Abstract
Single-point turbulence models will be discussed from a somewhat analytical point of view. The lowest level of modelling considered here is that of eddy-viscosity-based two-equation models, but particular attention is given to explicit algebraic Reynolds stress models (and explicit algebraic scalar flux models). Some new trends in models based directly on the Reynolds stress transport equations are also discussed.
The author wants to thank Dr Stefan Wallin for various valuable contributions, and Gustaf Mårtensson and professor Fritz Busse for many useful comments on the manuscript.
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References
Adumitroaie, V., Taulbee, D.B. & Givi, P. (1997). Explicit algebraic scalar flux models for turbulent reacting flows. A. i.ch.e.J. 43: 1935–2147.
Alvelius, K. & Johansson, A.V. (1999). Direct numerical simulation of rotating channel flow at various Reynolds numbers and rotation numbers. In PhD thesis of K. Alvelius, Dept. of Mechanics, KTH, Stockholm, Sweden
Aupoix, B., Cousteix, J. & Liandrat, J. (1989). MIS: A way to derive the dissipation equation Turbulent Shear Flow vol. 6 (ed. J.-C. André ), Springer
Batchelor, G.K. (1953). The theory of homogeneous turbulence. Cambridge University Press.
Champagne, F.H., Harris, V.G. & Corrsin, S. (1970). Experiments on nearly homogeneous turbulent shear flow. J. Fluid Mech. 41: 81–139.
Chasnov, J.R. (1994). Similarity states of passive scalar transport in isotropic turbulence. Phys. Fluids 6: 1036.
Chou, P.Y. (1945). On velocity correlations and the solutions of the equations of turbulent motion. Quart. of Applied Math. 3: 38–54.
Comte-Bellot, G. & Corrsin, S. (1966). The use of a contraction to improve the isotropy of grid-generated turbulence. J. Fluid Mech. 25: 657–682.
Daly, B.J. & Harlow, F.H. (1970). Transport equations in turbulence. Phys. Fluids 13:2634–2649.
Durbin, P.A. (1996). On the k–e stagnation point anomaly. Int. J. Heat and Fluid Flow 17: 89–90.
Gatski, T.B. & Speziale, C.G. (1993). On explicit algebraic Reynolds stress models for complex turbulent flows. J. Fluid Mech. 254: 59–78.
Gibson, M.M. & Launder, B.E. (1978). Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86: 491–511.
Girimaji, S.S. (1995). Fully-explicit and self-consistent algebraic Reynolds stress model. ICASE Report No. 95–82.
Girimaji, S.S. (1996). Improved algebraic Reynolds stress model for engineering flows. In Engineering Turbulence Modelling and Experiments 3 pp 121–129. Eds W. Rodi and G. Bergeles. Elsevier. Science B. V.
Girimaji, S.S. (1997). A Galilean invariant explicit Reynolds stress model for turbulent curved flows. Phys. Fluids 9: 1067–1077.
Girimaji, S.S. & Balachandar, S. (1997). Analysis and modeling of buoyancy-generated turbulence using numerical data. Int. J. Heat and Mass Transfer 41: 915–929.
Hallbäck, M., Groth, J. & Johansson, A.V. (1990). An algebraic model for nonisotropic turbulent dissipation rate in Reynolds stress closures. Phys Fluids A 2: 1859–1866.
Högström, C.M., Wallin, S. & Johansson, A.V. (2001). Passive scalar flux modelling for CFD. In Proceedings of Turbulence and Shear Flow Phenomena II, Stockholm, June 27–29, 2001, II: 383–388.
Imao, S., Itoh, M. & Harada, T. (1996). Turbulent characteristics of the flow in an axially rotating pipe. Int. J. Heat and Fluid Flow 17: 444–451.
Johansson, A.V. & Burden, A.D. (1999). An introduction to turbulence modelling. Chapter 4 in Transition, Turbulence and Combustion Modelling, ERCOFTAC Series vol. 6, Kluwer. pp 159–242.
Johansson, A.V. & Hallbäck, M. (1994). Modelling of rapid pressure-strain rate in Reynolds tress closures. J. Fluid Mech. 269: 143–168
Johansson, A.V. & Hallbäck, M. (1994). Modelling of rapid pressure-strain rate in Reynolds tress closures. J. Fluid Mech. 290: 405 (1995).
Johansson, A.V. & Wallin, S. (1996). A new explicit algebraic Reynolds stress model. In Proc. Sixth European Turbulence Conference, Lausanne, July 1996, Ed. P. Monkewitz, 31–34.
Johansson, A.V. & Wikström, P.M. (2000). DNS and modelling of passive scalar transport in turbulent channel flow with a focus on scalar dissipation rate modelling. Flow, Turbulence and Combustion 63: 223–245.
Jongen, T., Mompean, G. & Gatski, T.G. (1998). Accounting for Reynolds stress and dissipation rate anisotropies in inertial and noninertial frames. Phys. Fluids 10: 674–684.
Kim, J. (1989). Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech. 177: 133–166.
Kim, J., Moin, P. & Moser, R. (1987). On the structure of pressure fluctuations in simulated turbulent channel flow. J. Fluid Mech. 205: 421–451.
Kolmogorov, A.N. (1942). Equations of turbulent motion of an incompressible fluid. Izvestia Academy of Sciences, USSR; Physics 6: 56–58.
Komminaho, J. & Skote, M. (2001). Reynolds stress budgets in Couette and boundary layer flows. Submitted to Flow, Turbulence and Combustion.
Kristoffersen, R. & Andersson, H. (1993). Direct simulation of low-Reynolds-number turbulent flow in a rotating channel. J. Fluid Mech. 256: 163–197.
Lam, C.K.G. & Bremhorst, K.A. (1981). Modified form of K-e model for predicting wall turbulence. ASME, J. Fluids Engineering 103: 456–460.
Launder, B.E., Reece, G.J. & Rodi, W. (1975). Progress in the development of a Reynolds-stress turbulence closure. J. Fluid Mech. 41: 537–566.
Launder, B.E. & Spalding, D.B. (1972). Mathematical models of turbulence. Academic Press.
Launder, B.E., Tselepidakis, D.P. & Younis, B.A. (1987). A second-moment closure study of rotating channel flow. J. Fluid Mech. 183: 63–75.
Lindberg, P.A. (1994). Near-wall turbulence models for 3D boundary layers. Appl. Sci. Res. 53: 139–162.
Lumley, J.L. (1978). Computational modeling of turbulent flows. Adv. Appl. Mech. 18: 123–177.
Menter, F.R. (1992). Improved Two-Equation k - w Turbulence Model for Aerodynamic Flows. NASA TM-103975
Menter, F.R. (1993). Zonal Two Equation k - w Turbulence Models for Aerodynamic Flows. AIAA 93–2906
Mohammadi, B. & Pironneau, O. (1994). Analysis of the K - r model Wiley/Masson.
Naot, D., Shavit, A. & Wolfstein, M. (1973). Two-point correlation model and the redistribution of Reynolds stresses, Phys. Fluids 16: 738–743.
Piquet, J. (1999). Turbulent flows, models and physics Springer.
Pope, S.B. (1975). A more general effective-viscosity hypothesis. J. Fluid Mech. 72: 331–340.
Poroseva, S.V., Kassinos,S.C., Langer, C.A. & Reynolds, W.C. (2001). Simulation of turbulent flow in a rotating pipe using the structure-based model. In Proceedings of Turbulence and Shear Flow Phenomena II, Stockholm, June 27–29, 2001, II: 223–228.
Reynolds, W.C. (1976). Computation of turbulent flows. Ann. Rev. Fluid Mech. 8: 183–208.
Rodi, W. (1976). A new algebraic relation for calculating the Reynolds stresses. Z. angew. Math. Mech. 56: T219–221.
Rodi, W & Mansour, N.N. (1993). Low Reynolds number K-c modelling with the aid of direct simulation data. J. Fluid Mech. 250: 509–529.
Rotta, J (1951). Statistische theorie nichthomogener turbulenz I. Zeitschrift für Physik 129: 547–572.
R. Rubinstein, C.L. Rumsey, M.D. Salas, and J.L. Thomas, editors (2001). Turbulence modelling workshop ICASE Interim Report No. 37 NASA/CR-2001–210841.
Saffman, P.G. (1970). A model for inhomogeneous turbulent flow. Proc. Roy. Soc. London A 317: 417–433.
Saffman, P.G. (1967). The large-scale structure of homogeneous turbulence. J. Fluid Mech. 27: 581–593.
Shih, T.-H. & Lumley, J.L. (1986). Second-order modeling of near-wall turbulence. Phys. Fluids 29: 971–975.
Shih, T.-H., Reynolds, W.C. & Mansour, N.N. (1990). A spectrum model for weakly anisotropic turbulence. Phys. Fluids A 2: 1500–1502.
Shih, T.H., Zhu, J. & Lumley, J.L. (1992). A Realizable Reynolds Stress Algebraic Equation Model NASA TM 105993, ICOMP-92–27, CMOTT-92–14.
Sjögren, T.I.. (1997). Development and Validation of Turbulence Models Through Experiment and Computation. Doctoral thesis, Dept. of Mechanics, KTH, Stockholm, Sweden.
Sjögren, T.I.A & Johansson, A.V. (1998). Measurement and modelling of homogeneous axisymmetric turbulence. J. Fluid Mech. 374: 59–90.
Sjögren, T.I.A & Johansson, A.V. (2000). Development and calibration of algebraic non-linear models for terms in the Reynolds stress transport equations. Phys. Fluids 12: 1554–1572.
So, R.M.C., Zhang, H.S. & Speziale, C.G. (1991). Near-wall modeling of the dissipation rate equation. AIAA J. 29: 2069–2076.
Spencer, A.J.M. & Rivlin, R.S. (1959). The theory of matrix polynomials and its application to the mechanics of isotropic continua. Arch. Rat. Mech. Anal. 2: 309–336.
Speziale, C.G. (1991). Analytical methods for the development of Reynolds-stress closures in turbulence. Ann. Rev. Fluid Mech. 23: 107–157.
Speziale, C.G. Abid, R. & Anderson, E.C. (1992). Critical evaluation of two-equation models for near-wall turbulence. AIAA J. 30: 324–331.
Speziale, C.G., Sarkar, S. & Gatski, T.B. (1991). Modelling the pressure-strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech. 227: 245–272.
Speziale, C.G. & Xu, X.-H. (1996). Towards the development of second-order closure models for nonequilibrium turbulent flows. Int. J. Heat and Fluid Flow 17: 238–244.
Taulbee, D.B. (1992). An improved algebraic Reynolds stress model and corresponding nonlinear stress model. Phys. Fluids 4: 2555–2561.
Taulbee, D.B., Sonnenmeier, J.R. & Wall, K.M. (1994). Stress relation for three-dimensional turbulent flows. Phys. Fluids 6: 1399–1401.
Tavoularis, S. & Corrsin, S. (1981). Experiments in nearly homogeneous turbulent shear flow with a uniform mean temperature gradient. Part I. J. Fluid Mech. 104: 311–347.
Wallin, S. & Johansson, A.V. (2000). An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J. Fluid Mech. 403: 89–132.
Wallin, S. & Johansson, A.V. (2001). Modelling of streamline curvature effects on turbulence in explicit algebraic Reynolds stress turbulence models. In Proceedings of Turbulence and Shear Flow Phenomena II, Stockholm, June 27–29, 2001, 11:223–228. Also to appear in revised form in Int. J. Heat and Fluid Flow.
Wikström, P.M., Wallin, S. & Johansson, A.V. (2000). Derivation and investigation of a new explicit algebraic model for the passive scalar flux. Phys. Fluids 12: 688–702.
Wilcox, D.C. (1994). Turbulence modeling for CFD DCW Industries Inc. ISBN 0–9636051–0–0, USA 1994.
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Johansson, A. (2002). Engineering Turbulence Models and their Development, with Emphasis on Explicit Algebraic Reynolds Stress Models. In: Oberlack, M., Busse, F.H. (eds) Theories of Turbulence. International Centre for Mechanical Sciences, vol 442. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2564-9_5
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DOI: https://doi.org/10.1007/978-3-7091-2564-9_5
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