Regularization-based sub-grid scale (SGS) models for large eddy simulations (LES) of high-Re decaying isotropic turbulence

Abstract

Regularization-based subgrid-scale (SGS) turbulence models for large eddy simulations (LES) are quantitatively assessed for decaying homogeneous turbulence (DHT) and transition to turbulence for the Taylor-Green vortex (TGV) through comparisons to laboratory measurements and direct numerical simulations (DNS). LES predictions using the Leray-α, LANS-α, and Clark-α regularization-based SGS models are compared to the classic nondynamic Smagorinsky model. Regarding the regularization models, this work represents their first application to relatively high-Re decaying turbulence with comparison to the active-grid-generated decaying turbulence measurements of Kang et al. (J. Fluid Mech., 2003) at Re _λ ≈ 720 and the Re = 3000 DNS of transition to turbulence in the TGV of Drikakis et al. (J. Turbulence, 2007). For DHT the nondynamic Smagorinsky model is in excellent agreement with measurements for the turbulent kinetic energy and energy spectra but higher-order moments show slight discrepancies. For TGV too, the energy decay rates of Smagorinsky agree reasonably well with DNS. Regarding the regularization models stable results are not obtained as compared to the Smagorinsky model at the same grid resolution for various values of α; and at higher grid resolutions, they are in worse agreement. However, with additional dissipation such as in mixed α-Smagorinsky models, results are acceptable and show only slight deviations from Smagorinsky.

Keywords:

• isotropic turbulence
• large eddy simulation
• sub-grid scale modeling
• regularization

Acknowledgments

This work is partially supported by NSF Grant No. 0651788 and is gratefully acknowledged. Computing time was provided by the National Center for Supercomputing Applications (NCSA), Argonne National Laboratories, and Purdue University Supercomputing. We would like to thank Dr. Stephen Pope at Cornell, Dr. Gregory Blaisdell at Purdue, Dr. Charles Meneveau at Johns Hopkins, and Dr. Hyung Kang at Johns Hopkins universities, for all the insightful discussions during the initial development of the code and the generation and analysis of some of the results used in the current study.