Abstract
Large Eddy Simulation shows considerable promise as a more accurate turbulent flow prediction tool than RANS. For typical engineering problems, the geometrical complexity means that an unstructured mesh approach is preferable. The aim of this work is to consider the dierent treatments of the convective flux term, in an unstructured formulation, and how this aects the solution accuracy. The embedded LES, or MILES approach, relies upon the numerical dissipation to remove energy from the smallest resolved scales and so comparisons are shown between embedded LES and LES using a Sub-Grid Scale model. The median dual is constructed from a mixed element mesh to provide the control volumes for the finite volume integration of the Navier-Stokes equations. Two MUSCL type flux schemes are considered. The first uses linear reconstruction, coupled with a limiter, to compute the left and right states and the dissipation term is evaluated using Roe Flux Dierence Splitting. The dissipation term is scaled using a sensor based on vorticity and divergence in order to keep the dissipative terms small. The second is computationally simpler and does not use reconstruction. The dissipative term is computed using a pseudo-Laplacian so as to give a fourth order term. Again, the magnitude of this term is controlled by a sensor. Results are shown for two cases: a fully developed pipe flow with a bulk Reynolds number of 10,000, and free jet with a Reynolds number of 36,000 and a Mach number of 0.9. All calculations produce realistic turbulent structures with no sign of re-laminarisation due to excessive numerical dissipation. For the pipe flow, the scheme using reconstruction and the full Roe FDS with MILES is observed to give weaker large scale structures, and the solution is improved considerably by scaling down the numerical dissipation and incorporating a sub-grid scale model. Good agreement is found with experiment for all computations of the free jet case, although there is some sensitivity of the potential core length to numerical scheme and presence of sub-grid scale model.
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