Abstract
Results from full turbulence simulations incorporating the effects of chemical reaction are compared with simple closure theories and used to reveal some physical insights about turbulent reacting flows. Pseudospectral methods for homogeneous turbulent flows with constant physical and thermal properties in domains as large as 643 Fourier modes were used for these simulations. For the case of nonpremixed flows involving a two-species, second-order, irreversible chemical reaction, it is found that the scalar dissipation microscale is only a weak function of the reaction rate and that chemical reaction contributes very little to the decay of the variance of the reactant concentration. Examination of local values of the velocity and concentration fields shows that the local reaction rate is highest in regions of the greatest rates of strain and that vorticity tends to align with the reaction zone. Finally, difficulties associated with the evaluation of multipoint pdf's and with the archival of time-dependent data from the threedimensional simulations are described.
Similar content being viewed by others
References
Ashurst, W. T., Kerstein, A. R., Kerr, R. M., and Gibson, C. H. (1987). Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence,Phys. Fluids 30, 2343–2353.
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, vol. 44, Springer-Verlag, Heidelberg, pp. 65–113.
Brachet, M. E., Meiron, D. I., Orszag, S. A., Nickel, B. G., Morf, R. H., and Frish, U. (1983). Small-scale structure of the Taylor-Green vortex,J. Fluid Mech. 130, 411–452.
Buning, P. G., and Steger, J. L. (1985). Graphics and Flow Visualization in Computational Fluid Dynamics, AIAA Paper No. 85-1507.
Clark, R. A., Ferziger, J. H., and Reynolds, W. C. (1979). Evaluation of subgrid-scale models using an accurately simulated turbulent flow,J. Fluid Mech. 91, 1–16.
Eswaran, V., and O'Brien, E. E. (1988). Simulations of scalar mixing in grid turbulence using an eddy-damped closure model,Phys. Fluids (accepted for publication).
Givi, P., and McMurtry, P. A. (1987). Numerical experiments on mixing and chemical reaction in a homogeneous turbulent flow,Bull. Am. Phys. Soc. 32, 2033.
Herring, J. R., and Kerr, R. M. (1982). Comparison of direct numerical simulations with predictions of two-point closures for isotropic turbulence convecting a passive scalar,J. Fluid Mech. 118, 205–219.
Hill, J. C. (1976). Homogeneous turbulent mixing with chemical reaction,Ann. Rev. Fluid Mech. 8, 135–161.
Hill, J. C., Leonard, A. D., and Rogers, M. M. (1987). Direct numerical simulation of a homogeneous, turbulent reacting flow,Bull. Am. Phys. Soc. 32, 2120.
Ievlev, V. M. (1973). Equations for the finite-dimensional probability distributions of pulsating variables in a turbulent flow,Sov. Phys. Dokl. 18, 117–119.
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.
Kida, S., and Murakami, Y. (1987). Kolmogorov similarity in freely decaying turbulence,Phys. Fluids 30, 2030–2039.
Kim, J., Moin, P., and Moser, R. (1987). Turbulence statistics in fully developed channel flow at low Reynolds number,J. Fluid Mech. 177, 133–166.
Kosály, G. (1987). Non-premixed simple reaction in homogeneous turbulence,AIChE J. 33, 1998–2002.
Leonard, A. D., and Hill, J. C. (1986). Direct simulation of turbulent mixing with irreversible chemical reaction,Proc. World Cong. III Chem. Eng. 4, 177–180.
Leonard, A. D., and Hill, J. C. (1987). A Simple Chemical Reaction in Numerically Simulated Homogeneous Turbulence, AIAA Paper No. 87-0134.
Lundgren, T. S. (1972). A closure hypothesis for the hierarchy of equations for turbulent probability distribution functions, in Rosenblatt, M., and Van Atta, C. (eds.),Statistical Models and Turbulence, Lecture Notes in Physics, Vol. 12, Springer, New York, pp. 70–100.
O'Brien, E. E. (1986). Recent contributions to the statistical theory of chemical reactants in turbulent flows,PhysicoChem. Hydrodynam. 7, 1–15.
Oran, E. S., and Boris, J. P. (1987).Numerical Simulation of Reactive Flow. Elsevier, New York.
Orszag, S. A. (1971). Numerical simulation of incompressible flows within simple boundaries: accuracy,J. Fluid Mech. 49, 75–112.
Orszag, S. A. (1972). Comparison of pseudospectral and spectral approximation,Stud. Appl. Math. 51, 253–259.
Orszag, S. A., and Patterson, G. S. (1972). Numerical simulation of turbulence, in Rosenblatt, M., and Van Atta, C. (eds.)Statistical Models and Turbulence, Lecture Notes in Physics, Vol. 12, Springer, New York, pp. 127–144.
Patterson, G. K. (1981). Application of turbulence fundamentals to reactor modelling and scaleup,Chem. Eng. Commun. 8, 25–52.
Picart, J., Borghi, R., and Chollet, J. P. (1986). Numerical simulation of turbulent reacting flow, presented at Tenth Symposium on Turbulence, Rolla, Missouri.
Pope, S. B. (1985). Pdf methods for turbulent reactive flows,Prog. Energy Combust. Sci. 11, 119–192.
Riley, J. J., and Metcalfe, R. W. (1980). Direct Numerical Simulation of a Perturbed, Turbulent Mixing Layer, AIAA Paper No. 80-0274.
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.
Rogallo, R. S. (1981). Numerical Experiments in Homogeneous Turbulence, NASA TM 81315.
Rogers, M. M., and Moin, P. (1987). The structure of the vorticity field in homogeneous turbulent flow,J. Fluid Mech. 176, 33–66.
Rogers, M. M., Moin, P., and Reynolds, W. C. (1986). The Structure and Modeling of the Hydrodynamic and Passive Scalar Fields in Homogeneous Turbulent Shear Flow, Department of Mechanical Engineering Report No. TF-25, Stanford University, Stanford, California.
Rutland, C., El Tahry, S., Ferziger, J. H. (1987). Direct simulation of turbulent pre-mixed reacting flows,Bull. Am. Phys. Soc. 32, 2032.
Shirani, E., Ferziger, J. H., and Reynolds, W. C. (1981). Mixing of a Passive Scalar in Isotropic and Sheared Homogeneous Turbulence, Department of Mechanical Engineering Report No. TF-15, Stanford University, Stanford, California.
Toor, H. L. (1969). Turbulent mixing of two species with and without chemical reactions,Ind. Eng. Chem. Fundam. 8, 655–659.
Winkler, K. A., Chalmers, J. W. Hodson, S. W., Woodward, P. R., and Zabusky, N. J. (1987). A numerical laboratory,Phys. Today October, 28–37.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Leonard, A.D., Hill, J.C. Direct numerical simulation of turbulent flows with chemical reaction. J Sci Comput 3, 25–43 (1988). https://doi.org/10.1007/BF01066481
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01066481