Using perturbation method to obtain scaled numerical model for analyzing noise of supercavitation

Cavitation is changing liquid phase to gas phase due to decreasing local pressure of flow induced by increasing local velocity. In situation of maximum velocity, some bubbles that contain air and vapor are produced and traveled from point of high pressure to lower pressure, so bubbles are destroyed rapidly and produce acoustic noise. Providing sufficient numerical model for simulation of acoustic waves induced by cavitation or supercavitation is so important for monitoring and controlling of these phenomena. For analyzing propagation of acoustic waves in fluid, sound is part of fluid dynamics, so momentum, energy and mass conservation equations like fluid dynamics are basics equation for identification of supercavitation. In this paper, to provide a numerical model contains hydrodynamic and acoustic parts of fluid dynamics, first by using scaled analysis, non dimensional forms of conservation equations are generated. Then by using perturbation method and considering acoustic term as a term in lower order than hydrodynamic term, conservation equations can be separated to two group equations with different orders. Leading order is hydrodynamic equations and first order is acoustic form of conservation equations. Results in first order equation show coupling of acoustic terms with hydrodynamic terms of fluid flow.