A new method is proposed for the stability analysis of cavitating flow. In combination with the singularity method, a closed cavity model is employed allowing the cavity length freely to oscillate. An eigen-value problem is constituted from the boundary and supplementary conditions. This method is applied for the analysis of rotating cavitation in a cascade with a finite pitch and a finite chordlength. Unlike previous semi-actuator disk analyses (Tsujimoto et al., 1993 and Watanabe et al., 1997a), it is not required to input any information about the unsteady cavitation characteristics such as mass flow gain factor and cavitation compliance. Various kinds of instability are predicted. One of them corresponds to the forward rotating cavitation, which is often observed in experiments. The propagation velocity ration of this mode agrees with that of experiments, while the onset range in terms of cavitation number is larger than that of experiments. The second solution corresponds to the backward mode, which is also found in semi-actuator disk analyses and identified in an experiments. Other solutions are found to be associated with higher order cavity shape fluctuations, which have not yet been identified in experiments.

1.
de Bernardi, J., Joussellin, F., and Von Kaenel, A., 1993, “Experimental Analysis of Instabilities Related to Cavitation in a Turbopump Inducer,” Proceedings of 1st International Symposium on Pump Noise and Vibrations.
2.
Furuya, O., 1982, “Dynamic Characteristics of Cavitating Pumps and Inducers,” ASME Paper, pp. 147–155.
3.
Geurst
J. A.
,
1959
, “
Linearized Theory for Partially Cavitated Hydrofoils
,”
International Shipbuilding Progress
, Vol.
6
, No.
60
, pp.
369
384
.
4.
Hashimoto
T.
,
Yoshida
M.
,
Watanabe
M.
,
Kamijo
K.
, and
Tsujimoto
Y.
,
1997
, “
Experimental Study on Rotating Cavitation of Rocket Propellant Pump Inducers
,”
AIAA Journal of Propulsion and Power
, Vol.
13
, No.
4
, pp.
488
494
.
5.
Horiguchi, H., Watanabe, S., Tsujimoto, Y., and Aoki, M., 1998, “A Theoretical Analysis of Alternate Blade Cavitation in Inducers,” Proceedings of ASME Fluids Engineering Division Summer Meeting, Cavitation and Multiphase Flow Forum, FEDSM98-5083.
6.
Huang
J. D.
,
Aoki
M.
, and
Zhang
J. T.
,
1996
, “
Alternate Blade Cavitation on Inducer
,”
JSME International Journal
, Series B, Vol.
41
, No.
1
, pp.
1
6
.
7.
Kamijo
K.
,
Yoshida
M.
, and
Tsujimoto
Y.
,
1993
, “
Hydraulic and Mechanical Performance of LE-7 LOX Pump Inducer
,”
AIAA Journal of Propulsion and Power
, Vol.
9
, No.
6
, pp.
819
826
.
8.
Ryan, R. S., Gross, L. A., Mills, D., and Mitchell, P., 1994, “The Space Shuttle Main Engine Liquid Oxygen Pump High-Synchronous Vibration Issue, the Problem, the Resolution Approach, the Solution,” AIAA Paper, 94-3153.
9.
Tsujimoto
Y.
,
Kamijo
K.
, and
Yoshida
Y.
,
1993
, “
A Theoretical Analysis of Rotating Cavitation in Inducers
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
115
, No.
1
, pp.
135
141
.
10.
Tsujimoto
Y.
,
Yoshida
Y.
,
Maekawa
M.
,
Watanabe
S.
, and
Hashimoto
T.
,
1997
, “
Observations of Oscillating Cavitations of an Inducer
,”
ASME JOURNAL OF FLUIDS ENGINEERING
, Vol.
119
, No.
4
, pp.
775
781
.
11.
Wade
R. B.
,
1967
, “
Linearized Theory of a Partially Cavitating Cascade of Flat Plate Hydrofoils
,”
Applied Scientific Research
, Vol.
17
, pp.
169
188
.
12.
Watanabe
S.
,
Tsujimoto
Y.
,
Kamijo
K.
, and
Furuya
O.
,
1998
, “
An Analysis of Unsteady Cavitation Characteristics by a Singularity Method
,” (in Japanese)
Transactions of JSME
, Series B, Vol.
64
, No.
621
, pp.
1285
1292
.
13.
Watanabe, S., Yokota, K., Tsujimoto, Y., and Kamijo, K., 1997a, “Three-Dimensional Analysis of Rotating Cavitation in Inducers—Linear Cascade Model Spanning between Two Parallel Plates—,” Proceedings of JSME Centennial Grand Congress, International Conference on Fluid Engineering, Tokyo, Vol. 111, pp. 1377–1382.
14.
Watanabe, S., Yokota, K., Tsujimoto, Y., and Kamijo, K., 1997b, “Theoretical Analyses of Rotating Cavitation in Inducers,” Proceedings of the 8th International Symposium on Aerdynamics and Aeroelastisity of Turbomachines, T. H. Fransson, ed., Kluwer Academic Press, pp. 3–17.
This content is only available via PDF.
You do not currently have access to this content.