Turbulence modeling for computational fluid dynamics, Part I: Conceptual outlook[

The motivations like economics, and in house availability of powerful computers advocates the use of numerical methods as a complementary tool for experiments. Resolving all time and length scales as in the case of Direct Numerical Simulation (DNS), computational solutions are equivalent to experimental ones. However, as a result of memory limitations, even in supercomputers, most of engineering problems encountered in nature can not be attained numerically by means of DNS. Therefore, a large variety of turbulence models are developed in order to account for the effect of turbulence. Large Eddy Simulation (LES) is at the highest level in modeling. Its modeling concept is based on the computation of large energy-carrying structures and modeling the small structures. LES is computationally cheaper than DNS and enables the solution of complex flows. Resulting subgrid-scale models are simpler in comparison to models for Reynolds-averaged Navier-Stokes equations (RANS), which build second level in turbulence modeling. There is no unique turbulence model that applies to wide range of flows encountered in nature. Hence, modeling requires that it must be verified by experiment. This paper is the first part of two. In this part, we present conceptual view of turbulence modeling concepts in order to provide a perspective for those unfamiliar with the current status and a basis for those new in this field. In the second part, we will present some key solutions with various turbulence models to provide more details.

___

[1] Uygun, M., Tuncer, I.H., "Viscous Flow Solutions over CN-235 Cargo Aircraft,"accepted to appear in AIAA Journal of Aircraft,2004

[2] Uygun, M., "A Computational Study of Subsonic Flows over A Medium Range Cargo Aircraft," M.S. Thesis, Middle East Technical University, Turkey, 2000.

[3] Uygun, M., "Development of Scripts for Building Computational Grids for a Model Submarine," DRDC Atlantic CANADA, TN 2003-160, August 2003.

[4] Reynolds, O., "On the Dynamical Theory of Incompressible Viscous Fluid and the Determination öf the Criterion," Phil. Tran. Ro.Soc. Lon., Series A, Vol. 186,123-161,1874.

[5] Cebeci, T.; Smith, A.M.O., "Analysis of Turbulent Boundary Layers," Academic Press,New York, 1974.

[6] Wilcox, D.C., "Turbulence Modeling for CFD,"DCW Industries, Inc., La Canada, California,USA, 1993.

[7] Favre, A., "Equations des gaz turbulents compressible, part 1: formes generates," Journal de Mechanique Vol. 4, 361-390,1965.

[8] Morkovin, M.V., "Effects of Compressibility on Turbulent Flows," The mechanics of Turbulence,Fordon and Breach, New York, 1961.

[9] Boussinesq, J., "Essai sur la theorie des eaux courantes," Mem. Pres. Acad. Sci., XXIII, 46,Paris, 1877.

[10] Reynolds, W.C., "Computation of Turbulent Flows," Thermoscience Division, Dept. of Mechanical Engineering, Standford Univ.,Standford Calif., Rept. TF-4,1975.

[11]Shur, M.; Strelets, M.; Travin, A.; Spalart, P.,"Turbulence Modeling in rotating and Curved Channels: Assessment of the Spalart-Shur Correction term," AIAA Paper 98-0325,1998.

[12] Shin, T.H.; Zhu, J.; Liou, W.W.; Chen, K.H.; Liu, N.S.; Lumley, J., "Modeling of Turbulent Swirling Flows," NASA TM-113112,1997.

[13]Abdel Gawad, A.F.; Abdel Latif, O.E.; Ragab,S.A.; Shabaka, L.M., "Turbulent Flow and Heat Transfer in Rotating Non-Circular Ducts with Nonlinear k-e Model," A1AA Paper 98-0326, 1998.

[14]Lumley, J.L.; "Computational Modeling of Turbulent Flows," Advances in Applied Mechanics, Vol. 18,123-176,1978.

[15]Shur, M.; Strelets, M.; Travin, A.; Spalart, P., "Turbulence Modeling in Rotating and Curved Channels: Assessment of the Spalart-Shur Correction Term," A1AA Paper 98-0325,1998.

[16]Deardorff, J.W.; "A Numerical Study of Three-Dimensional Turbulent Channel Flow at Large Reynolds Number," Journal of Fluid Mechanics, Vol. 41,453-480, 1970

[17]Bardina, J.; Ferziger, J.H.; Reynolds, W.C., "Improved Sub-grid Models for Large Eddy Simulation," AIAA Paper 80-1357,1980.

[18]Moin, P.; Kim, J.; "Numerical Investigation of Turbulent Channel Flow," Journal of Fluid Mechanics, Vol. 118,341-377,1982.

[19]Hallback, M.; Henningson, D.S.; Johansson, A.V.; Alfredsson, P.H., "Turbulence and Transition Modeling," ERCOFTAC Series, Vol.2, Dordrecht, the Netherlands, 1996.

[20] Chapman, D.R.; "Computational Aerodynamics Development and Outlook," AIAA Journal, 17 (1979),pp.l293-1313.

[21] Vasilyev, O.V.; Lund, T.S.; Moin, P., "A General Class of Commutative Filters for LES in Complex Geometries," Journal of Computational Physics, Vol. 146 82-104,1998.

[22] Moin, P.; Squires, K.D.; Cabot, W.H.; Lee, S.: A Dynamic Subgrid-Scale Model for Compressible Turbulence and Scalar Transport. Physics of Fluids, Vol. 3, 2746-2757,1991.

[23]Vreman, B.; Geurts, B.; Kuerten, H.; Broeze, J.; Wasistho, B.; Streng, M.: Dynamic Subgrid-Scale Models for LES of Transitional and Turbulent Compressible Flow id 3-D Shear Layers. 10th Symposium on Turbulent Shear Flows, The Pennsylvania State University, PA, Volume 1, August 14, 1995.

[24]Lenormand, E.; Sagaut, P.; Phuoc, L.T.; Comte,P.: Subgrid-Scale Models for Large-Eddy Simulations of Compressible Wall Bounded Flows. AIAA Journal, Vol. 38,1340-1350, 2000.

[25] Smagorinsky, J., "General Circulation Experiments with the primitive Equations,"Monthly Weather Review, Vol. 91,99-165,1963.

[26] Gerrnano, M.; Piomelli, U.; Moin, P.; Cabot,W.H.: A Dynamic Sub-grid Scale Eddy Viscosity Model. Physics of Fluids, Vol. 3, 1760-1765,1991. "

[27] Ghosal, S.; Lund, T.S.; Moin, P.; Akselvoll, K.: A Dynamic Localization Model for Large-Eddy Simulation of Turbulent Flows. Journal of Fluid Mechanics, Vol. 286, 229-255, 1995.

[28] Marvin, J.G., "Advancing Computational Aerodynamics through Wind-Tunnel experimentation," AGARD Fluid Dynamics Panel Meeting on Integration of Computers and Wind Tunnel Testing, Chattanooga, Tenn. Sept. 24,1980.