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Incompressible turbulent flow simulation using the \(\kappa -\varepsilon \) model and upwind schemes. (English) Zbl 1360.76104

Summary: In the computation of turbulent flows via turbulence modeling, the treatment of the convective terms is a key issue. In the present work, we present a numerical technique for simulating two-dimensional incompressible turbulent flows. In particular, the performance of the high Reynolds \(\kappa -\varepsilon \) model and a new high-order upwind scheme (adaptative QUICKEST by Kaibara et al. (2005)) is assessed for 2D confined and free-surface incompressible turbulent flows. The model equations are solved with the fractional-step projection method in primitive variables. Solutions are obtained by using an adaptation of the front tracking GENSMAC (Tomé and McKee (1994)) methodology for calculating fluid flows at high Reynolds numbers. The calculations are performed by using the 2D version of the Freeflow simulation system (Castello et al. (2000)). A specific way of implementing wall functions is also tested and assessed. The numerical procedure is tested by solving three fluid flow problems, namely, turbulent flow over a backward-facing step, turbulent boundary layer over a flat plate under zero-pressure gradients, and a turbulent free jet impinging onto a flat surface. The numerical method is then applied to solve the flow of a horizontal jet penetrating a quiescent fluid from an entry port beneath the free surface.

MSC:

76F60 \(k\)-\(\varepsilon\) modeling in turbulence

Software:

FREEFLOW; GENSMAC
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References:

[1] B. P. Leonard, “Simple high-accuracy resolution program for convective modelling of discontinuities,” International Journal for Numerical Methods in Fluids, vol. 8, no. 10, pp. 1291-1318, 1988. · Zbl 0667.76125 · doi:10.1002/fld.1650081013
[2] A. Harten, “On a class of high resolution total-variation-stable finite-difference schemes,” SIAM Journal on Numerical Analysis, vol. 21, no. 1, pp. 1-23, 1984. · Zbl 0547.65062 · doi:10.1137/0721001
[3] A. Varonos and G. Bergeles, “Development and assessment of a variable-order non-oscillatory scheme for convection term discretization,” International Journal for Numerical Methods in Fluids, vol. 26, no. 1, pp. 1-16, 1998. · Zbl 0906.76060 · doi:10.1002/(SICI)1097-0363(19980115)26:1<1::AID-FLD603>3.0.CO;2-N
[4] V. G. Ferreira, M. F. Tomé, N. Mangiavacchi, et al., “High-order upwinding and the hydraulic jump,” International Journal for Numerical Methods in Fluids, vol. 39, no. 7, pp. 549-583, 2002. · Zbl 1010.76068 · doi:10.1002/fld.234
[5] V. G. Ferreira, N. Mangiavacchi, M. F. Tomé, A. Castelo, J. A. Cuminato, and S. McKee, “Numerical simulation of turbulent free surface flow with two-equation k - \epsilon eddy-viscosity models,” International Journal for Numerical Methods in Fluids, vol. 44, no. 4, pp. 347-375, 2004. · Zbl 1085.76047 · doi:10.1002/fld.641
[6] B. Song, G. R. Liu, K. Y. Lam, and R. S. Amano, “On a higher-order bounded discretization scheme,” International Journal for Numerical Methods in Fluids, vol. 32, no. 7, pp. 881-897, 2000. · Zbl 0974.76052 · doi:10.1002/(SICI)1097-0363(20000415)32:7<881::AID-FLD2>3.0.CO;2-6
[7] M. A. Alves, P. J. Oliveira, and F. T. Pinho, “A convergent and universally bounded interpolation scheme for the treatment of advection,” International Journal for Numerical Methods in Fluids, vol. 41, no. 1, pp. 47-75, 2003. · Zbl 1025.76024 · doi:10.1002/fld.428
[8] M. K. Kaibara, V. G. Ferreira, H. A. Navarro, J. A. Cuminato, A. Castelo, and M. F. Tomé, “Upwinding schemes for convection dominated problems,” in Proceedings of the 18th International Congress of Mechanical Engineering (COBEM ’05), Ouro Preto, MG, Brazil, November 2005.
[9] V. G. Ferreira, C. M. Oishi, F. A. Kurokawa, et al., “A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows,” Communications in Numerical Methods in Engineering, vol. 23, no. 6, pp. 419-445, 2007. · Zbl 1262.76065 · doi:10.1002/cnm.900
[10] A. Castello, M. F. Tomé, C. N. L. César, S. McKee, and J. A. Cuminato, “Freeflow: an integrated simulation system for three-dimensional free surface flows,” Journal of Computing and Visualization in Science, vol. 2, no. 4, pp. 199-210, 2000. · Zbl 0979.76067 · doi:10.1007/s007910050040
[11] L. D. Landau and E. M. Lifshitz, Fluid Mechanics, vol. 6 of Course of Theoretical Physics, Butterworth-Heinemann, Newton, Mass, USA, 1975. · Zbl 0146.22405
[12] R. Peyret and T. D. Taylor, Computational Methods for Fluid Flow, Springer Series in Computational Physics, Springer, New York, NY, USA, 1983. · Zbl 0514.76001
[13] D. C. Wilcox, Turbulence Modeling for CFD, DCW Industries, La Ca\?ada, Calif, USA, 1993.
[14] D. L. Sondak and R. H. Pletcher, “Application of wall functions to generalized nonorthogonal curvilinear coordinate systems,” AIAA journal, vol. 33, no. 1, pp. 33-41, 1995. · Zbl 0824.76036 · doi:10.2514/3.12329
[15] H. L. Norris and W. C. Reynolds, “Turbulent channel flow with a moving wavy boundary,” Tech. Rep. TR TF-7, Departament of Mechanics Engineering, Stanford University, Palo Alto, Calif, USA, 1980.
[16] P. Bradshaw, Ed., Turbulence, vol. 12 of Topics in Applied Physics, Springer, Berlin, Germany, 2nd edition, 1978. · Zbl 0348.00024
[17] D. C. Wilcox, “Reassessment of the scale-determining equation for advanced turbulence models,” AIAA journal, vol. 26, no. 11, pp. 1299-1310, 1988. · Zbl 0664.76057 · doi:10.2514/3.10041
[18] F. M. White, Viscous Fluid Flow, McGraw-Hill, New York, NY, USA, 1991.
[19] F. Menter and T. Esch, “Elements of industrial heat transfer predictions,” in Proceedings of the 16th International Congress of Mechanical Engineering (COBEM ’01), Ouro Uberlndia, MG, Brazil, November 2001.
[20] B. P. Leonard, “The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection,” Computer Methods in Applied Mechanics and Engineering, vol. 88, no. 1, pp. 17-74, 1991. · Zbl 0746.76067 · doi:10.1016/0045-7825(91)90232-U
[21] P. K. Sweby, “High resolution schemes using flux limiters for hyperbolic conservation laws,” SIAM Journal on Numerical Analysis, vol. 21, no. 5, pp. 995-1011, 1984. · Zbl 0565.65048 · doi:10.1137/0721062
[22] P. H. Gaskell and A. K. C. Lau, “Curvature-compensated convective transport: SMART, a new boundedness-preserving transport algorithm,” International Journal for Numerical Methods in Fluids, vol. 8, no. 6, pp. 617-641, 1988. · Zbl 0668.76118 · doi:10.1002/fld.1650080602
[23] M. F. Tomé and S. McKee, “GENSMAC: a computational marker and cell method for free surface flows in general domains,” Journal of Computational Physics, vol. 110, no. 1, pp. 171-186, 1994. · Zbl 0790.76058 · doi:10.1006/jcph.1994.1013
[24] V. G. Ferreira, Análise e Implementa de Esquemas de Convec e Modelos de Turbulência para Simula de Escoamentos Incompressíveis Envolvendo Superfícies Livres, M.S. thesis, Departament of Computer Science and Statistics, USP - University of São Paulo, São Carlos, Brazil, 2001.
[25] S. Armfield and R. Street, “An analysis and comparison of the time accuracy of fractional-step methods for the Navier-Stokes equations on staggered grids,” International Journal for Numerical Methods in Fluids, vol. 38, no. 3, pp. 255-282, 2002. · Zbl 1027.76033 · doi:10.1002/fld.217
[26] F. H. Harlow and J. E. Welch, “Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface,” Physics of Fluids, vol. 8, no. 12, pp. 2182-2189, 1965. · Zbl 1180.76043 · doi:10.1063/1.1761178
[27] A. Chorin, “A numerical method for solving incompressible viscous flow problems,” Journal Computational of Physics, vol. 2, no. 1, pp. 12-26, 1967. · Zbl 0149.44802 · doi:10.1016/0021-9991(67)90037-X
[28] J. Eaton and J. P. Johnston, “Turbulent flow reattachment: an experimental study of the flow and structure behind a backward-facing step,” Tech. Rep. TR MD-39, Stanford University, Stanford, Calif, USA, 1980.
[29] S. Thangam and C. G. Speziale, “Turbulent flow past a backward-facing step:a critical evaluation of two-equation models,” AIAA Journal, vol. 30, no. 5, pp. 1314-1320, 1992. · Zbl 0775.76069 · doi:10.1016/0020-7225(92)90148-A
[30] A. C. Brandi, Estratégias “Upwind” e Modelagem k - \epsilon para Simula Numérica de Escoamentos com Superfícies Livres em Altos Números de Reynolds, M.S. thesis, Departament of Computer Science and Statistics, USP - University of São Paulo, São Carlos, Brazil, 2005.
[31] F. M. White, Fluid Mechanics, McGraw-Hill, New York, NY, USA, 1979. · Zbl 0471.76001
[32] E. J. Watson, “The radial spread of a liquid jet over a horizontal plane,” Journal of Fluid Mechanics, vol. 20, pp. 481-499, 1964. · Zbl 0129.20002 · doi:10.1017/S0022112064001367
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