Hermite regularization of the Lattice Boltzmann Method for open source computational aeroacoustics

The lattice Boltzmann method (LBM) is emerging as a powerful engineering tool for aeroacoustic computations. However, the LBM has been shown to present accuracy and stability issues in the medium-low Mach number range, that is of interest for aeroacoustic applications. Several solutions have been proposed but often are too computationally expensive, do not retain the simplicity and the advantages typical of the LBM, or are not described well enough to be usable by the community due to proprietary software policies. We propose to use an original regularized collision operator, based on the expansion in Hermite polynomials, that greatly improves the accuracy and stability of the LBM without altering significantly its algorithm. The regularized LBM can be easily coupled with both non-reflective boundary conditions and a multi-level grid strategy, essential ingredients for aeroacoustic simulations. Excellent agreement was found between our approach and both experimental and numerical data on two different benchmarks: the laminar, unsteady flow past a 2D cylinder and the 3D turbulent jet. Finally, most of the aeroacoustic computations with LBM have been done with commercial softwares, while here the entire theoretical framework is implemented on top of an open source library (Palabos).Comment: 34 pages, 12 figures, The Journal of the Acoustical Society of America (in press

Numerical studies towards practical large-eddy simulation

Large-eddy simulation developments and validations are presented for an improved simulation of turbulent internal flows. Numerical methods are proposed according to two competing criteria: numerical qualities (precision and spectral characteristics), and adaptability to complex configurations. First, methods are tested on academic test-cases, in order to abridge with fundamental studies. Consistent results are obtained using adaptable finite volume method, with higher order advection fluxes, implicit grid filtering and "low-cost" shear-improved Smagorinsky model. This analysis particularly focuses on mean flow, fluctuations, two-point correlations and spectra. Moreover, it is shown that exponential averaging is a promising tool for LES implementation in complex geometry with deterministic unsteadiness. Finally, adaptability of the method is demonstrated by application to a configuration representative of blade-tip clearance flow in a turbomachine

Aeroelastic simulations of stores in weapon bays using Detached-Eddy simulation

Detached-Eddy Simulations of flows in weapon bays with a generic store at different positions in the cavity and with flexible fins are presented in this paper. Simulations were carried out to better understand the fluid–structure interactions of the unsteady, turbulent flow and the store. Mach and Reynolds numbers (based on the missile diameter) were 0.85 and 326.000 respectively. Spectral analysis showed few differences in the frequency content in the cavity between the store with rigid and flexible fins. However, a large effect of the store position was seen. When the store was placed inside the cavity, the noise reduction reached 7 dB close to the cavity ceiling. The closer the store to the carriage position, the more coherent and quieter was the cavity. To perform a more realistic simulation, a gap of 0.3% of the store diameter was introduced between the fin root and the body of the store. Store loads showed little differences between the rigid and flexible fins when the store was inside and outside the cavity. With the store at the shear layer, the flexible fins were seen to have a reduction in loads with large fluctuations in position about a mean. Fin-tip displacements of the store inside the cavity were of the range of 0.2% of the store diameter, and in the range of 1–2% of store diameter when at the shear layer

Accuracy consideration by DRP schemes for DNS and LES of compressible flow computations

Several dispersion relation-preserving (DRP) spatially central discretizations are considered as the base scheme in the framework of the Yee & Sjögreen low dissipative nonlinear filter approach. In addition, the nonlinear filter of Yee & Sjögreen with shock-capturing and long time integration capabilities is used to replace the standard DRP linear filter for both smooth flows and flows containing discontinuities. DRP schemes for computational aeroacoustics (CAA) focus on dispersion error consideration for long time lin- ear wave propagation rather than the formal order of accuracy of the scheme. The resulting DRP schemes usually have wider grid stencils and increased CPU operations count compared with standard central schemes of the same formal order of accuracy. For discontinuous initial data and long time wave propa- gation of smooth acoustic waves, various space and time DRP linear filter are needed. For acoustic waves interacting with shocks and turbulence induced noise, DRP schemes with linear filters alone usually are not capable of simulating such flows. The investigation presented in this paper is focused on the pos- sible gain in efficiency and accuracy by spatial DRP schemes over standard central schemes having the same grid stencil width for general direct numerical simulations (DNS) and large eddy simulations (LES) of compressible flows. Representative test cases for both smooth flows and problems containing discontinuities for 3D DNS of compressible gas dynamics are included

Studies of Inviscid Flux Schemes for Acoustics and Turbulence Problems

The last two decades have witnessed tremendous growth in computational power, the development of computational fluid dynamics (CFD) codes which scale well over thousands of processors, and the refinement of unstructured grid-generation tools which facilitate rapid surface and volume gridding of complex geometries. Thus, engineering calculations of 10(exp 7) - 10(exp 8) finite-volume cells have become routine for some types of problems. Although the Reynolds Averaged Navier Stokes (RANS) approach to modeling turbulence is still in extensive and wide use, increasingly large-eddy simulation (LES) and hybrid RANS-LES approaches are being applied to resolve the largest scales of turbulence in many engineering problems. However, it has also become evident that LES places different requirements on the numerical approaches for both the spatial and temporal discretization of the Navier Stokes equations than does RANS. In particular, LES requires high time accuracy and minimal intrinsic numerical dispersion and dissipation over a wide spectral range. In this paper, the performance of both central-difference and upwind-biased spatial discretizations is examined for a one-dimensional acoustic standing wave problem, the Taylor-Green vortex problem, and the turbulent channel fl ow problem

Turbulent jet simulation using high-order DG methods for aeroacoustics analysis

In this work, a high-order discontinuous Galerkin (DG) method is used to perform a large-eddy simulation (LES) of a subsonic isothermal jet at high Reynolds number Re D = 10^6 on a fully un-structured mesh. Its radiated acoustic field is computed using the Ffowcs Williams and Hawkings formulation. In order to assess the accuracy of the DG method, the simulation results are compared to experimental measurements and a reference simulation based on a finite volume method. The comparisons are made on the flow quantities (mean, rms and spectra) and pressure far field (rms and spectra)

A source-extraction based coupling method for computational aeroacoustics

This thesis involves the computation of aerodynamically generated sound using a source-extraction based coupling approach. In the present coupling method, the unsteady aerodynamic calculation and the calculation of sound propagation are separated artificially. A set of acoustic perturbation equations is derived by decomposing all flow variables into their dominant part and their fluctuating part, and neglecting some small-magnitude terms, and further simplified into a set of isentropic perturbation equations. Accompanying the derivation of the acoustic perturbation equations, a new extracting formulation for the acoustic source terms contained in the unsteady flow field is proposed. The acoustic source terms required in solving the acoustic perturbation equations are computed numerically from the time-dependent solutions of the unsteady flow field. In the simulation of the unsteady flow, the unsteady Reynolds-Averaged-Navier-Stokes equations (RANS) based cell-centred finite volume method is mainly used. A large eddy simulation (LES) technique is also employed in the investigation of one application case. A powerful and efficient high order dispersion-relation-preserving (DRP) finite difference scheme with fully staggered-grid variable arrangements is implemented in the solution of the acoustic perturbation equations. The performance of a set of radiation boundary conditions is examined for various background flows. A suitable and efficient coupling procedure, in conjunction with the source-extraction formulation, is designed between the cell-centred finite volume based CFD solver and the fully-staggered finite difference based acoustic solver. A range of acoustic model problems are investigated with the purpose of assessing the feasibility and accuracy of the source-extraction formulation associated with the coupling procedure. These model problems include wave propagation, reflection, interaction, and scattering, of acoustic pulse with/without background mean flow. The accuracy of computational results from these model problems is very encouraging when reasonable computational mesh sizes and time steps are used in both the CFD solver and the acoustic solver. Several applications of the source-extraction based coupling method to some more complex cases have also been examined. These cases are: 1) generation and propagation of sound by a series of vortices impinging on a finite thin flat plate; 2) generation and propagation of sound from a subsonic flow past a finite thin flat plate with a small angle of attack; 3) generation and near field radiation of aerodynamic sound from an low speed, laminar flow over a two-dimensional automobile door cavity; 4) flow-induced noise from an open cavity turbulent flow. These application calculations have demonstrated preliminarily the capability and potential of the new source extraction formulation for solving more realistic aeroacoustic problems