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Publication# Simulation of benchmark and industrial unsteady compressible turbulent fluid flows

Abstract

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.

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Accurate microscale windfields computations over complex topography is crucial to many particle transport models but remains a challenging task. The objective of this work focuses on the numerical simulations of micro-scale windfields over the steep Gaudergrat ridge, located in the Swiss Alps. These windfields are computed with the objective of driving a snowdrift model, consequently the work concentrates on meteorological situations close to snow storms. As snow transport occurs in the first meters above the surface, this implies a very fine resolution of order tens of meters. Airflow simulations are performed using the meteorological model ARPS (Advanced Regional Prediction System), which is based on a Large Eddy Simulation (LES) formulation of the compressible Navier-Stokes equations. The turbulent airflow features play an important role in the transport of particles. Therefore ARPS turbulence models, the Smagorinsky-Lilly and the 1.5 order Turbulent Kinetic Energy (TKE) closures, have been examined in neutral atmosphere conditions over flat terrain. ARPS mechanical turbulence schemes has hence been tested and the parameters of the Subgrid-Scales (SGS) models have been tuned. ARPS has already been proven suitable for reproducing qualitative features of airflow and over complex alpine terrain with a careful choice of the artificial initialisation and periodic boundary conditions. When lateral periodic boundary conditions are applied for airflow computations over real complex topography, instabilities arise quickly. For a quantitative and stable description of airflow presented in this work, the initialisation and boundary conditions have consequently been improved. In this study, the simulations over the Gaudergrat ridge presented are performed a one-way nesting approach. ARPS is first driven by the outputs of the MeteoSwiss model aLMo which produce initial and time dependent lateral boundary conditions. Then the application of the nesting technique permit to bridge spatial resolutions from 7km (aLMo grid resolution) to 25 m (horizontal resolution in the finer ARPS grid). Such a fine resolution is also required for Large-Eddy Simulations (LES) configuration and it is expected that a large part of the energy is resolved explicitly. The nesting technique has been applied to reproduce two selected days during the Gaudergrat Experiment (Gaudex) with stronger wind, to have conditions as close as possible to winter conditions and when thermal winds are weak. The field measurement campaign, Gaudergrat Experiment (Gaudex), in collaboration with the University of Leeds, was held from June to October 2003 at the Gaudergrat ridge, near Davos, Switzerland. The collected data are used to develop a better understanding of the airflow characteristics and turbulence features as well as to check the model results. The comparison with field data show satisfactory results for the mean flow quantities, whereas the lateral boundary condition forcing suppresses the small scales turbulent motion. A simple method is proposed to spin up turbulent motions in the finer resolution domain. This method is based on the introduction of turbulent perturbations from a precursor simulation onto the mean wind profile at the lateral boundaries. This new configuration facilitate the development of turbulence and resolves explicitly smaller scale motions without altering the mean flow. The spectral analysis of the Gaudex data highlights the fact that the turbulence on the lee side of the Gaudergrat ridge is influenced by local features, whereas at the crest, the effect of the surrounding mountains is recognisable. The statistical analysis of wind speed fluctuations shows that the turbulence in complex terrain is highly intermittent, but can be interpreted as a combination of subsets of isotropic turbulence. In complex terrain, the production of turbulence is not continuous, it is hence difficult to apply the traditional scaling and averaging laws developed for homogeneous horizontal surfaces. The heterogeneous surface conditions are likely to create additional length and time scale to generalise the statistical properties.

The research work reported in the present dissertation is aimed at the analysis of complex physical phenomena involving instabilities and nonlinearities occurring in fluids through state-of-the-art numerical modeling. Solutions of intricate fluid physics problems are devised in two particularly arduous situations: fluid domains with moving boundaries and the high-Reynolds-number regime dominated by nonlinear convective effects. Shear-driven flows of incompressible Newtonian fluids enclosed in cavities of varying geometries are thoroughly investigated in the two following frameworks: transition with a free surface and confined turbulence. The physical system we consider is made of an incompressible Newtonian fluid filling a bounded, or partially bounded cavity. A series of shear-driven flows are easily generated by setting in motion some part of the container boundary. These driven-cavity flows are not only technologically important, they are of great scientific interest because they display almost all physical fluid phenomena that can possibly occur in incompressible flows, and this in the simplest geometrical settings. Thus corner eddies, secondary flows, longitudinal vortices, complex three-dimensional patterns, chaotic particle motions, nonuniqueness, transition, and turbulence all occur naturally and can be studied in the same geometry. This facilitates the comparison of results from experiments, analysis, and computation over the whole range of Reynolds numbers. The flows under consideration are part of a larger class of confined flows driven by linear or angular momentum gradients. This dissertation reports a detailed study of a novel numerical method developed for the simulation of an unsteady free-surface flow in three-space-dimensions. This method relies on a moving-grid technique to solve the Navier-Stokes equations expressed in the arbitrary Lagrangian-Eulerian (ALE) kinematics and discretized by the spectral element method. A comprehensive analysis of the continuous and discretized formulations of the general problem in the ALE frame, with nonlinear, non-homogeneous and unsteady boundary conditions is presented. In this dissertation, we first consider in the internal turbulent flow of a fluid enclosed in a bounded cubical cavity driven by the constant translation of its lid. The solution of this flow relied on large-eddy simulations, which served to improve our physical understanding of this complex flow dynamics. Subsequently, a novel subgrid model based on approximate deconvolution methods coupled with a dynamic mixed scale model was devised. The large-eddy simulation of the lid-driven cubical cavity flow based on this novel subgrid model has shown improvements over traditional subgrid-viscosity type of models. Finally a new interpretation of approximate deconvolution models when used with implicit filtering as a way to approximate the projective grid filter was given. This led to the introduction of the grid filter models. Through the use of a newly-developed method of numerical simulation, in this dissertation we solve unsteady flows with a flat and moving free-surface in the transitional regime. These flows are the incompressible flow of a viscous fluid enclosed in a cylindrical container with an open top surface and driven by the steady rotation of the bottom wall. New flow states are investigated based on the fully three-dimensional solution of the Navier-Stokes equations for these free-surface cylindrical swirling flows, without resorting to any symmetry properties unlike all other results available in the literature. To our knowledge, this study delivers the most general available results for this free-surface problem due to its original mathematical treatment. This second part of the dissertation is a basic research task directed at increasing our understanding of the influence of the presence of a free surface on the intricate transitional flow dynamics of shear-driven flows.

Several authors have proposed studying randomly forced turbulent hows (e.g., E. A. Novikov, Soviet Physics JETP, 20(5), 1290 1965). More recently, theoretical investigations (e.g., renormalization group) have focused on whim-noise forced Navier-Stokes equations (V. Yakhot and S. A. Orszag, J.Sci.Comput. 1(1), 3 1986), The present article aims to provide an appropriate numerical method for the simulation of randomly forced turbulent systems. The spatial discretization is based on the classical Fourier spectral method. The time integration is performed by a second-order Runge-Kutta scheme. The consistency of an extension of this scheme to treat additive noise stochastic differential equations is proved. The random number generator is based on lagged Fibonacci series. Results are presented for two randomly forced problems: the Burgers and the incompressible Navier-Stokes equations with a white-noise in time forcing term characterized by a power-law correlation function in spectral space. A variety of statistics are computed for both problems, including the structure functions, The third-order structure functions are compared with their exact expressions in the inertial subrange. The influence of the dissipation mechanism (viscous or hyperviscous) on the inertial subrange is discussed. In particular, probability density functions of velocity increments are computed for the Navier-Stokes simulation, Finally, for both Burgers and Navier-Stokes problems, our results support the view that random sweeping is the dominant effect of the large-scale motion on the small-scales. (C) 1998 Academic Press.

1998