Abstract
The filtered density function (FDF) is implemented for a two-dimensional, large eddy simulation (LES) of a gas phase, spatially developing, reacting and non-reacting, constant-density, plane mixing layer in a flow regime prior to the mixing transition where the flow is mainly two-dimensional. The unresolved scalar fluctuations are taken into account by considering the probability density function (PDF) of subgrid scale (SGS) scalar quantities following the FDF approach. In the derived FDF transport equation, the effect of chemical reactions appears in a closed form. The Lagrangian Monte Carlo scheme is used to solve the FDF transport equation. The applicability and performance of the FDF for LES of a reacting plane mixing layer are assessed by comparisons with experimental measurements. In non-reacting flow, the calculated mean streamwise velocity profiles and mean mixture fraction profiles relax to self-similarity, which is in satisfactory agreement with the measurements. In reacting flow, the FDF calculation provided a satisfactory accuracy in comparison with measurements of mean reactant and product concentration. The increase in the total amount of product formation in the flip case demonstrates the asymmetric characteristics of the entrainment and mixing characteristics in the mixing layer.
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References
Schumann, U., Large eddy simulation of turbulent diffusion with chemical reactions in the convective boundary layer. Atmos. Environ. 23 (1989) 1713–1730.
Jou, W.H. and Riley, J.J., Progress in direct numerical simulations of turbulent reacting flow. AIAA J. 27 (1989) 1543–1556.
McMurty, P.A., Menon, S. and Kerstein, A.R., A linear eddy sub-grid model for turbulent reacting flows: Application to hydrogen-air combustion. In: Proceedings of the 24th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1992) pp. 271–278.
Fureby, C. and Lofstrom, C., Large-eddy simulations of bluff body stabilized flames. In: Proceedings of the 25th Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1994) pp. 1257–1264.
Branley, N. and Jones, W.P., Large eddy simulation of a turbulent non-premixed flame. In: Proceedings of the Eleventh Symposium on Turbulent Shear Flows, Grenoble, France. Institut National Polytechnique, Université Joseph Fourier (1997) pp. 21–1-21-6.
Cook, A.W., Riley, J.J. and Kosaly, G., A laminar flamelet approach to subgrid-scale chemistry in turbulent flow. Combust. Flame 109 (1997) 332–341.
Cook, A.W., Riley, J.J. and de BruynKops, S.M., A sub-grid model for nonpremixed turbulent combustion. In: Proceedings of the Eleventh Symposium on Turbulent Shear Flows, Grenoble, France. Institut National Polytechnique, Université Joseph Fourier (1997) pp. 16–13-16-18.
de Bruyn Kops, S.M., Riley, J.J. and Kosaly, G., Investigation of modeling for non-premixed turbulent combustion. Flow, Turbulence and Combustion 60 (1998) 105–122.
Mathey, F. and Chollet, J.P., Large eddy simulation of turbulent reactive flows. In: Proceedings of the Eleventh Symposium on Turbulent Shear Flows, Grenoble, France. Institut National Polytechnique, Université Joseph Fourier (1997) pp. 16–19-16-24.
Dopazo, C., Probability density function approach for a turbulent axisymmetric heated jet: Center line evolution. Phys. Fluids A 18(2) (1975) 389–404.
Pope, S.B., PDF methods for turbulent reactive flows. Prog. Energy Combust. Sci. 11 (1985) 119–192.
Dopazo, C., Recent developments in PDF methods. In: Libby, P.A. and Williams, F.A. (eds), Turbulent Reacting Flow. Academic Press, San Diego (1994) p. 375–474.
Givi, P., Model free simulation of turbulent reactive flows, Prog. Energy Combust. Sci. 15 (1989) 1–107.
Cook, A.W. and Riley, J.J., A subgrid model for equilibrium chemistry in turbulent flows. Phys. Fluids 6 (1994) 2868–2870.
Pope, S.B., Computations of turbulent combustion: Progress and challenges. In: Proceedings of the 23rd Symposium (International) on Combustion. The Combustion Institute, Pittsburgh (1990) pp. 591–612.
Gao, F. and O'Brien, E.E., A large-eddy simulation scheme for turbulent reacting flows. Phys. Fluids A 5 (1993) 1282–1284.
Colucci, P.J., Jaberi, F.A., Givi, P. and Pope, S.B., Filtered density function for large eddy simulation of turbulent reacting flows. Phys. Fluids 10(2) (1998) 499–515.
Jaberi, F.A., Colucci, P.J., James, S., Givi, P. and Pope, S.B., Filtered mass density function for large-eddy simulation of turbulent reacting flows. J. Fluid Mech. 401 (1999) 85–121.
Masutani, S.M. and Bowman, C.T., The structure of a chemically reacting plane mixing layer. J. Fluid Mech. 172 (1986) 93–126.
Riley, J.J., Metcalfe, R.W. and Orszag, S.A., Direct numerical simulations of a chemically reacting turbulent mixing layers. Phys. Fluids 25 (1986) 406–422.
Metais, O. and Lesieur, M., Spectral large-eddy simulation of isotropic and stably stratifed turbulence, J. Fluid Mech. 239 (1992) 157–194.
Dopazo, C. and O'Brien, E.E., Statistical treatment of non-isothermal chemical reactions in turbulence. Combust. Sci. Technol. 13 (1976) 99–122.
Borghi, R., Turbulent combustion modeling. Prog. Energy Combust. Sci. 14 (1988) 245–292.
Pope, S.B., Lagrangian PDF methods for turbulent flows. Annu. Rev. Fluid Mech. 26 (1994) 23–63.
Monkewitz, P.A., Subharmonic resonance, pairing and shredding in the mixing layer. J. Fluid Mech. 188 (1988) 223–252.
Ghoniem, A.F. and Ng, K.K., Numerical study of the dynamics of a forced shear layer. Phys. Fluids 30(3) (1987) 706–721.
Durst, F., Pereira, J.C.F. and Tropea, C., The plane symmetric sudden-expansion flow at low Reynolds numbers. J. Fluid Mech. 248 (1993) 567–581.
Leonard, B.P., A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comput. Methods Appl. Mech. Engrg. 19 (1979) 59–98.
Chen, X.Q. and Pereira, J.C.F., Large-eddy simulation of particle dispersion in plane mixing layers. In:Rodi,W. and Bergeles, G. (eds), Engineering TurbulenceModeling and Experiments, Vol. 3 (1996) pp. 259–271.
Sousa, J.M.M., Silva, C.F.B. and Pereira, J.C.F., Accuracy comparison of high-order finite difference schemes for the evolution of two-dimensional finite amplitude disturbances. In: Ilin, A.V. and Scott, L.R. (eds), Proceedings of the Third International Conference on Spectral and High Order Methods, Houston, Texas, 5–9 June 1995. Houston J. Math., University of Houston (1996) 389-396.
Brown, G.L. and Roshko, A., On density effects and large structure in turbulent mixing layers. J. Fluid Mech. 64 (1974) 775–816.
Browand, F.K. and Latigo, B.O., Growth of the two-dimensional mixing layer from a turbulent and non-turbulent boundary layer. Phys. Fluids 22 (1979) 1011–1019.
Batt, R.G., Turbulent mixing of passive and chemically reacting species in a low-speed layer, J. Fluid Mech. 82 (1977) 53–95.
Mass, U. and Pope, S.B., Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space. Combust. Flame 88 (1992) 239–264.
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Zhou, X., Pereira, J. Large Eddy Simulation (2D) of a Reacting Plane Mixing Layer Using Filtered Density Function Closure. Flow, Turbulence and Combustion 64, 279–300 (2000). https://doi.org/10.1023/A:1026595626129
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DOI: https://doi.org/10.1023/A:1026595626129