Cavitation void fragmentation as acoustic source: mathematical model

Abstract

Object and purpose of research. This paper is intended to develop a mathematical model of cavitation void fragmentation into separate collapsing bubbles as an acoustic source for further implementation in Logos software package. The study was performed on propeller models in cavitating environment. Subject matter and methods. Volume and quantity of bubbles appearing after fragmentation of a cavitation void on propellers, as well as amplitude and frequency properties of a single bubble collapse are studied as per CFD methods. Viscous flow properties are found from finite-volume (FVM) solution to unsteady Reynolds equations (RANS) closed by a biparametric semi-empirical turbulence model. The coefficients in the mathematical model of acoustic source thus obtained were calibrated through validation that included noise measurements at KSRC Cavitation Tunnel. Main results. This work included numerical simulation of collapse dynamics for a single cavitation bubble at different initial conditions, with approximation of the pressure impact created by bubble collapse in the infinite fluid and near a solid wall. The study estimated volume and quantity of the bubbles created by the fragmentation of cavitation void on propellers (3 propellers of different shape operating at different advance ratios and cavitation numbers). The mathematical model representing above-mentioned process could be further implemented in Logos software as a finite-volume algorithm with k-ω SST turbulence model. The study also created a validation base for further testing and calibration of the mathematical model thus developed. Conclusion. The study was performed as part of project Mathematical simulation on exa- and zetaflops class supercomputers launched by National Centre for Physics and Mathematics (Russia). The analysis of obtained results has shown that the mathematical model suggested in this paper does have practical potential, but it needs additional empirical data for greater flexibility and more accurate estimates. Without this model, these practical tasks still could be handled but at a cost of considerable and, most importantly, unnecessary increase in required hardware resources.