turbulent mixing of two fluids
i want to model the mixing of two fluids in a tube bend. the fluids have the same density but very different molecular viscosities. the flow is turbulent (Re about 5000).
in fact, i want to solve the problem by using a two fluid model, i.e. i will use two momentum equtions, one mass transport equation and one continuity equation. however, i think that a turbulent viscosity which is calculated independently for each fluid will not lead to correct results.
i would be glad is someone who has already modeled this problem can give me some advise how to model physically corret the mixing of two fluids.
thanks in advance
Re: turbulent mixing of two fluids
You are working in a complex area. No wonder you are kind of lost! Let me give you some references for you--
McMurtry, P.A., Jou, W.-H., Riley, J.J. and Metcalfe, R.W. "Direct Numerical Simulations of a
Reacting Mixing Layer with Chemical Heat Release," AIAA Journal, 24, pp. 962-970, 1986.
McMurtry, P.A., Riley J.J., and Metcalfe, R.W. "Effects of Heat Release on the Large Scale
Structures in a Turbulent Reacting Mixing Layer," Journal of Fluid Mechanics, 199, pp. 297-332,
Son, S.F., McMurtry, P.A., and Queiroz, M. "The Effects of Heat Release on Various Statistical
Properties of a Reacting Shear Layer," Combustion and Flame, 85, pp. 51-67, 1991.
McMurtry, P.A. and Givi, P. "Direct Numerical Simulations of a Reacting, Turbulent Mixing Layer
By A Pseudospectral-Spectral Element Method," Finite Element Methods in Fluids, 8, pp. 355-378,
McMurtry, P.A., Menon, S. and Kerstein, A.R. "A Linear Eddy Subgrid Model for Turbulent
Reacting Flows: Application to Hydrogen-Air Combustion,"Proceeding of the 24th (International)
Symposium on Combustion, the Combustion Institute, pp. 271-278, 1992.
McMurtry, P.A., Gansauge, T. and Kerstein, A.R "Linear Eddy Simulations of Mixing and Reaction
in A Homogeneous Turbulent Flow," Phys. Fluids A, 5, pp. 1023-1034, 1993.
McMurtry, P.A. and Menon, S. "Linear Eddy Simulations of Turbulent Combustion," J. Energy &
Fuels, 7, pp. 817-826, 1993.
Kerstein, A.R. and McMurtry, P.A. "Mean-Field Theories of Random Advection," Physical Review
E, 49, pp. 474-482, 1994.
Cremer, M., McMurtry, P.A., and Kerstein, A.R. "Effects of Turbulent and Scalar Length-Scale
Distributions on Turbulent Mixing Processes," Phys. Fluids A, 6, pp. 2143-2153, 1994.
Kerstein, A.R. and McMurtry, P.A. "Low Wavenumber Statistics of Randomly Advected Passive
Scalars," Physical Review E, 50, pp. 2057-2063, 1994.
Kerstein, A.R., Cremer, M.A. and McMurtry, P.A. "Scaling Properties of Differential Molecular
Diffusion Effects in Turbulence," Physics of Fluids, 7, pp. 1999-2007, 1995.
Guilkey, J.E., Gee, K.R., McMurtry, P.A. and Klewicki, J.C. "Use of Caged Fluorescent Dyes for
the Study of Turbulent Passive Scalar Mixing," Experiments in Fluids, 21, pp. 237-242, 1996.
McMurtry, P.A. "Turbulence," in Encyclopedia of Climate and Weather, pp. 786-793, Oxford
University Press, 1996.
Guilkey, J.E., Kerstein, A.R., McMurtry, P.A. and Klewicki, J.C. "Long-tailed Probability
Distribution Functions in Turbulent Pipe Flow Mixing," Physical Review E, 56, (2), 1753, 1997.
Krueger, S.K., Su, C.-W., and McMurtry, P.A. "Modeling Entrainment and Fine- Scale mixing in
Cumulus Clouds," Journal of the Atmospheric Sciences, 54, 2697- 2712, 1997.
Maynes, D., Klewicki, J.C., McMurtry, P.A. and Robey, H. "Hydrodynamic Scalings in the Rapid
Growth of Crystals From Solution," J. Crystal Growth, 178, 545-558, 1997.
Maynes, D., Klewicki, J.C., McMurtry, P.A. "Time Resolved Torque of Rotating Bluff Bodies in a
Cylindrical Tank," J. Fluids Eng., 120, 23-28, 1998.
Su, C-W., Krueger, S.K., McMurtry, P.A. and Austin, P.H., "Linear Eddy Modeling of Droplet
Spectral Evolution During Entrainment and Mixing in Cumulus Clouds," Atmospheric Research, 47,
Cremer, M. and McMurtry, P.A. "A Model of Turbulent Mixing and Reaction for H2- air
Combustion," Journal of Propulsion and Power, 14, 3, 309--317, 1998.
Re: turbulent mixing of two fluids
(1). In the mixing zone, the turbulent Reynolds number will be of O(100) or less. (2). So, I don't think the difference in the molecular viscosity between two fluid is important in the mixing process.
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