. be madeo However, he observed a ve'ry strong thermodynamic effect for those fluidso That a significant thermodynamic effect in the anticipated direction (ioeo, less loss for a given visual extent of cavitation region for hot than for cold water) was found for the venturi loss coefficient with well-developed cavitation may be t;he result of the fact that this parameter is much more sensitive to changes in the flow than is the cavitation numberO 2. Reynolds2 Number Effects Assuming on the basis of the previous discussion that thermodynamic effects are negligibly small in the present tests with the single exception mentioned, there are three groups of data to'be considered for Reynolds' number and velocity effects: (a) Thoma cavitation parameter for the pump tests (which is in effect a cavitation number), (b) cavitation number, and (c) loss coefficient for the venturi tests o

~28~ Without exception, the cavitation number, both for pump and venturi, and for all degrees of cavitation tested, decreased substantially for increased Reynolds? nurmber or velocity. An examination of the existing literature regarding scale effects in pumps and on stationary objects(2^35,6J7,89.^0,!O,12) shows that the cavitation number sometimes increased with. increased Reynolds? number or velocity and sometimes decreasedo The only pump tests found in the literature, aside from the present results, giving constant temperature data, at different speeds are those quoted by Stepanoff(7) from a Russian paper (12)* These results are quantitatively almost identical to those of the present testso Also, some of the other results quoted by Stepanoff(7) to substantiate the existence of thermodynamic effects could. be taken instead to show, at least partially, Reynolds, number effectso They show a decrease of cavitation number for the impeller with, increased temperature for a given fluid at fixed pump speed, Since the viscosity decreases rapidly with increasing tem'peratture, these effects could be attributed to an increase of Reynolds? nu.mber as well as'to a change in thermodynamic parameters Other results shown by tche same authors, concern the comparison between water and organic fluidso For these, the thermodynamic effects unquestionably predominateo A summarization of the scale effects for stationary bodies is presented by Holl and Wislicenuso(5) Data for CIT reported by Kermeen et alo2) and from Pennsylvania State University are includedo It is reported that results from a low pressure coefficient body * Similar results are available from unpublished sources.(l,

-29" (an NACA 16012 hydrofoil) show a decrease of cavitation number with increased Reynolds' number or velocity as do the present testso On the other hand, a high pressure coefficient body such as an ogive shows the opposite trend. The hydrofoil and the present venturi, being well streamlined bodies, seem somewhat comparable, as do the hydrofoil and the blades of a centrifugal pump Hence the results of the present tests seem in at least quantitative agreement with the literature However, it should be mentioned that the previous scale effects results reported (2-95) as opposed to the present results, involve mainly variation of velocity and sizeo The tests of Reference 2 do include a small temperature variation (from 550to 770F) As previously noted, Figures 7 through 9 show that the venturi loss coefficient cannot be correlated in terms of Reynolds? number alone except for the case of cavitation initiation'which is virtually singlephase flowo This may be taken to indicate the basic inadequacy of Reynolds? number as a unique correlating parameter 3. Velocity, Weber N'Niber, and. Time Effects The reasoning behind the expectation of a correlation in terms of Reynolds? number has been previously discussedo However, the use of velocity per se, for a given fluid9 as a correlation parameter can also be justifiedo Such a presentation'would also tend to include Weber number effects as discussed belowo For a constant cavitation number, both the time of exposure to the region of underpressluore, and the amount of this underpressure, are functiorns of velocity; one inversely as the velocity, the other

-30directly as the velocity squared, It may not be unreasonable to assume that the gross cavitation pattern is largely controlled by the nucleation process, which is itself not as yet entirely understood. It is not inconceivable that the nucleation process may depend upon time of exposure to underpressure and absolute value of this underpressure in such a way that the effects are not cancelled for constant cavitation numbero The Weber number, for a given fluid and over a moderate temperature range, is almost entirely a function of velocity since surface tension does not change substantially over such a rangeo Therefore, nucleation effects which, from a slightly different viewpoint might be considered as Weber number effects, are uniquely related to velocity under these conditionso V. CONCLUSIONS The following significant conclusions can be drawn~ 1) Significant scale effects have been observed in stationary components for various degrees of cavitation and substantial variations in velocity, size, and temperatureo Also such effects have been observed in rotating equipment over a range of velocity and temperatureo The direction of these effects is consistent with the present literatureo 2) The cavitation numibers, for stationary and rotating components, can be correlated either in terms of Reynolds? number or velocity if size and temperature

-31is not variedo Reynolds6 number appears to account adequately for size variation, and partially for temperature variation in the stationary component (venturi) No size variation was available for the rotating component (pump impeller)o 3o Venturi loss coefficient cannot in general be correlated solely in terms of Reynolds: number or velocityo 4o Thermodynamic effects are significant in. the present tests only for the venturi loss coefficient for welldeveloped cavitation. Over the temperature range tested, this is not inconsistent with the existing literature.

VI. BIBLIOGRAPHY 1L Hammitt, Fo Go, et alo Fluid-Dynamic Performance of a Cavitating Venturi - Part II, UI-U I Report 034 T University of Michigan Dec,, 1960o 2, Kermeen, Ro W,, et alo "Mechanism of Cavitation Inception and the Related Scale-Effects Problem'" Trans, ASME, May, 1955o 30 Stahl, Ho and Stepanoff, A. Jo "Thermodynamic Aspects of Cavitation in Centrifugal Pumpso" Trans, ASME, 1956, po 1691-6993 4, Daily, J, W, and Johnson, V E, "Turbulence and Boundary Layer Effects on Cavitation Inception from Gas Nuclei." Trans. ASME, Vol. 78, Nov, 1956, po 1703-1706, 5. Holl, Jo W, and Wislicenus, Go F, "Scale Effects of CavitationT Paper No, 60-WA-151, ASMEo 6. Oshima, R "Theory of Scale Effect of Cavitation Inception on Axial Symmetric Bodies," Paper No. 60-WA-136, ASMEO 7o Stepanoff, Ao Jo "Cavitation in Centrifugal Pumps with Liquids Other Than Water." Paper No, 59-A-158, ASMEo 80 Jacobs, Ro B,, et alo Pumping Gryogenic Liquids, NBS Report No, 3569, Technical Memorandum No 36 ational Bureau of Standards, Feb., 1956o 9o Jacobs, R, B., et alo "Direct Measurement of Net Positive Suction Heado" Trans. ASME, Series D, Journal of Basic Engro, Volo 81, 1959, p o 1t 7 10o Salemann, Vo "Cavitation and NPSH Requirements of Various Liquidso' Trans, ASME, Series D, Journal of Basic Engr,, Volo 81, 1959, po 167-173, 11o Hammitt, F, G. "Liquid-Metal Cavitation - Problems and Desired Research " Paper No, 60-HY~D-13, ASME, 12, Esman, I, G,, Editor, Centrifugal Pumps for the Oil Industryo Gostoptech-Izdat, Moscow, 1951, p 2 6-27 in Russian), 13. Personal communications from G. Wood, Pratt, and Whitney Aircraft Co., D. Sandercock, NASA Lewis Laboratory, M, Keresman, ThompsonRamo-Wooldridge, Inc. Cleveland, Ohio. -32

LIST OF FIGURES Figure 1. Cavitation Number vs. Throat Reynolds Number in a Cavitating Venturi for Sonic Initiation. Figure 2. Cavitation Number vso Throat Reynolds' Number in a Cavitating Venturi for Visible Initiationo Figure 35 Cavitation Number vso Throat Reynolds? Number in a Cavitating Venturi for Cavitation to First Marko Figure 4. Cavitation Number vso Throat Reynolds' Number in a Cavitating Venturi for Cavitation to Second Marko Figure 5o Cavitation Number vso Throat Velocity in a Cavitating Venturi for Visible Initiationo Figure 6. Cavitation Number vso Throat Velocity in a Cavitating Venturi for Cavitation to Second Marko Figure 7. Loss Coefficient vso Throat Reynolds' Number in a Cavitating Venturi for Visible Initiation, Figure 80 Loss Coefficient vso Throat Reynolds? Number in a Cavitating Venturi for Cavitation to First Marko Figure 9. Loss Coefficient vso Throat Reynolds' Number in a Cavitating Venturi for Cavitation to Second Mark. Figure 10o Loss Coefficient vso Throat Velocity in a Cavitating Venturi. for Visible Initiationo Figure 11. Loss Coefficient vso Throat Velocity in a Cavitating Venturi for Cavitation to First Marko Figure 12. Loss Coefficient vso Throat Velocity in a Cavitating Venturi for Cavitation to Second Marko Figure 1_3 Thoma Cavitation Parameter vs. Normalized Reyn.olds Numbero Figure 14. Thoma Cavitation Parameter vso Normalized Pump Speedo Figure 15. Suction Specific Speed vs. Normalized Pump Speedo