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Effects of heat release on the large-scale structure in turbulent mixing layers

Published online by Cambridge University Press:  26 April 2006

P. A. Mcmurtry
Affiliation:
University of Utah, Salt Lake City, UT 84112, USA
J. J. Riley
Affiliation:
University of Washington, Seattle, WA 98195, USA
R. W. Metcalfe
Affiliation:
University of Houston, Houston, TX 77004, USA

Abstract

The effects of chemical heat release on the large-scale structure in a chemically reacting, turbulent mixing layer are investigated using direct numerical simulations. Three-dimensional, time-dependent simulations are performed for a binary, single-step chemical reaction occurring across a temporally developing turbulent mixing layer. It is found that moderate heat release slows the development of the large-scale structures and shifts their wavelengths to larger scales. The resulting entrainment of reactants is reduced, decreasing the overall chemical product formation rate. The simulation results are interpreted in terms of turbulence energetics, vorticity dynamics, and stability theory. The baroclinic torque and thermal expansion in the mixing layer produce changes in the flame vortex structure that result in more diffuse vortices than in the constant-density case, resulting in lower rotation rates of the large-scale structures. Previously unexplained anomalies observed in the mean velocity profiles of reacting jets and mixing layers are shown to result from vorticity generation by baroclinic torques.

Type
Research Article
Copyright
© 1989 Cambridge University Press

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References

Acton, E.: 1976 The modelling of large eddies in a two-dimensional shear layer. J. Fluid Mech. 76, 561592.Google Scholar
Aref, A. & Siggia, E. D., 1980 Vortex dynamics of the two-dimensional turbulent shear layer. J. Fluid Mech. 100, 5395.Google Scholar
Ashurst, W. T. & Meiberg, E., 1988 Three-dimensional shear layers via vortex dynamics. J. Fluid Mech. 189, 87110.Google Scholar
Bernal, L. P.: 1981 The coherent structure of turbulent mixing layers. I. Similarity of the primary vortex structures. II. Secondary streamwise vortex structure. Ph.D. thesis, California Institute of Technology.
Breidenthal, R. E.: 1981 Structure in turbulent mixing layers and wakes using a chemical reaction. J. Fluid Mech. 109, 124.Google Scholar
Brown, G. L. & Roshko, A., 1974 On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 91, 319335.Google Scholar
Buckmaster, J. D.: 1985 An introduction to combustion theory. In The Mathematics of Combustion. (ed. J. Buckmaster), pp. 346. SIAM.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A., 1988 Spectral Methods in Fluid Dynamics. Springer.
Corcos, G. M. & Sherman, F. S., 1984 The mixing layer: deterministic models of a turbulent flow. Part 1. Introduction and the two-dimensional flow. J. Fluid Mech. 139, 2965.Google Scholar
Dimotakis, P. E.: 1986 Entrainment and growth of a fully developed, two-dimensional shear layer. AIAA J. 24, 17911796.Google Scholar
Givi, P., Jou, W.-H. & Metcalfe, R. W. 1986 Flame extinction in a temporally developing mixing layer. Twenty-first Symp. (Intl) on Combustion, pp. 12511261. The Combustion Institute.
Gollahalli, S. R., Saval, Ou., Huang, R. F. & Azara, J. L. R. 1986 Structure of attached and lifted gas jet flames in hysteresis region. In Twenty-first Symp. (Intl) on Combustion, pp. 14631471. The Combustion Institute.
Gottlieb, D. & Orszag, S. A., 1977 Numerical Analysis of Spectral Methods. Philadelphia: SIAM.
Hermanson, J. C.: 1985 Heat release effects in a turbulent shear layer. Ph.D. thesis, California Institute of Technology.
Hottel, H. C. & Hawthorne, W. R., 1953 In Third Symp. (Intl) on Combustion, p. 254. Williams and Wilkens.
Jou, W. H. & Riley, J. J., 1989 Progress in direct numerical simulations of turbulent reacting flows. AIAA J. (to appear). Also AIAA paper 87–1324.Google Scholar
Karagozian, A.: 1982 An analytical study of diffusion flames in vortex structures. Ph.D. thesis, California Institute of Technology.
Keller, J. O. & Daily, J. W., 1985 The effects of highly exothermic chemical reaction on a two-dimensional mixing layer. AIAA J. 23, 19371945.Google Scholar
Konrad, J. H.: 1976 An experimental investigation of mixing in two-dimensional turbulent shear flows with application to diffusion limited chemical reactions. Ph.D. thesis, California Institute of Technology.
Koochesfahani, M. M.: 1984 Experiments on turbulent mixing and chemical reactions in a liquid mixing layer. Ph.D. thesis, California Institute of Technology.
Lasheras, J. C., Cho, J. S. & Maxworthy, T., 1986 On the origin and evolution of streamwise vortical structures in a plane, free shear layer. J. Fluid Mech. 172, 231258.Google Scholar
Libby, P. A. & Williams, F. A., 1980 Fundamental aspects of turbulent reacting flows. In Turbulent Reacting Flows (ed. P. A. Libby & F. A. Williams), pp. 143. Springer.
Lin, S. J. & Corcos, G. M., 1984 The mixing layer deterministic models of a turbulent flow. Part 3. The effect of plain strain on the dynamics of streamwise vortices. J. Fluid Mech. 141, 139178.Google Scholar
Lowrey, P. S. & Reynolds, W. C., 1986 Numerical simulation of a spatially-developing, forced, plane mixing layer. Rep. TF-26. Department of Mechanical Engineering, Stanford University.
Majda, A. & Sethian, J., 1985 The derivation and numerical solution of the equations for zero Mach number combustion. Combust. Sci. Tech. 42, 185205.Google Scholar
Marble, F. E. & Broadwell, J. E., 1977 The coherent flame model of turbulent chemical reactions. Project SQUID Tech. Rep. TRW-9-PU.Google Scholar
Masutani, S. M.: 1985 An experimental investigation of mixing and chemical reaction in a plane mixing layer. Ph.D. thesis, Stanford University.
McMurtry, P. A.: 1987 Direct numerical simulations of a reacting mixing layer with chemical heat release. Ph.D. thesis, University of Washington.
McMurtry, P. A., Jou, W.-H., Riley, J. J. & Metcalfe, R. W., 1986 Direct numerical simulations of a reacting mixing layer with chemical heat release. AIAA J. 24, 962970.Google Scholar
Metcalfe, R. W., Orszag, S. A., Brachet, M. E., Menon, S. & Riley, J. J., 1987 Secondary instability of a temporally growing mixing layer. J. Fluid Mech. 184, 207243.Google Scholar
Michalke, A.: 1964 On the inviscid instability of the hyperbolic tangent velocity profile. J. Fluid Mech. 19, 543556.Google Scholar
Mungal, M. G. & Dimotakis, P. E., 1984 Mixing and combustion with low heat release in a turbulent shear layer. J. Fluid Mech. 148, 349382.Google Scholar
Orszag, S. A. & Pao, Y., 1974 Numerical computation of turbulent shear flows. Adv. Geophys. 18, 225236.Google Scholar
Orszag, S. A. & Patterson, G. S., 1972 Numerical simulation of turbulence. In Statistical Models and Turbulence (ed. M. Rosenblatt & C. Van Atta). Lecture Notes in Physics, vol. 12, pp. 127147. Springer.
Patnaik, P. C., Sherman, F. S. & Corcos, G. M., 1976 A numerical simulation of Kelvin Helmholtz waves of finite amplitude. J. Fluid Mech. 73, 215240.Google Scholar
Peters, N.: 1983 Local quenching due to flame stretching and non-premixed turbulent combustion. Combust. Sci. Tech. 30, 117.Google Scholar
Pierrehumbert, R. T. & Widnall, S. E., 1982 The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech. 114, 5982.Google Scholar
Rehm, R. G. & Baum, H. R., 1978 The equations of motion for thermally driven, buoyant flows. Natl. Bur. Stand. J. Res. 83, 297308.Google Scholar
Riley, J. J. & Metcalfe, R. W., 1980a Direct numerical simulations of the turbulent wake of an axisymmetric body. In Turbulent Shear Flows II (ed. L. S. Bradbury, F. Durst, B. E. Launder, F. W. Schmidt & J. H. Whitelaw), pp. 7893. Springer.
Riley, J. J. & Metcalfe, R. W., 1980b Direct numerical simulations of a perturbed, turbulent mixing layer. AIAA Paper 80–0274.Google Scholar
Riley, J. J. & Metcalfe, R. W. & Orszag, S. A. 1986 Direct numerical simulations of chemically reacting mixing layers. Phys. Fluids 29, 406422.Google Scholar
Rogallo, R. W. & Moin, P., 1984 Numerical simulation of turbulent flows. Ann. Rev. Fluid Mech. 16, 99137.Google Scholar
Saval, Ö. & Gollahalli, S. R. 1986 Flow structure in near-nozzle region of gas jet flames. AIAA J. 24, 11371140.Google Scholar
Sivashinsky, G. O.: 1979 Hydrodynamic theory of flame propagation in an enclosed volume. Acta 'Astronaut. 6, 631645.Google Scholar
Takagi, T., Shin, H.-D. & Ishio, A. 1980 Local laminarization in turbulent diffusion flames. Combust. Flame 37, 163170.Google Scholar
Takeno, T. & Kotani, Y., 1975 An experimental study on the stability of jet diffusion flames. Acta Astronaut. 2, 9991008.Google Scholar
Wallace, A. K.: 1981 Experimental investigation on the effects of chemical heat release on shear layer growth and entrainment. Ph.D. thesis, University of Adelaide.
Whol, K., Gazley, C. & Kapp, A. J., 1949 Diffusion Flames. In Third Symp. on Combustion Flame and Combustion Phenomena, pp. 288300. Combustion Institute, Pittsburgh, Pa.
Winant, C. D. & Browand, F. K., 1974 Vortex pairing, the mechanism of turbulent mixing-layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237255.Google Scholar
Yule, A. J., Chigier, N. A., Ralph, S., Boulderstone, R. & Ventura, J., 1981 Combustiontransition interaction in a jet flame. AIAA J. 19, 752760.Google Scholar