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October 9, 1999, 07:00 
turbulent mixing of two fluids

#1 
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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 ulrich 

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October 9, 1999, 13:57 
Re: turbulent mixing of two fluids

#2 
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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. 962970, 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. 297332, 1989. 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. 5167, 1991. McMurtry, P.A. and Givi, P. "Direct Numerical Simulations of a Reacting, Turbulent Mixing Layer By A PseudospectralSpectral Element Method," Finite Element Methods in Fluids, 8, pp. 355378, 1992. McMurtry, P.A., Menon, S. and Kerstein, A.R. "A Linear Eddy Subgrid Model for Turbulent Reacting Flows: Application to HydrogenAir Combustion,"Proceeding of the 24th (International) Symposium on Combustion, the Combustion Institute, pp. 271278, 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. 10231034, 1993. McMurtry, P.A. and Menon, S. "Linear Eddy Simulations of Turbulent Combustion," J. Energy & Fuels, 7, pp. 817826, 1993. Kerstein, A.R. and McMurtry, P.A. "MeanField Theories of Random Advection," Physical Review E, 49, pp. 474482, 1994. Cremer, M., McMurtry, P.A., and Kerstein, A.R. "Effects of Turbulent and Scalar LengthScale Distributions on Turbulent Mixing Processes," Phys. Fluids A, 6, pp. 21432153, 1994. Kerstein, A.R. and McMurtry, P.A. "Low Wavenumber Statistics of Randomly Advected Passive Scalars," Physical Review E, 50, pp. 20572063, 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. 19992007, 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. 237242, 1996. McMurtry, P.A. "Turbulence," in Encyclopedia of Climate and Weather, pp. 786793, Oxford University Press, 1996. Guilkey, J.E., Kerstein, A.R., McMurtry, P.A. and Klewicki, J.C. "Longtailed 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, 545558, 1997. Maynes, D., Klewicki, J.C., McMurtry, P.A. "Time Resolved Torque of Rotating Bluff Bodies in a Cylindrical Tank," J. Fluids Eng., 120, 2328, 1998. Su, CW., 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, 4158, 1998. Cremer, M. and McMurtry, P.A. "A Model of Turbulent Mixing and Reaction for H2 air Combustion," Journal of Propulsion and Power, 14, 3, 309317, 1998. 

October 9, 1999, 16:15 
Re: turbulent mixing of two fluids

#3 
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(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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