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New explicit algebraic stress and flux model for active scalar and simulation of shear stratified cylinder wake flow. (English) Zbl 1422.80004

Summary: On the numerical simulation of active scalar, a new explicit algebraic expression on active scalar flux was derived based on Wikström, Wallin and Johansson model (\(a^{WWJ}\) model). Reynolds stress algebraic expressions were added by a term to account for the buoyancy effect. The new explicit Reynolds stress and active scalar flux model was then established. Governing equations of this model were solved by finite volume method with unstructured grids. The thermal shear stratified cylinder wake flow was computed by this new model. The computational results are in good agreement with laboratorial measurements. This work is the development on modeling of explicit algebraic Reynolds stress and scalar flux, and is also a further modification of the \(a^{WWJ}\) model for complex situations such as a shear stratified flow.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
80M12 Finite volume methods applied to problems in thermodynamics and heat transfer
80-05 Experimental work for problems pertaining to classical thermodynamics
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[1] Mcguirk J J, Rodi W. Mathematical modeling of three-dimensional heated surface jets. J Fluid Mech, 1979, 95(4): 609–633 · Zbl 0415.76010 · doi:10.1017/S0022112079001610
[2] Rodi W. Turbulence models for environmental problems. In: Kollmann W, eds. Prediction methods for turbulent flows. New York: Hemisphere Publishing Corporation, 1980
[3] Gibson M M, Younis B A. Calculation of swirling jets with a Reynolds stress closure. Phys Fluids, 1986, 29(1): 38–48 · doi:10.1063/1.865951
[4] Cheng G C, Farokhi S. On turbulent flows dominated by curvature effects. J Fluids Eng, 1992, 114(1): 52–57 · doi:10.1115/1.2909999
[5] Walker D T, Chen C Y. Evaluation of algebraic stress modeling in free-surface jet flows. J Fluids Eng, 1996, 118(1): 48–54 · doi:10.1115/1.2817509
[6] Jiang C B, Xu X Q. Computation of three-dimensional nonisotropic turbulent buoyant flows by finite element method (in Chinese). J Hydr Engrg, 1991, (7): 8–18
[7] Ni H Q, Shen Y M. Numerical Simulation of Turbulent Flows, Heat and Mass Transfer in Engineering (in Chinese). Bejing: China Water Power Press, 1996
[8] Pope S B. A more general effective-viscosity hypothesis. J Fluid Mech, 1975, 72(2): 331–340 · Zbl 0315.76024 · doi:10.1017/S0022112075003382
[9] Taulbee D B. An improved algebraic Reynolds stress model and corresponding nonlinear stress model. Phys Fluids, 1992, 4(11): 2555–2561 · Zbl 0762.76041 · doi:10.1063/1.858442
[10] Taulbee D B, Sonnenmeier J R, Wall K M. Stress relation for 3-dimentsional turbulent flows. Phys Fluids, 1994, 6(3): 1399–1401 · Zbl 0821.76037 · doi:10.1063/1.868252
[11] Gatski T B, Speziale C G. On explicit algebraic stress models for complex turbulent flows. J Fluid Mech, 1993, 254: 59–78 · Zbl 0781.76052 · doi:10.1017/S0022112093002034
[12] Wallin S. Engineering Turbulence Modeling for CFD With a Focus on Explicit Algebraic Reynolds Stress Models. Dissertation of Doctoral Degree. Norsteds Tryckeri AB, Stockholm, Sweden, 2000
[13] Gatski T B, Wallin S. Extending the weak-equilibrium condition for algebraic Reynolds stress models to rotating and curved flows. J Fluid Mech, 2004, 518: 147–155 · Zbl 1068.76039 · doi:10.1017/S0022112004000837
[14] Wikström P M, Wallin S, Johansson A V. Derivation and investigation of a new explicit algebraic model for the passive scalar flux. Phys Fluids, 2000, 12(3): 688–702 · Zbl 1149.76584 · doi:10.1063/1.870274
[15] Launder B E. Heat and Mass Transfer. Berlin: Springer, 1976
[16] Högström C M, Wallin S, Johansson A V. Passive scalar flux modelling for CFD. In: Proceedings of Turbulence and Shear Flow Phenomena II. Stockholm, 2001, II: 383–388
[17] Adumitroaie V, Taulbee D B, Givi P. Explicit algebraic scalar-flux models for turbulent reacting flows. AICHE J, 1997, 43(8): 1935–1946 · doi:10.1002/aic.690430803
[18] Wallin S, Johansson A V. An explicit algebraic Reynolds stress model for incompressible and compressible turbulent flows. J Fluid Mech, 2000, 403: 89–132 · Zbl 0966.76032 · doi:10.1017/S0022112099007004
[19] Hua Z L, Xing L H, Gu L. Application of a modified QUICK scheme to depth-averaged k-{\(\epsilon\)} turbulent model based on unstructured grid. J Hydrodyn, 2008, 20(4): 514–523 · doi:10.1016/S1001-6058(08)60088-8
[20] Jasak H. Error Analysis and Estimation for The Finite Volume Method With Applications to Fluid Flows. Dissertation of Doctoral Degree. London: University of London, 1996
[21] Saad Y, Schultz M H. GMRES-A generalized minimal residual algorithm for solving nonsymmetric linear-systems. SIAM J Sci Stat Comput, 1986, 7(3): 856–869 · Zbl 0599.65018 · doi:10.1137/0907058
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