Abstract
One commonly-used method for deriving the RANS equations for multicomponent flow is the technique of conditional averaging. In this paper the concept is extended to LES, by introducing the operations of conditional filtering and surface filtering. Properties of the filtered indicator function \(\bar b\) are investigated mathematically and computationally. These techniques are then used to derive conditionally filtered versions of the Navier–Stokes equations which are appropriate for simulating multicomponent flow in LES. Transport equations for the favre-averaged indicator function \(\bar b\) and the unresolved interface properties (the wrinkling and the surface area per unit volume) are also derived. Since the paper is directed towards modelling premixed combustion in the flamelet regime, closure of the equations is achieved by introducing physical models based on the picture of the flame as a wrinkled surface separating burnt and unburnt components of the fluid. This leads to a set of models for premixed turbulent combustion of varying complexity. The results of applying one of this set of models to propagation of a spherical flame in isotropic homogeneous turbulence are analysed.
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References
Angelberger, C., Veynante, D., Egolfopoulos, F. and Poinsot, T., Large eddy simulation of combustion instabilities in turbulent premixed flames. In: Proceedings of the Summer Program (1998) pp. 61–82.
Boger, M., Veynante, D., Boughanern, H. and Trouvé, A., Direct numerical simulation analysis of flame surface density concept for large eddy simulation of turbulent premixed combustion. In: Twenty-Seventh Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1988) pp. 917–925.
Bourlioux, A., Semi-analytical validation of a dynamic large-eddy simulation procedure for turbulent premixed flames via the G-equation. Combust.Theory Modelling 4 (2000) 363–389.
Bradley, D., Hicks, R.A., Lawes, M. and Sheppard, C.G.W., Final Report, CEC Contract JOU2-CT-92-0162. Technical report, Combustion Research Group, University of Leeds (1996).
Bradley, D., Hicks, R.A., Lawes, M., Sheppard, C.G.W. and Woolley, R., The measurement of laminar burning velocities andMarkstein numbers for iso-octane-air and iso-octane-n-heptaneair mixtures at elevated temperatures and pressures in an explosion bomb. Combust.Flame 115 (1998) 126–144.
Bray, K.N.C., The challenge of turbulent combustion'. In: Twenty-Sixth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1996) pp. 1–26.
Butler, T.D. and O'Rourke, P.J., A numerical method for two-dimensional unsteady reacting flows. In: Sixteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1977) pp. 1503–1515.
Candel, S.M. and Poinsot, T.J., Flame stretch and the balance equation for the flame area. Combust.Sci.Technol. 70 (1990) 1–15.
Cant, R., Pope, S. and Bray, K., Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion. In: Twenty-Third Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1990) pp. 809–815.
Colin, O., Ducros, F., Veynante, D. and Poinsot, T., A thickened flame model for large eddy simulations of turbulent premixed combustion. Phys.Fluids 12(7) (2000) 1843–1863.
Dopazo, C., On conditional averages for intermittent turbulent flows. J.Fluid Mech. 81 (1977) 433–438.
Fureby, C. and Tabor, G., 1997, Mathematical and physical constraints on large eddy simulations'. Theor.Comput.Fluid Dynam. 9(2) (1997) 75–83.
Fureby, C., Tabor, G., Weller, H. and Gosman, A.D., A comparative study of sub grid scale models in homogeneous isotropic turbulence. Phys.Fluids 9(5) (1997) 1416–1429.
Gülder, Ö.L., Turbulent premixed flame propagation models for different combustion regimes. In: Twenty-Third Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1990) pp. 743–750.
Hawkes, E. and Cant, S., A flame surface density approach to large eddy simulation of premixed turbulent combustion. Proc.Combust.Inst. 28 (2000) 51–58.
Im, H.G., Lund, T.S. and Ferziger, J.H., Large Eddy Simulation of turbulent front propagation with dynamic subgid bodels. Phys.Fluids 9(12) (1997) 3826–3833.
Jasak, H., Error analysis and estimation for the finite volume method with applications to fluid flows. Ph.D. Thesis, Imperial College (1996).
Jasak, H. and Weller, H.G., Interface tracking capabilities of the inter-gamma differencing scheme. Technical report, Imperial College of Science, Technology and Medicine (1995).
Kerstein, A.R., Ashurst, W.T. and Williams, F.A., Field equations for interface propagation in an unsteady homogeneous flowfield. Phys.Rev.A 37 (1988) 2728–2731.
Marble, F.E. and Broadwell, J.E., The coherent flame model of chemical reactions. Technical Report TRW-9-PU, Project Squib Rep. (1977).
Menon, S., Simulation and control of combustion instability in a dump combustor. In: Sixth International Conference on Numerical Combustion, New Orleans, Louisiana (1996).
Menon, S. and Jou,W.H., Large eddy simulations of combustion instability in an axusymmetric ramjet. Combust.Sci.Technol. 75 (1991) 53.
Nwagwe, I.K., Weller, H.G., Tabor, G., Gosman, A.D., Lawes, M., Sheppard, C.G.W. and Wooley, R., Measurements and large eddy simulations of turbulent premixed flame kernel growth. Proc.Combust.Inst. 28 (2000) 59–66.
Peters, N., Wenzel, H. and Williams, F.A., 2000, ‘Modification of the turbulent burning velocity by gas expansion. Proc.Combust.Inst. 28 (2000) 235–243.
Pitz, R.W. and Daily, J.W., Combustion in a turbulent mixing layer formed at a rearward-facing step. AIAA J. 21 (1983) 1565–1570.
Poinsot, T.J., Veynante, D. and Candel, S., Quenching processes and premixed turbulent combustion diagrams. J.Fluid Mech. 228 (1991) 561–606.
Pope, S.B., The evolution of surfaces in turbulence. Internat.J.Engrg.Sci. 26(5) (1988) 445–469.
Schroeder, W., Martin, K. and Lorensen, W., The Visualisation Toolkit: An Object-Oriented Approach to 3d Graphics. Prentice Hall, Englewood Cliffs, NJ (1997).
Shewchuk, J.R., http://www.cs.cmu.edu/ quake/triangle.html.
Shewchuk, J.R., Triangle: Engineering a 2D quality mesh generator and Delaunay triangulator. In: First Workshop on Applied Computational Geometry, Philadelphia, PA (1996) pp. 124–133.
Spalding, D.B., ‘Mixing and chemical reaction in steady confined turbulent flames. In: Thirteenth Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1970) pp. 649–657.
Tabor, G., Nwagwe, I.K., Weller, H. and Gosman, A.D., Visualisation of results from LES of combustion. J.Vis. 2(2) (1999) 177–184.
Vervisch, L., Bidaux, E., Bray, K. and Kollmann, W., Surface density function in premixed turbulent combustion modelling, similarities between probability density function and flame surface approach. Phys.Fluids 7(10) (1995) 2496–2503.
Weller, H., The development of a new flame area combustion model using conditional averaging. Thermo-Fluids Section Report TF 9307, Imperial College of Science, Technology and Medicine (1993).
Weller, H., Uslu, S., Gosman, A., Maly, R., Herweg, R. and Heel, B., Prediction of combustion in homogeneous-charge spark-ignition Engines. In: International Symposium COMODIA 94 (1994) pp. 163–169.
Weller, H.G., Marooney, C.J. and Gosman, A.D., A new spectral method for calculation of the time-varying area of a laminar flame in homogeneous turbulence. In: Twenty-Third Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1990) pp. 629–636.
Weller, H.G., Tabor, G., Gosman, A.D. and Fureby, C., Application of a flame-wrinkling LES combustion model to a turbulent mixing layer. In: Twenty-Seventh Symposium (International) on Combustion. The Combustion Institute, Pittsburgh, PA (1998) pp. 899–907.
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Tabor, G., Weller, H. Large Eddy Simulation of Premixed Turbulent Combustion Using Ξ Flame Surface Wrinkling Model. Flow, Turbulence and Combustion 72, 1–27 (2004). https://doi.org/10.1023/B:APPL.0000014910.06345.fb
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DOI: https://doi.org/10.1023/B:APPL.0000014910.06345.fb