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Direct Numerical Simulation and Simple Closure Theory for a Chemical Reaction in Homogeneous Turbulence

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Turbulent Reactive Flows

Part of the book series: Lecture Notes in Engineering ((LNENG,volume 40))

Abstract

The direct numerical simulation of turbulent flows serves as a useful test of simple closure theories, since one can examine the dynamics of the concentration and veloCity fields in more detail than in laboratory experiments and learn how the interaction of turbulent motion and molecular diffusion affects the overall reaction rate. A brief review of the most popular methods available for full turbulence simulations is presented, and a demonstration of the usefulness of direct numerical simulation is given for simple single-point closure theories (viz., those of Toor and of Patterson) applied to the irreversible, second-order chemical reaction of initially unmixed reactants.

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References

  • Anderson, D. A., Tannehill, J. C. and Pletcher, R. H. (1984). Computational Fluid Mechanics and Heat Transfer. McGraw-Hill: New York.

    MATH  Google Scholar 

  • Ashurst, W. T., Peters, N. and Smooke, M. D. (1986). Numerical simulation of turbulent flame structure with non-unity Lewis number, Combust. Sci. Tech. 53, 339–375.

    Article  Google Scholar 

  • Bilger, R. W. (1980). Turbulent flows with nonpremixed reactants. In Libby, P. A. and Williams, F. A. (eds.) Turbulent Reacting Flows, Topics in Applied Physics, 44, Springer-Verlag: Berlin, pp. 65–113.

    Google Scholar 

  • Boris, J. P. and Book, D. L. (1976). Solution of the continuity equation by the method of flux-corrected transport, Methods in Computational Physics 16, 85–129.

    Google Scholar 

  • Corrsin, S. (1964). The isotropic turbulent mixer: Part II. Arbitrary Schmidt number, AIChE J. 10, 870–877.

    Article  Google Scholar 

  • Eswaran, V. and O’Brien, E. E. (1987). Chemically reacting scalars in homogeneous, isotropic, turbulent flows. Submitted for publication.

    Google Scholar 

  • Eswaran, V. and Pope, S. B. (1987). Direct numerical simulations of the turbulent mixing of a passive scalar. Fluid Dynamics and Aerodynamics Report FDA-87-12. Cornell University: Ithaca, New York.

    Google Scholar 

  • Feiereisen, W. J., Reynolds, W. C. and Ferziger, J. H. (1981). Numerical simulation of a compressible, homogeneous turbulent shear flow. Dept. Mech. Engng. Rep. TF-13, Stanford University: Stanford, California.

    Google Scholar 

  • Fujiwara, T., Taki, S. and Arashi, K. (1986). Numerical analysis of a reacting flow in H2/O2 rocket combustor. Part 1: Analysis of turbulent shear flow, AIAA Paper 86-0528.

    Google Scholar 

  • Ghoniem, A. F. and Givi, P. (1987). Vortex-scalar element calculations of a diffusion flame, AIAA Paper 87-0225.

    Google Scholar 

  • Givi, P. and McMurtry, P. A. (1987). Non-premixed simple reaction in homogeneous turbulence: Direct numerical simulation, AIChE J. To be pubished.

    Google Scholar 

  • Gotlieb, D. and Orzsag, S. A. (1977). Numerical Analysis of Spectral Methods: Theory and Applications. SIAM: Philadelphia. Hesselink, L. (1988). Ann. Rev. Fluid Mech., to appear.

    Google Scholar 

  • Hill, J. C. (1976). Homogeneous turbulent mixing with chemical reaction, Ann. Rev. Fluid Mech. 8, 135–161.

    Article  ADS  Google Scholar 

  • Hussaini, M. Y., Salas, M. D. and Zang, T. A. (1985). Spectral methods for inviscid, compressible flows. In Habashi, W. G. (ed.) Advances in Computational Iranson-ics. Pineridge: Swansea, Wales, pp. 875 912.

    Google Scholar 

  • Hussaini, M. Y. and Zang, T. A. (1987). Spectral methods in fluid dynamics, Ann. Rev. Fluid Mech. 19, 339–367.

    Article  ADS  Google Scholar 

  • Jou, W.-H. and Riley, J. J. (1987). On direct numerical simulations of turbulent reacting flows, AIAA Paper 87-1321.

    Google Scholar 

  • Kerr, R.M. (1985). Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence, J. Fluid Mech. 153, 31–58.

    Article  ADS  MATH  Google Scholar 

  • Korczak, K. Z. and Patera, A. T. (1986). An isoparametric spectral-element method for solution of the Navier-Stokes equations in complex geometry, J. Comp. Phys. 62, 361–382.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  • Kosály, G. (1987). Non-premixed simple reaction in homogeneous turbulence, AIChE J. 33, 1998–2002.

    Article  Google Scholar 

  • Leonard, A. (1985). Computing three-dimensional incompressible flows, Ann. Rev. Fluid Mech. 17, 523–559.

    Article  ADS  Google Scholar 

  • Leonard, A. D. and Hill, J. C. (1986). Direct simulation of turbulent mixing with irreversible chemical reaction, Proc. World Congress III of Chem. Eng., 4, 177–80.

    Google Scholar 

  • Leonard, A. D. and Hill, J. C. (1987a). A simple chemical reaction in numerically simulated homogeneous turbulence, AIAA Paper 87-0134.

    Google Scholar 

  • Leonard, A. D. and Hill, J. C. (1987b). Direct numerical simulation of turbulent flows with chemical reaction. Second Nobeyama Workshop on Fluid Dynamics and Supercomputers. Nobeyama, Japan.

    Google Scholar 

  • Lowery, P. S., Reynolds, W. C. and Mansour, N. N. (1987). Passive scalar entrainment and mixing in a forced, spatially-developing mixing layer, AIAA Paper 87-0132.

    Google Scholar 

  • McMurtry, P. A., Jou, W.-H., Riley, J. J. and Metcalfe, R. W. (1986). Direct numerical simulations of a reacting mixing layer with chemical heat release, AIAA J. 24 962–970.

    Article  ADS  Google Scholar 

  • O’Brien, E. E. (1986). Recent contributions to the statistical theory of chemical reactions in turbulent flows, PhysicoChem. Hydrodyn. 7, 1–15.

    MathSciNet  ADS  Google Scholar 

  • Oran, E. S. and Boris, J. P. (1987). Numerical simulation of reactive flow. Elsevier, New York.

    MATH  Google Scholar 

  • Oran, E., Young, T. R., Boris, J. P., Picone, J. M. and Edwards, D. H. (1982). A study of detonation structure: The formation of unreacted gas pockets, Nineteenth Symp. (Int.) Combust., 573–582.

    Google Scholar 

  • Orszag, S. A. (1972). Comparison of pseudospectral and spectral approximations, Studies Appl. Math. 51, 253–259.

    MATH  Google Scholar 

  • Patterson, G. K. (1981). Application of turbulence fundamentals to reactor modelling and scaleup, Chem. Eng. Commun. 8, 25–52.

    Article  Google Scholar 

  • Peyret, R. and Taylor, T. D. (1983). Computational Methods for Fluid Flow. Springer-Verlag: New York.

    MATH  Google Scholar 

  • Picart, J., Borghi, R. and Chollet, J. P. (1987). Numerical simulation of turbulent reactive flows. Sixth Symposium on Turbulent Shear Flows, Toulouse, France.

    Google Scholar 

  • Pope, S. B. (1985). Pdf methods for turbulent reactive flows, Prog. Energy Combust. Sci. 11, 119–192.

    Article  MathSciNet  ADS  Google Scholar 

  • Riley, J. J., Metcalfe, R. W. and Orszag, S. A. (1986). Direct numerical simulations of chemically reacting turbulent mixing layers, Phys. Fluids 29, 406–422.

    Article  ADS  Google Scholar 

  • Rogallo, R. S. (1981). Numerical experiments in homogeneous turbulence. NASA TM 81315.

    Google Scholar 

  • Taki, S. and Fujiwara, T. (1981). Numerical simulation of triple shock behavior of gaseous detonation, Eighteenth Symp. (Int.) on Combust., 1671–1681.

    Google Scholar 

  • Toor, H. L. (1969). Turbulent mixing of two species with and without chemical reactions, Ind. Eng. Chem. Fundam. 8, 655–659.

    Article  Google Scholar 

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Leonard, A.D., Hill, J.C. (1989). Direct Numerical Simulation and Simple Closure Theory for a Chemical Reaction in Homogeneous Turbulence. In: Borghi, R., Murthy, S.N.B. (eds) Turbulent Reactive Flows. Lecture Notes in Engineering, vol 40. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9631-4_25

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  • DOI: https://doi.org/10.1007/978-1-4613-9631-4_25

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-0-387-96887-2

  • Online ISBN: 978-1-4613-9631-4

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