Coupled compressible and incompressible finite volume formulations for the large eddy simulation of turbulent flow with and without heat transfer

摘要

A coupled finite volume approach for solving the time-dependent Navier-Stokes equations is developed for application to the large eddy simulation (LES) of turbulent flow. The preconditioning strategy of coupling the incompressible N-S equations and providing acceleration of iterative convergence in both compressible and incompressible formulations is employed. Three different spatial discretization schemes along with the regular/staggered grid arrangements are evaluated on both two-dimensional laminar flows and three-dimensional turbulent flows;No distinctive differences are found in laminar flow cases, but the staggered grid appears to provide a better resolution of the turbulence statistics over a regular one in the simulation of turbulence. Comparisons are also presented between LES and coarse-grid direct numerical simulation (DNS) for the channel flow, and effects of grid refinement are examined. Further, the dynamic subgrid scale model is successfully applied to the LES of the square-duct flow as well;While the upwinding scheme offers an advantage in laminar cases, in incompressible turbulent flows it appears to have accuracy only comparable to the central differencing schemes on the staggered grid. However, the central differencing schemes fail both on the regular grid arrangement for incompressible simulations and on the staggered grid for compressible flow; this seems to make upwinding the optimal choice;Finally, the turbulent channel flow with fluid property variations caused by low and significant heat transfer (with the hot to cold wall temperature ratio of 1.02 and 3.0) is simulated using a compressible dynamic model. Different flow statistics are compared. For the significant heat transfer case, while the low order statistics such as variances and correlations generally tend to exhibit noticeable variations in the cold and hot wall regions, higher order moments such as the skewness and flatness factors are observed to be mostly insensitive to the present heat transfer rate. Further, the Reynolds shear stress budget is also found not to be affected by the heat transfer rate change, while the temperature variance budget is slightly altered in the very near-wall regions;Overall, the dynamic subgrid scale model seems to perform well and does not require the specification of the turbulent Prandtl number for heat transfer cases.