Investigation of high-resolution methods in large-eddy simulation of subsonic and supersonic wall turbulent flows

Abstract

This thesis presents the motivation, objectives and reasoning behind the undertaken PhD to investigate the capability of compressible Implicit Large Eddy Simulation (ILES) in simulating wall-bounded inhomogeneous flows with particular interest in the near wall region and further presents the progress achieved to date. Investigation includes the assessment of current ILES methods to resolve inhomogeneous turbulence as well as compressible turbulent boundary layers and to improve on those models further. A channel flow is an excellent problem to use to investigate the properties of a SGS model near a wall. The presence of a solid boundary tends to alter the behaviour of the turbulent flow in a number of ways that need to be modeled by the SGS model in order to correctly represent the flow near the wall and most importantly the boundary layer. The presence of the wall inhibits the growth of the small scales, alters the exchange mechanisms between the resolved and unresolved scales and finally gives rise in the SGS near wall region to important Reynolds-stress producing events. A literature survey was carried out to identify other numerical investigations in simulating channel flow as well as data that could be used for validation purposes. The main parameters used to validate the level of resolution in simulating channel flow are identified and a number of tools are developed. The primary parameters extensively used to validate LES simulations of channel flow throughout the literature are mean flow velocity profiles, turbulent kinetic energy, dissipation and shear stress profiles, wall shear stress and friction velocities as well as energy spectra in the spanwise and streamwise homogeneous directions. Compressible viscous ILES of inhomogeneous anisotropic turbulence in an incompressible channel flow at wall normal grid resolutions of 68, 96 and 128 cells are carried out with grid clustering applied to the wall normal direction. Initial results conducted in the compressible regime show that in order to obtain satisfactory results, medium and fine grids are required whereas on coarser grids, some additional numerical method is required. Each reconstruction scheme introduces a numerical dissipation characteristic to itself that maybe regarded as a sort of turbulence model. Thus depending on the required dissipation, a suitable limiter can be chosen. The investigation then moves on to supersonic turbulent flow incorporating shockboundary layer interaction. Only the slope-limiters that prove to simulate the flow in the fully developed turbulent channel best are favoured and then also utilised in the subsequent compressible ramp simulations. The capabilities of modelling the shock boundary layer interaction, mean turbulent profiles and shockwave angle are investigated and compared against those obtained by DNS simulations. It is found that the grid at the inlet of the ramp plays a significant role, since it needs to be fine enough to maintain the turbulent in flow at an acceptable level before reaching the shock-boundary layer interaction zone. Further, very high-order numerical reconstructions were found to have difficulties in remaining stable in the high gradient regions of the flow when formulated in conservative form and therefore solutions were not possible to obtain. Nonetheless, lower order reconstruction methods run smoothly and the momentum profiles obtained, matched closely those obtained by DNS.