Development of LES-High-Order Spectral Difference Method for Flow Induced Noise Simulation

Matteo Parsani, Ghader Ghorbaniasl, Chris Lacor
2010 16th AIAA/CEAS Aeroacoustics Conference   unpublished
The filtered fluid dynamic equations are discretized in space by a high-order spectral difference (SD) method coupled with large eddy simulation (LES) approach. The subgridscale stress tensor is modeled by the wall-adapting local eddy-viscosity model (WALE). We solve the unsteady equations by advancing in time using a second-order backward difference formulae (BDF2) scheme. The nonlinear algebraic system arising from the time discretization is solved with the nonlinear lower-upper symmetric
more » ... s-Seidel (LU-SGS) algorithm. The SD-LES method provides the acoustic sources for aerodynamic sound field simulation in the time domain. The numerical noise simulation is based on the Ffowcs-Williams Hawkings (FW-H) approach, which provides noise contributions for monopole, dipole and quadrupole acoustic sources. This paper will focus on the validation and assessment of this hybrid approach using different test cases. The test cases used are: a laminar flow over a two-dimensional (2D) open cavity at Re = 1.5 × 10 3 and M = 0.15 and a laminar flow past a 2D square cylinder at Re = 200 and M = 0.5. In order to show the application of the numerical method in industrial cases and to assess its capability for sound field simulation, a three-dimensional (3D) turbulent flow in a muffler at Re = 4.665 × 10 4 and M = 0.05 has been chosen as a third test case. The flow results show good agreement with numerical and experimental reference solutions. Comparison of the computed noise results with those of reference solutions also shows that the numerical approach predicts noise accurately. * PhD student, † Senior Research Scientist, on unifying several of the popular methods including the DG method, the SV method and the SD method with a technique that does not require the evaluation of the integral. [28] [29] [30] Although spatially high-order accurate numerical schemes guarantee the accurate resolution of small scales, their application for the simulation of general turbulent flows implies that particular attention has still to be paid to subgrid models. In this framework, we couple a high-order SD scheme on unstructured hexahedral grids with the Wall-Adapted Local Eddy-viscosity (WALE) model 31, 32 to perform large eddy simulations 33 (LES). We have implemented the high-order SD method for the three dimensional (3D) Navier-Stokes (N-S) equations and extended to 3D LES in the COOLFluiD collaborate simulation environment developed at the von Karman Institute for Fluid Dynamics (see Quintino 34 and the COOLFluiD project website 35 ). Usually, explicit temporal discretizations such as multi-stage Total Variation Diminishing (TVD) Runge-Kutta schemes 4 are used to advance the solution in time. In general, explicit schemes and their boundary conditions are easy to implement, vectorize and parallelize, and require only limited memory storage. However, for large-scale simulations and especially for high-order solutions, the rate of convergence slows down dramatically, resulting in inefficient solution techniques. In addition, the solver must also be able to deal with the geometrical stiffness imposed by the N-S grids where high-aspect ratios occur near walls. In the case of compressible solvers there is an additional stiffness when solving for low speed flows caused by the disparate eigenvalues of the system. Therefore, to exploit the potential of high-order methods efficient solvers are needed. In order to speed up convergence, a multi-grid strategy and/or an implicit temporal discretization is required. Implicit schemes can advance the solution with significantly larger time steps compared to explicit methods. However, they are more expensive than explicit schemes if the algebraic solver employed is not efficient. 36, 37 In the present study, the governing equations are solved by advancing in time using a second-order backward difference formula (BDF2). The nonlinear algebraic systems arising from the time discretization is then solved with the nonlinear lower-upper symmetric Gauss-Seidel (LU-SGS) algorithm. 33, [38] [39] [40] [41] In CAA, the problem of sound field simulations can be separated into two parts, one describing the nonlinear generation of sound, while the other describing the transmission of sound. In this work, we have proposed a CAA tool where an unsteady flow field in the near field is computed by using the implicit high-order SD/SD-LES methods and the far-field sound pressure is predicted by using the acoustic source information provided by the first step simulation. The noise prediction is based on the Ffowcs Williams-Hawkings (FW-H) approach, which is a particular case of the Lighthill's acoustic analogy to predict the noise generated in the presence of moving bodies. The sound levels can be very sensitive to the accuracy of the computed retarded time and the position of the moving sources, especially for highly unsteady loads. As a result, severe validation and verification tests are required. Ghorbaniasl and Hirsch 42 presented a series of test cases which are help validate the numerical implementation of noise simulations. The present article will focus on the assessment of capability of high-order SD/SD-LES methods to provide a noise propagation tool with acoustic pressure sources. The main contribution of this work is the evaluation of two verification test cases and one industrial validation case, for the proposed hybrid farfield acoustic propagation. The test cases are: a laminar flow over a two-dimensional (2D) open cavity at Re = 1.5 × 10 3 and M = 0.15, a laminar flow past a 2D square cylinder at Re = 200 and M = 0.5, and a 3D muffler at Re = 4.665 × 10 4 and M = 0.05. The remainder of this article is organized as follows. A brief summary of the filtered N-S equations for a compressible flow and the description of the WALE model are given in Section II. Section III is devoted to the description of the SD method and the treatment of the diffusive terms with the second approach of Bassi and Rebay 43 (BR2). In the same section the coupling of the SD method and the WALE model through a new definition of the grid filter width presented in Parsani et al. 33 is given. The nonlinear LU-SGS algorithm combined with BDF2 is described in Section IV. The FW-H approach is briefly revised in Section V. Section VI deals with the numerical results, before finally drawing the conclusions in Section VII.
doi:10.2514/6.2010-3816 fatcat:kldaqcc32zcyfpyfpcfmmrj5e4