Reformulated Flow-Acoustics Splitting for RANS/CAA based Acoustic Metrics: Tip Leakage Flow Problem

Abstract

A novel acoustic metric is derived from reduced order modeling of turbulent near-field flow to characterize sources of sound caused by flow around complex geometry. The acoustic metric can serve as a physics based aeroacoustics cost function in 3-D optimization workflow. Quick turnaround times of less than 50-100 Core·h are deemed a crucial prerequisite for 3-D optimization in an industrial environment and can be accomplished with the new approach where an evaluation of the acoustic metric requires only the resolution of the source region of interest. The approach relies on an alternative flow/acoustics splitting of the Linearized Euler Equations (LEE) into Acoustic Perturbation Equations (APE) and linear equations for the split velocity fluctuations that govern vorticity transport. A specific dilatation based cross-coupling term can be identified that describes vortex sound generation. From this source term the acoustic metric is deduced. RANS informed stochastic forcing with the Fast Random Particle Mesh (FRPM) method is applied for obtaining inflow turbulence in the vortical velocity equations. In this paper, the acoustic metric is evaluated for a generic tip-gap flow problem typically encountered in industrial fan applications and for which noise reduction via geometrical optimization is of high interest. Besides the near-field simulations, additional acoustic simulations are carried out and resulting sound spectra are juxtaposed to near-field acoustic metric data by varying flow velocity and tip-gap size. Different discretization schemes for the split linear equations are applied, viz. a 4th order Discontinuous Galerkin based approach and a 4th order hierarchical-cartesian finite difference solver that combines the DRP scheme with an immersed/embedded boundary method. Proper trends are reproduced by the acoustic metric. The extension of the approach to a stochastically Forced Linear Advection Diffusion equation as the ultimate means to realize fully RANS-conformal synthetic turbulence on the foundations of well established numerics is discussed.