Mathematical modeling and decomposition of hydrodynamics-acoustic fields using perturbation methods

作者：Riahi M^*; Nouri N M; Valipour A

来源：Scientia Iranica, 2014, 21(1): 213-221.

• Mathematics modeling
• Cavitation
• Supercavitation
• Perturbation method
• Scale analysis

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 effects is not as high as that of hydrodynamics. Therefore, in this paper, initially, for comparing different 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 flow, are selected. By regarding acoustics as lower order phenomena, compared to the hydrodynamics of flow, and simultaneously using the perturbation method, two equations containing leading and first orders and different terms can be attained. Obtained results indicate that leading order equations represent the hydrodynamics of the cavitating flow, and first order equations indicate the acoustics of cavitation or supercavitation. Acoustic equations of the present study contain terms related to fluid viscosity, density and pressure changes, and background flow velocity. As acoustic equations are coupled with leading order equations, in order to find the noise of cavitation, equations of fluid flow for compressible flow should be resolved.

• 出版日期2014-2