Turbulent Shear Flows 7 pp 331-343 | Cite as

# Large Scale Structures in Reacting Mixing Layers

## Abstract

The role of large-scale coherent structures in the enhancement of mixing and chemical reaction in turbulent free shear flows has been investigated by analyzing direct numerical simulations of temporally growing reacting mixing layers. The streamwise vortical modes are found to enhance the reaction rate by convoluting the reaction surface and enhancing the mixing of the two species, although the relative significance of this effect is very sensitive to the species diffusivity. For certain Schmidt numbers, the effects of flame shortening are balanced by flame sheet stretching by the vortex pairing process. The behavior of the helicity density, dissipation, and enstrophy production in the braid region has been examined. There does not appear to be a simple correlation between the amplitude of the helicity density and the position of some very strong coherent structures in this flow.

## Keywords

Direct Numerical Simulation Coherent Structure Large Scale Structure Streamwise Vortex Damkohler Number## Preview

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## References

- Bernai, L. P., Roshko, A. (1986): Streamwise vortex structure in plane mixing layers. J. Fluid Mech.
**170**, 499–525ADSCrossRefGoogle Scholar - Buell, J. C., Huerre, P. (1988): Inflow/outflow boundary conditions and global dynamics of spatial mixing layers. Proceedings of the 1988 Summer Program, Center for Turbulence Research, pp. 19–28Google Scholar
- Cantwell, B., Coles, D. (1983): An experimental study of entrainment and transport in the turbulent near wake of circular cylinder. J. Fluid Mech.
**136**, 321–374ADSCrossRefGoogle Scholar - Canuto, C., Hussaini, M. Y., Quarteroni, A., Zang, T. A. (1988): Spectral Methods in Fluid Mechanics, Springer-Verlag, New YorkGoogle Scholar
- Corcos, G. M., Sherman, F. S. (1984): The mixing layer: deterministic models of a turbulent flow, part I. Introduction and the two-dimensional flow. J. Fluid Mech.
**139**, 29–65ADSMATHCrossRefGoogle Scholar - Givi, P. (1988): Model free simulations of turbulent reactive flows: a review. Progress in Energy and Combustion Science, in pressGoogle Scholar
- Hunt, J. C. R., Hussain, F. (1989): Private communicationGoogle Scholar
- Hussain, F. (1984): Coherent structures and incoherent turbulence. In Turbulence and Chaotic Phenomena in Fluids, IUTAM Symposium. (T. Tatsumi, ed.), pp. 453–460Google Scholar
- Hussain, A. K. M. F. (1983): Coherent structures and incoherent turbulence. IUTAM Symposium on Turbulence and Chaotic Phenomena in Fluids, IUTAM, Kyoto, Japan, pp. 1–7Google Scholar
- Hussain, A. K. M. F. (1986): Coherent structures and turbulence. J. Fluid Mech. 173, 303–356ADSCrossRefGoogle Scholar
- Hussain, F., Moser, R., Colonius, T., Moin, P., Rogers, M. M. (1988): Dynamics of coherent structures in a plane mixing layer. Proceedings of the 1988 Summer Program, Center for Turbulence Research, pp. 49–56Google Scholar
- Lin, S. J., Corcos, G. M. (1984): The mixing layer: deterministic models of a turbulent flow. Part 3. The effect of plane strain on the dynamics of streamwise vortices. J. Fluid Mech.
**141**, 130–178ADSCrossRefGoogle Scholar - Metcalfe, R. W., Orszag, S. A., Brachet, M. E., Menon, S., Riley, J. J. (1987a): Secondary instability of a temporally growing mixing layer. J. Fluid Mech.
**184**, 207–243ADSMATHCrossRefGoogle Scholar - Metcalfe, R.W., Hussain, F., Menon, S., Hayakawa, M. (1987b): Coherent Structures in a Turbulent Mixing Layer: A Comparison Between Direct Numerical Simulations and Experiments. Turbulent Shear Flows, Vol 5, pp. 110–123Google Scholar
- Michalke, A. (1964): On the inviscid instability of the hyperbolic tangent velocity profile. J. Fluid Mech.
**19**, 543–556MathSciNetADSMATHCrossRefGoogle Scholar - Moffatt, H. K. (1985): Magnetostatic equilibria and analogous Euler flows of arbitrarily complex topology. Part 1. Fundamentals. J. Fluid Mech.
**173**, 303–356Google Scholar - Orszag, S. A. (1971): Numerical simulation of incompressible flows within simple boundaries: accuracy. J. Fluid Mech.
**49**, 75–112MathSciNetADSMATHCrossRefGoogle Scholar - Orszag, S. A., Pao, Y.-H. (1974): Numerical computation of turbulent shear flows. Adv. Geophys.
**18A**, 225ADSGoogle Scholar - Peyret, P., Taylor, T. D. (1983): Comp. Methods for Fluid Flows. Springer-Verlag, New YorkGoogle Scholar
- Pierrehumbert, R. T., Widnall, S. E. (1982): The two- and three-dimensional instabilities of a spatially periodic shear layer. J. Fluid Mech.
**114**, 50–82ADSCrossRefGoogle Scholar - Riley, J. J. Metcalfe, R. W. (1985): Direct numerical simulations of chemically reacting turbulent mixing layers. Paper in AIAA 23rd Aerospace Sciences MeetingGoogle Scholar
- Riley, J. J., Metcalfe R. W., Orszag, S. A. (1986): Direct Numerical Simulations of Chemically Reacting Turbulent Mixing Layers. Phys. Fluids
**29**, 406–422ADSCrossRefGoogle Scholar - Riley, J. J., Mourad, P. D., Moser, R. D., Rogers, M. M. (1988): Sensitivity of mixing layers to three-dimensional forcing, Proceedings of the 1988 Summer Program, Center for Turbulence Research, pp. 91–116Google Scholar
- Williams, F. A. (1985): Combustion Theory. The Benjamin/Cummings Publishing Co., Menlo ParkGoogle Scholar
- Shtilman, L., Levich, E. Orszag, S. A., Pelz, R. B. Tsinober, A. (1985): On the role of helicity in complex fluid flows. Phys. Lett.
**113A**, 32–37ADSGoogle Scholar