A rescaling method for correcting log-layer mismatch in detached eddy simulation

Abstract

In order to correct the unphysical log-layer mismatch commonly encountered in detached eddy simulation (DES) of flows with attached boundary layers, a function lM,ML, which has a multi-layer structure with scaling laws in each layer and a plateau related to the Karman constant, is defined. The height of this plateau is found to be crucial for obtaining the correct log-layer. A target scaling function is designed which equals lM,ML in the near-wall region, but with the height of plateau determined analytically from the classical log-law. This scaling function is used as a target function according to which the resolved turbulent fluctuations are renormalized, in order to recover the height of plateau prescribed by the log-law. The renormalization procedure guarantees the height of lM,ML required by log-law, resulting in correct log layer slope. The method is also shown to maintain similar turbulent properties in the large eddy simulation (LES) region of DES method. Hence it predicts the turbulent intensity correctly. The results demonstrate the relationship between constant lM,ML and log-law profile of mean velocity, and relate the Karman constant to turbulent fluctuations, implying a complete description of turbulent structural ensemble dynamics. The proposed method can be extended to more general flows with log layers since it uses only the log-law with Karman constant as the input, while the intercept of log layer depends on the solution of Spalart-Allmaras (SA) model in the near-wall field, where Reynolds-averaged Navier-Stokes (RANS) solutions are accurate.