Large Eddy Simulation with the unstructured collocated arrangement

TitleLarge Eddy Simulation with the unstructured collocated arrangement
Publication TypeThesis
Year of Publication2006
AuthorsBenhamadouche, S
DegreePhD Thesis, The University of Manchester
UniversityUniversity of Manchester
AbstractSeveral industrial applications of CFD, such as thermal fatigue, aero-acoustic noise or fluid-structure interaction need to capture the unsteady behaviour of an incompressible flow. Large Eddy Simulation is the only reasonable approach in CFD to obtain a time-dependent solution, as well demonstrated on academic cases. However, performing LES on fully unstructured finite-volume grids, as required for complex industrial geometries, as well as to locally adapt the grid resolution to the large spatial variations of turbulent scales, remains challenging. The main purpose of the present work is to deal with the collocated arrangement implemented in the in-house ´Electricit´e De France (EDF) code Code Saturne and to show whether reasonable LES computations are feasible with this discretization. Several numerical issues such as numerical dissipation are first analyzed in a discrete sense. It is found that the Rhie and Chow interpolation, widely used in all the collocated approaches, introduces a numerical dissipation which drains energy equally at all the wave-numbers. Removing this interpolation on regular Cartesian grids allows, with a second order Crank-Nicolson scheme and sub-iterations on the predictor-corrector algorithm for pressure/velocity coupling, to strictly conserve kinetic energy. Nevertheless, the interpolation is maintained as it has a stabilizing effect on skewed grids and as it avoids odd-even decoupling phenomenon. It is also found that a ’symmetrical’ formulation allows to strictly conserve kinetic energy for the convection term. The use of this formulation alters the second order precision of the code. Thus, a second order approach for the convection term is kept with implicit gradient reconstruction for non-orthogonal grids. Finally, sub-iterations on the predictor-corrector algorithm for pressure/velocity coupling are retained as this allows to reduce time splitting errors. A particular attention is then paid to the Decaying Isotropic Turbulence in order to identify the implicit filter induced by the discretization and to find the appropriate Smagorinsky constant. It is found that the implicit filter induced by the numerical discretization with a Smagorinsky model resembles to a Gaussian filter with a filter-width equal to 2h where h is the grid-spacing in a regular mesh. The value of the Smagorinsky constant is between 0.16 and 0.18 what corresponds to consensual values found in the literature for highly accurate discretizations. The explicit filter employed for the dynamic model is a smoothing operator that involves all the neighbours of a cell which share a node with it. The filter-width of this explicit filter is equal, on uniform meshes, to 3h. The averaging of the Smagorinsky constant is done for its numerator and denominator separately. It is also shown that local averaging gives reasonable results with the DIT which is encouraging for industrial simulations in which no homogeneous direction is available. The last two academic cases to be tested are the standard and the oscillating channel flows. After usual tests on structured Cartesian meshes, the ability of nonconforming meshes to adapt the resolution large eddy scale variations at the wall is pointed out. The global over-estimation of the mean velocity often observed with Cartesian meshes is cured by introducing local refinements in the near-wall region using the capabilities of a collocated approach to naturally handle non-conforming meshes. This solution is very promising to run industrial cases at moderate to high Reynolds numbers without artificial wall functions. To conclude the channel flow simulations, a distributed non-conforming mesh is created following the behaviour of the Kolmogorov scales in each direction in order to obtain a very fine mesh compatible with a Direct Numerical Simulation resolution but with a lower number of computational cells than in the conforming cases. The results are very satisfactory compared to previous DNS calculations on structured grids. This capability can be exploited to run DNS calculations at higher Reynolds numbers with much less nodes than in the structured case. Finally, The potential of LES to predict complex vortical separation is reported using a 3D axi-symmetric bump considered very challenging by the CFD community as all Reynolds Averaged Navier-Stokes attempts totally failed. The calculations give satisfactory quantitative results. The main physical structures observed in the experiment are captured. The quantitative results are globally satisfactory except for the wall-normal component of the velocity which is far from the experimental results and for the Reynolds stresses which are overestimated.