The unsteady dynamics of cavitating cascades and inducer pumps were studied with a view to understanding (and possibly predicting) the dynamic characteristics of these devices. The chronology of the research is summarized as well as the final conculsions for each task. The construction of a dynamic pump test facility and its use in making experimental measurements of the transfer function is described as well as tests conducted using a scale model of the low pressure liquid oxygen turbopump inducer in the shuttle main engine. Auto-oscillation and unsteady inlet flow characteristics are discussed in addition to blade cavity influence and bubbly cavitation

Acosta, A. J.

Brennen, C. E.

English

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wCALIFORNIA INSTITUTE OF TECHNOLOGY
PASADENA. CALIFORNIA 011215
01VIE1011 OF KNOINKIrRI NG
AND AWPLIKO 6COWNCK IOA•A ♦
FINAL REPORT
ON NAS 8-29313
NATIONAL AERONAUTICS & SPACE ADMINISTRATION
"DYNAMICS OV CAVITATING CASCADES"
by
C.E. Brennen
A.J. Acosta
(NAS A-CR-16 1673) DYNAN.LCS OF CAV,ITATING	 N81-20382
CASCADES Filial 12eport (Cdl inrAia ,Inst. Of
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G3/34 19413
January 1980
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1. Introductlon
This document represents the final report on Contract NAS 8-29313
with the National Aeronautics b Space Adminiatration, George Marshall Space
Flight Center, Huntsville, Alabama. The fundamenzal purpcpe of this contract
was to study the unsteady dynamics of cavitating cascades arad inducer pumps
with a view to understanding (and possibly predicting) the dynamic character-
Istics of these devices. As a result of the present work we believe that
significant advances have indeed been made toward this objective. Some
evidence of this is the .fact that we received the American Society of
Mechanical l tagineers Robert, T. Knapp Award for publication [7) .
The primary results of the work performed are contained in, the
publications :Listed at the end of this report. It would be superfluoua to
repeat all that technical material In this report since we believe that
,01, dwumentfation bas already been achieved. However, it may be of some
vs:luc, to briefly review the chronolo ,y of the research and then summarize
the final, conclusions.
2. Review of Technical 1^ >r^ss
The initial contracts on this project were. entirely concerned
with theoretical, analyses of- the dynamics of c,;avitating, cascades and inducer
pumps. At that time it was widely believed that cavitatinl pumps could be
modelled t ►sing simple L,R,C models Find that progress only required sensible
casid accurate evaluation of the few key unknowns in these models such as
the cavitation compliance. Our first few pub].ications, were directed toward
that end. Types of cay.ittat:ion c ► mirzring in cas(, ades and inducer pet ►r),ps were
identified. Publications [11 and [2a presented quas:istatic analyses and
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7-2,-
results for the compliance resulting from attached blade cavities. Publica-
tion (3) presented analys.as and results for the compliance characteristics
of bubbly cavitation. Publication [4) extended the work of publications
[1) and [2) to consider the truly dynamic rather than quasi-static effecto
for blade cavities. We still regard these efforts as having considerable
merit; however, the results have to be seen in the wider context of pump
dynamiesas revealed In, the later work particularly the experimental research.
The next st,.k^p forward wap the recognition of the need to define
a more general form for the dynamics of a device like a cavitating inducer
pump. The concept of the dynamic transfer, figiction was the result of this
work and was presented in. Publications [6) and [71, For example, these
publications identified the need to evaluate the mass flow galn factor and
presented analyses 
and 
results for the cont--,:ibution.,q to the mass flow gain
factor due to attached blade cavities.
3.	 Measurements of Transifer Functiotis
Simultineotiqly it was recognized that real progress beyond this
point could only be made if complete transfer functions could be measured
experiniou tally. Conseqttently we embarked on an experimental program to
accomplish this. A facility constructed for , the express purpose of study-
iug the. unsteady, dynamic rospon.Be of cavitating inducer pumps was con-
s tructed; it was called the Dynamic Pump lost Facility (D] ITF) . Details of
this facility are primarily found in. publications (81,[9), (111, (16), [17).
(Publication [5] resulted from one of the many In,4truti ►entation difficulties
which had to be?, surmounted.) The facility as originally coastructed utilized
water and as member of 3 in. dialtieter imp0,11el-S. CompliAe dynamic transfer
funo.tions for varioti,4 mcai% show coviditions, (including cavitation nur^bel)
-3-
over a range of frequencies up to ^4Z Itz. were presented in publications
(81, (9) and 11,11.
The evidence of these transfer functions showed that
(i) even in the absence of cavitation the pump impo-lance
departed significantly from its quasi-static value for
reduced frequencies bald on tip speed and Made spacing
above about 0.03. The trends were consistent with these
observed in some early dynamic measurements on centrifugal
pumps made at NASA Lewis.
(ii'* In the presence of even a modest amount of cavitation the
dynamic characteristics became quite complex and none of
the elements of the general transfe r. function could be
regarded as negligible. As a result the simplistic 1,,R,C
models appeared to be inadequate represtmitations of the
dynamic response.
(iii) Evaluation of the determinant of the experimentally mea-
sured transfer functions revealed that the inducer pump
became increasingly "active" dynamic device as the cavita-
tion number was reduced. Consequently, it would be capable
of exciting instabilities in otherwise passive hydraulic
oysteins.
4. 'Bubbly Flow Model-Theoretical Transfer Ftaictions
The identification of the source of this active feature of
cavitation dynatnics and better understanding of tine overall transfer func.-
tiotis became they 	task. 'rho result was Oie Bubbly Flow Model for the
dynamics of cavitathig, poops (Publication .12) which we believe to be the
i 4
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i
beat analytical approach to date. It yielded transfer functions which were
in good qualitative and fair qua>.ntitative agreement with those measured
experimentalIv. The model was based on a bubbly, two-phase flow representa-
tion of the flow in the blade passages of the inducerr``,
	
Essential
features were the dynamic waves in this flow caused by pressure fluctuations
and the kinematic waves caused by fluctuating production of cavitation bub-
bles (in the vicinity of pump inlet) due, in turn, to the fluctuating flow
rate. The latter phenomena is re4^ponsible for the active dynamic behavior
of the pump in the model.;
5. Further Experimental Transfer Functions
The first part of the experimental program involved measurements
111
of the dynamic transfer functions for 3 in. diameter inducers in water at
normal temperatures. Simple helical inducers as well as a scale model of
the low pressure liquid oxygen turbopump inducer (LPOTP) in the Space
Shuttle Main Engine were used. Questions then arose concerning (i) the
manner in which this data should be scaled to larger inducers (ii) the
scaling for other liquids given the fact that thermodynamic effects are
often observed in the steady cavitatiog performance of inducers and (iii)
the possible effects of non-uniform inlet flow on the transfer functions.
Consequently an alternative working section for the D.P.T.F.
was designed and built which would allow measurements on 4 in. diameter
inducers. Again the tests utilized several helical inducers as well as a
4 in. model of the LPOTP inducer. The results (which are presented in
Publication 16) essentially indicated that we had anticipated the correct
scaling laws when setting up the non-dimensionalization. There was sub-
stantial agreement between both sets of transfer functions and the bubbly
a-5-
flow model. Tudeed with the benefit of the earlier, experiences the 4 in.
transfer functions were probably more ac:urate and showed less scatter than
the 3 in.transfer functions.
The results of tests desiped to investigate the thermal. effects
(the water was heated to about 70°() and the effects of non-uniform inlet
flow are also presented in Publication 16. The answer, was simply that
virtually no effect was observed over and above the effects on mean flow
p^rformance.
6. Auto-oscillation Studies
The active dynamic feature of cavitatit,g inducers which leads to
instabilities in many applicat I,ons could also be demonstrated in the bPTF.
When the latter was op".:ated under certain conditions without external
perturbation of the flow the entire facility could become unstable result-
ing in large pressure and flow rate fluctuations. This instability which
is referred to as auto-osIcil.lation became the subject of rIn i.nve;;tlgat:i,on
parallel and complementary to the measurement of the transfer functions.
Measurements of the frequency and onset cavitation number of auto-oscilla-
tion were made as well as the pressure and :flow rate fluctuation magnitudes.
This data is reported in publications [15], [17] and [l$].
A primary objective of this work was to determine whether the
frequency and onset cavitation number could be predicted fr(-,,i knowledge of
the transfer functions over a range of cavitation numbers. This does in-
deed appear to be the case., The predicted .frequencies were close to those
observed and the scaling with inducer rotating speed and diameter confoa;`m
ed with expectations. The onset cavitation number could also be predicted
but with less accuracy. Consequently auto-oscillation does appear to be
I
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the outward manifestation of global instabilities caused by the active
dynamic characters of cavitating inducers.
7. Unsteady Inlet Flow Characteristics
Additional studies of the details of the flow at or near , inlet to
a cavitating inducer W,,re carried out because so much of the preceding re-
search suggested that this was the crucial region i,'asofar as the global
dynamics were concerned. Detailed surveys of the axial and swirl wean.
velocity profiles were made (see publications 16,17,19). Unsteady pressure
fluctuations on the walls of inlet duct were monitored at various axial
locations during the auto-oscillation experiments (see publications 17,1$,
19).
The general conclusion of these studies was that the complicated
swirling flow at inlet which is integrally coupled with the backf low plays
a major role in determining not only the steady state performance of the
inducer but also its dynamic characteristics. Even in the absence of cavita-
tion the dynamic response of such a swirling flow is riot well documented
and for this reason we up,dertook the theoretical analyses of wave propaga-
tion in such flows which are described in publication 19 and in an appendix
to pcablicatcion 17.
Although we believe we have knowledge of the global effects result-
ing from these flows it andthat the detailed local measurements made thus far
are yaluable,it must be concluded that complete details remain to be un-
covered. Specifically we would suggest a detailed survey of both the steady
and unsteady flow velocity profiles in this region. We hope to complete
such a survey of the unsteady flow velocity profiles as part of a separate
study; the results will be reported to GMSFC.
8: Other Studies
Other kinds of flow involving phase change will probably exhibit
the same kind of active dynamic characteristics demonstrated for c%vitating
inducers. One such example was investigated theoretica,y, namely a con- .
densation or evaporation process in a pipe. The resulra';!ere (resented in
publication 14 and provide a useful clue as to the source of the fluctuating
energy injected by the inducer pump. In summary, any phaso change process
is capable of modulating a steady energy supply (for example, the energy
released or absorbed during condensation or evaporation) into flow fluctu?tiona.
9. Acknowledgments
We would like to take this opportunity to acknowledge and thank the
many people who participated in this research effort. First, our thanks to
the graduate students Jong Kim; S.L. Ng, D.M. Braised and R. Bernier with
whom it was our pleasure to work. However, a number of undergraduates'also
played a large role in the experimental program; we are very grateful to
Javier del Valle, George, Hendrikson, Phil Engelauf, Sui Cheung, Curtis Meissner,
Gregory Hoffman, Edmond Lo, Daniel Rovner and the others who participated
for shorter times. Also we were greatly aided by the expert help of the
Institute staff, particularly Norman Keidel, George Yamamoto and 'Elton Daly.
Finally, we wish to express out sincerest thanks to the technical
personnel at the George Marshall Space Flight Center with whom it was a
great pleasure to work. A large measure of the credit for the success of
this effort should go to them.
PUBLUNCIONS
(1)	 Brennen, C. and Acosta, A.J., "A note on turbopump blade cavitation
compliance for the POGO instability," ASME Polyphase Flow Forum,
1972, pp. 23-24.
[2) Brennen, C. and Acosta, A.J., ""Theoretical, quasi-static analysis of
c4 ►vitation compliance in tu-rbopuwps II , J. Spacecraft and Rockets,
Vol. 10, No. 3, 1973, pp. 175-180. [Also translated ic.to Russian
(without our, knowledge) and, published as "Analysis of the elasticity
of cavitation caverns in the pumps of liquid-propelled rocket engines"
(retranslation of Russian title) in Voprosy Raketnoi Tekhniki, No. 3.1
[3) Brennen, C., "The dynamic behavior and compliance of a stream of
cavitoting bubbles", ASME J. Fluids Eng., Vol. 95, 197.", pp. 533-542.
[4) Kf,.,I,, J.H. and Acosta, A.J., "Unsteady flow in cavitating turbopump",
ASM, J. Fluids Eng., Vol. 97, 1975, pp. 412-437.
[5) Acosta, A.J. , "Unsteady effects in flow rate measurement of the
entrance of a, pipe'", ASME J. Fluids, Eng., Vol.. 98, No. 3, 1976, pp.
562-563.
[6]	 Brennen, C. and Acbrita, A.J., "The dynamic performitice of cia-vitating
turboptimps", Proc. 5th Conf. on Fluid Mach., Akademiai Kiado,
Budapest, Hungary, pp. 121-136, 1975.
(7) Brennen, C. and Acost,,,i,-A.3., "The dynamic transfer function for a
cavitating inducer", ASME J. Fluids Dig., Vol. 98, 1976, pp. 182-
191.
(8) Ng, S.L., "Dynamic response. of cavitating turbomachines", Ph.D.
Thesis, California Ttistituto of Technology, Pasadena, Calif. , 1,976
(Report 'P 184.1, Div. of Eng. and Appl. Soi., Aug. 3.976).
[91	 Ng, S.L., Brennen, C, rand Acosta, A.J., "The'lie dynamics of cavitating
inducer pumps"", Proc. Int'. Conf. o 'Wn o Phase, Flow and Cavitation,
I.Am.R., Grenoble, France, 1976.
[10)	 Brennen, C., "On non-cavitating axial inducer perforrizatice, a brief
unpublished note, 1977.
(111	 Ng, S.L, and Brennen, C., "Experiments on the dynamic behavior of
cavitating pump,,-,", ASME J. Fluids Eng., Vol. 100, 1978, pp. 166-
176.
[12)
	
Brennen, C. , "Bubble flow model for the dynamic characteristics of
cavitating pumps", J. Fluid Mech., Vol. 89, Part 2, 1978, pp. 223-
240.
[13] Brennen, C. , "The unsteady dynamic characteris tics of hydraulic
systems with emphasis on cavitation and turbomachines", Proc. Joint
ASCE/TAI-IR/ASMB Synip. on design and operation of fluid macbinery
(Fort Collins, Colorado, June 1978), Vol. 1, pp. 97-1-07.
[14] Drennen, C., "The unsteady, dynamic response of phase changes in
Hydraulic systems", in "Wo-phase momentum, heat and mass transfer"
(Eds: Durat, F., Ts-Lklatiri, C.V. and Afgan, N.11.) Hemispbere Publ.
Co., ;Dash., 1979, Vol. 2, pp. 747-758.
[15] traisted, D.M. and Brennen, C., "Observations on instabilities of
cavitating inducers", ASME Cavitation and Polyphase Flow, June 1,978.
[16] Brennen, C.F., MWissoer, C., Lo , E.Y. and 11offman, G.S., "Scale of-
fec,ts in the dynamic transfer functions for eavitattng inducers",
1979, submitted to J. 'Fluids tn8ineering.
1171	 Braisted, DJt., "Cavitation induced instabilities associated with
turbomachines" P Ph. D. Thasts, California Institute of Technology,
Pasadena, Calif., '1979 (Report No. F,184,2,, Div. of Eng. & Appl. Set.,
Sept. 1979).
[18] Bra,isted, D.M. and Brennen, C.E., "Auto-oscillation. of cavitatiag
inducers", 1979, submitted to ASME J. Fluids Engineering.
[19] Braisted, D.M. and Brennen, C.E., "Dynamic charac t emis ties of swirl-
ing pipe flows with particul,ir reference to pump inlet flows", 1980,
in preparation.
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Dynamics of cavitating cascades

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