Fundamental research on DES for practical calculation of wall-bounded turbulence at high Reynolds number

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Hybrid method combining the Reynolds-averaged Navier-Stokes equation (RANS) and the large eddy simulation (LES) is a useful approach to numerical simulation of wall-bounded turbulence at high Reynolds number. A fundamental research was carried out on hybrid simulation including the detached eddy simulation (DES). The main results are as follows:1. Analysis and improvement of the mismatch of velocity profile in turbulent channel flowA numerical simulation of turbulent channel flow was carried out to reproduce the mismatch of the velocity profile at the RANS/LES interface. The mixing length model and k-ε model were used to simulate the turbulent flow. The reason for the mismatch was investigated by obtaining the statistics such as the turbulent kinetic energy and by examining the structure of velocity fluctuations. In order to incorporate nonlocal effect, a new filtering was introduced at the RANS/LES interface and two velocity components referred to from the RANS and LES regions were defined. It was shown that the mismatch can be removed by optimizing the filter width and its location.2. Theoretical analysis of the hybrid filter and its applicationThe formalism of the hybrid filter introduced by Germano was extended to theoretically investigate the additional filtering at the interface. It was shown that the additional filtering can be considered as a finite difference approximation to Germano's hybrid filter. This result gives the physical justification of the additional filtering. An expression for the filter width and its location was derived and applied to the turbulent channel flows at low and high Reynolds numbers. It was shown that the velocity mismatch is removed and good velocity profile is obtained. Moreover, the relation between the Germano's hybrid filter and the stochastic forcing was investigated to improve the hybrid simulation.