University of Michigan Department of Mechanical Engineering Cavitation and Multiphase Flow Laboratory UMICH - 01357-34-T PUMP AND OTi-IER C(:!)MPONEI\NT CAViTAT-T C N COIfPT RA IS O(NS BTiI'WEEN ALICALI LICQUID IMETALS AND WATgER by F. G. Hammitt Financial Support Provided by: National Science Foundation Grant No. GK-1889 and the Argonne National Laboratory December 1973

Table of Contents Table of Contents................................ List of Tables..-,, * * ii'a a. ~ 0 List of Figures..................... i Abstract..........0 * P,,.iii 1. Introduction.............1 II. Pertinent Applications and Data............................1 A. Pratt and Whitney Air-craft - CNEL,....1 1. General Background Information...........................2 2. Actual Tests and Results...................... a. Cavitation Performance in Water and High-Temperature Potassium...............................,..,.,.... b. Detailed Cavitation Performance inl Water............ 6 c. Cavitation Dama g Tests. c. Cavitation Damago Tests.............................. * B. Oak Ridge National Laboratory................I........... 8 1. General Background inforGn altiond o........................... 2. Actual Tests and Results............................. a. Comparison of Cavitation PSStI - Water and'at. *........ b. Cavitation ),amage Tests........................11 c. Vellt:,ri Soditn Cavitation Tests..............a..... * 12 d. Cavitation Tests with Potassium in Electromagnetic (EMl) Ptunps..........................13 C. French Atomic Energy Commission Tests - Cadarache and Electricite de?rance (EdF.. 14 1. General Background Information....................14 2. Specific Results.5.................* 15 D. NASA Program and Results....................16 1. General Background Jnformation...........................16 2. Specific Results Obtained........................ 17 a. Water Tump 2c vitation Stu(dy...................... 1

-i-aTable of Contents (cont.) b, Cavitation Damn age Studies*...........................17 c. Cavitation Performance Comparisons with Differellt Fluids.* 1 &~~~~~~~~~~~~~~.................*...l I.11 Conclusions................ 1 9l A. Cavitation Inception in Water and Alkali Liquid Metals in iIfdentical Comp.onents................................ 1 9 B. Non-Cavitating Performance Comparisons between Water and Alkali Liquid Metals.................. 19 C. Detailed Cavitation Inception Comparisons between Wlater and Alkali Liquid Metals..............................1') D. Cavitation-Pree Operation.................................. 20 E. Cavitation Damage........................,.,. 21 References........................................... Tables.........................................................25 Figures.......2,

-iiList of Tables 1. Comparison Centrifugal Pump Cavitation inception Test Results (13), ORNL Tests. 2. Suction Specific Speeds for ORNL Tests. 3. Pumnp Operating Conditions - c(NL,' Tests (12). List of FiM..:res 1. Water and Potassinnm Tlurbopump Performance Compared - CArTEL Tests.('I 2. Schematic of Venturi Tube - EdF Tests (!K,1G6) 3. Water Cavitation Inception Tests - EdFi' (j17) 4. Sodium Cavitation inception Tests - EdFl(4-'j1) 5. Cavitation Sigma vs. LReynolds I`tmiber in Vcnturi for Water and Sodiiu (EdF and U-M Tests ) (341,9) 6. -lypothetical Cverall Depeliderice of -Inception Sigma n.,d Erosion Rate on Relative Air Content (4-323)

Abstract The presently existing and available world data on cavitation perform:aice an,! damage in alkali licluid metals, particularly as i.t pertains to cases where water tests of the same or identical components are avail. able, has been surveyed. Jt is generally concluded that there exists no difference in cavitating (or non-cavitating) performance between water and alkali liquid metals of such components as pumps or venturis observed within the various pertinent experimental inaccuracies. Hence, for most engineering purposes, ordinary water tests may be taken as an approximate indication of sodiul results. MIore precise results will require tests wherein the gas content of both fluids, including the size and population spectra of entrained nuclei, has been measured. However, within the usual engineering range of interest (moderate gas contents) gas content is niparently not of over-riding importance. Long-term operation of liquid metal powerplant pumps within or near the cavitating range is impractical from the viewpoint of damage. However, design of complex truly cavitation-free licquid metal components is not within the 1)resent state-of-the-art without a sol)histicated research program involving visualization and aimed at a p-irticular com-ponent.

-1I. Introduction As recently discussed by the author (1), for the design and specification of complex fluid handling machinery such as centrifugal pumps, e.g., in cases where cavitation is limiting, it may actually be necessary for optimum results, to test the prototype machine under prototype conditions. However, in many cases such as those involving either very large machines or machines handling difficult fluids (such as sodium), this may not be feasible. Both the above conditions may be present to some extent in the case of the coolant pumps for large sodium-cooled reactors. It is quite possible that the pump manufacturer may not be able to fully test the full-scale unit in his own laboratory even in water, and certainly not (at least in most cases) in sodium. Hence it is necessary to know reliably the relationship between cavitation performance of the unit in question in ordinary water and in sodium (or other alkali liquid metals, assuming thiat there is little important difference between these different coolant liquids). While only relatively limited pertinent information is yet available, that which exists, and is pertinent to centrifugal pumps, will be surveyed in this report. Conclusions pertinent to the presentstate of knowledge and recommended future research will then be drawn. At thepresent, there are three sources of information, jPertinent particularly to centrifugal (or axial and mixed-flow) pumps, which will be discussed. These are the studies made by the following groups: 1. Pratt and Whitney Aircraft - CANEL 2. Oak Ridge National Laboratory 4. N1ASA 3. French /iEC II. Pertinent Applications and Data A. Pratt and Whitney Aircraft - CANEL

-21. General Background Information (1-8) The program at Pratt and Whitney Aircraft's Connecticut Advanced Nuclear Engineering Laboratory (CANEL), primarily in the early 1960(s), was aimed at the development of alkali liquid metal turbopumps primarily for use in the SNAP-50 program. Fluids to be pumped were sodium, potassium, NaK, and lithium. Since this program was oriented toward the development of space hardware, minimization of volume and weight of machinery was of predominant importance. Thus, turbopum speeds were to be maximized and suppression pressures minimized. For these reasons, pump cavitation became a limiting parameter. Since long machinery life was also a requisite (one year of unattended operation for example), cavitation damage could not be tolerated, as opposed, e.g., to rocket turbopumps, where life requirements are sufficiently short that cavitation damage is not a major problem. Thus, the CANEL SNAP-50 requirements are rather similar to those of the present fast reactor coolant pumps in that both cavitation damage and performance effects are important. These applications differ in that space and weight minimization for the SNAP-50 pumps are relatively very important, so that a more aggressive design philosophy with respect to cavitation is required for these pumps. Hence, one of the major gols of the CANEL work (and also that of NASA, to be discussed later) was to determine how much cavitation was tolerable in light of the particular life requirements. The CANEL program involved complete and comprehensive testing of the same pump impellers in both water and liquid metals, eventually including some cavitation damage testing of one of the same impellers in potassium. I assume at this point that there is no difference in kind between the various alkali liquid metals with re

-3spect to cavitation performance, so that sodium, potassium or NaK tests when compared directly with water, are equally valid for the present purpose. The pumps involved are of the mixed-flow type (part radial and part axial) with specific speed of about 8200, and are designed for maximum cavitation performance, with inlet sections something like the conventional "cavitating inducers" used in rocket turbopumps. They are "unshrouded", i.e. the outer tips of the blades run with close clearance to the casing, thius providing a small leakage flow between casing and blade tips, where the first evidence of cavitation is often found. Nevertheless, this type of pump (unshrouded) has been found to be more resistant to cavitation than the conventional shrouded design (3), perhaps because of the reduced degree of restraint applied to the fluid. One difficulty with the unshrouded design, for the study of cavitation performance in different conditions, is the fact that performance depends closely on the value of tip clearance. This parameter proved difficult to maintain when comparing pump performance in water and liquid metal tests. These CANEL impellers perform excellently with regard to cavitation, being operable at suction specifi c speed (S-value)"' 20,000. This compares with S of perhaps 7000 maximum for conventional reactor coolant pumps. The CANEL program included first the very careful testing of a group of quite similar'pen-shrouded impellers of the type described above in a water tunnel constructed for the purposeswherein water could be deaerated to somn extent and total air content measured. The pump casings were of plexiglass so that high-speed pictures of the flow could be taken, and the first appearance of cavitation accurately measured. In addition *S=6700 and 5200, e.g., for primary and secondary sodium pumps for the British 250 NWE Prototype Fast Reactor (18). Hydraulic Institute recommends S -8140 for cavitation-free performance (15), e.g.

-4acoustic measurements were made to correlate cavitation noise with other observable flow parameters, and the location of later cavitation damage was determined by using an acrylic coating easily removed by the beginni of cavitation attack. Once the impellers had been so "calibrated" in the water tunnel it wa planned that they would be operated in high-temperature liquid metal, ar their full cavitation performance obtained. Later, long duration cavitat damage tests would be made at selected S-values, to determine how much cavitation could be tolerated in the SYAP-50 system. Actually this rathe ambitious program was never completed due to curtailment of the entire CANEL operation. However, one of the impellers which had been very carefully tested in water was calibrated in high-temperature potassium for cavitation performance, and then was operated under cavitating conditior (S=20,000) for 350 hours, after which some head fall-off occurred and vibrations increased markedly so that the test was terminated. Tt was then found that considerable cavitation damage occurred under this condi tion. The direct comparison of cavitation in water and potassium is unfortt nately weakened by the fact that the piping leading up to the impeller i the potassium and water loops was not identical, and also that the blade tip leakage flow may not have been properly modeled. This clearance was quite pressure-sensitive in the water-loop because of the deflection of the plexiglass housing under pressure. Also it was temperature-sensitivc in the high-temperature potassium loop, but not appreciably pressuresensitive since the casing there is of stainless steel. 2. Actual Tests and Results (1-8) a. Cavitation Performance in Water and HtJih-Temoeratulre Potassi Fig. 1 shows the comparative cavitation performance curves obtained for the same open-shrouded impeller tested in partially deaerated cold

-5water and in potassium at 141000F. For the liquid metal test only "constant throttle" operation for the driving gas-turbine was feasible, so for comparative purposes a similar test was run for water. This is not precisely the conventional constant flow test, but the flow variation is relatively small. A comparison between results for the constant flow and constant throttle test for water is shown in Fig. 1. From the present viewpoint of comparing cavitation performance in water and alkali liquid metals, the most important result of this test must be that the 3f drop-off point from maximum head (usually defined as the "cavitation inception point" in commercial pump tests) for potassium occurs at an NPSH ("net positive suction head" (Pi -P)/2/2g ) which is approximately twice that required for water, i.e., from this particular test it appears that potassium cavitates much more readily than water in the same pump impeller,indicating that tests in water are not "conservative." This trend is also verified if the start of head falloff from the maximum head is called the cavitation inception point. This is in fact an alternative method for defining the inception of cavitation. Inspection of Fig. 1 indicates that in this case the ratio between inception NPSH for potassium and water would be about 60/35 = 1.7. However, as will be developed later, this result disagrees with other pertinent information, and in fact there seems to be no theoretical reason to believ ethat the trend it indicates is valid. There are other interesting features indicated in Fig. 1. For example, the water and potassium curves are not similar, probably indicating that there exist some significant difference in the test geometry. According to the authors (1,2), this is inevitable in that the arrangement of inlet and discharge piping in the water and liquid metal loops is not identical. The differences are also partly the result of differences ir the blade tip to casing clearance between the water and liquid metal

-6tests. In the water tests this clearance, which is very important in determining pump head, increases significantly with pressure, i.e., NPSH, due to the significant deformation of the plexiglass casing because of the relatively small elastic modulus of plexiglass. On the other hand, in the potassium test, the tip-casing clearance is significantly temperature-dependent, and is thus not precisely know~n, since it is impossible to measure at operating temperature. For these reasons the observed difference in FPI>SII between water and potassium may not be meaningful. b. Detailed Cavitation Performance in Water (1-8) The CANEL water cavitation studies, using the same impellers for which the potassium test was made, are among the most detailed and comprehensive presently existing,.and in themselves shed important light on the problem of designing "cavitation-free" sodium coolant pumps. The CANEL tests used transparent pump casings (only useful with the unshrouc type of impellers used) so that high-speed photogra!phy could be used to observe carefully the first appearance of vapor, i.e., the initial onset of "cavitation", long before it affects measurably pump head or floi Whether or not such "micro-cavitation" is damaging is another presently unresolved question, but it is certain (19,e.g.) that it will provide a characteristic bubble-collapse noise signal, no doubt making difficult the acoustic determination of boiling nucleation. In the CANTEL tests it was found (5) that micro-cavitation appeared at an NPSH about 8 x that corresponding to the conventional Y:PSHT inception point as defined by a 3' pump head fall-off. Similar results (multiplying factor oftv3.5) were found in the N-ASA tests (9). Tn my opinion, these results are probably typical of most pumps, so that today, in my opinion <and that of others (18,e.g.), it is probably beyond tI

-7state of the art to design a true "cavitation-free" pump for a given application (without considerable research) which is not prohibitively conservative otherwise, i.e., the S-value would have to be extremely low (perhaps order of 3000-4000 for a typical case). This would require a costly, large and bulky unit, operating at low speed with high inlet pressures. co Cavitation Dama.e Tests (1-3,7-8) As previously indicated, one of the primary objectives of the CAVEL experiments was to determine the maximum degree of cavitation which could be tolerated consistent with the SNAP-50 objectives, i.e., the maximum S-value for these impellers suitable for long-term operation in high-temperature liquid metal. Also as previously indicated, the impellers were first "calibrated" in water to determine a degree of cavitation which appeared feasible for long-term operation, at least from the viewpoint of noise, vibration,.and lhead (or efficiency) fall-off. HTn addition, an acrylic coating was used in the water tests to determine the location of probable cavitation attack anld obtain at least some idea of its intensity. As a result of these water tests it was decided that an NPSH corresponding to S=20,000 was likely to be successful from all the above viewpoints. The 14000F potassium test was hence performed under this condition. However, during the first 350 hours of operation a significant pump flow and head fall-off occurred. During the first 250 hours operation was entirely normal. At 350 hours a sudden jump in vibration level caused the test to be terminated at that point. Upon disassembly (1) it was determined that the ca.use of the vibration was rubbing between the impeller and casing. Fo cause fo this could be assigned. Cavitation damage was fairly general over te blade surfaces, reaching a maximum depth of about 0.050 in. Full details on the form and distribution of damrnage are given in ref. 1. The inmpeller was of

cast type 316 stainless steel. I't was a general conclusion from this danmage test that a long-term o]erating condition corresponding to an S-value of 20,000 is too optimistic for this type of coolant pump (1). B. Oak!idge National Laboratory 1. General Background 1informa tion The program at the ()Oak Ridge Na-tional Laboratory ((.1'RL) wras motivatec at first by the (since abandonned) nuclear aircraft project in the 1550( In fact a. small reactor (10,11 ) of 2.5. Mgrst, the Aircraft Reactor Experiment (ARE), was actually constructed at Oak Ridge and operated in the late 1950(s). This was a "molten-salt" cooled reactor, wherein the primary molten salt (11,12) coolant exchanges heat with a helium heat-dump loop. Also, the reflector is sodium-cooled, also heat-exchanging with a helium heat-dump loop. The ORNL pump group program was then aimed primarily at the development of pumps for both alkali liquid metals (Na, NaK, and K) and molten salts. (;nce the aircraft nuclear project was curtailed during the 1950(s), the same work may have been partially motivated by the SNAP-50 system development (which also motivated the CAYNEL work already described). Eventually a molten salt reactor project for possible central station reactors was commenced (during 19'60(s)) and hlas resulted in the construction and continued operation of the Molten Salt Reactor (MSR) at ORNLo The MSR has thus profitted from the initial and continued pump work at ORNL i volving molten salt pumps. As in most pump development rojects, particularly those utilizing fluids for which great amounts of previous experience are not available, one of the primary problems to be researched is that of cavitation. The work at Oak Ridge involves the following pertinent items: 1 ) Direct comparison of cavitation IPSH for the same pump operated in water and also in NaK (13). *Density - 3.25 g/cc; i.e., zvll x sodium density. Salt is NaF -ZrF4- U4 (50 - 46 - 4 mol,).

2) Long-term operation of centrifugal pumps under cavitating conditions in molten salt and in sodiumn (12,14). 3) Venturi cavitation tests with sodium (15), blot no direct comparison to water. 4) Cavitation tests with E]'M pumps in potassium with argon cover gas and simple potassium vapor pressurization, noting differences in cavitation inception due presumably to entrained gas (16,17). 2. Actual Tests and Results a. Comparison of Cavitation NPSH - Water and NlaK (13) The cavitation tests at ORNl differ from those at CANEL in that the pumps are more or less purely centrifugal pumps of conventional (shrouded) design, rather than the axial-mixed-flow units tested at CANMEL. Mechanically, the ORNL pumps are vertical sump-type uni.ts with shaft overhung from relatively conventional bearings. A gas space separates the liquid metal from a mechanical shaft seal.* The specific speed of the pumps is of the order of 1000 (vs..v 8,000 for the CANEL pumps), and the suction speed the order of 2000-300C(vs.'20,000 for the CAN7ECL pumps), i.e., they are relatively very poor pumps from the viewpoint of cavitation suppression, but are probably closer to commercial design in this regard th,.an are the CANIEL designs. For the specific comparison of cavitation inception performance between water (150-2000F) and NaK (14950F), a pump of specific speed,:s= 955 with impeller of 10 inch diameter running at 3150 RPM, 290 foot head and 450 GPM was used. The cavitation inception N'PStI was defined as that NPSH below which a continuous drop in pump head is produced. This point was found graphically as the intersection of lines tangent to the generally horizontal portion of the NPSH vs. head curve to that tangent to the generally vertical portion of this curve. Typical.PSHI values in *A dynamic shaft seal ("vortex seal") was used in the CAI:JDL SIAP-50 pump]s since their operations specified conditions included negative "g".

-1 0these tests are the order of 20-35 ft. The cover gas for the water test was air, and heliumn for the tests in NaK. Five tests were made for both water and NaK, respectively, in the sat loop with the same instrumentation. The effect of pump speed over the range 2600-3400 rpm was explored. Correcting for the differences in vapor pressure for th2 different fluids, it was found that there was le: than a 6% difference between the NPStI values required for the two fluid: in each pair of tests. However, as in the previously discussed CANEL tests, the required NPSH for NaK was greater (on the average, though noalways) than that for water. However, the difference was so small as to be considered negligible (and perhaps within experimental error) in my opinion (_-1 ft. in general). According to the author (13) there was in fact a possible error in the potassium ~PSII values of about 1 ft. due t( lack of precision in control of the temperature. The detailed results are summarized in Table 1(reproduced from the original paper - (13)). Table 2 shows the suction specific speed values from these tests, indicating in general that it is not constant, but increases markedly with pump speed (-20of) for a speed change of -30%. Such an increase of S with rN is quite common for pumps of this specific speed range (20, e.g. but there is some indication that S will maximize and then reduce with further increase of T; (21, e.g.). Similar results have been observed for venturis, e.g. (23,24). This result is simply one of the numerous fairly major departures from the "classical" laws of cavitation scaling, descri bed in the literature as "cavitation scale effects," and largely of unresolved origin and unpredictable magnitude, thus adding only to the general uncertainties concerned with cavitation tests (22,23,24,e.g.). While it is fairly well verified from all the tests here described, as well as other miscellaneous sources (25,e.g.) that the non-cavitating

-11liquid metal performance of a given alkali metal pump can be predicted accurately by water tests, the indications regarding cavitating perform;ance are only those herein discussed. In summary, from the ORCIL centrifugal pump cavitation inception comparison between water and balK, it can be concluded that the inception NPSH (or S) is virtually identical between the two fluids (within about 6% for NPSH or about 4.57!, for S), with the water test being "non-conservative." However, the experimental error is at least of the same order as the observed difference. b. Cavitation Damage Tests (12,14) Long-term cavitation damage tests were conducted at (ARYL (12,14) with molten salt and sodium, using centrifugal pumps of somewhat different type for the two fluids (N s=1900 for sodium and 4300 for molten salt and the head rise for sodium is 132 ft. and 40 ft. for molten salt). One test (2575 hours) was run with sodium at 1400~F at the 3!') drop-off point, in this case corresponding to S=3200, i.e., the pump is not well-designed for cavitation resistance. Two tests were run in pumps of somewhat different design in molten salt: the first for 3550 hours, again at the 3Y drop-off point, but in this case S=9300. The second was for 25,000 hours but at an NPSII about 1.5 x that for the 3?%;o drop-off point, corresponding to S=7000 in this case. The temperature for the sodium test was varied in 516 continuous there-o7f cycles over the range 1050-1250 F throughout the test, whereas for molten salt the temperature was held at 1200~F throughout, for the longer test. The temperature was varied over the range 1100-14000F in 652 thermal cycles for the shorter of the molten salt tests. The material from which the pumps are constructed in all cases is ]nconel, and the nlolten salt is of the same components previously described. Table 3 directly reproduced from ref. 12 gives full details of the tests.

-12Considerable cavitation danmage occurred in,1ll cases, thu s being con sistent with the previously described CANEL tests to the extent that operation of liquid metal ptumps well within the cavitating region (3< drop-off, e.g.) is generally not feasible from the viewpoint of damage. In the ORNL tests (as opposed to those at CANEL) there was no measurabl performance deterioration due to cavitation damage. However, in all the ORNL tests pits of depth greater than v in. were found. Thus damage was relatively very substantial, since the impeller diameters were of the order of 6 in. Considering the low S-values involved, these pumps are certainly not optimum from the viewpoint of cavitation design, and this fact may be partly responsible for the rapid accumulation of cavitation damage. An interesting point concerning the 25,000 hour test, which was performed at an NPSH-value 1.5 x that corresponding to the conventionally defined (3% drop-off point) cavitation inception point, was that even fthis "non-cavitating" point, substantial damage is accrued in a long-te: test, i.e., continuous operation for about a 3-year period. Presumably, this operating condition, as well as those of the shorter tests, would then be prohibitive for sodinum-cooled or molten salt reactor powerplant: c. Venturi Sodium Cavitation Tests (15) Part of the effort of the ORVL pump group consisted of cavitation te, in sodium in a venturi with 70 diffuser cone-angle (15). Unfortunately, there was no direct comparison made with water in the same facility. Ho% ever, the cavitation performance of the venturi was roughly as expected, in that cavitation was found at the venturi throat at a pressure _1.4 pE above vapor pressure, thus pobably indicating al ample supply of en*Another possible partial explanation may be that the minimum pressure was not measured, and that the friction drop downstream of the pressure tap may not have been properly included. However, this is estimated at only about x- psi.

-13trained gas. I'o mecasiurement of entraije(d gas wns made and of course that capability is still undeveloped. Jt is presumed that the gas originated from the centrifugal stunp-type pump with argon (and sometimes helium) blanket, which was used to drive the loop. It is mentioned that there is also a large sodium-gas interface in one of the loop tanks. Although it was investigated, no change in cavitation sigma was found dlue to changing from argon to helium as pressurizing gas. This observation is at variance with those made by a. French AEC group (Cadarache) working with cavitating orifices and nozzles with helium and argon as pressuri.zir. g gas. This work (26,27) will be described later. No indication of actual sodium conditions such as velocity, pressure, or Reynolds' nlunber are given. The venturi throat diameter is v1 in.T=1215-1475 F. d. Cavitation Tests with Potassium in U]lectromagnetic(EI,) umps (16,17) Cavitation tests were made onl 3 electromagnetic (EM4) pumps in potassium 0 at temperature ranging from &,00-1300 F. The pumps were of different types. Argon pressurizrtion was used and cavitation results compared with another system where pressurization was provided by potassium vapor alone, heated to attain the desired vp,-or pressure in a tank included for this purpose and connected to the loop through a small-bore tube. Thus, in the argons.. pressurized tests, at least a small supply of entrained gas nuclei waS available, whereas these were apparently nearly absent in the vaporpressurized tests. These tests are of interest in the present context in showing the dependence of cavitation inception sigma upon entrained gas nuclei content. The result of these tests is that cavitattion could not be attained at all in the vapor-pressurized runs (within the capabilities of the equipment), and in fact negative NPSII-values up to -7 psi were found (with no cavitation). For the argon-pressurized tests, on the other *tS~S do te French AEC tests described later (26,27).

-1!hand, the:PSH for cavitation inception was up to +~3 psi. For directly comparable tests, the differenlce (due presumably only to the method of pressurization) is -K ft. -It is inot possible to compute sigma, since no inlet velocity is given. However, the total pump head rise is high, "750 ft. The significance of these tests from the present viewpoint is the demonstration of the potential major importance of entrained nuclei content in the liquid metal fluids. C. French Atomic Ener9_Y Commission Tests - Cadarache (2_ _) and EleCtricit'e de France EdF 26,27) 1. General Background Information A program has existed in France over the past several years to invesi igate cavitation in sodium, motivated by their fast reactor program. OnE facet of their sodium work has been to evaluate the applicability of water cavitation inception data to sodium. In this connection both water and sodium (26,27) cavitation tests were made in a venturi which was identical in flowpath to one used by our own laboratory for cavitation studies. No significant difference i.n inception sigma between the fluids was found, although there was fairly considerable data scatter (as is common with cavitation inception tests) as well as strong dependence on velocity (or Reynolds' number),amounting, however, in total to a varia.ti in NPSH of only %6 ft. Hence, perhaps this difference is negligible from the engineering viewpoint. The water data obtained in the French venturi tests wan consistent with that obtained with water in cur own tests on the similar unit. These tests are summarized in Fig. 2-5 (reproduced directly from ref. 26,27), Tile experimental results and the venturJ flow-path are shown. To try to resolve tile somewhat inconclusive results of the above tests and to obtain additional pertinent data, a further test program has been undertaken by the French Atomic Erlergy Commission in their laboratory at Cadarache. So far they have measured cavitation sigma in

-15orifices and converging nozzles (28). It is planned eventually to cavitation-test these sanme components in water, and perhaps extend the program to others, but comparative results are not available as yet. The sodium results (28) alone, however, are of interest in showing (as did the EM pump tests at ORNL) the importance of gas nuclei content in substantially affecting the cavitation inception sigma.'This leads them to conclude: (as translated) "This is why it seems important to rapidly start a pro-.ram to develop an apparatus to measure...(gas nuclei)..." J fully agree that this is in fact the key issue needing resolution before further substantial progress in the prediction of cav:it- ton in]ception in sodium can be made. There is such an active program at Cadarache now. 2, Specific Results The Electricite de France - University of Michigan venturi tests in water and sodium are reported in detail in our previous report (26), and the results repeated here for convenience, Fig. 2-5. The major result is that inception sigma for water and sodium lay within the same scatter band of data, which, even considering the substantial effects of velocity or Iheynolds'number, is still small enough to be considered negligible from an engineering viewpoint. Since entrained gas nuclei spectra were not measured for either water er sodium (for which no practical i.nstrulment is yet available), no further light can be shed on the subject from these tests. However, the additional tests conducted by Cadarache do further emphasize the substantial importance of Rknowing these gas nuclei spectra (size and population density). In the Cadarache tests in sodium on orifices arnd nozzles (28), it was found that sigma for ince:tion (defined as fir,:t intermi-ttent cavitation noise), as well as sigma corresponding to cavitation characterized by the first steady noise depended significantly on whether argon or helium were the pressurizing.gats used in the expansion tank to control the overall

_16loop pressure level. Gas was entrained in the sodium from this source rather than from the driving rpump, since it wns a freeze-soeal unit iather than the sumll-type pulmp often used in such loops. Test results show that incepltion sigma is greater by about 0.3 for both orifices and nozzles when argon is the cover gtas than in cases when this is helium. This difference amounts to an NPiSH difference of about 6 ft. (2 psi), which is about the magnitude of overall scatter of the results in the previously discussed EdF tests. From an engineering viewpoint, the differenices may often well be negligible in both cases. In addition, it was found that inception sigma was modified by the pressure level in the expansion tank for a given flow rate. The vari ati in sigma in this case was about 0.1 for argon. The same phenomenon was noted for helium. Finally, the slope of the sigma vs. Reynolds' number curves appears to be somewhat steeper with helium than with argon. The larger sigma for argon as compared with helium appears to imply a greater quantity of entrained gas in the sodium when argon is the cover gas. These results may be related to different solubilities of t1: two gases in sodium, but they are generally unexplained at this point. Their imp)ortance in tile present context is thle definite demonstration that entrained gas effects are of major importance in determining cavit ation sigma, so that it appears impossible to make further significant progress in this field without the development of a technique for measuring entrained microbubble spectra in sodiumn. This is also the statec opinion of the authors of the Cadar.che report (2g8). D. 1X'ASA Pro gram and Results (9,29'-32) 1. General Background Informatinn A substantial program of liclluid-metal turbolpumpn development exi.sted primarily during the 1950(s) at the Lewis Research Laboratory of AS in support of the SNAP programns, particularly SNAP-50. The NASA progr rr was rather simnilar to that at CA1:EL, already discussed, and involved

-17especially work with the alkali liquid metals. Pests inl both wrater arlld liquid metals were included. The studies incl -ded cavitation performnrce effects as well as damage, and involved primarily axial-mixed-flow prunmes of high specific speed, somewhat like those tested at CANEL. 2. Specific Results O.btained a. Water.1[mu) Cavittion Stdy () Unshrouded impellers solnewhat similar to those used at CAT'tL in transparent housings were studied photographically under cavitating conditions. As in the CANEL work, it was found that cavitation first developed from the tip-clearance flow. tIn the NASA tests "micro-cavitation" of this type developed at NTPSII about 3.5 x tha1 1 corresponding to the 3%1 drop-off point (vs. about x8 in the CANEL tests). The appearance of the first photographically visible cavitation occurred at S=6650 vs. S'1'5,000 for the 3:, drop-off point. Hence, it is again emphasized tha.t the development of a truly "cavitation-free" piunmp is beyond the present state-of-the-art without a fairly extensive development program. b. Cavitation Damge Studies (29-31) Quite comprehensive cavitation damage studies in sodJumn at various temleratures and with various materials have been condclcted by the 1.ASALewis group (2("-32). A special unshrouded axial-mixed-flow impeller was constructed with removable blades for this study. Tests were run on materials such as Rene-41 (a nick]el-chromium-based superalloy), and 316 and 318 type stainless steels (2pi). ()f these materials, 316 SS was the least resistant to cavitation damage, and Rene-41 the most. Tests were conducted at 1000 F:-.nd 1500 F. it was found that the rate of damage was virtually independent of temperature over this range. Thus, these tests do not agree with vibratory damage tests in this regard. There, thereis a very great fall-off of damage for 15000F sodium vs. 10000F (22,33,e.g.) presunmably due to the "cavitation thermodynamic effects" as they are termed in the

-1 8literature. Of course this "built-in" fluid effect is countered to some extent by the reduced strength of the materials as temperature is increased, particularly in a high-temperature range such as 1000-1500 F. in the vibratory tests (33,e.g. ) the fluid "thermodynamic effect" great outweighed the material weakenling effect. IHowever, this was apparently not the case for the NASA tests (2>9-31 ). This "paradox" merely emphasiz the difficulty of transferring cavitati<cn test results from test model prototype, etc, which exists ill many chases. The NASA cavitation tests were generally of 200-300 hours duration, and considerable damage was produced on all the materials. Trn at least one case (2'S) the test duratioin for which siJgnificant damage was produc was only 32 hours. Jit was determined (as expected) that the rate of dam age increases very rapidly with pump speed for tests at constant S (25') Hence, suction s)pecific speed alone cannot be used as a predictor for damage. It was also found (2C9) that the NfiSH1 corresponding to a given point on the cavitation curve (the 3' fall-off point, e.g. ), was much 1 at 1500 F than at 1')000F (13 ft. in one case), due primarily also to "tllermodynamic effecats." Thi-ls, for this case, an NYPSH decrease of about 15%, occurs at higher temperature, corresponding to an increase in S of about 1 1 o. in summary, the NASA ciamage tests appear to prove, as did those at CARNEL and at ORNI, -hat operation ~withlin or near the cavitating region i not practical for liquid-metal pTowerplant nrumps. c. Cavitation Performance Comparisons with Different Fluids Cver the past decade or so there has beern a continuous program at NASA-Lewis (partially in conjunction with NfS, Boulder, Colo.) to study cavitation inception in various fluids, using a venturi-type geometry for tihe studies (32,e.g.). Comparisons between water and cryogenics have been emphasized rather than licuid metals, btut in so far as basic theor,

-1 9ical models are evolved (as they have been to some extent), this work is also applicable to liquid mnet.-ls. 1]]. Conclusions The major conclusions whicll can be drawn frozm the present study follow. A. Cavitation ncel ti ion ii Water and Alklcali Li uid.,etals in -denticl Comp o.nents Available evidence, where direct comparisons between water and alkali liquid metal cavitation tests exist, show in general that there is no major difference in inceptioni sigma for pumps of venturis (the only components for which there is experimenta::. evidence) between water and any of the alkali liquid metals. ]t is also reasonable to assume thlat there is no significant difference in this regard between sodium and the other alkali liquid metals. The above statements are confirmed by tests at 0]TrNL and Electricite de France (coordinated with University, of Michigrn tests). Tests at Pratt and Whitney Aircraft (CANhEL) disagree in showing that the NPSH required for a potassiumn pvump may be twice that for the -::ame pump in water. However, there are special reasons pertinent only to this work and explained in detail in this report, which lead to the conclusion that this result is invalid. Furthermore, there is no theoretical reason to believe that N'a, aK, or K should cavitsate more easily than water. Theoretical reasoning leads, in fact, to the opposite conclusion. D..Non-Cavitating Performnance Comparisons between Water and Alka]li Liouid Mietals Non-cavitating performance of alkali liquid metal pumps and other flow components can be accurately enough predicted by water tests, applying the conventional scaling law-s. C. Detailed Cavi.tationn Incepttion Compnarisons between!rater and Alkali Liquid Metals Detailed differences betwreen cavitation performance with water ~rnd alkali liquid metals, pointed out in all the tests here reviewed, can

-20only be further s'esolved if complete gas content measurements are made in all the fluids involved, i.e., size and population density spectra c entrained gas "microbubbles" must be measured as well as total (or dissolved) gas. Though there exist in general no relatively available inst inents for this pulrpose for any fluid, such measurements are being made routi.lely now in various laboratories (including our own) for wa ter, ar apparently feasible technitques exist for liquid metals. The best approre for sodiwn at present to obtain such spectra is through the use of an ultrasonic absorption or scattering technique using high-temperatlure tranisducers of a type already developed at ANL, and already used j..i 12C sodium. Within practical engineering limits, applicable at least in most cas but not always if good precisi n is required as it might sometimes be, the effect of gas content (judging from a vast amount of water data (24 e.g.)) appears to be small within a moderate range of gas contents (not very high or very low),applying to most actual lara;e scale machines. These results for both cavitation inception sigma and for cavitation damage are summarized in Fig. 6-a,b (reproduced for convenience from re 24). The results so far available for alkali liquid metals seem to indi that the same genieral situation applies, at least for cavitation as it affects component pTerformance, but probably not such phenonmena as.oisc or boiling superheat. D. Cavitation-Free 0perntion it is sometimes desired that completely cavitation-free operation be specified for sodium reactor components. However, the design of comrple:. fluid-flow components which are truly "cavitation-free," i.e., no bubbles capable of producing noise or damage exist, is probably not withirn the present stat —of-the-art without sophisticated research nrograms, involving model tests cand flow visualization, aimed at that particular

-21 - component. This is the case at present for ally licui. includirg water and all liquid metals. These statements are based on the NASA and CANqEL work. E. Cavitation Damage It is in general impractical to operate liquid metal pumps over long periods in or near the conventional cavitation zone due to the rapid a-ccumulation of dmnage. This has been observed in various cases for tests as short as 100-500 hours.

-22References 1. R.S. Kulp and J.V. Alteri, "Cavitation Damage of Mechanical Pump Impeller Operating in Liquid Metal Space Power Loops, " NASA Cr-165, July 1965. (Pratt and Whitney Aircraft - CANEL contractor report) 2. G. M. Wood, personal communication, Pratt and Whitney Aircraft, East Hartford, Conn., Dec. 1973. 3. G. M. Wood, W. G. Whippen, "Cavitation Effects in Turbomachinery, " Cavitation State of Knowledge, ASME, edit. J. M. Robertson and G. F. Wislicenus, 1969, p. 148-165. 4. G. M. Wood, J. S. Murphy, J. Farquhar, "An Experimental Study of Cavitatio in Mixed Flow Pump Impeller, " Trans. ASME, J. Basic Engr., 82, 1960, p. 929-940. 5. G. M. Wood, "Visual Cavitation Studies of Mixed Flow Pump Impellers, " Trar ASME, J. Basic Engr., 85, 1, 1963, p. 17-28. 6. G.M. Wood, H. Welna, R.P. Lamers, "Tip-Clearance Effects in Centrifugal Pumps," Trans. ASME, J. Basic Engr., Dec. 1965, p. 932-940. 7. R.S. Kulp and J. V. Alteri, "Investigation of Cavitation Damage of a Mechanic Pump Impeller in High Temperature Potassium, " Quart. Prog. Rept. No. 1, NASA CR-54383, 1965. 8. Ibid #7, Prog. Rept. No. 2, NASA CR-54440, 1965. 9. M. J. Hartmann and R. F. Soltis, "Observation of Cavitation in Low Hub-Tip Ratio Axial Flow Pump, " ASME Preprint No. 60-Hyd-14, 1960. 10.W. B. Cottrell, H.E. Hungerford, J.K. Leslie, J.L. Meem, "Operation of the Aircraft Reactor Experiment, " ORNL-1845(Del. ), Oak Ridge National Laboratory, Oak Ridge, Tennessee, Sept. 1955. 11. A.G. Grindell, W. F. Boudreau, H.W. Savage, "Development of Centrifugal Pumps for Operation with Liquid Metals and Molten Salts at 1100-1500 F, " Nucl. Sci. & Engr.,, 1, Jan. 1960, p. 83-91. 12. P. G. Smith, J. H. deVan, A.G. Grindell, "Cavitation Damage to Centrifugal Pumg Impellers during Operation with Liquid Metals and Molten Salt at 10501400 F," Trans. ASME, J. Basic Engr., 85, 1963, p. 329-337. 13.A.G. Grindell, "Correlation of Cavitation Inception Data for Centrifugal Pump Operating in Water and Sodium-Potassium Alloy (Nak)," Trans. ASME, J. Basic Engr., D, 82, 1960, p. 821-828.

-23References (cont. ) 14. J. H. deVan, "Examination of Pump Impellers from Sodium and Fused Salt Pump Endurance Tests, " Internal ORNL Memo of April 10, 1961, (ORNL Central File No. 61-4-77). 15. J. M. Trummel, "Some Observations Made of Cavitating Sodium Flow in Venturi, " Internal ORNL Memo to H. W. Savage, Aug. 31, 1954. 16. W.R. Huntley, H. C. Young, A.G. Grindell, "The Cavitating Characteristics of Two Types of Electromagnetic Pumps in Potassium, " Cavitation Forum, ASME, 1966, p. 15-16. 17. W.R. Huntley, A.G. Grindell, "Performance and Cavitation Characteristics of Two Helical Electromagnetic Induction Pumps Operating with Potassium, " ORNL-TM-1793, Dec. 1967. 18. L.F. Bowler and D. Taylor, "The Sodium Pumps for the PFR," NTuclear Engineering, May 1967, p. 361-366. 19. R.F. Saxe and L.W. Lau, "Cavitation Noise in NYuclear Reactors," Nuclear Engineering and DesigTn, 8, 1968, p. 229-240. 20. F.G. Hammitt, "Observations of Cavitation Scale and Thermodynamic Effects in Stationary and Rotating Components," Trans. AS.ME, J. Basic Engr., D,, March 1963, p. 1-16. 21. W. Jekat, "A New Approach to Reduction of Pump Cavitation - HIubless inducer," and discussion by F.G. Hammitt, Trans. AS?>W;8, J. Basic ~ngr., D, b_9, 1, March 1967, p. 130-139. 22o R.T. InapIp, J.W. Daily, F.G. Hammitt, Cavitation, McGraw-Iill, 1 70. 23. F.G. Hammitt, J.F. Lafferty, D.M. Ericson, M.J. Robinson, "Gas Content, Size, Temperature, Velocity Effects on Cavitation Tnception in a Venturi," ASME P'aper No 67-WA/FE-22, 1 967. 24o E.G. lIammitt, "Effects of Gas Content upon Cavitation inception, Performance and Damage," J. Hydraulic Research T.AJR1, 10, 3, 1972, p. 259-2 90. 25. R.E. Ball, D.E. Cullman, RW. Atz, "Design and Testing of Sodium Pumps for I-allam Nuclear Power Facility," ASME Paper No. 61-SA-39, 1961. 26. F.G. Hammitt, "Cavitation Inception in Venturi in Sodiwun and Water," ORA Rept. LUTDClI 01357-21-ai, Uiiv. Mich., Ann Arbor, lich., Nov. 1973. 27. J. Boniin, R. Bonnafoux, J. C-icquel, "Comparaison des Seuils d' Apparition de la Cavitation dans un Tulbe de Venturi dans 1l'Eau et le Sodium iq1~1ide," EdF Bull. de la Direction des Etudes et Rechrches, Serie A, Ilucleaire, Iyd., Thermi que, No. 1, 1 9,71, p. 5-12.

References (cont. ) 28. J.C. Duquesne and A. Arr'ellier, "Etude Experimentale de la Cavi tat: dans un Ecoulement de Sodium a Travers des Diaphragmes et i!ne Tulye] Note Technique SDER/73/163, Service de Technologie des Reacte~rs a Sodium, Dept. des Reacteurs a Neutrons Rapides, Commissariat a tEne: Atomique, Cadarache, March 9, 1973. 29. W.S. Cunnan and D.C. Rleemsnyder, "Cavitation Damage and the Effect of Fluid Temperature on the Perform(arnce of an Axial-Flow Pump in Liquid Sodium"."ASA TN-D-5484, Oct. 19;9. 30. Reemsnyder, D.C., Cunnan, W.S., Weigel, C., "Performance and Cavit Damage of an ALxial-Flow 1PUmp in 1 5000F Liquid Sodium," NASA TrN D5138, 1969. 31. Cunnan, W.S., Kovichl, G., Reernsnyder, D.C., "Effect of a Fluid Ter. erature on the Cavitation Performance of a High HIub-Tip Ratio Axia Flow Pump in Water to 250 F," NASA TN D-5318, 1969. 32. Ruggeri, R.S., Moore, R.D., "Method for Prediction of Itmnp Cavitat Performance for Various Liquids, Liquid Temperatures, and Rotative Speeds," NASA TN D-5292, 1969. 33. R. Garcia, F.G. Hammitt, "Cavitation Damage and Correlations with Material and Fluid Properties," Trans. ASME, J. Basic Engr., D, 4, Dec. 1967, p. 753-763.

_25TABLE 1 Comrnrison Centrifu gal Pumprn Cavitation Incetion Test Results (.INL (13) Water Teats Sodium-Potassium Teats Eatimated Alloy Teat.Nv av T HI. 11v Nay Qav T H Hci Hci Difference (rpm) (gpm) (OF) (ft ab) (ft(rpm) (gpm (F) (ft aba) (ft aba) (ft) (~) Run I 3375 306 168 45. 2 Z1.3 Run 1 3390 308 1490 40.5 64.3 63.3 +1.0 +1.6 Run 2 3374 436 138 39.3 6. 4 Run 2 3383 435 1501 43.0 76. 1 79.8 -3. 7 -4. 7 Hun 3 3003 306 158 43.Z Zl. 1 Run 3A 3018 310 1502 43. 65.1 68.0 -2.9 -4.3 Run 3B 3030 305 149? 42. 1 64.0 65.5 -1.5 -2.3 Run 3C 3047 30? 1500 42. 7 64.6 65.0.0.4 -0. 6 Run 4 2999 436 138 37.0 6.4 Run 4A 3000 432 1493 41.2 71.6 75.4 -3.6 -4.8 Run 4B 3000 43Z 1503 43.5 74. I 79.0 -4.o -6. Run 4C 2985 435 1503 43.5 74. 1 77.6 -3.5 -4.5 Run 5 2603 304 165 40.2 l21.3 Run 5 2601 30! 1481 1i 5 57 4 59.0 -1.6 -'. 7 4'934

-26TABLE 2 ORL Pumps a Suction Spe.f ic Sneed S N q NPSH S (RPM) GPI Ft. 33}90 308 63.3 2610 3383 435 7'.8 2640 3030 307 66.o 2310 300( 433 7.0 2360 2601 303 5,.0 2130 4935

-27TABLE 3 Pumnp -p eieratim. Conditions OJUNL (12) Sodium Molten Molten pump salt pump salt pump test test I test 2 Test fluid Sodium Molten salt* Molten salt* Temperature, F 1050-1250 1100-1400 1200 Shaft speed, rpm 3550 2700 2700 Pump flow, gpm'440 -645 645 Static suction head, ft abs 61-69 14.1-14.8 21 Total head, ft -132 -40 40 Design specific speed 1900 4300 4300 NPSH, ft abs 60-65 14.1-14.8 21 Average suction specific speed 3200 9300 7000 Impeller relative inlet velocity, ft/see 53.1 37.7 37.7 Test duration, hr 2576 3550 25,000 *NaF-ZrF-JUF4, 50-404 mole %. 4936

-2~ WATER A.~,D POTAS S JyLTM TURBOPUMP CAVITATION PERFORMANCE COMPARED AT CONSTA~NT FLOW AND CONSTANT THROTTLE (Ref. l) (Pratt and Whitney Aircraft -CANEL) ~.......,........o..............................~..........o...........................................................................................................................,....o................................................................ o ~~~~~~~~~ ~ ~ ~ ~ ~..............................................................: ~:::::::::.......... ~~~~~~~~~.............................................................................~~~~~~~~~~~~~~~~~~~...:':.....':'.:: I'...'...'.......''~.'::-:.... ~::~:~~.... ~...~ ~ ~ i'.:::~: ~.:::'.'.'::::.'::::.::'....-:.:. ~.. ~:-'::'.'.:::.::.. -... = = == = = = = = = = == = = = = = =.........:::..... -::..:!...- -: -:......................'......~~~~~~~~....:.......;~.........::........:..................,............:.........::'::::::::::'::::::: —:::::~~~~~~ ~ ~ ~ ~ ~ ~ ~.:~:.'..........'.::: "':....2_...~~~~~~~~ ~...........o::.+?[!..:.:::.!...:..C...................... ~~~~~~~~:;...,;:i.:.:.,'.:: ii..~.......... n,' - - -.:7':' ~..............:...::.:..:"....._::.......................................'.i.....................'.........::::': ============' 240:::................;::..;.,:.,iii.::!:.:.ii.::::[ii::;i::.:............ uJ 18 0 T!TT'TTTT~T'TT'TT'TiTT:::::::::::::::::::::::..............:..::.......~ ~~~~~~~~............. U.......... ~~~~~~J P..................................................................... 1 6 0;:.......................::::::::::::..................................................:........... -:~~~~~~~~~~~.:.....:.:........:.:..:.:....: ~~~~~~~~~~~__,.........:_.......__::.....:_......!..... ~..:... - 3. ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~.

4,, 16 -2'i~~~0Fig. e Schematic of Venturi Tube (Dimensions in mm.) Electicite de France Tests (27) i I0 I__ III _II!I I'__ i- _,__ oat~rebe a \o \ " * -2 --. _ 0,*_ Lai a _. at s w h I _. ~ i aat O r _. Throat Reynolds Number 4917 Filg. 3 Water Cavitation Inception Tests (27) Electricite de France

-30-.0-~~0- - - 4... i.. -,, i f or il- -- 0== _ _ ___X....... ~ 1-+= - _- _ 0_,0T w1 -. I -\I flr I 1 I' I~ ~.(..... z _ o-, 0 _ab-T -60 -a' _____ -0,04 O a 160 - -' r 160C - -o H. OOt C - -o,.. -_ _ " _-_ X 400*C - - - - -,3 4 7 _ _ Throat Revnolds Number 4918 Fig. i Sodium Cavitation Inception Tests Electricite' de France (z)

0.140. lz -33% (Air content by Volum I 0. 10a —- - ~~~~Ithroat 0.08 - - - - Uof M water 0. 06 t E %~ ~~Z I I _I I I I ~~~~~~~~~~~~wate~r tests o' 3. Bo04in Sod (1/4" throat) 80 0. 00.To 0R.0. 04 8 9 ~10 z34 7 8 9 TIhroat Reynolds Number, Re 3499 FIG. S CAVITATION SIGMA VS. REYNOLDS NUMBER IN VENTURI FOR WATER AND SODIUM Electricite de Fr-ance%7) and University oi Michiganft-")

-32(Pc' Pv) c p v /2 Region of Exptl. Data Pc = pression au seuil de cavitation Hypothetical I a, = teneur saturante en gaz Pc a Pressure at Point of a =teneur en gaz Cavltatlon Inception / (P - P)> O as Saturated Gas Content (I atr) a * Actual GasContent, a. Inception Sigma vs. Relative Air Content (hypothetical example). (Pc - P) < 0 a de debut en fonction de la teneur relative /.I 1 vI 1 I en air 0.001 0.01 0.1 1.0 10.0 a/as b. Erosion Rate vs. Relative Air Content 3 - Demonstrated (hypothetical example). a: --— Hypothetical Vitesse d'erosion en fonction de la teneur o Z0 relative en air w Fig. 6. Hypothetical Overall Dependence of Incepz_0 ( _tion Sigma and Erosion Rate on Relative Air Content. >1 a et taux d'6rosion en fonction de la teneur,3! en air (extrapolation des r6sultats d'exp-,___ _ J'"...rience). 0. I 1.0 2.0 3.0 a/as (Ref. 24) 4323 UNIVERSITY OF MICHIGAN L1111111111111111111LI1111]111 111111llllll111 1111 3 an9015 0302 nn7 7118