Abstract
An algebraic eddy viscosity model, based on a new length scale has been developed. The model proposes the eddy viscosity as a solution of a quartic (Q 4) equation. The turbulent length scale for attached and separated flows is defined by employing a vorticity functionF =yΩD introduced in the Baldwin-Lomax model. The algebraic-Q 4 eddy viscosity model was incorporated into Navier-Stokes code and tested for complex transonic airfoil flows with separation. The results are compared with the experimental data.
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References
Baldwin B. S., and Lomax, H. (1978). Thin layer approximation and algebraic model for separated turbulent flows. AIAA Paper 78-257.
Caughey, D. A. (1988). Diagonal implicit multigrid algorithm for the Euler equations.AIAA Journal 26(7), 841–851.
Cebeci, T., and Smith, A. M. O. (1974).Analysis of Turbulent Boundary Layers. Academic Press.
Coles, D. (1956). The law of the wake in turbulent boundary layer.Journal of Fluid Mechanics, Part 21, 191–226.
Harris, D. H. (1981). Two-Dimensional Aerodynamic Characteristics of the NACA0012 Airfoil in Langley 8-foot Transonic Pressure Tunnel. NASA TM 81927.
Holst, T. L. (1988). Viscous transonic airfoil workshop compendum of results. AIAA Paper 87-1640.
Johnson, D. A., and King, L. S. (1985). A mathematically simple turbulence closure model for attached and separated turbulent boundary layers.AIAA Journal 23(11), 1684–1692.
Kirtley, K. R. (1992). Renormalization group based algebraic turbulence model for three-dimensional turbomachinery flows.AIAA Journal 30(6), 1500–1506.
Lund, T. (1990). Application of the Algebraic RNG Model Transition Simulation. In Hussaini, M. Y. and Voigt, R. G. (eds.).Instability and Transition, Springer-Verlag2, 463–473.
Martinelli, L., and Yakhot, V. (1989). RNG-based turbulence transport approximation with applications to transonic flows. AIAA Paper 89-1950.
Monin, A. S., and Yaglom, A. M. (1971).Statistical Fluid Mechanics. Vol. 1, MIT Press.
Patankar, S. V., and Spalding, D. B. (1967).Heat and Mass Transfer in Boundary Layers. Morgan-Grampian, London.
Sakya, A. E., Nakamura, Y., and Yasuhara, M. (1993). Evaluation of an RNG-based algebraic turbulence model.Computers Fluids 22(2/3), 207–214.
Schlichting, H. (1979).Boundary-Layer Theory. McGraw-Hill, New York.
Stock, H. W., and Haase, W. (1987). The determination of turbulent length scales in algebraic turbulence models for attached and slightly separated flows using Navier-Stokes methods. AIAA Paper 87-1302.
Varma, R. R., and Caughey, D. A. (1991). Diagonal implicit multigrid solution of compressible turbulent flows. AIAA Paper 91-1571.
Yadlin, Y., and Caughey, D. A. (1990). Block multigrid implicit solution of the Euler equations of compressible fluid flow.AIAA Journal 29, 712–719.
Yakhot, V., and Orszag, S. A. (1986). Renormalization group analysis of turbulence. 1. Basic theory.J. Sci. Comput. 1, 3–51.
Yakhot, A., Kedar, O., and Orszag, S. A. (1992). Algebraic-Q 4 turbulent eddy viscosity model: Boundary layer flow over a flat plate and flow in a pipe.J. Sci. Comput. 7, 229–239.
Yakhot, A., Shalman, E., Igra, O., and Yadlin, Y. (1995). An algebraic-Q 4 turbulence model for transonic airfoil flows. AIAA Paper 95-0395.
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Yakhot, A., Shalman, E., Igra, O. et al. An algebraic-Q 4 turbulence model for attached and separated airfoil flows. J Sci Comput 11, 71–98 (1996). https://doi.org/10.1007/BF02088818
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DOI: https://doi.org/10.1007/BF02088818