Analysis of Rotating Cavitation in a Finite Pitch Cascade Using a Closed Cavity Model and a Singularity Method

Abstract

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 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 ratio 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 experiment. Other solutions are found to be associated with higher order cavity shape fluctuations, which have not yet been identified in experiments. Transactions of the ASME Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 06/13/2015 Terms of Use: http://asme.org/terms Conclusions A new method was proposed for the stability analysis of cavitating flow. This method was applied for the analysis of rotating Journal of Fluids Engineering DECEMBER 1999, Vol. 121 / 839 Downloaded From: http://fluidsengineering.asmedigitalcollection.asme.org/ on 06/13/2015 Terms of Use: http://asme.org/terms

Higher Order Rotating Cavitation in an Inducer

“…The higher order rotating cavitation and higher order cavitation surge occur at higher flow rate than the design flow rate. As we decrease the flow rate, these instabilities start to occur at higher cavitation number, as predicted by the analysis (Watanabe et al, 1999;Horiguchi et al, 2000).…”

“…However, Watanabe et al (1999) and Horiguchi et al (2000) theoretically predicted the higher order rotating cavitation which has higher propagation speed ratio (about 3-6). In the present study, the higher order rotating cavitation with a propagation speed ratio of about 5 is reported.…”

Theoretical Analysis of Thermodynamic Effect of Cavitation in Cryogenic Inducer Using Singularity Method

“…We have developed a simple analysis of unsteady cavitating flow combining a free streamline theory and a singularity method, and succeeded in simulating the cavitation instabilities of hydrofoil (Watanabe et al [9]) as well as those of cascade such as rotating cavitation and cavitation surge (Watanabe et al [10]). More recently, we have constructed an analytical method of the thermodynamic effect on steady, partially cavitating flow (Watanabe et al [11]).…”

Analytical Study of Cavitation Surge in a Hydraulic System

“…Kawata et al [11] showed an example in which the negative gradient of the pressure performance curve under quasi-steady conditions becomes positive under unsteady conditions due to the phase delay. Brennen and Acosta [4], Otsuka et al [12], Watanabe et al [13], and Rubin [14] showed that the mass flow gain factor and the cavitation compliance have the phase delay under the unsteady conditions. Therefore, the unsteady characteristics of performance curves and cavitation characteristics are important to discuss the stability of the hydraulic system.…”