On Predicting The Turbulence-induced Secondary Flows Using Nonlinear K-∈ Models

Low turbulent Reynolds number direct simulation data are used to calculate the invariants of the Reynolds stress and the turbulent dissipation rate in a square duct. The results show that, depending on the region where the analysis is carried out, the turbulent flow field comes close to one-, two-, and three-component states. Modeling such flows - even at higher Reynolds numbers - will require models that can approach all three states. A number of related nonlinear k-∈ models are tested a priori using the direct simulation data. The numerical simulation using Reynolds averaged Navier-Stokes equations with these models was performed. Their ability to predict the secondary flows, with a low-Reynolds k-∈ model, cannot be gauged from realizability. © 1996 American Institute of Physics.8718561868Speziale, C.G., Analytical methods for the developments of Reynoldsstress closures in turbulence (1991) Annu. Rev. Fluid Mech., 23, p. 107Speziale, C.G., On non-linear k-l and k-∈ models of turbulence (1987) J. Fluid Mech., 178, p. 459Joseph, D.D., (1984) Fluid Dynamics of Viscoelastic Liquids, , Springer-Verlag, New YorkShih, T., Zhu, J., Lumley, J.L., (1993) A Realizable Reynolds Stress Algerbraic Equation Model, , NASA Tech. Memo TM-105993Rubinstein, R., Barton, J.M., Nonlinear Reynolds stress models and the renormalization group (1990) Phys. Fluids A, 8, p. 1472Demuren, A.O., Rodi, W., Calculation of turbulence-driven secondary motion in non-circular ducts (1984) J. Fluid Mech., 140, p. 189Gatski, T.B., Speziale, C.G., On explicit algebraic stress models for complex turbulent flows (1993) J. Fluid Mech., 254, p. 59Pope, S.B., A more general effective-viscosity hypothesis (1975) J. Fluid Mech., 72, p. 331Huser, A., Biringen, S., Hatay, F.F., Direct simulation of turbulent flow in a square duct: Reynolds-stress budgets (1994) Phys. Fluids, 6, p. 3144Gibson, M.M., Launder, B.E., Ground effects on pressure fluctuations in the atmospheric boundary layer (1979) J. Fluid Mech., 86, p. 491Cheesewright, R., McGrath, G., Petty, D.G., (1990) LDA Measurements of Turbulent Flow in a Duct of Square Cross Section at Low Reynolds Number, , Aeronautical Engineering Department, University of London, Report No. ER 101Huser, A., Biringen, S., Direct numerical simulation of turbulent flow in a square duct (1993) J. Fluid Mech., 257, p. 65Gavrilakis, S., Numerical simulation of low-Reynolds-number turbulent flow through a straight square duct (1992) J. Fluid Mech., 244, p. 101Gavrilakis, S., (1993) Turbulent Velocity Structures Derived from POD Analyses, , Institute de Machines Hydrauliques et de Mécanique des Fluides, École Polytechnique Fédérale de Lausanne, Report No. T-93-30Antonia, R.A., Kim, J., Browne, L.W.B., Some characteristics of small-scale turbulence in turbulent duct flow (1991) J. Fluid Mech., 233, p. 369Bradshaw, P., Blair Perot, J., A note on turbulent energy dissipation in viscous wall region (1993) Phys. Fluids, 5, p. 3305Kim, J., Moin, P., Moser, R., Turbulent statistics in fully developed channel flow at low Reynolds number (1987) J. Fluid Mech., 177, p. 133Tennekes, H., Lumley, J.L., (1972) A First Course in Turbulence, , MIT Press, Cambridge, MALumley, J.L., Computational Modeling of Turbulent Flows (1978) Advances in Applied Mechanics, 18, p. 123. , Academic Press. New YorkGavrilakis, S., Large-scale structures in the turbulent flow near a right-angled corner (1994) 1st ERCOFTAC Workshop on Direct and Large-Eddy Simulation, , SurreyGessner, F.B., The origin of secondary flow in turbulent flow along a corner (1973) J. Fluid Mech., 58, p. 1Speziale, C.G., The dissipation rate correlation and turbulent secondary flows in noncircular ducts (1986) Trans. Am. Soc. Mech. Eng. J. Fluid Eng., 108, p. 118Durbin, P.A., Near-wall turbulence closure modeling without damping functions (1991) Theor. Comput. Fluid Dyn., 3, p. 1Rodi, W., Mansour, N.N., Low Reynolds number k-∈ modeling with the aid of direct simulation (1993) J. Fluid Mech., 250, p. 509Mompean, G., Three-equation turbulence model for prediction of the mean square temperature variance in grid-generated flows and round jets (1994) Int. J. Heat Mass Transfer, 37, p. 1165Chien, K.Y., Prediction of channel and boundary-layer flows with a low-Reynolds-number turbulence model (1982) AIAA J., 20, p. 33Lam, C.K.G., Bremhorst, K., A modified form of the k-∈ model predicting wall turbulence (1981) Trans. Am. Soc. Mech. Eng. J. Fluid. Eng., 103, p. 456Reynolds, W.C., Computation of turbulent flows (1976) Annu. Rev. Fluid Mech., 8, p. 183Lindberg, P.A., (1994), private communicationNisizima, S., A numerical study of turbulent square-duct flow using an anisotropic k-∈ model (1990) Theor. Comput. Fluid Dyn., 2, p. 61Launder, B.E., Tselepidakis, D.P., Contribution to the modelling of near-wall turbulence (1993) Turbulent Shear Flows 8, p. 81. , edited by F. Durst, R. Friedrich, B. E. Launder, F. W. Schmidt, and J. H. Whitelaw, MunichNaimi, N., Gessner, F.B., A calculation method for developing turbulent flow in rectangular ducts of arbitrary aspect ratio (1995) J. Fluid Eng., 117, p. 249Launder, B.E., Reece, G.J., Rodi, W., Progress in the development of a Reynolds-stress turbulence closure (1975) J. Fluid Mech., 68, p. 537Hanjalic, K., Launder, B.E., A Reynolds stress model of turbulence and its application to thin shear flows (1972) J. Fluid Mech., 52, p. 60

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