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On explicit algebraic stress models for complex turbulent flows

Published online by Cambridge University Press:  26 April 2006

T. B. Gatski  and
C. G. Speziale
T. B. Gatski
Affiliation:
NASA Langley Research Center, Hampton, VA 23681, USA
C. G. Speziale
Affiliation:
ICASE, NASA Langley Research Center, Hampton, VA 23681, USA Present address: Aerospace and Mechanical Engineering Department, Boston University, Boston, MA 02215, USA.
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Abstract

Explicit algebraic stress models that are valid for three-dimensional turbulent flows in non-inertial frames are systematically derived from a hierarchy of second-order closure models. This represents a generalization of the model derived by Pope (1975) who based his analysis on the Launder, Reece & Rodi model restricted to two-dimensional turbulent flows in an inertial frame. The relationship between the new models and traditional algebraic stress models – as well as anisotropic eddy viscosity models – is theoretically established. A need for regularization is demonstrated in an effort to explain why traditional algebraic stress models have failed in complex flows. It is also shown that these explicit algebraic stress models can shed new light on what second-order closure models predict for the equilibrium states of homogeneous turbulent flows and can serve as a useful alternative in practical computations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 254 , September 1993 , pp. 59 - 78
Copyright
© 1993 Cambridge University Press

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References

Bardina, J., Ferziger, J. H. & Reynolds, W. C. 1983 Improved turbulence models based on largeeddy simulation of homogeneous, incompressible turbulent flows. Stanford University Tech. Rep. TF-19.
Demuren, A. & Rodi, W. 1984 Calculation of turbulence-driven secondary motion in non-circular ducts. J. Fluid Mech. 140, 189–222.Google Scholar
Gibson, M. M. & Launder, B. E. 1978 Ground effects on pressure fluctuations in the atmospheric boundary layer. J. Fluid Mech. 86, 491–511.Google Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.
Johnston, J. P., Halleen, R. M. & Lezius, D. K. 1972 Effects of a spanwise rotation on the structure of two-dimensional fully-developed channel flow. J. Fluid Mech. 56, 533–558.Google Scholar
Launder, B. E. 1990 Phenomenological Modeling: Present and Future (ed. J. L. Lumley). Lecture Notes in Physics, vol. 357, pp. 439–485. Springer.
Launder, B. E., Reece, G. & Rodi, W. 1975 Progress in the development of a Reynolds stress turbulence closure. J. Fluid Mech. 68, 537–566.Google Scholar
Launder, B. E. & Spalding, D. B. 1974 The numerical computation of turbulent flows. Comput. Methods Appl. Mech. Engng 3, 269–289.Google Scholar
Lumley, J. L. 1970 Toward a turbulent constitutive equation. J. Fluid Mech. 41, 413–434.Google Scholar
Lumley, J. L. 1978 Computational modeling of turbulent flows. Adv. Appl. Mech. 18, 123–176.Google Scholar
Pope, S. B. 1975 A more general effective viscosity hypothesis. J. Fluid Mech. 72, 331–340.Google Scholar
Reynolds, W. C. 1987 Fundamentals of turbulence for turbulence modeling and simulation. Lecture Notes for Von Kármán Institute, AGARD Lecture Series 86, North Atlantic Treaty Organization.
Rivlin, R. S. 1957 The relation between the flow of non-Newtonian fluids and turbulent Newtonian fluids. Q. Appl. Maths 15, 212–215.Google Scholar
Rodi, W. 1976 A new algebraic relation for calculating the Reynolds stresses. Z. angew. Math. Mech. 56, T219–T221.Google Scholar
Rosenau, P. 1989 Extending hydrodynamics via the regularization of the Chapman–Enskog expansion. Phys. Rev. A 40, 7193–7196.Google Scholar
Rubinstein, R. & Barton, J. M. 1990 Nonlinear Reynolds stress models and the Renormalization group. Phys. Fluids A 2, 1472–1476.Google Scholar
Saffman, P. G. 1977 Results of a two-equation model for turbulent flows and development of a relaxation stress model for application to straining and rotating flows. Proc. Project SQUID Workshop on Turbulence in Internal Flows (ed. S. Murthy), pp. 191–231. Hemisphere.
Spencer, A. J. M. 1971 Theory of invariants. In Continuum Physics (ed. A. C. Eringen), vol. 1, pp. 240–352. Academic.
Speziale, C. G. 1987 On nonlinear K—I and K—ε models of turbulence. J. Fluid Mech. 178, 459–475.Google Scholar
Speziale, C. G. 1991 Analytical methods for the development of Reynolds stress closures in turbulence. Ann. Rev. Fluid Mech. 23, 107–157.Google Scholar
Speziale, C. G., Gatski, T. B. & Mac Giolla Mhuiris, N. 1990 A critical comparison of turbulence models for homogeneous shear flows in a rotating frame. Phys. Fluids A 2, 1678–1684.Google Scholar
Speziale, C. G. & Mac Giolla Mhuiris, N. 1989 On the prediction of equilibrium states in homogeneous turbulence. J. Fluid Mech. 209, 591–615.Google Scholar
Speziale, C. G., Mansour, N. N. & Rogallo, R. S. 1987 The decay of isotropic turbulence in a rapidly rotating frame. Proc. 1987 Summer Program of the Center for Turbulence Research (ed. P. Moin, W. C. Reynolds & J. Kim), pp. 205–211. Stanford University Press.
Speziale, C. G., Sarkar, S. & Gatski, T. B. 1991 Modeling the pressure–strain correlation of turbulence: an invariant dynamical systems approach. J. Fluid Mech. 227, 245–272.Google Scholar
Speziale, C. G., So, R. M. C. & Younis, B. A. 1992 On the prediction of turbulent secondary flows. ICASE Rep. 92-57, NASA Langley Research Center.
Taulbee, D. B. 1992 An improved algebraic Reynolds stress model and corresponding nonlinear stress model. Phys. Fluids A 4, 2555–2561.Google Scholar
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.Google Scholar
Wigeland, R. A. & Nagib, H. M. 1978 Grid-generated turbulence with and without rotation about the streamwise direction. IIT Fluids and Heat Transfer Rep. R78-1.
Wolfram, S. 1988 Mathematica. Addison-Wesley.
Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B. & Speziale, C. G. 1992 Development of turbulence models for shear flows by a double expansion technique. Phys. Fluids A 4, 1510–1520.Google Scholar
Yoshizawa, A. 1984 Statistical analysis of the deviation of the Reynolds stress from its eddy viscosity representation. Phys. Fluids 27, 1377–1387.Google Scholar