Abstract
Numerical predictions with a differential Reynolds stress closure, which in its original formulation explicitly takes into account possible states of turbulence on the anisotropy-invariant map, are presented. Thus the influence of anisotropy of turbulence on the modeled terms in the governing equations for the Reynolds stresses is accounted for directly. The anisotropy invariant Reynolds stress model (AIRSM) is implemented and validated in different finite-volume codes. The standard wall-function approach is employed as initial step in order to predict simple and complex wall-bounded flows undergoing large separation. Despite the use of simple wall functions, the model performed satisfactory in predicting these flows. The predictions of the AIRSM were also compared with existing Reynolds stress models and it was found that the present model results in improved convergence compared with other models. Numerical issues involved in the implementation and application of the model are also addressed.
Similar content being viewed by others
References
Lumley, J.L., Newman, G.: Return to isotropy of homogeneous turbulence. J. Fluid Mech. 82, 161–178 (1977)
Lumley, J.L.: Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176 (1978)
Jovičić, N., Breuer, M., Jovanović, J.: Anisotropy–invariant mapping of turbulence in a flow past an unswept airfoil at high angle of attack. J. Fluids Eng. 128(3), 559–567 (2006)
Jovanović, J.: The Statistical Dynamics of Turbulence. Springer, New York (2004)
Shir, C.C.: A preliminary study of atmospheric turbulent flow in the idealized planetary boundary layer. J. Atmos. Sci. 30, 1327–1339 (1973)
Hällback, M., Groth, J., Johansson, A.V.: An algebraic model for non-isotropic turbulent dissipation rate in Reynolds stress closure. Phys. Fluids A 2, 1859–1866 (1990)
Kolmogorov, A.N.: Local structure of turbulence in an incompressible fluid at very high Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 299–303 (1941)
Speziale, C.G., Sarkar, S., Gatski, T.B.: Modeling of pressure-strain correlation of turbulence: an invariant dynamical system approach. J. Fluid Mech. 227, 245–272 (1991)
Launder, B.E., Reece, G.J., Rodi, W.: Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 68, 537–566 (1975)
Durst, F., Schäfer, M., Wechsler, K.: Efficient simulation of incompressible viscous flows on parallel computers. Notes Numer. Fluid Mech. 52, 87–101 (1996)
Grotjans, H.: Turbulenzmodelle höherer Ordnung für komplexe Anwendungen. PhD thesis, TU München (1999)
Jakirlic, S. Hanjalić, K.: A new approach to modelling near-wall turbulence energy and stress dissipation. J. Fluid Mech. 459, 139–166 (2002)
Manceau, R., Hanjalić, K.: Elliptic blending model: a new near-wall Reynolds-stress turbulence closure. Phys. Fluids 14(2), 744–754 (2002)
Launder, B.E., Li, S.-P.: On the elimination of wall-topography parameters from second-moment closure. Phys. Fluids 6(2), 999–1006 (1994)
Dianat, M., Fairweather, M., Jones, W.P.: Reynolds stress closure applied to axisymmetric, impinging turbulent jets. Theoret. Comput. Fluid Dyn. 8, 435–447 (1996)
Craft, T.J., Launder, B.E.: A Reynolds stress closure designed for complex geometries. Int. J. Heat Fluid Flow 17(3), 245–254 (1996)
Moser, R.D., Kim, J., Mansour, N.N.: Direct numerical simulation of turbulent channel flow up to Re τ = 590. Phys. Fluids 11, 943–946 (1999)
Obi, S., Aoki, K., Masuda, S.: Experimental and computational study of turbulent separated flow in an asymmetric diffuser. In: Proc. 9th Symp. on Turbulent Shear Flows, Kyoto (1993)
Buice, C.U., Eaton, J.K.: Experimental investigation of flow through an asymmetric plane diffuser. Technical report, Center of Turbulence Research, Stanford University, CTR Annual Research Briefs (1996)
Durbin, P.A.: On the k-ϵ stagnation point anomaly. Int. J. Heat Fluid Flow 17, 89–91 (1996)
Iaccarino, G.: Predictions of a turbulent separated flow using commercial CFD codes. ASME J. Fluids Eng. 123, 819–828 (2001)
Apsley, D.D., Leschziner, M.A.: Advanced turbulence modelling of separated flow in a diffuser. J. Flow Turbul. Combust. 63, 81–112 (1999)
Kaltenbach, H.J., Fatica, M., Mittal, R., Lund, T.S., Moin, P.: Study of flow in a planar asymmetric diffuser using large-Eddy simulation. J. Fluid Mech. 390, 151–185 (1999)
Schlüter, J.U., Wu, X., Pitsch, H.: Large-Eddy Simulation of a Separated Plane Diffuser. AIAA Paper (2005)
Driver, D.M., Seegmiller, H.L.: Feature of a reattachment turbulent shear layer in a divergent channel flow. AIAA J. 23, 163–171 (1985)
Lasher W.C., Taulbee, D.B.: On the computation of turbulent backstep flow. Int. J. Heat Fluid Flow 13(1), 30–40 (1992)
Hanjalić, K., Jakirlić, S.: Contribution towards the second-moment closure modelling of separating turbulent flows. Comput. Fluids 27(2), 137–156 (1998)
Guilmineau, E., Piquet, J., Queutey, P.: Two-dimensional turbulent viscous flow simulation past airfoils at fixed incidence. Comput. Fluids, 26, 135–162 (1997)
Coles, D., Wadcock, A.J.: Flying hot-wire study of flow past a NACA 4412 airfoil at maximum lift. AIAA J. 17, 321–329 (1979)
Wadcock, A.J.: Two-dimensional stalled airfoil. In: Proceedings of the 1980-81 AFOSR-HTTM-Stanford Conference on Complex Turbulent Flows, pp. 234–252. Thermosciences Divison, Mechanical Engineering Department, Stanford University, Stanford, California (1981)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kumar, V., Frohnapfel, B., Jovanović, J. et al. Anisotropy Invariant Reynolds Stress Model of Turbulence (AIRSM) and its Application to Attached and Separated Wall-Bounded Flows. Flow Turbulence Combust 83, 81–103 (2009). https://doi.org/10.1007/s10494-008-9190-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10494-008-9190-y