A Renormalized Detached Eddy Simulation Method Without Log-Layer Mismatch

Abstract

In order to correct the log-layer mismatch (LLM) commonly encountered in detached eddy simulation (DES) of attached or weakly-detached flows, a multi-layered order function $\ell _\mathrm{{M,ML}}$ is defined. One of the layers of $\ell _\mathrm{{M,ML}}$ is a plateau and is crucial to the log-law of the mean velocity profile. The plateau height can be determined theoretically from the usual log-law formulation. A target function $\ell _\mathrm{{M,target}}$ is defined which inherits near wall scaling of SA model and extends it to reach the correct plateau. The function is used to renormalize (stretching/compressing) turbulent fluctuations during DES calculation. This renormalized DES (RNDES) is tested in both an incompressible channel flow and a ${\text {Ma}}=2.25$ compressible boundary layer (CBL) flow. RNDES predicts correct mean velocity profiles free of LLM and correct turbulent intensities as well, indicating that RNDES develops correct turbulent structural ensemble under the constraint of statistical quantities.