Low Mach number approximated linearized perturbed Euler equations-based unified computational flow-induced acoustic model for 2D planar/axisymmetric complex geometry

Abstract

This article is on proposition of a unified 2D planar and axisymmetric differential formulation—for both fluid dynamics and acoustic governing equations. Further, using hydrodynamic splitting method for computational acoustics, a differential formulation is proposed by performing low Mach number approximation on Linearized Perturbed Euler Equations (LPEE). Finally, using the differential formulations, a unified numerical methodology is proposed for Computational Flow-induced Acoustics (CFiA)—involving complex geometry—on a body-fitted curvilinear grid. A finite volume and finite difference methods-based hybrid method is presented for algebraic formulation in CFiA. Further, solution methodology is presented with a semi-implicit pressure projection method for fluid flow, four step Runge-Kutta method along with sub time-stepping for acoustic perturbations, and a one-way explicitly coupled solution algorithm for the CFiA. A detailed validation study is presented separately for the present in-house computational-acoustic and CFiA solvers—by considering various test problems, involving 2D planar and axisymmetric complex geometry problems. Further, using an order of accuracy study, the present acoustic and CFiA solvers are demonstrated as IV-order and II-order accurate, respectively. Finally, using the CFiA solver, a superior performance is demonstrated for the proposed low Mach number approximated LPEE as compared to the traditional LPEE-based solver. For low Mach number CFiA, involving 2D planar and axisymmetric complex geometries, a novel method is presented here for computationally efficient CFiA development.