A simple model of mixing and chemical reaction in a turbulent shear layer

Arguments are presented to show that the concept of gradient diffusion is inapplicable to mixing in turbulent shear layers. A new model is proposed for treating molecular mixing and chemical reaction in such flows at high Reynolds number. It is based upon the experimental observations that revealed the presence of coherent structures and that showed that fluid elements from the two streams are distributed unmixed throughout the layer by large-scale inviscid motions. The model incorporates features of the strained flame model and makes use of the Kolmogorov cascade in scales. Several model predictions differ markedly from those of diffusion models and suggest experiments for testing the two approaches.

[1]  G. M. Corcos,et al.  A numerical simulation of Kelvin-Helmholtz waves of finite amplitude , 1976, Journal of Fluid Mechanics.

[2]  S. Feldman,et al.  A new model for mixing and fluctuations in a turbulent wake , 1965 .

[3]  D. Spalding,et al.  A General Theory of Turbulent Combustion , 1978 .

[4]  Peter Bradshaw,et al.  Effect of free-stream turbulence on large structure in turbulent mixing layers , 1978, Journal of Fluid Mechanics.

[5]  A. Roshko,et al.  On density effects and large structure in turbulent mixing layers , 1974, Journal of Fluid Mechanics.

[6]  Forman A. Williams,et al.  Some Implications of Recent Theoretical Studies in Turbulent Combustion , 1980 .

[7]  R. Breidenthal,et al.  Structure in turbulent mixing layers and wakes using a chemical reaction , 1981, Journal of Fluid Mechanics.

[8]  R. Breidenthal.  A chemically reacting, turbulent shear layer , 1979 .

[9]  G. M. Corcos,et al.  Vorticity concentration and the dynamics of unstable free shear layers , 1976, Journal of Fluid Mechanics.

[10]  S. Corrsin.  Limitations of Gradient Transport Models in Random Walks and in Turbulence , 1975 .

[11]  Manuel Rebollo Rebollo,et al.  Analytical and experimental investigation of a turbulent mixing layer of different gases in a pressure gradient , 1973 .

[12]  P. Dimotakis,et al.  The mixing layer at high Reynolds number: large-structure dynamics and entrainment , 1976, Journal of Fluid Mechanics.

[13]  D. Coles.  Prospects for useful research on coherent structure in turbulent shear flow , 1981, Proceedings of the Indian Academy of Sciences Section C: Engineering Sciences.

[14]  Parampreet Singh,et al.  Turbulent mixing in a two‐dimensional jet , 1975 .

[15]  John Harrison Konrad,et al.  An Experimental Investigation of Mixing in Two-Dimensional Turbulent Shear Flows with Applications to Diffusion-Limited Chemical Reactions , 1977 .

[16]  B. Walker.  Turbulence Model Comparisons for Shear Layers and Axisymmetric Jets. , 1979 .

[17]  F. E. Marble,et al.  The coherent flame model for turbulent chemical reactions. Final report 1 Mar 75--31 Jan 77 , 1977 .

[18]  H. L. Toor.  Mass transfer in dilute turbulent and non‐turbulent systems with rapid irreversible reactions and equal diffusivities , 1962 .

[19]  H. C. Hottel.  Burning in laminar and turbulent fuel jets , 1953 .

[20]  H. Fiedler,et al.  Transport of Heat Across a Plane Turbulent Mixing Layer , 1975 .

[21]  Laboratory Simulation of Atmospheric Turbulence: Generation of Arbitrary Velocity Distributions and Model Experiment on Flow Around Mt. Fuji , 1975 .

[22]  H. Hottel,et al.  Mixing and combustion in turbulent gas jets , 1948 .

[23]  G. L. Brown,et al.  A small, Fast-Response Probe to Measure Composition of a Binary Gas Mixture , 1972 .