CAVITAT9ION P-IVOR{ANCE -OF BEI HYMODESL 1.4/2 Sa UENMtIFUGAL -ThMPF Internal Report No. 3 UitI P1roject 033424 Frederick Go antt January 22, 1

The Lmajor rm-a4-e og &iate reduci.a.ones and the calculations tor this report;sr car3wde d oizt by, and, undesi: t re supefrvisions of,,Mr Paulr TX Chut. ThR e ntest.nstrumefatiom was ia.rgely coneivred and installed by C. L. ~akamo, assisted by J3.,ch midt. The tests were superiseI aemd i;ondmtctad by V. F.. Cramer3 assisted by U. J.3 Rlobimnoono Majotr corn'tributions to the th e iesg. Fprogram were also Ima!by T, A. Sheaf ln rand AN. Travers,

I Introduct~#fonr I BEquipsen:t and Instrutmentation l A. Limitations B. Instrumentation 3 III Test Results 3 IV %scusion of Rassult 5 A. General 5 B. Predicted Mercury Performance 11 V Conclusions 12 V: Appendix 14 A. Error Anaiysis!4 B. Date Processing 15 VIX Nomenclature 18 VII Bib1iosraphy 19 I Summarization of Results and Standfatr Deviation 13

1 S0.eagitc of S et-upr for Pur,? Cavitation Tets 2. ma R s 8Cari.a: ion Pareameer~ cNJ vas Nornmalized Ptmrp Spsed, N/N 3. Suction SpccificL Spyeed vr. Normalized ump Speed 4. Thcis (iav.ation Paramtexr, rs. NormalizAsd Reynols Neuer 5.X Representative Pumpi Cavitatn Perfoiance Curve 6. Cavitat;ion ]N1belr -V, Reynol8s''NFxmer a7t Throat.n a l m it atn t Venhtutri 7. Catritati -on NtM-wber vs. NormaGlied Throat Ve.ocity in a Cavitatir VemttLri 8o Plot of ThMe.adynmic Parwatfer vs* Tmpwes'ature

1. Introductito Cavitation perfo=-aate te$ts have been conducted on the Berked'o ley Pump Company Model 1-1/2 WSR centrif ugal pump, which is used to powear the liquid metal cavitati.on loop forI tnm basic purposes: 1) To obtain a direct comparison of cavitating performance in a turbonachine under conditionls of iderticar. geometry bietween hot and col1d wmter on the one hand and various liquid metals on the otherl, 2) To obtain basic information on cavitation in a turbomachine for cpau rison with similaer information from a statioenary component as a venturi, which is also employed in the present project, Due to the fact th:at the facility and ptmp were designed prit mrily for operatioa tith high-temperaure liquid metals.$, and hen7e somewhat tompromised to avoid mechanical compVleidties, the cavitating performance of the pump cannot be o7btained as easily or accurately as might be expected under ordinary conditionso. owever, the difficualties were overscome to the eattent that meaningful data could be obtained IU. uipmnt' and Instrumentation A. Limitations The Berkeley pump is a sump-aype centrifugal pump with smaft overhung from a bearing housing losated.bo. ~the sut tank, It is conI nected into a closed piping loopo The. facility and the pump ave been previously pictured and de$cribed in detail'2o The ssaugp is sealed by a stuffing-box from atmosphaere In liuiud metal operation i.t s intended that the saup be blanketed witih inert gas at a pressure slightly

above atmospheric allowing a small, cont:rolled out-leakage. Even with the mnaxim allo wable speed of the pump (pump drive is through a variable-speed fluid coupling from an induIctUson wrtor), cavitation with water can only be attained in the pump if the samp pressure is reduced to a near vacuum or the water vapor pressure is raised to values near ati:ospheric. It was desired to use both approaches in order to determine the possible'1thermodiiynamic effects," since the parameter denoting the ratio between vapor and liquid volume under equilibrium conditions in the cavitating regions3'4 changes very considerably between, for eammple, water at 80 F and 160 F. It was also desired to cover a range of operating speeds to obtain information on "'cale effects." Usin5b either approach to obtain cavitation (both were used to cover the desired range of parameters), it is difficult to obtain accurate data. For cold water or low speed t:ests, it is necessary to p.rodluce by quite a considerable vacuum in the sump This was done/using a vacuum pUMp, the capacity of which was balanced against thea stuffing-box leakage and a controlled by-pass valve (Figure 1). Since the stuffing-box leakage was not constant or negligible (overheating difficulties ware experienced if i~t were unduly tightened), it proved very difficult to obtain steady-state even for brief periods. * Vacuum requtrements for high temperature or high speed runs were of couraee lessso that the above difficulties etre somewhat reduced in these caseso HIowever, date obtained at the higher temperatures inelutade ienreased inaccarasl elue to temperature measurements, since th.e *These difficulties should nEo be present with mrcury since the atmospheric pressure in the sump is only about 21/2. feet of suppression head in this case.

dependence of vapor pressure on temperati=e increatses reatly. The value of NPSH becomes quite sensitive to te merature since the vapor pressure is nearly as large as the static pressure, It should be noted that this difficulty, which is naot excessively severe in the present case, exista onaly f-or tests with 1ow NPS puSmps (Swghich was occasioned in this case by the very low flowg, i.e., 40-100 GPM, rather than good cavitation performanc) B; Instrumentation To asets of tests were made teing quite different instrumenti a tion arrangements. The first was quite conventional, using manometers and/or calibrated gages for pressure measurement. The second used high.response rate p ressure trtansducers feeding a recording5 potentiometer, It was felt that these were neassary because of the previously mentioned difficulty of attaining steady-atete conditions. Actually, the trawn ducers did not give as great an Improvement in precision as had been hoped, probably because of drift during the runs. The remaining iltrumntation was typical. Flow was measured by calibrate1d venturi teperature by a thertocouple inserted at first into the puM p, later into the dischaege line. No significant dif - farences between theso ae locations Were observedo Pump speed was measured through a magnetic pick-up feeding an electronic countero Accuracy is believed to have been extremely good. Gas content of the water was measured by a Van Slyke Meteir Ill, Test Results Twelve distinct astegories of test runs were planned. Thease are classified accrding to pups speed as a proportion of deslgn speed,

flow as proportion of design f lows at the applicable speed, and tenperature (approxinately 90 R. orP 165 Fo A temperature of approximately 90 F, rather tian say 60 F, was used to avoid vaporization in the iustrntent lines which were cooled by the somewhat lower room air temperature. ) Actually, three speeds were used (1750, 2420, and 3000 rpm),and two flow ratios (0.93 and 1..20), Atsufly, only, 10 of the possible 12 categories %vree run, since it proved tmpossible to provide suf ficient vacuum in the sump to obtain cavitation at the low speed with cold water. The runs and their results are listed in Table 1t Each rutn consisted actually of several passes through the cavitating perfomiance region (an average of approximately four per run), Thus some information is available upon teich to base a calculation of standard deviation. This was done for all runs having more than two. pessea, and the results are also listed in Table I. The standard devia-' tion is shown on the points in Figures 2, 3, and 4, where it is seen to be sufficiently smll that the trend of the curves is significant This is particularly true in the case of the Thora cavitation parametero A eypical plot of the ra &data from a run having a sScmwhat less than avSerage standard deviation i shon in Figure 5 as pump pressure rise versus Hvo. The Hay value upon which the cavitation parameters are based is defited as that value for which the pump pressure rise has decrease3d to 95% of the noncavitating value. Hv itself was inferred from a static pressure tap located ap.proxitately 6 diameters upstream from the elbow leadinag directly to piump auction (Figure 1), c:orrected for a small calculated frictioan loss and elevation chane to impeller cente Prliane. Pup disLhrge also was corrected for the elevration cge o to The impeller centerline Howver, the frictional effects wre negligible in thils case. The calculation details

are given in the Appendix, Hsv values wane ta kem from plots of the data as, for eauiple, Figure 5, aed used to compute the Thoma cavitation par.aster, CT and the suction specific speedfic S For the presentation of these results, (Figures 2 and 3), pump speed and flow were nolized by diveiding,. by the design speed (1800 rpm) and design flow (40 gpm), respectively. RXamination of these curves shows a considerable "scale effect" in that — r decreases bevteen 30 and 50% (depending upon flowy) for a speed increase of about 75% Simtilar, but inverse, behavior is noted for S. The curves are clearly divided acco:rding to the flow ratio.. S is appreciably loxer for the lower. flow and S higherO. Te standard deviweffect and the flow effect ation of the points is such as to make t:he scale/both unquestionably sigr nificant ~for In the case of 3, the scale effect is certaint.y asi{g aificant, while the flow effect is also, but lese so. There is uo significant differentiation betaeen hot and cold vater points, or noticeable effe~t of gas content (as long as water is settled over a period of severa1 hours to remve large entrained bubbles, as it was for these tests) Horwever t$hie gas content could only be varied over a tange from saturation to about 50% of saturation. IV. Digsussion of Results A. General Fminaution of Figure 3 show the auction specific speed for the aunit is about 2500 at the design poin$t and about 4500 at 1.66 design speed (and 0.93 x destign flOw) The faca t th aht thalese ales are less thanEs conventional practice would indicate is beieved due to two lEac3tors 1) There is a standrd 1ong-radius elbow directly upstream of the pusp suction. This is ot a part off the pump itself, but rather o[ the loop.

2) The impelleer,vs not especially designed for good cavitation performance, The lo~.7 8 values are not believed injurious to the overall test objectives since only a comparison between fluids in the same geometrical configuration was desired, No attempt to develop a high suction specific speed impeller is involved at presentO The low values are an advantage in that cavitation wsith ligquid metals should be re easily obtained. B Scale and The.rmod.Sic Effects It has become incrteasingly recogpized of late that significant scale effects and also thermodynamic effects, causing departures from the idealized theory (on which the concept of the Thora parameter and suction specif~ic speed are based, for exaple) do exist in cavitation perfore e6,,7,,>etoo RbAn almost identical effect (wherein suction specific speed increased 40% for a speed increase of 50%) to tha shown in Figtre 3 is lirsed by Stepanof;, quoting a fussian paper8 Also a somewhat similtar effect (significant decrease of cavitation number for tncreasL of Reyolids' number has been =oted in the present investigation for cavitae tlon in a venturi (Figures 18 through 21,f R aierenc 2}c Thel venturi tests C0rr0late V6l3. in terms of ReylnoLds nmw ber (Figure 6), but only very poorly in texms of velocity (Figure 7). These fig~ure are replotted from the data of Reference 2; Figure 6 is BFigure 19 of Reference 2 with standard deviations added, and Figure 7 is the same data plotted against normalized throat velocity. This partial cortelation i trse of two different parath ters is posible bcause of thue relatively small temperaturee range, ad the fact thbat osat of the high Reygnrolds' numsber points are also high temperature points, and hence tQo soe extent all shift together when the

abcissa iS cznged from Re-molds' numebe? to velocity. Visible initiation in the vernuri was chosen for comparisXon with the p=mp data because the proportional head effects are similar and hence, presumably, t-he degree of cavitacion. The pump Curves were shown in Figures 2 and 3 plotted against normalized velocity, It is noted that the correlation is quite good in terms of the standa.:cd deviation which is showa. Figure 4 is a replot of the data of Figure 2 in terms of Reynolds' number. A reasonably good correlation is obteal-ned alathough not gquite so good as that in terms of velocity. The shape of the curves is similar, but the slope of the curve in termns of velocity is somewhat ateepe,'. trly clear-cut arguments can be asdvanced to explain the correlations ir terms of Reynold8s' numbert although it seems unlikely that Reynolds' number should be the only factor of significance. A summarisation of these arguments follows. If it is consi.dered that cavitation bubbles originate in the tboundatry layer and also that local under-pressures in the fluid are a function of deg of degree of turbulence, it is not surprising that Reynolds' number should to some exteat at least correlate cavitation data. Othetr possible parameters, as listed for instance in Reference 5, include Froude number, atch number, Weber number, and Peclet number. If tests at a fixed temperature and over only a moderate velocity range are considered, it seems unlikely that effects due toa variation of Mach or Peclet numbers could be serious. Weber number does not vary significantly over the test temperaturea range since swurface tension is only a weak function of terS'perature. PFroude number does not vary significantly in the testso Hnce, it might be cncluded thst, at least for fiaed eavperatiure oaynoldso' number alone tnould be significantv In fact, a variation of cavitation

number with Reynolds' n-mber has recently been derived by Oshima6 by considering only inertial, pressure, and surface tenston effects. However, the predicted variation is in the opposite direction to that observed ain the present tests. In the pump tests, the cavitation conditions are defined as those producing a pump hlead reduction of 5%. As suggested by Stepanoff4 and Saleuann,. tentatively this can be taken to mean a given vapor vollme within the pUmpe. Again, as originally suggested by Stepanoff,, considertably greater local head depression for hot than for cold water, at 1east under constant equilibrium conditions, is required to produce the sensible heat from the surrounding liquid for production of the requisite vapor. This was presentred in slightly different form by th present author3 as a parameter equal to the ratio of vapor volume to liquid volu per unit head depression. This parameter is plotted over the range of the present test teperaturtes in Figure 8, where it is seen to vary by a factor of about 5. In other words, under equilibrium conditions, a head depression, 5-ol crd increased over the cold water tests, should be required to produce the sme proportionate head reduction in the hot water tests. It is apparent that this is not quantitatively meaningfu in the present casea since the head depression for the cold water tests is of the order of 4 feet, and about the a=s for the hot water tests. However, the trend characterised as "thermodaic effects' in the current literature certainly exists as shown by the test results of StepSnofe- and Salmann5 and also Jacob10 It thus eeans reasonable to assu that separate Reynol$ds' n.mn ber and theradynaic effects exist. Assume for centrifa ugal pumps, on the basis of the present tests, aa well as those of Referenlce 8, that the

Remomlda' Wuiber effect alone, for testis at costanrt temperature, results in a decrease of the Thoema parameter with increase of Reynaolds' -M.boer (pump speed), and tmat the tih.ermodPynmic effects result in a further decrease of Thoma parameter (assuming a fixed proportionate head 1oss) for 1increasesd Blfactor43, i.e. as occasioned by increased temperature for a given flu6d. Then the data shown in Figure 4, which is plotted in terms of Rey. olds' number, should sho separate hot and cold water curves. That this is not the'case either with the pmup (PFigure 4) or ventnri (Fig'uare 6) date may be the result of the fact that the thertdynamic effect is relatively negligible over the temperat'ure range tested. No direct comparison can be made with the test results listed by Stepanoff and Salemann since the vapor pressure values for the preasent tests are far below those for which they testedo However, extrapolation of their data does tindicate that the thermodyamic effect would naot be ap preaiable in these tests. The venturi cavitation date2 from the present research investiconsiderably gation correlates/better in terms of Reynolds' Tlumber than of velocity, (Figtures 6 and 7). Howriever, in these tests, a fixed proportionate head loss for the different tests does not exist. Rather, the extent of the cavitating region was fixed visually, and it was shown that the head loss, under these conditions, for substantial cavitation weas greater for cold water than for hot, as expected (see Figuzre 28 and 29 of Reference 2, although the differentiationa for visible initiation, for which comparison should be made, is too small to be significant within the precision of these tests F Figure 27, Reference 2), However, the argumenat aupon which prediction of the thermod ic effects is based, ieo., tixed proportionate head loss, does not apply. If the points of Figure 6 (visible

iiti&atiotn for the oventurij, o, o-i;L lilar curves fos amore advanced cav.ation (Figures 20 aand 21 o4 Reference 2), are adjusted according to the venturi loss data (Figure:es 28 and 29 of Reference 2, for example) t!o that the head loss scatio for points at a givten Reyno.Aldst nmbear is conse.ntX, then the hot vwater point for a;iiven Reiolds' number should be considered at a greaser visual degree of cavit:ation (as visually observoed) to give the same haad toss as a cold point at that same Reynolds' nube-x This Would result an a separate curve for hot water which would be at somewhat lower cavitation numbers than the cold rhater curve (i.e., the present curves of Figures l8-21 of Reference 2), since cavitation i=umber generally decreases as the cavitating rkg!ion ~s increased (Figure 2' 2 of Reference 2). If curves on this basis ea're psot@ted against velocity rather then ReyPolds' number, the separation between hot and cold xtsater curves would be increased, rather than te-ndiVg. to collapse into a l-ingle curve when plotted in this fasion as the puip curves apparently do. No ratiolization is at s present possible of the fact that the pump data correlateF best in teras of v.elocity and the venturi dat. onlj in terms of Reynolds' anmber. The above arguments regarding thermodywamzic effects indicate adjustments in the wrong directionr if it were to be as — sumed that the venturi and putmp plots %ere equivalent. Of course, there are basic differences betweren rotating znsad stationary systems which may be responsible~. It is noted that a similar correlation of cavitation number over a raestricted temperature range witih Reynolds' number for carbitation on a stationary body %was presented in Reference 7. An em nrnation of the existig literature regarding sca.e effects in pumps and on stationary objects2'4'5'7'8 slhows that caritation indiex sosmetimes increases with increased velocity or Remyno&.i'

trifrizgal pups (6tQ p:ce sent tcsZs and R-ferene 8 2) show a decrearae Tih resrlts on. pesu (setf:cent bo%-die s, a sumarized in Referiee S, s^howE the o2ppostte r-erti'iraitiea:i.n~ue-er, esuuts`tor a low prressire coef. ~ic'i,~ernti bo4 in IRA 160'2 Vdr.Bo SA.l it Reference 5) shosm a dereac mdth Er9.3r lds' aui.-, ass does ~the data from the veat uer tests o. h-e present izrestigatL cn2 1 Is3e hyitofoil:22nd venMt~z'i seet sohmewat coiparatYb e in:hisa x tep.. Ao.. So6.nitc'ity.t betwaen a hydrofDoil a nr.c the blades of a cnntr iu;J xnan may be jus tified Predicted gYrc ry?erforjangj?7or;imi ar vsel cities in the ame en Zipment, the Reynolc&' nurmbers for me:curjy Id.1 be cons.:derably greater. tlk-n those for -t:-iatar (% ectr of 3 t& 8 dcpeanc.PaUg tpoa- tepexsruatre). The 1ther4codynamic i tf se $S 3as compared thb-ough the equi ibC. it vol tiSe ratio (B-factor) cb t.oulC not bt grtit s inche thei v2apocr vr e per Iiu4 n- TI.. e r u nit hea8 depre sioa irs a factor of 07 e IneL.tx k:a- for cbI tfotreh.L Stn ace te..n.a let head dspress3ir reAured t.o o tair> gi $ en.S ca-vt:aition effect or pump head diftfere'ial i3 on.y a sai.l poNrtion of ttV b.Vt. col;d water, and seince:I. will be prestmably greatly i-ecweaseed for mercury, tihe cmange i.n cavitation p[~arme; er fronm this effect should wot be %v~ery substantial. Wfhile this is in the opposite direction from kthe lReylds. nw ber effect: an, eartadint4ioin of Figures 2 and 3 indicates that the Reynolds nember effect,wi i robably'be airly la xge Hence, T thes-. effects alone contr'A.. tt;could be etpet 7eed that the cai itat:ion p sa:arters for earcu~ry w ilt i e sb 1 $tantlally less taa for irater. On the other hand, the effect of surface tension is proportisonately E.lss for mecury, erhaps akirg cavitiati1 oeg sir and rintg. the cettitation nt etr.

V, Conclusions It is concluded from the pump cavitation tests with water that the TFhoia cavitation parameter decreases subs$tantially for increasing pump speed for a fi:xed flow coefficient. Curves for hot and cold tmater over the range from 90 to 160 F coincide. Corresponding comments apply to suction specific speed. These trends are in approximate quantitative agreement with the only similar tests knomwn to the author in the literature. It i.s tentatively concluded that major effects resulting in deviation from classical theory in a ptmp or a stationary member can be divided into either Reynolds' number or velocity effects (it is not certain at present which is most suitable, although tests with mercury in the present facility may go far to resolve the uncertaibnty) and thermodynaamic effectso detailed examination of- the results indicates, however, that these alone a're probably not sufficient, and the correlations are probably partly fortuitouso The direction of variation o: cavitation number with Rteynolds the nauber in/venturi tests was the same as in the pump tests. This does not conflict with present literature which shows Reynolds' number effects i.n either direction for stationary objects. No similar tests on vent.uris are known to the author for direct comparisono It is also tentatively concluded that cavitation numbers for mercury in the same geometry and at the same velocity will be less than for water because of the large Reynolds' number effect and the relatively s thermod icetal in thedynamic e in ppliable rane of variables. Howver a counater trend could be indicated by a Weber number effect.

13;. Termp. Run N oo o F. N/NO Q/Qo S C< 9 166 0097 0.93 0.1732 2351 0.033 353 10 162 1.102 O. 232 2572 to-... 2 83 1,343 0.93 0.802 4144 0.0067 247 1 g 12 85 1.2 0.209 2927 0.0251 240 8 167 t 0.93 0, 1071 3437 0.0301 569 11 162 1.2 0.2065 3033 0.0216 225 3 88 1.665 O. 93 O, 0865 3930 - b 13 97 1.2 0. 1846 3192 0.0155 216 7 166 0. 93 0. 0687 4935 0. 0182 979 6 161 1.2 0. 1599 3516 0. 0046 83 -4 93 1.2 0.192 3747 0.0163 274 20 120 1.343 0,93 0O1214 3200 0.0438 725 21 110 1.2 0. 1925 3650 0.o 0239 345 22 125 1.665 0.93 0.0884 4240 23 125 1t o 2 O. 1618 4040..w. Averages 0.023 387 TABLE I Sumnarization of *Results and Standard Deviation

ZA. xro Anaiy.'Vsivc Each of the exrer.t.ntal po.ti:Zs tsE t9ifh o n escepticr') is tUe resaul of 8iseveral:sc;gual.~:ru1ns, uouK,1 4.on: t, Accor4ingT to'3st~.$-Idard procedures*, these are us'ed to cwpute the standard dev.iations fo- eac pon't Whicht' consists of zrae t Ulan tiwo sparate uns, T...vheseM are s..i:...G ized in TIable 1, where "it s nsted t ~t. hat t he average.s;:tan.darcd deviation for the T.hon cavitation paraxeter is 0.023 and that for the suction specif.e speed i~s 387T Te^ Ct tual values tio no t vary by orders of rguitde fr.oam the average vatlues. The runs'~ita sta..dard pressure gages,.ather than higho-response trasyie~ ars (rur sAs 20-23) show somewthat greater devia-. tion bu-t not by an order of nmagnitude. The average devia'tions are saown o-n the figures with each po:int. to give some idea of the- reliability Of the poin'ts.0 The standard deviations co:puted Srn the repetitive run ido aot: qui.te includ.e a.1 possible e:rors. The runs wtere made in quick suc —,essaion so tahat a single temap eratuee readi;g was used for all. For the ow? teperature runs, the depenaence of vapor pressure on temperat iure is so small as -to tmiake error on this account definitely negligible. For ahe highest temp4eratures used, an er:rFor of 1OF corresponds to a vapor pressure error of about 0.2 feet. On. this basis i:t is believed that the likely -vapor pressure error is: o rore than 0.1 feet, corresponding to an error in Msy of no Pare.thz:n 2% and in m$st cases lenss tNh.n 1%. This is quite neg igible compared to the scat:ter of the d4tao where Xi s data R average of si n nmaber of runs

S. Daa?roessinj The a-mlc eqt.aauCos z3etd in retduc'e U uct: n specific.aat S atea are 9S. -.tZ-)t 8jS & $. S_) Fco- (POs~tSc) in ^;&AZ { 2' The meaning o, the aboe ave syto@ls is.irted in:omencl.ature. Thus, according to the above t0-pzations, the measured quantities shCould be RFAD~ GWP;, temperature anmd the static pressures at both ends of the pump. 3ince the transduicer regitZers only pressure differecres, the barometer pressura read6in becores necessary. As mentionred In the ts-xt, pressure readings are obtained di' rectly from a::ecording potentiometer ti most of the tests aad frC4; &urdon gages in sr;me. Eqs. (3) and (4) are them computed. Hsv in. gEq (2) can be calculated from the result of Eq. (3). AP of the pump is e eadily obtained from?o2ut'tin. One thus plo!s A1P n. ys.H The critical H8'~ is taken at the poinrt fihereI the pump presuasre differential is reducted by 5%. A typical curve is $hown by Figure 5. Follbo.wing is a repres~nem~intative calculatio::

Tempt = 83OF The~rmocos le correc tr.c 0 65 fro.i ca lfbr ration curvete Actual floiid temp, = n 3.65p3 F Saturated vapor pressure = 0.5643;psia (Reference n I) Barometric pressure 14f035 psia Flow rate = 52 SCa f:~'cm ven-:uri ca&ibration cuve ~RPM~ of pp = 242lt (1) ID of the pipe 1.61 i nches Velocity of the fluid = 881 1ps Re 1.141 x 105 f 0, 017 for pipe of p and a~ above Reynolds, tubaer (2) Suction side prasourei correction AZ,. g525 1 0= 04;58 ft. Equivaslent lentgthL of piping 4=-J4. f40t. h 0s,s 52 5'It. 4A +.a~h = 0.933 ft. = 0.425 psi ~" Pin = (?2ti c)i -.... —opsia (3) Density of water= 6 2.I 1/ft3 P, T 1.31 __-=1.04 (4) Discharge side presmsre corre f:tiona aZ= I ft Equivalent: en~:h of piping 0,91 ft. az = 0,066 fto

(5) Daroi-eti ic psres rsue =a14.35 psla Teerefore the o-mrkidt equations are Pity = (Pstatcitin + 13.925.-.......ia Pout = (esta, tic?) t + 14,85..p..a Hi. = 2. 31 sin' 2 0 27....."...OWlm P = Pcz' Pil.............pi

VII Nomenclature: P Pressure S Suctn Suction fic speed of pump N RPM of pump Hsv WNet positive suction head Saturated vapor pressure feight V Velocity of the fluid Depending on the topic, C may symbolize the cavitation number which, by definition, dT ( AP On the other head, T may symbolize the "Standard Deviation"' in the conm.on statistical sensr. Thus means the standard deviation of cavitation mmber G. means Thome cavitation parameter B Thermodynamic coefficient, equilibrium vapor volume per liquid,volume per unit head depression {L C(P (AT/,) Density of liquid t BDensity of vapor Cp Specific heat of liquid a H Head depression below saturation pressure a T Temperature change of liquid corresponding to A H hg %Latent heat of evaporation

19.'VIII Bibliogra h 1l eHaimiatt, F. G., "Liquid-Metal Cavitation - rosion Research Investigation." Final Report, Project 02824, University of Michigan, Jan. 1960 2. aitt, et al, "Fluid Dynamic Performance of a Cavitating Venturi - Part II'". UHRi Report 03424-3-T, University of Michigan, Dec. 1960 3. Hitt, F. G., "Liquid-Metal Cavitation - Problems and Desired Research." Paper No. 60-HYD-13, ASE, April 11, 1960 4. Stepanoff, A J. J, "Cavitation in Centrifugal Pumps with Liquids Other Than Water." Paper No. 59-A-158, ASME, Jan. 11, 1960 meeting 5. Roll, J. W., Wislicenus, G. F., "Scale Effects on Cavitation." Paper No. 60-WA-151, ASME, Jan. 10, 1961 6. Oshima R., "Theory of Scale Effect of Cavitation Inception on Axial Sysetric Bodies." lASM Paper No. 60-WA-136 7. Kermeen, R. W., McGraw, J. T. Parkin, B, P.,'"Mechanism of Cavitation Inception and the Related Scale-Effects Problem' Trans. ASME, May, 1955 8. I. G. B8man, Editor, "Centrifugal Pumps for the Oil Industry." Gostoptech-lzdat, Moscow, 1951, pp. 26 and 27 (in Russian) 9. Salemann, V., "Cavitation and NPSH Requirements of Various Liquids," Trans. ASHE, Series D, Journal of Basic Engineering, Vol. 81, 1959, ppO 167-173 10. Jacobs, IR. B., Martin, K. B., Hardy, aR. J., "Direct Measurement of Net Positive Suction Head," Trans. ASME, Series D, Journal of Basic Engineering, Vol. 81, 1959, p. 147 11. Keenan, J. H., and Keyes, Fo G., "Thermodynamic Properties of Steam," 1936, John Wiley and Sons, Inc.

SCHEMATIC OF PUMP TEST SET- UP DRIVE PULLEY FROM VARIABLE SPEED FLUID COUPLING BEARING HOUSING STUFFING BOX THROTTLE VALVE Li TO AT M. ~NEEDLE VALVE VALVE TO VACUUM PUMP \\DISCHARGE PRESSUR TAP I |_ _ I I — S R I Z CLO ED LOOP LIQUID LEVEL kt g g -- 0X f P MP SUMP V l ~ r ~LONG RADI S ELBOW PUMP IMPELLER/ SUCTION PRESSURE TAP FIGUREI

THOMA CAVITATION PARAMETER VS. NORMALIZED PUMP SPEED.26 24.22.201: Q/Q0.1.2.18.16.14 12 Q/Qo =.93.10.08 TEMP FLOW \.06 0 HOT o MEDIUM Q/Qo= 2 04 A COLD O HOT n STANDARD DEVIATION (TO SCALE).02 l O MEDIUM Q/Qo=.93 V COLD 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 2

SUCTION SPECIFIC SPEED VS. NORMALIZED PUMP SPEED 5000 4000 - - 0/Q=.93 o O 0 Q 3000 Qo/o= 1.2 2000 TEMP FLOW O HOT o3 MEDIUM Q/Q =1.2 1000 A COLDt —- - O OT T STANDARD DEVIATION (TO SCALE) o 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 3

THOMA CAVITATION PARAMETER VS. NORMALIZED REYNOLDS' NUMBER.26.24.22.20 A.18 04 1 COL Q _/Qo=.93 0 HOT STANDARD DEVIATION (TO SCALE).02 l >MEDIUM Q/Q.93 T COLD l 0 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/ Re. FIGURE 4

PUMP CAVITATION PERFORMANCE CURVE, RUN NO. 2 46 2 ~ 3 42 0 X f-XL- rCI —-. —-.. /. 38 I i 22' 3 31 38. tiP 408 418 40.0 41.8 40.4 404 (I) ~~~~~~~NC P 38.8 39.7 38.0 39.7 38.4 38.4 xC /aoc 34 i! H 6.9 7.2 6.5 7.7 6.3 6.3 1 sv __ _ __ _ _____-.- - xI t R A ciASI I <34 I Isi TRIA 30. TEMP 83 v 2 nd TRIAL RPM =2420 3 XJ 1 ~~~~~~~~~~~~~~~3rd TRIAL FLOW 52 GPM. —. 26 2 6 10 14 18 22 26 30 34 H, FT. OF WATER FIGURE 5

CAVITATION NUMBER vs. THROAT REYNOLD'S NUMBER IN A CAVITATING VENTURI FOR VISIBLE INITIATION 0.22 0.20. i..... LARGE (I/2)TEST SMALL(i/4 ) SECTON DATA FLUID CONDITION TEST SECTION SECTION DATA DATA 018 * \ a * COLD WATER 0.16 b A L - HOT WATER v 0.14 I.-.,. _ _ a_ 0_12__\ I STANDARD DEVIATION(tO scale) E 0.12 0. Io \ z Z O 0.06..-. i 0.04 0.02, e -0.02 2 3 4 5 6 7 8 9 10 2 3 4 5 6 7 8 9 10 REYNOLDS NUMBER AT THROAT OF THE TEST SECTIONS, Ret FIG. 6

CAVITATION NUMBER vs. THROAT VELOCITY IN A CAVITATING VENTURI FOR VISIBLE INITIATION 0.20 0.181 LARGE (1/2")TEST I I SMALL (1/4') FLUID CONDITINTS ETO SEC.TION DATA COLD WATER 0.14, _ _ _ _ i i,, _ __ ~~~~~b A i ~ i j HOT WATOE 0.12 ----- s I I I~STANDARFUD DEVIATIONTOS SCALE)TN I~~~~ i............., w~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 0.10 V.i _ —-*7.i....___......... z I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ __ ~ ~ ~ ~ L __.-~-. i- __ —— ~ —- __-C -—. __- I — - I - I;, ) ---— i.~~~~~~~~~-1 —~~~__ _ ___I:~- __:~~.:- *t. — **- t ----- __ —- _- — I 0. 06 C.) I I ~e i ~ i i 0.04 iIi ~0.~- I02 -0~~~ ~ ~ ~ ~ ~~.02 55 60 65 70 75 80 85 90 95 VELOCITY AT THROAT fps FIG. 7

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