Mathematical modeling and decomposition ofhydrodynamics-acoustic fi elds using perturbationmethods

Conservation of mass, momentum, energy and state equations are recognized as basic mathematical models in analysis of the acoustic behavior of cavitation, as well as supercavitation. Also, it is known that the order of acoustic eects is not as high as that of hydrodynamics. Therefore, in this paper, initially, for comparing dierent terms of equations, using scale analysis, conservation equations are converted into dimensionless ones. Then, by comparing all conditions, coupled with weighting terms available in those equations, groups of parameters most appropriate with the hydrodynamics and hydroacoustics of the cavitating ow, are selected. By regarding acoustics as lower order phenomena, compared to the hydrodynamics of ow, and simultaneously using the perturbation method, two equations containing leading and rst orders and dierent terms can be attained. Obtained results indicate that leading order equations represent the hydrodynamics of the cavitating ow, and rst order equations indicate the acoustics of cavitation or supercavitation. Acoustic equations of the present study contain terms related to uid viscosity, density and pressure changes, and background ow velocity. As acoustic equations are coupled with leading order equations, in order to nd the noise of cavitation, equations of uid ow for compressible ow should be resolved