Analysis of filtered Navier–Stokes equation for hybrid RANS/LES simulation

Abstract

Hybrid Reynolds-averaged Navier-Stokes/large eddy simulation ͑RANS/LES͒ is expected to accurately predict wall-bounded turbulent flows at high Reynolds numbers. It is known that extra terms due to the noncommutivity between the hybrid filter and the spatial derivative appear in the hybrid-filtered equations. In this paper the filtered Navier-Stokes equation is investigated using direct numerical simulation data of turbulent channel flow. In particular, the transport equations for the resolved and modeled energies are evaluated to examine the contribution of the extra terms. The RANS and LES regions are located by setting the width of the hybrid filter varying from the grid spacing to the channel half width. In the first case the RANS region is located near the wall for wall modeling in LES. In the second case the RANS and LES regions are located upstream and downstream, respectively. The extra terms in the Navier-Stokes and continuity equations show fairly large values in the RANS/LES interface region in both cases. The extra terms for the convection and the turbulent diffusion represent the energy transfer from the modeled part to the resolved part. This energy transfer suggests that conventional hybrid simulations neglecting the extra terms may underpredict velocity fluctuations in the interface region, causing an insufficient momentum transport and velocity mismatch in channel flow. These results show that the effect of the extra terms should be taken into account in the filtered Navier-Stokes equation as well as in the turbulent-energy equation in hybrid simulations.

Effects of resolution inhomogeneity in large-eddy simulation

“…Specifically, 105 uniform grid points on the domain [6π/2 − 0.059882471808, 6π/2] are mapped to the domain [0, 4π] through equation (12). The offset value is determined to ensure the points exactly span a 4π interval.…”

“…Nevertheless, correction of the commutation error is crucial for developing robust subgrid stress (SGS) models for practical LES applications. Furthermore, Hamba [12] showed that the impact of resolution inhomogeneity on hybrid RANS/LES applications can be significant because the resolution must change drastically when transitioning to/from LES and RANS regions. Modeling of commutation effects will, therefore, also be necessary for these more sophisticated turbulence modeling techniques, which inherit the deficiencies of the traditional SGS models they are based upon.…”

Simulation and optimization of control parameters in energy hybrid filter

“…This filter passes frequencies up to 60Hz. Influence of higher harmonics on fi50 -angle (directly on sine and cosine of the angle) is avoided in this way which can be calculated next from so sine and cosine values prepared by using are tangent function [7]. where f 0 is mains frequency [8].…”

Verification and Validation: the Path to Predictive Scale-Resolving Simulations of Turbulence

“…This turns SRS models grid dependent, precluding the evaluation of modeling and numerical errors separately, a requirement for reliable V&V exercises. Also, dynamic SRS formulations lead to commutation errors since the filtering operator of the model does not commute with spatial and temporal differentiation [50]. iv) Numerical setup -a precise validation exercise requires numerical simulations and reference experiments performed on the same flow conditions, i.e., domain, boundary conditions, material properties, and initial or inflow conditions.…”