A simplified chemistry based three-dimensional Direct Numerical Simulation (DNS) database of freely propagating statistically planar turbulent premixed flames with a range of different values of turbulent Reynolds number has been used for the a priori modelling of the curvature term of the generalised Flame Surface Density (FSD) transport equation in the context of Large Eddy Simulation (LES). The curvature term has been split into the contributions arising due to the reaction and normal diffusion components of displacement speed and the term originating from the tangential diffusion component of displacement speed. Subsequently, these contributions of the curvature term have been split into the resolved and subgrid contributions. New models have been proposed for the subgrid curvature terms arising from the combined reaction and normal diffusion components and the tangential diffusion component of displacement speed. The performances of the new model and the existing models for the subgrid curvature term have been compared with the corresponding quantity extracted from the explicitly filtered DNS data. The new model for the subgrid curvature term is shown to perform satisfactorily in all cases considered in the current study, accounting for wide variations in LES filter size. 1. Introduction Flame Surface Density (FSD) based reaction rate closure is one of the popular methods of turbulent premixed combustion modelling in the context of Reynolds Averaged Navier Stokes (RANSs) simulations [1, 2]. The FSD based modelling has recently been extended to Large Eddy Simulations (LESs) [3–12]. The generalised FSD is defined as [3–10] where is the reaction progress variable and the overbar indicates a LES filtering operation. The transport equation of is given by [1, 4–7, 9, 11]: where is the th component of flame normal vector and is the displacement speed, and are the surface-weighted and Favre filtered values of a general quantity . The final term on the right hand side of (1) originates due to flame curvature and thus this term (i.e., ) is referred to as the curvature term [4–7, 9, 11]. It is evident from (1) that the curvature dependence of plays a key role in the statistical behaviours of？？ and this was confirmed in previous a priori Direct Numerical Simulation (DNS) based analyses [9, 11]. It was previously demonstrated [9, 11] that the existing models for the subgrid curvature term often do not capture its correct qualitative and quantitative behaviours, particularly in the Thin Reaction Zones (TRZ) regime flames. Moreover, the model parameters for the
References
[1]
R. S. Cant, S. B. Pope, and K. N. C. Bray, “Modelling of flamelet surface-to-volume ratio in turbulent premixed combustion,” Proceedings of the Combustion Institute, vol. 23, no. 1, pp. 809–815, 1991.
[2]
S. Candel, D. Veynante, F. Lacas, E. Maistret, N. Darabhia, and T. Poinsot, “Coherent flamelet model: applications and recent extensions,” in Recent Advances in Combustion Modelling, B. E. Larrouturou, Ed., pp. 19–64, World Scientific, Singapore, 1990.
[3]
M. Boger, D. Veynante, H. Boughanem, and A. Trouve, “Direct numerical simulation analysis of flame surface density concept for large eddy simulation of turbulent premixed combustion,” Proceedings of the Combustion Institute, vol. 27, pp. 917–925, 1998.
[4]
F. Charlette, A. Trouvé, M. Boger, and D. Veynante, “A flame surface density model for Large Eddy Simulations of turbulent premixed flames,” in Proceedings of the Joint Meeting of the British, German and French Sections of the Combustion Institute, Nancy, France, 1999.
[5]
E. R. Hawkes, Large Eddy Simulation of premixed turbulent combustion [Ph.D. thesis], Cambridge University Engineering Department, Cambridge, UK, 2000.
[6]
E. R. Hawkes and R. S. Cant, “A flame surface density approach to large-eddy simulation of premixed turbulent combustion,” Proceedings of the Combustion Institute, vol. 28, no. 1, pp. 51–58, 2000.
[7]
E. R. Hawkes and R. S. Cant, “Implications of a flame surface density approach to large eddy simulation of premixed turbulent combustion,” Combustion and Flame, vol. 126, no. 3, pp. 1617–1629, 2001.
[8]
R. Knikker, D. Veynante, and C. Meneveau, “A dynamic flame surface density model for large eddy simulation of turbulent premixed combustion,” Physics of Fluids, vol. 16, no. 11, pp. L91–L94, 2004.
[9]
N. Chakraborty and R. S. Cant, “A priori analysis of the curvature and propagation terms of the flame surface density transport equation for large eddy simulation,” Physics of Fluids, vol. 19, no. 10, Article ID 105101, 2007.
[10]
N. Chakraborty and M. Klein, “A priori direct numerical simulation assessment of algebraic flame surface density models for turbulent premixed flames in the context of large eddy simulation,” Physics of Fluids, vol. 20, no. 8, Article ID 085108, 2008.
[11]
N. Chakraborty and R. S. Cant, “Direct Numerical Simulation analysis of the Flame Surface Density transport equation in the context of Large Eddy Simulation,” Proceedings of the Combustion Institute, vol. 32, pp. 1445–1453, 2009.
[12]
F. E. Hernandez-Perez, F. T. C. Yuen, C. P. T. Groth, and O. L. Gulder , “LES of a laboratory-scale turbulent premixed Bunsen flame using FSD, PCM-FPI and thickened flame models,” Proceedings of the Combustion Institute, vol. 33, pp. 1365–1371, 2011.
[13]
J. H. Chen, A. Choudhary, B. De Supinski et al., “Terascale direct numerical simulations of turbulent combustion using S3D,” Computational Science and Discovery, vol. 2, no. 1, Article ID 015001, 2009.
[14]
N. Peters, P. Terhoeven, J. H. Chen, and T. Echekki, “Statistics of flame displacement speeds from computations of 2-D unsteady methane-air flames,” Proceedings of the Combustion Institute, vol. 1, pp. 833–839, 1998.
[15]
T. Echekki and J. H. Chen, “Analysis of the contribution of curvature to premixed flame propagation,” Combustion and Flame, vol. 118, no. 1-2, pp. 308–311, 1999.
[16]
T. J. Poinsot, “Boundary conditions for direct simulations of compressible viscous flows,” Journal of Computational Physics, vol. 101, no. 1, pp. 104–129, 1992.
[17]
K. W. Jenkins and R.S. Cant, “DNS of turbulent flame kernels,” in Proceedings of the 2nd AFOSR Conference on DNS and LES, D. Knight and L. Sakell, Eds., pp. 192–202, Kluwer Academic Publishers, Rutgers University, 1999.
[18]
N. Peters, Turbulent Combustion, Cambridge University Press, Cambridge, UK, 2000.
[19]
F. Charlette, C. Meneveau, and D. Veynante, “A power-law flame wrinkling model for LES of premixed turbulent combustion—part I: non-dynamic formulation and initial tests,” Combustion and Flame, vol. 131, no. 1-2, pp. 159–180, 2002.
[20]
E. R. Hawkes and J. H. Chen, “Evaluation of models for flame stretch due to curvature in the thin reaction zones regime,” Proceedings of the Combustion Institute, vol. 30, pp. 647–653, 2005.
[21]
I. Han and K. Y. Huh, “Roles of displacement speed on evolution of flame surface density for different turbulent intensities and Lewis numbers in turbulent premixed combustion,” Combustion and Flame, vol. 152, no. 1-2, pp. 194–205, 2008.
[22]
W. R. Grout, “An age extended progress variable for conditioning reaction rates,” Physics of Fluids, vol. 19, no. 10, Article ID 105107, 2007.
[23]
N. Chakraborty, G. Hartung, M. Katragadda, and C. F. Kaminski, “Comparison of 2D and 3D density-weighted displacement speed statistics and implications for laser based measurements of flame displacement speed using direct numerical simulation data,” Combustion and Flame, vol. 158, no. 7, pp. 1372–1390, 2011.
[24]
H. Kobayashi, T. Kawahata, K. Seyama, T. Fujimari, and J. S. Kim, “Relationship between the smallest scale of flame wrinkles and turbulence characteristics of high-pressure, high-temperature turbulent premixed flames,” Proceedings of the Combustion Institute, vol. 29, pp. 1793–1799, 2002.
[25]
N. Chakraborty, M. Klein, and R.S. Cant, “Effects of turbulent reynolds number on the displacement speed statistics in the thin reaction zones regime of turbulent premixed combustion,” Journal of Combustion, vol. 2011, Article ID 473679, 19 pages, 2011.
[26]
E. R. Hawkes and R. S. Cant, “Physical and numerical realizability requirements for flame surface density approaches to large-eddy and Reynolds averaged simulation of premixed turbulent combustion,” Combustion Theory and Modelling, vol. 5, no. 4, pp. 699–720, 2001.
