Large-eddy simulation of the temporal mixing layer using the Clark model
Tóm tắt
The Clark model for the turbulent stress tensor in large-eddy simulation is investigated from a theoretical and computational point of view. In order to be applicable to compressible turbulent flows, the Clark model has been reformulated. Actual large-eddy simulation of a weakly compressible, turbulent, temporal mixing layer shows that the eddy-viscosity part of the original Clark model gives rise to an excessive dissipation of energy in the transitional regime. On the other hand, the model gives rise to instabilities if the eddy-viscosity part is omitted and only the “gradient” part is retained. A linear stability analysis of the Burgers equation supplemented with the Clark model is performed in order to clarify the nature of the instability. It is shown that the growth-rate of the instability is infinite in the inviscid limit and that sufficient (eddy-)viscosity can stabilize the model. A model which avoids both the excessive dissipation of the original Clark model as well as the instability of the “gradient” part, is obtained when the dynamic procedure is applied to the Clark model. Large-eddy simulation using this new dynamic Clark model is found to yield satisfactory results when compared with a filtered direct numerical simulation. Compared with the standard dynamic eddy-viscosity model, the dynamic Clark model yields more accurate predictions, whereas compared with the dynamic mixed model the new model provides equal accuracy at a lower computational effort.
Tài liệu tham khảo
Bardina, J., Ferziger, J.H., and Reynolds, W.C. (1984). Improved turbulence models based on LES of homogeneous incompressible turbulent flows Report No. TF-19, Department of Mechanical Engineering, Stanford, CA.
Chatelin, F. (1993).Eigenvalues of Matrices. Wiley, Chichester.
Clark, R.A., Ferziger, J.H., and Reynolds, W.C. (1979). Evaluation of subgrid-scale models using an accurately simulated turbulent flow.J. Fluid Mech.,91, 1–16.
Comte, P., Lesieur, M., and Lamballais, E. (1992). Large-and small-scale stirring of vorticity and a passive scalar in a 3D temporal mixing layer.Phys. Fluids A,4, 2761.
Erlebacher, G., Hussaini, M.Y., Speziale, C.G., and Zang, T.A. (1992). Toward the large-eddy simulations of compressible turbulent flows.J. Fluid Mech.,238, 155.
Favre, A. (1983). Turbulence: space-time statistical properties and behavior in supersonic flows.Phys. Fluids,26, 2851–2863.
Germano, M. (1992). Turbulence: the filtering approach.J. Fluid Mech.,238, 325–336.
Germano, M., Piomelli, U., Moin, P., and Cabot, W.H. (1991). A dynamic subgrid-scale eddy viscosity model.Phys. Fluids A,3, 1760.
Henningson, D.S., and Reddy, S.C. (1994). On the role of linear mechanisms in transition to turbulence.Phys. Fluids,6, 1396.
Humi, M. (1990). Optimal large eddy simulation in one dimension.Phys. Fluids A,2, 1046.
Lilly, D.K. (1992). A proposed modification of the Germano subgrid-scale closure method.Phys. Fluids A,4, 633.
Liu, S., Meneveau, C., and Katz, J. (1994). On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet.J. Fluid Mech., to appear.
Love, M.D. (1980). Subgrid modelling studies with Burgers' equation.J. Fluid Mech.,100, 87.
Moin, P., and Jimenez, J. (1993). Large eddy simulation of complex turbulent flows.Proc. AIAA 24th Fluid Dynamics Conference, Orlando, FL.
Moser, R.D., and Rogers, M. (1993). The three-dimensional evolution of a plane mixing layer: pairing and transition to turbulence.J. Fluid Mech.,247, 275.
Piomelli, U., Zang, T. A., Speziale, C.G., and Hussaini, M.Y. (1990). On the large-eddy simulation of transitional wall-bounded flows.Phys. Fluids A,2, 257.
Ragab, S.A., and Wu, J.L. (1989). Liner instabilities in two-dimensional compressible mixing layers.Phys. Fluids A,1, 957.
Rogallo, R.S., and Moin, P. (1984). Numerical simulation of turbulent flows.Ann. Rev. Fluid Mech.,16, 99–137.
Sandham, N.D., and Reynolds, W.C. (1991). Three-dimensional simulations of large eddies in the compressible mixing layer.J. Fluid Mech.,224, 133.
Schumann, U. (1991). Direct and large eddy simulation of turbulence—summar of the state-of-the-art 1991.Introduction to the Modeling of Turbulence, Lecture Series 1991-02, Von Karman Institute, Brussels.
Smagorinsky, J., (1963). General circulation experiments with the primitive equations. I. The basic experiment.Monthly Weather Rev.,91, 99–164.
Speziale, C.G. (1985). Galilean invariance of subgrid-scale stress models in the large eddy simulation of turbulence.J. Fluid Mech.,156, 55–62.
Vreman, A.W., Geurts, B.J., Kuerten, J.G.M., and Zandbergen, P.J. (1992). A finite volume approach to large eddy simulation of compressible, homogeneous, isotropic, decaying turbulence.Internat. J. Numer Methods Fluids,15, 799–816.
Vreman, B., Geurts, B., and Kuerten, H. (1993). A priori tests of large eddy simulation of the compressible plane mixing layer. Memorandum No. 1152, University of Twente, Enschede.
Vreman, B., Geurts, B., and Kuerten, H. (1994a). Realizability conditions for the turbulent stress tensor in large eddy simulation.J. Fluid Mech.,278, 351–362.
Vreman, B., Geurts, B., and Kuerten, H. (1994b). On the formulation of the dynamic mixed subgrid-scale model.Phys. Fluids,6, 4057–4059.
Vreman, B., Geurts, B., and Kuerten, H. (1994c). Subgrid-modelling in LES of compressible flows.Proc. First ERFOCTAC Workshop on Direct and Large Eddy Simulation, Guildford.
Vreman, B., Geurts, B., and Kuerten, H. (1994d). Subgrid-modelling and numerical errors in the large eddy simulation of the temporal mixing layer. Memorandum No. 1208, University of Twente, Enschede.
Zang, Y., Street, R. L., and Koseff, J.R. (1993). A dynamic mixed subgrid-scale model and its application to turbulent recirculating flows.Phys. Fluids A,5, 3186.