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Publication# Intercomparison of Terrain-Following Coordinate Transformation and Immersed Boundary Methods for Large-Eddy Simulation of Wind Fields over Complex Terrain

Résumé

We here perform an intercomparison of TFCT and IBM for large-eddy simulation of a turbulent wind field over a three-dimensional hill, for which wind-tunnel measurements are available for validation. The experimental dataset contains both vertical and horizontal profiles of mean velocities and variances, which allows an in-depth comparison of the numerical models. For the TFCT, a new algorithm for solving the pressure Poisson equation in the transformed coordinate system is proposed and first validated for a laminar flow over periodic two-dimensional hills by comparing with available benchmark solutions. Since the slopes of the three-dimensional hill are not steep, TFCT, which is free from implementation errors for the wall model, is preferable to IBM. The effects of sub-grid scale models and different schemes used to implement wall boundary conditions for IBM are studied. Discrepancies between the results obtained by TFCT and IBM are observed near the surface. The source of errors and possible ways to improve the IBM implementation are discussed.

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Large-eddy simulation (LES) is a very promising technique for the numerical computation of unsteady turbulent flows, and seems to be the perfect tool to simulate the compressible air flow around a high-speed train in a tunnel, providing unsteady results for aerodynamic and aeroacoustic analysis. To look into this possible future application of LES, two major lines of investigation are pursued in this thesis: first, the study of the effective ability of shock-capturing schemes to predict fundamental turbulent phenomena; second, the analysis of the aerodynamic phenomena induced by a high-speed train in a tunnel. The numerical simulation of compressible flows requires the use of shock-capturing schemes. These schemes can be relatively dissipative and mask the subgrid-scale contribution introduced in a large-eddy simulation to account for the unresolved turbulence scales. To estimate their effective dissipation and their ability to resolve turbulence phenomena, shock-capturing schemes widely used for aeronautical applications, from second- to fifth-order space accuracy, are employed here for simulating well-known fundamental flows in subsonic and supersonic regimes. Direct and large-eddy numerical simulations are undertaken for the inviscid and viscous Taylor-Green vortex decay problem, the freely decaying homogeneous and isotropic turbulence, and the fully developed channel flow. For all the turbulent flows investigated, several turbulence statistics are computed and the numerical dissipation of the schemes tested is interpreted in terms of subgrid-scale dissipation in a LES context, yielding an equivalent Smagorinsky or dynamic coefficient. This coefficient is for all schemes of the same order of magnitude as the commonly accepted values in LES for the subgrid-scale term. On the grounds of this analysis and of the comparisons of the turbulence statistics with accurate data obtained in the literature, the addition of explicit subgrid-scale models to the shock-capturing schemes tested is not recommended. It is thus concluded that the use of the LES technique for compressible turbulent flows is not yet suitable for industrial applications. The aerodynamic phenomena generated by a high-speed train travelling in a tunnel are also discussed, their importance on the design of high-speed lies is pointed out, and the analysis tools commonly employed for their study are reviewed. To study numerically the three-dimensional, compressible and turbulent air flow around a high-speed train accelerating in a tunnel, by accounting for the unsteady effects at inlet and outlet boundaries due to the propagation of pressure waves generated at the train departure, new coupling conditions between one-dimensional and three-dimensional domains are developed. These conditions are applied successfully to the numerical simulation of the unsteady wake developing behind two- and three-dimensional vehicles, where the averaged Navier-Stokes equations are solved with the turbulence modelling approach. The influence on the wake of the length of the vehicle tail is also discussed and results of multi-dimensional simulations are compared with one-dimensional data.

Jiannong Fang, Fernando Porté Agel

Accurate modeling of complex terrain, especially steep terrain, in the simulation of wind fields remains a challenge. It is well known that the terrain-following coordinate transformation method (TFCT) generally used in atmospheric flow simulations is restricted to non-steep terrain with slope angles less than 45 degrees. Due to the advantage of keeping the basic computational grids and numerical schemes unchanged, the immersed boundary method (IBM) has been widely implemented in various numerical codes to handle arbitrary domain geometry including steep terrain. However, IBM could introduce considerable implementation errors in wall modeling through various interpolations because an immersed boundary is generally not co-located with a grid line. In this paper, we perform an intercomparison of TFCT and IBM in large-eddy simulation of a turbulent wind field over a three-dimensional (3D) hill for the purpose of evaluating the implementation errors in IBM. The slopes of the three-dimensional hill are not steep and, therefore, TFCT can be applied. Since TFCT is free from interpolation-induced implementation errors in wall modeling, its results can serve as a reference for the evaluation so that the influence of errors from wall models themselves can be excluded. For TFCT, a new algorithm for solving the pressure Poisson equation in the transformed coordinate system is proposed and first validated for a laminar flow over periodic two-dimensional hills by comparing with a benchmark solution. For the turbulent flow over the 3D hill, the wind-tunnel measurements used for validation contain both vertical and horizontal profiles of mean velocities and variances, thus allowing an in-depth comparison of the numerical models. In this case, TFCT is expected to be preferable to IBM. This is confirmed by the presented results of comparison. It is shown that the implementation errors in IBM lead to large discrepancies between the results obtained by TFCT and IBM near the surface. The effects of different schemes used to implement wall boundary conditions in IBM are studied. The source of errors and possible ways to improve the IBM implementation are discussed.

2016