DNS/LES Simulations of Separated Flows at High Reynolds Numbers

Direct numerical simulations (DNS) and large-eddy simulations (LES) simulations of flow through a periodic channel with a constriction are performed using the dynamic Smagorinsky model at two Reynolds numbers of 2800 and 10595. The LES equations are solved using higher order compact schemes. DNS are performed for the lower Reynolds number case using a fine grid and the data are used to validate the LES results obtained with a coarse and a medium size grid. LES simulations are also performed for the higher Reynolds number case using a coarse and a medium size grid. The results are compared with an existing reference data set. The DNS and LES results agreed well with the reference data. Reynolds stresses, sub-grid eddy viscosity, and the budgets for the turbulent kinetic energy are also presented. It is found that the turbulent fluctuations in the normal and spanwise directions have the same magnitude. The turbulent kinetic energy budget shows that the production peaks near the separation point region and the production to dissipation ratio is very high on the order of five in this region. It is also observed that the production is balanced by the advection, diffusion, and dissipation in the shear layer region. The dominant term is the turbulent diffusion that is about two times the molecular dissipation.

[1]  J. Deardorff.  A numerical study of three-dimensional turbulent channel flow at large Reynolds numbers , 1970, Journal of Fluid Mechanics.

[2]  Roger L. Simpson,et al.  Turbulent Boundary-Layer Separation , 1989 .

[3]  Ken-ichi Abe,et al.  Investigation of Anisotropy-Resolving Turbulence Models by Reference to Highly-Resolved LES Data for Separated Flow , 2002 .

[4]  P. Moin,et al.  Turbulence statistics in fully developed channel flow at low Reynolds number , 1987, Journal of Fluid Mechanics.

[5]  Christopher L. Rumsey,et al.  DNS, Enstrophy Balance, and the Dissipation Equation in a Separated Turbulent Channel Flow , 2013 .

[6]  D. Wilcox.  Turbulence modeling for CFD , 1993 .

[7]  Ugo Piomelli,et al.  Large-Eddy Simulations: Theory and Applications , 1996 .

[8]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[9]  Jochen Fröhlich,et al.  Highly resolved large-eddy simulation of separated flow in a channel with streamwise periodic constrictions , 2005, Journal of Fluid Mechanics.

[10]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[11]  A. W. Vreman,et al.  Direct and Large-Eddy Simulation of the Compressible Turbulent Mixing Layer , 1995 .

[12]  Christopher L. Rumsey,et al.  Summary of the 2004 Computational Fluid Dynamics Validation Workshop on Synthetic Jets , 2006 .

[13]  Michael A. Leschziner,et al.  LARGE EDDY SIMULATION OF SEPARATED FLOW IN A STREAMWISE PERIODIC CHANNEL CONSTRICTION , 2001, Proceeding of Second Symposium on Turbulence and Shear Flow Phenomena.

[14]  Stefan Becker,et al.  Flow and Turbulence Structures in the Wake of a Simplified Car Model (Ahmed Modell) , 2002 .

[15]  S. Pope.  Turbulent Flows: FUNDAMENTALS , 2000 .

[16]  Jean-Philippe Laval,et al.  Direct numerical simulation of a separated channel flow with a smooth profile , 2007, 0710.3729.

[17]  Jochen Fröhlich,et al.  A Comparative Study of the Turbulent Flow Over a Periodic Arrangement of Smoothly Contoured Hills , 2006 .

[18]  P. Sagaut.  BOOK REVIEW: Large Eddy Simulation for Incompressible Flows. An Introduction , 2001 .

[19]  S. Stolz,et al.  Large-Eddy Simulation of Separated Flow in a Channel with Streamwise-Periodic Constrictions , 2005 .

[20]  J. Deardorff,et al.  On the magnitude of the subgrid scale eddy coefficient , 1971 .

[21]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[22]  Anthony E. Washburn,et al.  Experimental Investigation of Separation Control Part 1: Baseline and Steady Suction , 2006 .

[24]  Christopher L. Rumsey.  Effect of Turbulence Models on Two Massively-Separated Benchmark Flow Cases , 2003 .

[25]  P. Sagaut,et al.  Large eddy simulation of subsonic and supersonic channel flow at moderate Reynolds number , 2000 .

[26]  Michael A. Leschziner,et al.  Large-eddy simulation of turbulent boundary layer separation from a rounded step , 2012 .

[27]  M. Y. Hussaini.  On Large-Eddy Simulation of Compressible Flows , 1998 .

[28]  Miguel R. Visbal,et al.  On the use of higher-order finite-difference schemes on curvilinear and deforming meshes , 2002 .

[29]  Chi-Wang Shu,et al.  A new class of central compact schemes with spectral-like resolution I: Linear schemes , 2013, J. Comput. Phys..

[30]  Michael Manhart,et al.  Flow over periodic hills – Numerical and experimental study in a wide range of Reynolds numbers , 2009 .

[31]  P. Moin,et al.  DIRECT NUMERICAL SIMULATION: A Tool in Turbulence Research , 1998 .