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Application of CFD to LE-7A OTP Alternate Inducer Development

Naoki Tani1 Japan Aerospace Exploration Agency, 2-1-1 Sengen Tsukuba-Shi, Ibaraki, 305-8505, JAPAN

Chisachi Kato2 The University of Tokyo, 4-6-1 Komaba Meguro-ku, Tokyo, 153-8505, JAPAN

Koichi Okita3, Nobuhiro Yamanishi4 Japan Aerospace Exploration Agency, 2-1-1 Sengen Tsukuba-Shi, Ibaraki, 305-8505, JAPAN

and

Tsutomu Mizuno5 IHI, 229 Tonogaya Mizuho, Nishitama, Tokyo, 190-1297, JAPAN

The alternate oxidizer turbo-pump inducer development has been carried out to improve the suction performance of the LE-7A rocket engine. CFD was utilized for the design and development of the alternate inducer. For the first step, non-cavitating CFD was applied to verify the blade the design concept. Next, steady state cavitating CFD was carried out to predict suction performance. Finally, large-scale unsteady cavitating CFD was performed to evaluate the cavitation-induced instability. In the present paper, the application of CFD for the development of the alternate inducer will be presented.

Nomenclature N = Rotational speed Pin = Inlet pressure Pload = Blade pressure load pND = Non-dimensionalized pressure Pout = Outlet pressure PP.S. = Pressure surface blade surface pressure PS.S. = Suction surface blade surface pressure

I. Introduction N 1999, the H-II launch vehicle failed due to the fatigue breakdown of the fuel turbo-pump (FTP) inducer. Soon, FTP inducer improvement was carried out for the new launch vehicle, H-IIA. The development had successfully

ended, and a new inducer was installed to the H-IIA Flight #2. On the contrary, the oxidizer turbo-pump (OTP) inducer design has not been modified until today. However, in order to achieve higher reliability, an alternate inducer development began in 2006. The primary objective of the development is the improvement of suction performance and achieving lower cavitation inducer instability. The use of CFD has been quite limited due to small computational resources in the past. However, today, high performance computers which can be purchased at a relatively low cost, can provide results within reasonable interval with sufficient accuracy. In addition, many experimental and numerical studies on the inducer1, 2 have obtained useful knowledge on the design and

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1 Engineer, JAXA’s Engineering Digital Innovation Center, Member AIAA 2 Professor, University of Tokyo, Non Member AIAA 3 Senior Engineer, Space Transportation Engineering Department, Member AIAA 4 Associate Senior Engineer, JAXA’s Engineering Digital Innovation Center, Member AIAA 5 Assistant Manager, Space Technology Group, Member AIAA

American Institute of Aeronautics and Astronautics

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43rd AIAA/ASME/SAE/ASEE Joint Propulsion Conference & Exhibit 8 - 11 July 2007, Cincinnati, OH

AIAA 2007-5542

Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

understanding of the internal flow of inducers. The present paper focuses its attention on the utilization of CFD in inducer development.

Presently, several different CFD calculations were applied at each development stage. Steady state non-cavitating calculation was used to verify blade design concept, such as blade pressure distribution and recirculation flow. Next step is a steady state cavitating flow calculation, which is expected to estimate suction performance of each inducer. In addition, several inducers were applied to unsteady cavitation calculation to confirm cavitation-induced instability.

II. Inducer Design and Shape Presently, inducers were designed by three different design methods. The helical blade inducer holds a

conventional shape, and blade design procedure also follows the traditional way. In order to search a wide range of blade design space, two different kinds of helical inducers were chosen for comparison in the present paper. Three-dimensional blade inducer was also designed for comparison with the helical blade inducer. In addition to these two different design concept inducers, an inverse solution blade inducer was designed. This blade was designed by explicitly set blade loading at each blade position, and blade shape is designed to fulfill the blade loading distribution. Several different shape parameters were considered in each inducer, but comparison was carried out about each typical design inducer. Figure 1 shows the typical shape of each inducer. In order to classify, inducers are named as following.

1) Helical design forward load inducer : HF1

HF1 HA1 T1 I1Helical Front loading blade Helical Aft loading blade Three dimensional blade Inverse solution blade


Figure 1. Typical inducers of each design

2) Helical design aft load inducer : HA1 3) Three dimensional blade inducer : T1 4) Inverse solution blade inducer : I1 Definition of blade loading is pressure difference between pressure and suction surfaces. SSSPload PPP ... −= (1) According to above definition, HF1 inducer has large pressure difference between pressure-surface and suction-

surface at the inlet, as a result, it can easily be expect that inlet recirculation becomes large. On the contrary, aft blade load inducer, HA1, is likely to produce weak inlet recirculation, however, suction performance may become worse since tip vortex cavitation can easily grow into the blade passage. Both T1 and I1 inducers have aft-loading type blades, but these two inducers’ design procedures are completely different. The T1 inducer’s design process is similar to that of a helical inducer, and the difference is that blade loading is actively changed from hub to tip. On the contrary, the I1 inducer is designed by inverse solution method combined with an optimization technique.

III. Application of Non-cavitating CFD From a viewpoint of CFD analysis, the inducer is a very difficult objective. The blades are consisted by flat plate

with sharp leading edge, therefore, partial separation likely occurs at the leading edge. Another difficulty is the recirculation flow from the tip clearance. Kimura et al.1 has shown that recirculation flow takes an important role for cavitation instability, and which indicates that the estimation of recirculation flow is important at the design phase. Concerning these points, numerical simulations were carefully carried out.


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A. Evaluation of Inducer Blade Design Concept For the initial step, steady non-cavitating CFD calculations were

carried out to evaluate and confirm inducer blade design concept, namely, blade pressure distribution and recirculation flow region. In order to focus on blade characteristic evaluation, casing treatment, which is described later, is not considered. Figure 2 shows typical computational grid, which is consisted by hexahedral, tetrahedral, pyramid and prism grid. At the inducer tip region, hexahedral mesh was applied for precise recirculation flow estimation. Calculations were carried out by use of STAR-CD and FLUENT. Calculation method and boundary conditions are shown in Table 1.

Blade pressure-surface pressure distribution is shown in Fig. 3. Inducer HF1 shows radial pressure gradient around the leading edge, on the contrary, radial pressure gradient is weakened in other three inducers which have aft-loading type blade. This result means that pressure rise occurs smoothly in aft-loading blade inducer. Figure 3

Figure 2. Computational grid for

steady state CFD

Table 1. Computational conditions and turbulence models for steady state CFD

18300 / 7500 [RPM]Rotating Speed

LOX / WaterWorking Fluid

Calculation Conditions

Free outlet / Radial EquilibriumOutlet

Constant VelocityInlet

Boundary Conditions

RNG k-ε / Realizable k-εTurbulent Model

STAR-CD / FLUENTSolver

Calculation Methods

18300 / 7500 [RPM]Rotating Speed

LOX / WaterWorking Fluid


Free outlet / Radial EquilibriumOutlet


Boundary Conditions

RNG k-ε / Realizable k-εTurbulent Model

STAR-CD / FLUENTSolver

Calculation Methods


-0.85 1.1

Flow Flow FlowFlow

Front edge of recirculation region

Relative pressure against HF1 head rise

-0.17 2.3Relative backflow velocity normalized by inlet axial velocity


-0.85 1.1-0.85 1.1

FlowFlow FlowFlow FlowFlowFlowFlow


Relative pressure against HF1 head rise

-0.17 2.3-0.17 2.3Relative backflow velocity normalized by inlet axial velocity

Figure 3. Blade pressure surface pressure coefficient distribution (upper) and recirculation region (lower)


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also shows comparison of recirculation region. Strong backflow region can be observed in the HF1 inducer. On the contrary, other three induces have a small recirculation region. The driving force of recirculation flow is pressure difference between suction- and pressure-surfaces at the leading edge, and this is equivalent to the blade loading. This tendency can easily be estimated, but length and thickness of the backflow region are strongly influenced by turbulent boundary layer, therefore, response of recirculation strength against blade loading becomes non-linear. Such qualitative comparison between each inducer is important and meaningful.

B. Casing Treatment Casing treatment is often applied to reduce cavitation instability.

Figure 4 shows the typical casing treatment, which is a step near the leading edge. This casing treatment brings stable operation, however, there are no clear criteria for step size and length. Large step can suppress cavitation instability, but head drop occurs simultaneously, and suction

performance also becomes different. According to the comparison between numerical and experimental studies on HF1 inducer1, strong relation can be observed between backflow region and cavitation instability. Therefore, the primary objective of the investigation on casing treatment is recirculation region comparison. Presently, HF1 and HA1 inducers with casing step were calculated.

Calculated blade surface pressure distribution is shown in Fig. 5, and this comparison shows that, with stepped casing, leading edge pressure becomes lower in both inducers, but there is small influence to overall pressure distribution. Clear difference can be confirmed for the recirculation region length. Recirculation region becomes longer with stepped casing in the HF1 inducer, but recirculation region of the HA1 inducer becomes almost the same length. This result shows that recirculation of front loading type inducer can be controlled by casing treatment, on the contrary, aft loading type inducer recirculation is mainly decided by blade design itself.

Figure 4. Casing treatment

Without Step

Pressure-surface pressure Recirculation Region

With Step

Without Step

With Step

Recirculation Region


HA1 Inducer

HF1 Inducer

Without Step With Step

Pressure-surface pressureWithout Step With Step

Relative pressure against HF1 head rise-0.85 1.1

-0.17 2.3

Relative backflow velocity normalized by inlet axial velocity

Without Step

Pressure-surface pressure Recirculation Region

With Step

Without Step

With Step

Recirculation Region


HA1 Inducer

HF1 Inducer

Without Step With Step

Pressure-surface pressureWithout Step With Step

Relative pressure against HF1 head rise-0.85 1.1-0.85 1.1

-0.17 2.3-0.17 2.3

Relative backflow velocity normalized by inlet axial velocity

Figure 5. Casing treatment influence to blade surface pressure and recirculation region


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C. Leading Edge Cutback The inducer leading edge usually have cutbacks

for structural reason, however, experiments of Acosta et al.2 show that leading edge shape has great influence to inducer performance. In order to investigate an influence of leading edge cutback, two inducers, which are shown in Fig. 6, were compared. Both inducers’ blade shape are equivalent to the I1 inducer. Calculated result is shown in Fig. 7, and this comparison shows little influence on head rise, but recirculation backflow vortex structure becomes different. The bottom side of Fig. 7 shows the vortex core distribution. With small cutback leading edge, there is a clear circular vortex ring alongside the tip leakage vortex. The circular vortex ring shows front edge of recirculation region, and this shows that the length of recirculation region is almost the same at all circumference. On the contrary, circular vortex ring becomes wavelike shape when the leading edge is cutback, and vortex ring and tip leakage vortex becomes close at the tip throat. This implies that interaction between vortex ring and tip leakage vortex will likely occur with large cutback inducer blade. Some uncertainty still exists on the influence of such interaction, and understanding of the effect of leading edge shape is one of the future study.

100.9%

100.0%

0% 20% 40% 60% 80% 100% 120%

Type7A Cut

Type7A TD1Small

Cutback

Large Cutback

Relative HeadBaseline is a small cutback inducer

Vortex CoreSmall Cutback Large Cutback

Circular vortex ring

Tip Leakage Vortex

Wavelike shape vortex ring

100.9%

100.0%

0% 20% 40% 60% 80% 100% 120%

Type7A Cut

Type7A TD1Small

Cutback

Large Cutback



100.9%

100.0%

0% 20% 40% 60% 80% 100% 120%

Type7A Cut

Type7A TD1Small

Cutback

Large Cutback



Circular vortex ring

Tip Leakage Vortex

Wavelike shape vortex ring

Figure 7. Head rise (upper) and vortex core distribution (lower) comparison

Figure 6. Leading edge cutback shape Left: Small Cutback Right: Large Cutback

IV. Application of Cavitating CFD Suction performance prediction is most important but a difficult problem for an inducer, and several

computational analyses have been carried out to predict precise suction performance.3, 4 As widely known, cavitation instability, such as rotating cavitation, attached cavitation and cavitation surge, likely occur under some condition. And several numerical studies are carried out to simulate such cavitation instability.1, 6 From a viewpoint of practical usage, steady CFD suction performance prediction is usually applied, and unsteady CFD is often used to understand internal flow.1, 6 The same approach was applied in the present development, that is, RANS (Reynolds Averaged Navier-Stokes) simulations for suction performance prediction, and LES (Large Eddy Simulation) for evaluation of cavitation instability.

A. Suction Performance Prediction by Steady CFD For suction performance prediction by steady state CFD, FLUENT was applied as flow solver since the same

cavitation model of FLUENT was validated by inducer7. FLUENT uses the Full-Cavitation model as a cavitation model, which includes non-condensable gas and turbulent cavitation generation enhancement. Detailed explanation about the cavitation model is given in Ref. 7.

Figure 8 shows calculated cavity shape and suction performance of four inducers, and this plot shows that the HA1 inducer achieves the best suction performance. As mentioned before, the HA1 inducer suction performance is estimated to become worse at the design phase, but CFD analyses show opposite results. Blade passage width of the HA1 inducer was enlarged to maintain suction performance and computational result shows the effectiveness of this treatment. The same design policy was applied to the T1 inducer, and its suction performance also slightly improved


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compared to the HF1 inducer. Another feature of this suction performance is a negative gradient near the breakdown point, and this tendency is strongly observed in HA1 and T1 inducers, which have aft loading type blade design. Tsujimoto et al.8 have shown that such a negative suction performance is likely to introduce cavitation surge, which is a strong and low frequency vibration. In order to know the mechanism of this negative suction performance, some discussion was carried out.

Figure 9 shows calculated and schematic blade pressure distribution, and, in schematic drawing, solid and dotted lines show non-cavitating and cavitating condition, respectively. In Fig. 9, pressure distribution calculated under non-cavitating condition is shown. Pressure is non-dimensionalized as in Eq. 2.

0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6

HF1 inducer

HA1 inducer

T1 inducer

I1 inducer

HF1 HA1 T1 I1

Relative cavitation number

Rel

ativ

e he

ad a

gain

st

non-

cavi

tatin

g co

nditi

on0

0.2

0.4

0.6

0.8

1

1.2

0 0.1 0.2 0.3 0.4 0.5 0.6

HF1 inducer

HA1 inducer

T1 inducer

I1 inducer

HF1 HA1 T1 I1

Relative cavitation number

Rel

ativ

e he

ad a

gain

st

non-

cavi

tatin

g co

nditi

on

Figure 8. Cavity shape and Suction performance of each inducer

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

HF1 inducer

HA1 inducer

T1 inducer

I1 inducer

L.E. T.E.

Non-Cavitating Condition

Non-dimensionalized distancefrom leading edge

Non

-dim

ensi

onal

ized

pres

sure

: P

ND

Approximate Throat

Position

Angle from leading edge

Pre

ssur

e C

oeffi

cien

t

A

Pressure Surface

Suction Surface

Cavitating region

Throat region pressure gradient reduction

Non-cavitating conditionCavitating Condition

90% Span Position


Pre

ssur

e C

oeffi

cien

t

Pressure Surface

Suction SurfaceA

Cavitating region

Throat

Throat

-1

-0.5

0

0.5

1

1.5

0 0.2 0.4 0.6 0.8 1

HF1 inducer

HA1 inducer

T1 inducer

I1 inducer

L.E.L.E. T.E.T.E.

Non-Cavitating Condition

Non-dimensionalized distancefrom leading edge

Non

-dim

ensi

onal

ized

pres

sure

: P

ND

Approximate Throat

Position


Pre

ssur

e C

oeffi

cien

t

A

Pressure Surface

Suction Surface

Cavitating region

Throat region pressure gradient reduction

Non-cavitating conditionCavitating ConditionNon-cavitating conditionCavitating Condition

90% Span Position


Pre

ssur

e C

oeffi

cien

t

Pressure Surface

Suction SurfaceA

Cavitating region

Throat


Pre

ssur

e C

oeffi

cien

t

Pressure Surface

Suction SurfaceA

Cavitating region

Throat

Throat

Figure 9. Pressure distribution Left: Non-cavitating calculated blade surface pressure distribution

Right: Schematic drawing of pressure distribution


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inout

inND PP

PPp−−

= (2)

In usual case, pressure recovery occurs at cavity termination point, and pressure recovery value depends on surrounding flow. However, flow structure of inducer can be considered almost the same. Therefore, it can be assumed that pressure recovery at cavity termination point becomes constant in each inducer. Presently, suction surface pressure gradient at the cavity termination point is considered to be taking an important role to negative gradient of suction performance curve. Blade workload becomes proportional to a surrounded area of pressure distribution of Fig. 9, therefore, area comparison can explain the head rise change of cavitating inducer. Cavitating region pressure is maintained at saturation condition, and, if the pressure gradient at the cavitation termination point becomes smaller, cavity length becomes longer. As a result, region “A” in Fig. 9 becomes large, and blade workload is likely to increase compared to non-cavitating condition. Cavitation termination occurs around the throat position, therefore, small pressure gradient around the throat position may introduce negative suction performance gradient. Both the HA1 and the T1 inducers are aft-loading type inducers, and this means that pressure gradient at throat position becomes smaller compared to front loading type HF1 inducer. As a result, negative pressure gradient likely occur when blade loading becomes aft-loading type. In other words, suction performance is affected by suction surface pressure gradient at the throat.

B. Unsteady Cavitation Prediction Unsteady cavitation is another

major problem in inducer development, however, due to heavy computational load, unsteady CFD can be hardly used in the inducer development stage.

Experimental study show strong backflow may introduce cavitation instability1, therefore, the present objective was to investigate the influence of backflow vortex against cavitation. In order to fulfill such objective, resolving the large scale vortex is the most important demand, therefore, LES calculation was applied. Presently, Front Flow / Blue9 was used as a solver. Calculation condition and models are described in Table 2, and detailed description is given in Ref. 9. Presently, comparison of HF1 and HA1 inducers was carried out. Computational grid is shown in Fig. 10, which is consisted of hexahedral grids to maintain spatial accuracy. Since primary objective is a survey of interaction between backflow vortex and cavitation, cavitation number is adjusted to the point that inducer tip region cavitation reaches to the next blade. This is because unsteady of cavitation likely to occur when tip region is covered by cavitation.

Figure 10. Computational grid for LES calculation

Figure 11. Vorticity magnitude near inducer blade surface

Table 2 LES calculation models and conditions

7500 [RPM]Rotating Speed

WaterWorking Fluid


Constant PressureOutlet


Boundary Conditions

LES with Dynamic Smagorinsky modelTurbulent Model

Front Flow / BlueSolver

Calculation Methods

7500 [RPM]Rotating Speed

WaterWorking Fluid


Constant PressureOutlet


Boundary Conditions

LES with Dynamic Smagorinsky modelTurbulent Model

Front Flow / BlueSolver

Calculation Methods


7

Figure 11 shows vorticity magnitude contour at non-cavitating condition, and this figure shows turbulent streak on the inducer blades. It is widely known that cavity surface also shows such a streaky structure, therefore, LES calculation is quite valuable for high-speed cavitation.

Firstly, a cavity shape comparison, which is shown in Fig. 12, was carried out. On the cavity surface, streak shape cavity can be observed in LES

calculation, and this shows that cavity surface turbulence can qualitatively be treated. Cavity shape from inducer tip is similar between the two cases. This cavity is raised from strong tip vortex, which is a strong and large scale flow structure, and such flow is hardly affected by turbulence model. As a result, tip vortex cavitation show little difference. On the contrary, blade surface cavity shows clear difference, steady state RANS calculation shows large cavitation, but LES result shows quite small cavity. Such a surface cavity is strongly influenced by boundary layer, therefore, surface cavity shape can be affected by

turbulent model. Considering that such a large blade cavity can not be observed in experiment2, cavity shape of LES calculation seems to show a better result.

Backflow vortex comparison between the HF1 and the HA1 inducers is shown in Fig. 13. Large backflow vortex cavitation can be observed in HF1 inducer, on the contrary, in the HA1 inducer, clear backflow vortex cavitation can not be seen. The HA1 inducer is designed to reduce recirculation from tip clearance, which has been shown in Fig. 3, and the present result shows that small recirculation can also reduce backflow vortex. Although a relation between backflow vortex cavitation and cavitation instability can not be discussed since cavitation instability did not appeared in the present simulation, cavitation LES calculation capability was confirmed.

Inducer radial force induced by cavitation instability is one of the major sources of turbo-pump shaft vibration. Therefore, radial force frequency was estimated by use of LES calculation result. Figure 14 shows a sample of radial force frequency plot. There is no remarkable frequency peak in this plot, and this means that this inducer can be operated no cavitation instability.

RANS LESTime averaged Instantaneous

RANS LESTime averaged Instantaneous

Figure 12. Cavity shape comparison between RANS and LES

Backflow Vortex Cavitation

HF1 HA1

Backflow Vortex Cavitation

HF1 HA1 Figure 13. Backflow vortex cavitation comparison between

front loading type inducer (HF1) and aft loading type (HA1)

Frequency [Hz]

N 3N

Rad

ial F

orce

[N]

Frequency [Hz]

N 3N

Rad

ial F

orce

[N]

Frequency [Hz]

N 3N

Rad

ial F

orce

[N]

Figure 14. Inducer radial force frequency estimation of HF1 inducer

V. Summary In order to develop an alternate inducer for the LE-7A

oxidizer turbo-pump, a wide range of CFD calculations were applied. Non-cavitating steady-state CFD was applied for design phase, and its primary objective was to confirm the design concept and basic flow field, such as blade pressure distribution and recirculation region. Cavitation CFD was also carried out, and suction performance prediction about different design concept inducers were compared. This comparison reveals that the suction performance show different tendency when blade loading is changed from front loading type to aft loading. Large scale unsteady cavitation CFD was also carried out, and cavitation instability was


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estimated. By utilizing different types of CFD techniques, the development of the alternate inducer was carried out with high certainty. From a viewpoint of CFD research, applying such numerical approach to a wide range of experimental data greatly serves as a validation of such method and will give insight into future CFD development.

Acknowledgments Present work was supported by Ishikawajima-Heavy-Industry Space Technology Group, Advance Soft

Corporation, JAXA H-IIA project team and JAXA Rocket Engine Research Center’s Turbo-pump Section. The authors greatly appreciate their contributions and support. A part of this research was done in "Revolutionary Simulation Software for the 21st century (RSS21)" project supported by Research and Development for Next-generation Information Technology of Ministry of Education, Culture, Sports, Science and Technology (MEXT).

References 1 Kimura, T., Yoshida, Y., Hashimoto, T. and Shimagaki, M., “Numeral Simulation for Unsteady Cavitating Flow in a

Turbopump Inducer,” Proceedings of Sixth International Symposium on Cavitation on Disc [CD-ROM], Wageningen, The Netherlands, Sept. 2006.

2 Acosta, A.J., Tsujimoto, Y., Yoshida, Y., Azuma, S. and Cooper, P.., “Effects of Leading Edge Sweep on the Cavitating Characteristics of inducer pumps,” Proceedings of 8th Transport Phenomena and Dynamics of Rotating Machinary, Vol.1,2000, pp.181-188

3 Hosangadi, A., Hauja, V. and Ungewitter, R.J., “Generalized Numerical Framework for Cavitation in Inducers”, Proceedings of ASME FEDSM’03, FEDSM2003-45408, 2003.

4 Delagosya, O.C., et al., “3D Numerical Simulation of Pump Cavitating Behavior”, Proceedings of ASME FEDSM’02, FEDSM2002-31188, 2002.

5 Kamijo, K. and Suzuki, A., “An Experimental Investigation of Flat-Plate Helical Inducers for Rocket Turbopumps,” Technical Report of National Aerospace Laboratory, NAL-TR-345, Oct., 1973.

6 Delagosya, O.C., Reboud, J. L., Courtot, Y. and Patella, R. F., “A Numerical Model to Predict Unsteady Cavitating Flow Behavior in Inducer Blade Cascades,” Proceedings of Fourth International Symposium on Launcher Technology on Disc [CD-ROM], Liege, Belgium, Dec., 2002.

7 Athavale, M. M. and Singhal, A. K., “Numerical Analysis of Cavitating Flows in Rocket Turbopump Elements,” Proceedings of 37th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, AIAA 2001-3400, Salt Lake City, UT, July, 2001.

8 Tsujimoto, Y., Kamijo, K., and Yoshida, Y., “A Theoretical Analysis of Rotating Cavitation in Inducers,” ASME Journal of Fluid Engineering, Vol.115, No.1, 1993, pp.135-141.

9 Kato, C., et al., “Numerical prediction of sound generated from flows with a low Mach number,” Computers & Fluids, Vol.36, 2007, pp.53-68

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