Recovery of subgrid-scale turbulence kinetic energy in LES of channel flow

A methodology is presented for recovery of the subgrid-scale (SGS) turbulence kinetic energy in large-eddy simulations (LES) of turbulent channel flow. The formulation is based on extending the one-dimensional energy spectra computed in LES at each wall-normal location using a filtered form of one-dimensional energy spectra derived from the theoretical formulations of Pao [1] or Kraichnan [2]. The extended spectra are integrated to recover the SGS turbulence kinetic energy as a function of the wall-normal direction, from which the individual components of turbulence intensities are recovered using the formulation of Winckelmans et al. [3]. To account for the anisotropy of turbulence in the near-wall region, a transformation is introduced to map the ellipsoidal iso-surfaces of turbulence kinetic energy density in the spectralspace to a spherical surface, where the filtering operations can be applied to the theoretical spectra. The transformation parameters are determined from the dissipative scale in each direction, while the constants in the theoretical spectra are determined by minimizing the errors between the theoretical and LES spectra. The turbulence kinetic energy recovery procedure is applied at a post-processing stage and is independent of the SGS model employed. Validation studies performed using a DNS database of a turbulent channel flow at Re T ⊆ 570 show that the method can recover the total turbulence kinetic energy with errors of less than 1% and the SGS turbulence kinetic energy with errors of less than 10%. In application to LES data, the components of full turbulence intensities are recovered with an accuracy comparable to the accuracy with which the filtered statistics were predicted in LES.