A Field-Equation Turbulence Model Closed By Lagrange Method

Abstract

Abstract: First-order moment equations of hybrid second-order moment model are obtained by Euler method, while second-order moment equations are deduced by Lagrange equations. Equations for particle fraction and momentum are provided firstly. A Lagrange model with mean Langevin equations is obtained and Reynold stress equation is deduced, so that hybrid second-order moment model is closed without additional approximate assumptions. Wall-jet-flow loaded with solid particles is simulated. It shows that the model is effective.

Key words: field equation model, Euler method, Lagrange method, numerical simulation

CLC Number:

WANG Lu, XU Jiangrong, LIU Baoyin. A Field-Equation Turbulence Model Closed By Lagrange Method[J]. CHINESE JOURNAL OF COMPUTATIONAL PHYSICS, 2016, 33(3): 305-310.

References

[1] ZHANG Z S, CUI G X, XU C X. Theory and modeling of turbulence[M]. Beijing:Tsinghua University Press, 2005:209-216.
[2] REEKS M W. On the continuum equations for dispersed particles in non-uniform flows[J]. Phys Fluids A, 1992, 4(6):1290-1302.
[3] SIMONIN O, DEUTSCH E, MINIER J P. Eulerian prediction of the fluid-particle correlated motion in turbulent two-phase flows[J]. Flow, Turbulence and Combustion, 1993, 51(1-2):275-283.
[4] MINIER J P, PEIRANO E. The PDF approach to turbulent poly-dispersed two-phase flows[J]. Physics Reports, 2001, 352(1):1-214.
[5] POZORSKI J, MINTER J P. On the Lagrangian turbulent dispersion models based on the Langevin equation[J]. International Journal of Multiphase Flow, 1998, 24(6):913-945.
[6] van SLOOTEN P R, JAYESH Pope S B. Advances in PDF modeling for inhomogeneous turbulent flows[J]. Physics of Fluids, 1998, 10(1):246-265.
[7] ZHOU L X, LIN W Y, SUN K M. Simulation of swirling gas-particle flows using USM and k-ε-k_p two-phase turbulence models[J]. Journal of Engineering Thermophysics, 1995, 4:481-485.
[8] ZHOU L X, CHEN T. Simulation of swirling gas-particle flows using the unified second-order moment model[J]. Acta Mechanica Sinica, 1998, 30(4):385-390.
[9] ZHOU L X. A unified correlation moment closure model of turbulent gas-particle flows and combustion[J]. Journal of Engineering Thermophysics, 1991, 12(2):203-209.
[10] XU J, POPE S B. Assessment of numerical. accuracy of PDF/Monte carlo methods for turbulent reacting flows[J]. Journal of Computational Physics, 1998, 152:192-230.
[11] LI G, MODEST M F. An Effective particle tracing scheme on structured/unstructured grid in hybrid finite volume/PDF monte carlo methods[J]. Journal of Computational Physics, 2001, 173:187-207.
[12] LIU Z H, ZHENG C G, ZHOU L X. A DSM-LPDF two-phase turbulence model and Monte-Carlo simulation of swirling two-phase flow[J]. Journal of engineering thermophysics, 2001, 22(5):641-644.
[13] XU J R, ZHOU Z J, et al. Particles Reynolds stresses trajectory model and numerical simulation for a backward-facing step two-phase flow[J]. Chinese Journal of Computational Physics, 2004, 21(6):538-542.
[14] XU J R, WANG L. Two-order moment trajectory model of two-phase turbulence flow based on particle PDF transport equation[J]. Applied Mechanics and Materials, 2014, 668-669:318-321.
[15] MINIER J P, PEIRANO E. The PDF approach to turbulent poly-dispersed two-phase flows[J]. Physics Reports, 2001, 352(1):1-214.
[16] RISKEN H. The fokker-planck equation:Methods of solution and applications[M]. New York:Springer,1989.
[17] WANG L. A two-order moment Lagrange model based on PDF two-phase theory and its simulation[D]. Hangzhou:Hangzhou Dianzi University, 2013.
[18] SATO Y, HISHIDA K, MAEDA M. Effect of dispersed phase on modification of turbulent flow in a wall jet[J]. Journal of Fluids Engineering, 1996, 118:307-315.