07. Turbulence and Flow Instabilities

Numerical simulation of turbulence is an important tool for flow analysis in physics and engineering. This numerical simulations at practical Reynolds numbers using the DNS are still difficult to compute due to the large number of grid points required. Therefore, the utilization of turbulence models such as RANS and LES are essential for turbulence simulations. LES is becoming a useful tool for engineering design as computing power advances. LES models the effects of eddies smaller than sub-grid scale (SGS) in the form of eddy viscosity coefficients under a sufficiently fine grid size. Most of the currently proposed SGS models are modeled by assuming that the variation of the vortex energy spectrum from the inertial sub-region to the viscous dissipation region follows Kolmogorov's -5/3 power law. This assumption, however, causes errors in low-Reynolds number simulations where the range of the inertial sub-region is narrow. On the other hand, a simple one-dimensional dynamical model referred to as a shell model is known to represent very well the energy spectral characteristics of uniformly isotropic turbulence from the inertial sub-region to the viscous dissipative region. If the eddy viscosity effects of SGS can be evaluated using the shell model, the energy spectrum of SGS can be estimated by the shell model using the grid-scale flow field data obtained by LES, which may improve the accuracy of LES simulation in the low Reynolds number. This means that LES can provide an estimation equivalent to that of DNS. The present research attempted to develop an evaluation method for eddy viscosity that can continuously simulate the energy spectrum of eddies from the grid scale to the viscous dissipation region of the SGS by connecting the shell model with the LES calculation results based on the two-scale direct interaction approximation model proposed by Yoshizawa.

Shin-ichi Inage

Prof.