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Revisiting the modelling framework for the unresolved scalar variance
Published online by Cambridge University Press: 25 March 2024
Abstract
The unresolved scalar variance in large-eddy simulations of turbulent flows is a fundamental physical and modelling parameter. Despite its importance, relatively few algebraic models have been developed for this important variable with the most prominent models to date being the classic scale-similarity and gradient models. In this work a new generalized modelling framework based on reconstruction has been developed, which in contrast to classic modelling approaches allows the construction of base static variance models of arbitrary accuracy. It is demonstrated that higher-order reconstructions naturally lead to base static variance models of increased accuracy, and that the classic scale-similarity and gradient models are subsets of more general and higher-order models. The classic scale-similarity assumption for developing dynamic models is also revisited, and it is demonstrated that this can essentially be reinterpreted as a two-level reconstruction approach. Based on this result, a new general methodology is proposed that allows the construction of dynamic models for any given base static model, and a corresponding general reconstruction operator, algebraic or iterative. Consequently, improved static and dynamic models for the scalar variance are developed. The newly developed models are then thoroughly tested a priori using two high-fidelity direct numerical simulation databases corresponding to two substantially different flame and flow configurations, and are shown to outperform classic algebraic models for the variance.
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References
Adams, N. & Stolz, S. 2002 A sub-grid scale deconvolution approach for shock-capturing. J. Comput. Phys. 178, 391–426.CrossRefGoogle Scholar
Balarac, G., Pitsch, H. & Raman, V. 2008 Development of a dynamic model for the subfilter scalar variance using the concept of optimal estimators. Phys. Fluids 20, 035114.CrossRefGoogle Scholar
Bardina, J., Ferzinger, J.H. & Reynolds, W.C. 1980 Improved subgrid scale models for large eddy simulation. In AIAA 13th Fluid and Plasma Dynamics Conference, pp. 80–1357.Google Scholar
Bilger, R.W., Saetran, L.R. & Krishnamoorthy, L.V. 1991 Reaction in a scalar mixing layer. J. Fluid Mech. 233, 211–242.CrossRefGoogle Scholar
Boguslawski, A., Wawrzak, K., Paluszewska, A. & Geurts, B.J. 2021 Deconvolution of induced spatial discretization filters subgrid modeling in LES: application to two-dimensional turbulence. J. Phys. 2090, 1–10.Google Scholar
Borghi, R. 1988 Turbulent combustion modelling. Prog. Energy Combust. Sci. 14, 245–292.CrossRefGoogle Scholar
Bray, K.N.C. 1996 The challenge of turbulent combustion. Symp. (Intl) Combust. 26, 1–26.CrossRefGoogle Scholar
Bray, K.N.C., Libby, P.A. & Moss, J.B. 1985 Unified modeling approach for premixed turbulent combustion. Part I. General formulation. Combust. Flame 61, 87–102.CrossRefGoogle Scholar
Bray, K.N.C. & Moss, J.B. 1977 A unified statistical model of the premixed turbulent flame. Acta Astronaut. 4, 291–319.CrossRefGoogle Scholar
Bull, J.R. & Jameson, A. 2016 Explicit filtering and exact reconstruction of the sub-filter stresses in large eddy simulation. J. Comput. Phys. 306, 117–136.CrossRefGoogle Scholar
Carati, D., Winckelmans, G.S. & Jeanmart, H. 2001 On the modelling of the subgrid-scale and filtered-scale stress tensors in large-eddy simulation. J. Fluid Mech. 441, 119–138.CrossRefGoogle Scholar
van Cittert, P.H. 1931 Zum Einfluss der Spaltbreite auf die Intensitatsverteilung in Spektrallinien. II. Z. Phys. 69, 298–308.CrossRefGoogle Scholar
Clark, R.A., Ferzinger, H. & Reynolds, W.C. 1979 Evaluation of subgrid-scale models using an accurately simulated turbulent flow. J. Fluid Mech. 91, 1–16.CrossRefGoogle Scholar
Cook, A. & Riley, C. 1994 A subgrid model for equilibrium chemistry in turbulent flows. Phys. Fluids 6, 2868–2870.CrossRefGoogle Scholar
Datta, A., Mathew, J. & Hemchandra, S. 2022 The explicit filtering method for large eddy simulations of a turbulent premixed flame. Combust. Flame 237, 111862.CrossRefGoogle Scholar
Domingo, P., Nikolaou, Z., Seltz, A. & Vervisch, L. 2020 From Discrete and Iterative Deconvolution Operators to Machine Learning for Premixed Turbulent Combustion Modeling, pp. 215–232. Springer.Google Scholar
Domingo, P. & Vervisch, L. 2015 Large eddy simulation of premixed turbulent combustion using approximate deconvolution and explicit flame filtering. Proc. Combust. Inst. 35, 1359–1357.CrossRefGoogle Scholar
Domingo, P. & Vervisch, L. 2017 DNS and approximate deconvolution as a tool to analyse one-dimensional filtered flame sub-grid scale modelling. Combust. Flame 177, 109–122.CrossRefGoogle Scholar
Domingo, P., Vervisch, L. & Veynante, D. 2008 Large-eddy simulation of a lifted methane-air jet flame in a vitiated coflow. Combust. Flame 152 (3), 415–432.CrossRefGoogle Scholar
Dopazo, C. 1979 Relaxation of initial probability density functions in the turbulent convection of scalar fields. Phys. Fluids 22 (1), 20–30.CrossRefGoogle Scholar
Fox, R.O. 2003 Computational Models for Turbulent Reacting Flows. Cambridge University Press.CrossRefGoogle Scholar
Fukami, K., Fukagata, K. & Taira, K. 2020 Machine-learning-based spatio-temporal super resolution reconstruction of turbulent flows. J. Fluid Mech. 909, A9.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids 4, 1760–1765.CrossRefGoogle Scholar
Ghosal, S., Lund, T.S., Moin, P. & Akselvoll, K. 1995 A dynamic localization model for large eddy-simulation of turbulent flows. J. Fluid Mech. 286, 229–255.CrossRefGoogle Scholar
Girimaji, S.S. & Zhou, Y. 1995 Analysis and modeling of subgrid scalar mixing using numerical data. Phys. Fluids 8, 1224–1236.CrossRefGoogle Scholar
Gullbrand, J. & Chow, F.K. 2003 The effect of numerical errors and turbulence models in large-eddy simulations of channel flow, with and without explicit filtering. J. Fluid Mech. 495, 323–341.CrossRefGoogle Scholar
Gutheil, E., Balakrishnan, G. & Williams, F.A. 1993 Structure and extinction of hydrogen-air diffusion flames. In Reduced Kinetic Mechanisms for Applications in Combustion Systems (ed. N. Peters & B. Rogg), Lecture Notes in Physics. Springer.Google Scholar
Jimenez, C., Ducros, F., Cuenot, B. & Bedat, B. 2001 Subgrid scale variance and dissipation of a scalar field in large eddy simulations. Phys. Fluids 13, 1748–1754.CrossRefGoogle Scholar
Jimenez, J., Linan, A., Rogers, M.M. & Higuera, F.J. 1997 A priori testing of subgrid models for chemically reacting non-premixed turbulent shear flows. J. Fluid Mech. 349, 149–171.CrossRefGoogle Scholar
Jones, W.P. & Launder, B.E. 1972 The prediction of laminarization with a two-equation model of turbulence. J. Heat Mass Transfer 15, 301–314.CrossRefGoogle Scholar
Keil, F.B., Klein, M. & Chakraborty, N. 2021 Sub-grid reaction progress variable variance closure in turbulent premixed flames. Flow Turbul. Combust. 106, 1195–1212.CrossRefGoogle Scholar
Kim, H., Kim, J., Won, S. & Lee, C. 2021 Unsupervised deep learning for super-resolution reconstruction of turbulence. J. Fluid Mech. 910, A29.CrossRefGoogle Scholar
Klein, M., Kasten, C. & Chakraborty, N. 2015 A-priori direct numerical simulation assessment of sub-grid scale stress tensor closures for turbulent premixed combustion. Comput. Fluids 122, 1–11.CrossRefGoogle Scholar
Knudsen, E., Kim, S.H. & Pitsch, H. 2010 An analysis of premixed flamelet models for large eddy simulation of turbulent combustion. Phys. Fluids 22, 115109.CrossRefGoogle Scholar
Kolla, H., Rogerson, J.W., Chakraborty, N. & Swaminathan, N. 2009 Scalar dissipation rate modelling and its validation. Combust. Sci. Technol. 181, 518–535.CrossRefGoogle Scholar
Lecocq, G., Richard, S., Colin, O. & Vervisch, L. 2011 Hybrid presumed pdf and flame surface density approach for large-eddy simulation of premixed turbulent combustion. Part 1. Formalism and simulations of a quasi-steady burner. Combust. Flame 158 (6), 1201–1214.CrossRefGoogle Scholar
Lele, S.K. 1992 Compact finite-difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.CrossRefGoogle Scholar
Leonard, A. 1997 Large-eddy simulation of chaotic convection and beyond. In AIAA Meeting Papers on Disc, January 1997, A9715284, 97-0204.Google Scholar
Lilly, D.K. 1992 A proposed modification of the germano subgrid-scale closure method. Phys. Fluids 4, 633–635.CrossRefGoogle Scholar
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119.CrossRefGoogle Scholar
Lockwood, F.C. & Naguib, A.S. 1975 The prediction of the fluctuations in the properties of free, round-jet, turbulent, diffusion flames. Combust. Flame 24, 109–124.CrossRefGoogle Scholar
Loginov, M.A., Adams, N.A. & Zheltovodov, A.A. 2006 Large-eddy simulation of shock-wave/ turbulent-boundary-layer interaction. J. Fluid Mech. 565, 135–169.CrossRefGoogle Scholar
Mathew, J. 2002 Large eddy simulation of a premixed flame with approximate deconvolution modelling. Proc. Combust. Inst. 29, 1995–2000.CrossRefGoogle Scholar
Mathew, J., Foysi, H. & Friedrich, R. 2006 A new approach to LES based on explicit filtering. Intl J. Heat Fluid FLow 27, 594–602.CrossRefGoogle Scholar
Mathew, J., Lechner, R., Foysi, H., Sesterhenn, J. & Friedrich, R. 2003 An explicit filtering method for large eddy simulation of compressible flows. Phys. Fluids 15, 2279–2289.CrossRefGoogle Scholar
Maulik, R. & San, O. 2017 A neural network approach for the blind deconvolution of turbulent flows. J. Fluid Mech. 831, 151–181.CrossRefGoogle Scholar
Mesquita, C.C., Mastorakos, E. & Zedda, M. 2023 LES-CMC of high-altitude relight in an RQL aeronautical combustor. Proc. Combust. Inst. 39 (4), 4811–4820.CrossRefGoogle Scholar
Minamoto, Y., Fukushima, N., Tanahashi, M., Miyauchi, T. & Dunstan, T. 2011 Effect of flow geometry on turbulence-scalar interaction in premixed flames. Phys. Fluids 23, 125107.CrossRefGoogle Scholar
Moss, J.-B. & Bray, K.N.C. 1977 A unified statistical model of the premixed turbulent flame. Acta Astronaut. 4, 291–319.Google Scholar
Mukhopadhyay, S., van Oijen, J.A. & de Goey, L.P.H. 2015 A comparative study of presumed PDFs for premixed turbulent combustion modeling based on progress variable and its variance. Fuel 159, 728–740.CrossRefGoogle Scholar
Nambully, S., Domingo, P., Moureau, V. & Vervisch, L. 2014 A filtered-laminar-flame PDF sub-grid scale closure for LES of premixed turbulent flames. Part I. Formalism and application to a bluff-body burner with differential diffusion. Combust. Flame 161 (7), 1756–1774.CrossRefGoogle Scholar
Nikolaou, Z., Minamoto, Y. & Vervisch, L. 2019 Unresolved stress tensor modeling in turbulent premixed V-flames using iterative deconvolution: an a priori assessment. Phys. Rev. Fluids 4, 063202.CrossRefGoogle Scholar
Nikolaou, Z., Vervisch, L. & Domingo, P. 2022 Criteria to switch from tabulation to neural networks in computational combustion. Combust. Flame 246, 112425.CrossRefGoogle Scholar
Nikolaou, Z., Vervisch, L. & Domingo, P. 2023 An optimisation framework for the development of explicit discrete forward and inverse filters. Comput. Fluids 255, 105840.CrossRefGoogle Scholar
Nikolaou, Z.M. & Swaminathan, N. 2013 A 5-step reduced mechanism for combustion of 
$\textrm {CO}/\textrm {H}_2/\textrm {H}_2\textrm {O}/\textrm {CH}_4/\textrm {CO}_2$ mixtures with low hydrogen/methane and high $\textrm {H}_2\textrm {O}$ content. Combust. Flame 160, 56–75.CrossRefGoogle Scholar
$\textrm {CO}/\textrm {H}_2/\textrm {H}_2\textrm {O}/\textrm {CH}_4/\textrm {CO}_2$ mixtures with low hydrogen/methane and high 
$\textrm {H}_2\textrm {O}$ content. Combust. Flame 160, 56–75.CrossRefGoogle ScholarNikolaou, Z.M. & Swaminathan, N. 2015 Direct numerical simulation of complex fuel combustion with detailed chemistry: physical insight and mean reaction rate modelling. Combust. Sci. Technol. 187, 1759–1789.CrossRefGoogle Scholar
Nikolaou, Z.M. & Vervisch, L. 2018 A priori assessment of an iterative deconvolution method for LES sub-grid scale variance modelling. Flow Turbul. Combust. 101, 33–53.CrossRefGoogle Scholar
Nikolaou, Z.M., Vervisch, L. & Cant, R.S. 2018 Scalar flux modelling in turbulent flames using iterative deconvolution. Phys. Rev. Fluids 3, 043201.CrossRefGoogle Scholar
Pantano, C., Sarkar, R. & Williams, F.A. 2003 Mixing of a conserved scalar in a turbulent reacting shear layer. J. Fluid Mech. 481, 291–328.CrossRefGoogle Scholar
Pera, C., Reveillon, J., Vervisch, L. & Domingo, P. 2006 Modeling subgrid scale mixture fraction variance in les of evaporating spray. Combust. Flame 146, 635–648.CrossRefGoogle Scholar
Pierce, C.D. & Moin, P. 1998 A dynamic model for subgrid-scale variance and dissipation rate of a conserved scalar. Phys. Fluids 10, 3041–3044.CrossRefGoogle Scholar
Pierce, C.D. & Moin, P. 2004 Progress-variable approach for large-eddy simulation of non-premixed turbulent combustion. J. Fluid Mech. 504, 73–97.CrossRefGoogle Scholar
Poinsot, T. & Lele, S. 1992 Boundary conditions for direct simulations of compressible viscous flows. J. Comput. Phys. 101, 104–129.CrossRefGoogle Scholar
Schlatter, P., Stolz, S. & Kleiser, L. 2004 LES of transitional flows using the approximate deconvolution model. Intl J. Heat Fluid Flow 25, 549–558.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations. Mon. Weath. Rev. 91, 99–164.2.3.CO;2>CrossRefGoogle Scholar
Stolz, S. & Adams, N. 1999 An approximate deconvolution procedure for large-eddy simulation. Phys. Fluids 11, 1699–1701.CrossRefGoogle Scholar
Stolz, S. & Adams, N. 2001 An approximate deconvolution model for large-eddy simulation with application to incompressible wall-bounded flows. Phys. Fluids 13, 997–1015.CrossRefGoogle Scholar
Sutherland, J.C. & Kennedy, C.A. 2003 Improved boundary conditions for viscous, reacting compressible flows. J. Comput. Phys. 191, 502–524.CrossRefGoogle Scholar
Thompson, K.W. 1987 Time dependent boundary conditions for hyperbolic systems. J. Comput. Phys. 68, 1–24.CrossRefGoogle Scholar
Veynante, D. & Vervisch, L. 2002 Turbulent combustion modeling. Prog Energy Combust. Sci. 28, 193–266.CrossRefGoogle Scholar
Vreman, A.W., Albrecht, B.A., van Oijen, J.A., de Goey, L.P.H. & Bastiaans, R.J.M. 2008 Premixed and nonpremixed generated manifolds in large-eddy simulation of Sandia flame D and F. Combust. Flame 153, 394–416.CrossRefGoogle Scholar
Vreman, A.W., Bastiaans, R.J.M. & Geurts, B.J. 2009 a A similarity subgrid model for premixed turbulent combustion. Flow Turbul. Combust. 82, 233–248.CrossRefGoogle Scholar
Vreman, A.W., van Oijen, J.A., de Goey, L.P.H. & Bastiaans, R.J.M. 2009 b Subgrid scale modeling in large-eddy simulation of turbulent combustion using premixed flamelet chemistry. Flow Turbul. Combust. 82, 511–535.CrossRefGoogle Scholar
Wang, Q. & Ihme, M. 2017 Regularized deconvolution method for turbulent combustion modelling. Combust. Flame 176, 125–142.CrossRefGoogle Scholar
Wang, Q. & Ihme, M. 2019 A regularised deconvolution method for turbulent closure modelling in implicitly filtered large-eddy simulation. Combust. Flame 204, 341–355.CrossRefGoogle Scholar