Comparison of the Sigma and Smagorinsky LES models for grid generated turbulence and a channel flow

• Detailed comparison and verification of new Sigma and classical Smagorinsky SGS model.
• Novel test case: Grid turbulence as observed in an opposed jet configuration.
• Very first DNS is presented for this experimentally well-investigated test case.
• Static Sigma model was found to perform comparable to dynamic Smagorinsky model.
• Especially the near wall region has been captured more accurately by Sigma model.

Context: A new and promising Large-Eddy simulation (LES) subgrid model, the Sigma model, has been developed by Nicoud, Baya-Toda and co-workers. Its performance in different codes and test cases compared to the Smagorinsky model is of interest.Objective: The present work investigates how suitable different subgrid stress (SGS) models, i.e. the static and dynamic Smagorinsky and in particular Sigma models are for a Turbulent Opposed Jet (TOJ) configuration and evaluates the differences between the models for a TOJ and channel flow configurations.Method: The Sigma model has been implemented in a dedicated LES/DNS code and is tested against Direct Numerical Simulation (DNS) data from channel flow and grid turbulence data obtained from DNS and from measurements in a TOJ configuration. The flow through the turbulence generating plate (TGP) of the TOJ configuration constitutes a very sensitive test case for fluid flow simulations. Hence, it is a suitable case for a comparison of different SGS models for LES.To compare the SGS models, only the isothermal flow through one of the opposed nozzles, including the TGP has been simulated. LES and DNS have been performed using different grid resolutions down to a grid spacing smaller than the Kolmogorov length scale estimated for the region between the nozzles. The DNS results are being compared to experimental results, while LES results are compared to the DNS data in turn.To underline the differences between the SGS models and to show the general applicability of the newly implemented Sigma model, simulations of the turbulent channel flow have been performed additionally.Results: The TOJ and channel flow simulations show good agreement between DNS and LES. It has been found, that the Sigma model is a better alternative to the static Smagorinsky model with comparable results to the dynamic Smagorinsky model for most of the settings examined.