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Investigation of the influence of combustion-induced thermal expansion on two-point turbulence statistics using conditioned structure functions

  • V. A. Sabelnikov (a1) (a2), A. N. Lipatnikov (a3), S. Nishiki (a4) and T. Hasegawa (a5)

Abstract

The second-order structure functions (SFs) of the velocity field, which characterize the velocity difference at two points, are widely used in research into non-reacting turbulent flows. In the present paper, the approach is extended in order to study the influence of combustion-induced thermal expansion on turbulent flow within a premixed flame brush. For this purpose, SFs conditioned to various combinations of mixture states at two different points (reactant–reactant, reactant–product, product–product, etc.) are introduced in the paper and a relevant exact transport equation is derived in the appendix. Subsequently, in order to demonstrate the capabilities of the newly developed approach for advancing the understanding of turbulent reacting flows, the conditioned SFs are extracted from three-dimensional (3-D) direct numerical simulation data obtained from two statistically 1-D planar, fully developed, weakly turbulent, premixed, single-step-chemistry flames characterized by significantly different (7.53 and 2.50) density ratios, with all other things being approximately equal. Obtained results show that the conditioned SFs differ significantly from standard mean SFs and convey a large amount of important information on various local phenomena that stem from the influence of combustion-induced thermal expansion on turbulent flow. In particular, the conditioned SFs not only (i) indicate a number of already known local phenomena discussed in the paper, but also (ii) reveal a less recognized phenomenon such as substantial influence of combustion-induced thermal expansion on turbulence in constant-density unburned reactants and even (iii) allow us to detect a new phenomenon such as the appearance of strong local velocity perturbations (shear layers) within flamelets. Moreover, SFs conditioned to heat-release zones indicate a highly anisotropic influence of combustion-induced thermal expansion on the evolution of small-scale two-point velocity differences within flamelets, with the effects being opposite (an increase or a decrease) for different components of the local velocity vector.

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Email address for correspondence: andrei.lipatnikov@chalmers.se

References

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Antonia, R. A., Smalley, R. J., Zhou, T., Anselmet, F. & Danaila, L. 2003 Similarity of energy structure functions in decaying homogeneous isotropic turbulence. J. Fluid Mech. 487, 245269.
Aspden, A. J., Day, M. S. & Bell, J. B. 2016 Three-dimensional direct numerical simulation of turbulent lean premixed methane combustion with detailed kinetics. Combust. Flame 165, 266283.
Ballal, D. R. 1979 The structure of premixed turbulent flames. Proc. R. Soc. Lond. A 367, 353380.
Bray, K. N. C. 1995 Turbulent transport in flames. Proc. R. Soc. Lond. A 451, 231256.
Bray, K. N. C., Champion, M., Libby, P. A. & Swaminathan, N. 2011 Scalar dissipation and mean reaction rates in premixed turbulent combustion. Combust. Flame 158, 20172022.
Chaudhuri, S., Kolla, H., Dave, H. L., Hawkes, E. R., Chen, J. H. & Law, C. K. 2017 Flame thickness and conditional scalar dissipation rate in a premixed temporal turbulent reacting jet. Combust. Flame 184, 273285.
Danaila, L., Anselmet, F., Zhou, T. & Antonia, R. A. 1999 Similarity of energy structure functions in decaying homogeneous isotropic turbulence. J. Fluid Mech. 391, 359372.
Davidson, P. A. 2015 Turbulence: An Introduction for Scientists and Engineers, 2nd edn. Oxford University Press.
Drew, D. A. & Passman, S. L. 2006 Theory of Multicomponent Fluids. Springer.
Driscoll, J. F. 2008 Turbulent premixed combustion: flamelet structure and its effect on turbulent burning velocities. Prog. Energy Combust. Sci. 34, 91134.
Frisch, U. 1995 Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press.
Furukawa, J., Noguchi, Y. & Hirano, T. 2000 Investigation of flame generated turbulence in a large-scale and low-intensity turbulent premixed flame with a 3-element electrostatic probe and a 2-D LDV. Combust. Sci. Technol. 154, 163178.
Furukawa, J., Noguchi, Y., Hirano, T. & Williams, F. A. 2002 Anisotropic enhancement of turbulence in large-scale, low-intensity turbulent premixed propane-air flames. J. Fluid Mech. 462, 209243.
Furukawa, J., Okamoto, K. & Hirano, T. 1996 Turbulence characteristics within the local reaction zone thickness of a high-intensity turbulent premixed flame. Proc. Combust. Inst. 26, 405412.
Gökalp, I., Shepherd, I. G. & Cheng, R. K. 1988 Spectral behavior of velocity fluctuations in premixed turbulent flames. Combust. Flame 71, 313323.
Günther, R. 1983 Turbulence properties of flames and their measurement. Prog. Energy Combust. Sci. 9, 105154.
Hamlington, P. E., Poludnenko, A. Y. & Oran, E. S. 2011 Interactions between turbulence and flames in premixed reacting flows. Phys. Fluids 23, 125111.
Hill, R. J. 1997 Applicability of Kolmogorov’s and Monin’s equations of turbulence. J. Fluid Mech. 353, 6781.
Hill, R. J. 2001 Equations relating structure functions of all orders. J. Fluid Mech. 434, 379388.
Hill, R. J. 2002 Exact second-order structure-function relationships. J. Fluid Mech. 468, 317326.
Im, Y. H., Huh, K. Y., Nishiki, S. & Hasegawa, T. 2004 Zone conditional assessment of flame-generated turbulence with DNS database of a turbulent premixed flame. Combust. Flame 137, 478488.
Kadowaki, S. & Hasegawa, T. 2005 Numerical simulation of dynamics of premixed flames: flame instability and vortex–flame interaction. Prog. Energy Combust. Sci. 31, 193241.
Karlovitz, B., Denniston, D. W. & Wells, F. E. 1951 Investigation of turbulent flames. J. Chem. Phys. 19, 541547.
Kataoka, I. 1986 Local instant formulation of two-phase flow. Intl J. Multiphase Flow 12, 745758.
Kim, J., Bassenne, M., Towery, C. A. Z., Hamlington, P. E., Poludnenko, A. Y. & Urzay, J. 2018 The cross-scale physical-space transfer of kinetic energy in turbulent premixed flames. J. Fluid. Mech. 848, 78116.
Kolla, H., Hawkes, E. R., Kerstein, A. R., Swaminathan, N. & Chen, J. H. 2014 On velocity and reactive scalar spectra in turbulent premixed flames. J. Fluid Mech. 75, 456487.
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds number. Dokl. Akad. Nauk SSSR 30, 299303.
Kuznetsov, V. R. 1982 Limiting laws of propagation of a turbulent flame. Combust. Explos. Shock Waves 18, 172179.
Kuznetsov, V. R. & Sabelnikov, V. A. 1990 Turbulence and Combustion. Hemisphere.
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon Press.
Lapointe, S. & Blanquart, G. 2016 Fuel and chemistry effects in high Karlovitz premixed turbulent flames. Combust. Flame 167, 294–307.
Lesieur, M., Métais, O. & Comte, P. 2005 Large-Eddy Simulations of Turbulence. Cambridge University Press.
Libby, P. A. 1975 On the prediction of intermittent turbulent flows. J. Fluid Mech. 68, 273295.
Libby, P. A. & Bray, K. N. C. 1981 Countergradient diffusion in premixed turbulent flames. AIAA J. 19, 205213.
Lipatnikov, A. N. 2009 Can we characterize turbulence in premixed flames? Combust. Flame 156, 12421247.
Lipatnikov, A. N. & Chomiak, J. 2010 Effects of premixed flames on turbulence and turbulent scalar transport. Prog. Energy Combust. Sci. 36, 1102.
Lipatnikov, A. N., Chomiak, J., Sabelnikov, V. A., Nishiki, S. & Hasegawa, T. 2015a Unburned mixture fingers in premixed turbulent flames. Proc. Combust. Inst. 35, 14011408.
Lipatnikov, A. N., Chomiak, J., Sabelnikov, V. A., Nishiki, S. & Hasegawa, T. 2015b Influence of heat release in a premixed flame on weakly turbulent flow of unburned gas: a DNS study. In 25th International Colloquium on Dynamics of Explosions and Reactive Systems. ICDERS.
Lipatnikov, A. N., Chomiak, J., Sabelnikov, V. A., Nishiki, S. & Hasegawa, T. 2018a A DNS study of the physical mechanisms associated with density ratio influence on turbulent burning velocity in premixed flames. Combust. Theor. Model. 22, 131155.
Lipatnikov, A. N., Nishiki, S. & Hasegawa, T. 2014 A direct numerical simulation study of vorticity transformation in weakly turbulent premixed flames. Phys. Fluids 26, 105104.
Lipatnikov, A. N., Nishiki, S. & Hasegawa, T. 2015c DNS assessment of relation between mean reaction and scalar dissipation rates in the flamelet regime of premixed turbulent combustion. Combust. Theor. Model. 19, 309328.
Lipatnikov, A. N., Nishiki, S. & Hasegawa, T. 2019 A DNS assessment of linear relations between filtered reaction rate, flame surface density, and scalar dissipation rate in a weakly turbulent premixed flame. Combust. Theor. Model. (in press).
Lipatnikov, A. N., Sabelnikov, V. A., Chakraborty, N., Nishiki, S. & Hasegawa, T. 2018b A DNS study of closure relations for convection flux term in transport equation for mean reaction rate in turbulent flow. Flow Turbul. Combust. 100, 7592.
Lipatnikov, A. N., Sabelnikov, V. A., Nishiki, S. & Hasegawa, T. 2017 Flamelet perturbations and flame surface density transport in weakly turbulent premixed combustion. Combust. Theor. Model. 21, 205227.
Lipatnikov, A. N., Sabelnikov, V. A., Nishiki, S. & Hasegawa, T. 2018c Combustion-induced local shear layers within premixed flamelets in weakly turbulent flows. Phys. Fluids 30, 085101.
Lipatnikov, A. N., Sabelnikov, V. A., Nishiki, S. & Hasegawa, T. 2018d Does flame-generated vorticity increase turbulent burning velocity? Phys. Fluids 30, 081702.
Lipatnikov, A. N., Sabelnikov, V. A., Nishiki, S., Hasegawa, T. & Chakraborty, N. 2015d DNS assessment of a simple model for evaluating velocity conditioned to unburned gas in premixed turbulent flame. Flow Turbul. Combust. 94, 513526.
Matalon, M. 2007 Intrinsic flame instabilities in premixed and nonpremixed combustion. Annu. Rev. Fluid Mech. 39, 163191.
Monin, A. S. 1959 The theory of locally isotropic turbulence. Dokl. Akad. Nauk SSSR 125, 515518.
Monin, A. S. & Yaglom, A. M. 1975 Statistical Fluid Mechanics: Mechanics of Turbulence, vol. 2. MIT Press.
Mura, A., Robin, V., Champion, M. & Hasegawa, T. 2009 Small scale features of velocity and scalar fields in turbulent premixed flames. Flow Turbul. Combust. 82, 339358.
Mura, A., Tsuboi, K. & Hasegawa, T. 2008 Modelling of the correlation between velocity and reactive scalar gradients in turbulent premixed flames based on DNS data. Combust. Theor. Model. 12, 671698.
Nishiki, S., Hasegawa, T., Borghi, R. & Himeno, R. 2002 Modeling of flame-generated turbulence based on direct numerical simulation databases. Proc. Combust. Inst. 29, 20172022.
Nishiki, S., Hasegawa, T., Borghi, R. & Himeno, R. 2006 Modelling of turbulent scalar flux in turbulent premixed flames based on DNS databases. Combust. Theor. Model. 10, 3955.
O’Brien, J., Towery, C. A. Z., Hamlington, P. E., Ihme, M., Poludnenko, A. Y. & Urzay, J. 2017 The cross-scale physical-space transfer of kinetic energy in turbulent premixed flames. Proc. Combust. Inst. 36, 19671975.
Obukhov, A. M. 1941 The spectral energy distribution in a turbulent flow. Dokl. Akad. Nauk SSSR 32 (1), 2224.
Poinsot, T., Veynante, D. & Candel, S. 1991 Quenching processes and premixed turbulent combustion diagrams. J. Fluid Mech. 228, 561606.
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.
Renard, P.-H., Thévenin, D., Rolon, J. C. & Candel, S. 2000 Dynamics of flame/vortex interactions. Prog. Energy Combust. Sci. 26, 225282.
Roberts, W. L., Driscoll, J. F., Drake, M. C. & Goss, L. P. 1993 Images of the quenching of a flame by vortex – to quantify regimes of turbulent combustion. Combust. Flame 94, 5869.
Robin, V., Mura, A. & Champion, M. 2011 Direct and indirect thermal expansion effects in turbulent premixed flames. J. Fluid Mech. 689, 149182.
Robin, V., Mura, A., Champion, M. & Hasegawa, T. 2010 Modeling of the effects of thermal expansion on scalar turbulent fluxes in turbulent premixed flames. Combust. Sci. Technol. 182, 449464.
Sabelnikov, V. A. & Lipatnikov, A. N. 2017 Recent advances in understanding of thermal expansion effects in premixed turbulent flames. Annu. Rev. Fluid Mech. 49, 91117.
Sabelnikov, V. A., Lipatnikov, A. N., Chakraborty, N., Nishiki, S. & Hasegawa, T. 2016 A transport equation for reaction rate in turbulent flows. Phys. Fluids 28, 081701.
Sabelnikov, V. A., Lipatnikov, A. N., Chakraborty, N., Nishiki, S. & Hasegawa, T. 2017 A balance equation for the mean rate of product creation in premixed turbulent flames. Proc. Combust. Inst. 36, 18931901.
Sabelnikov, V. A., Lipatnikov, A. N., Nishiki, S. & Hasegawa, T. 2019 Application of conditioned structure functions to exploring influence of premixed combustion on two-point turbulence statistics. Proc. Combust. Inst. 37, 24332441.
Scurlock, A. C. & Grover, J. H. 1953 Propagation of turbulent flames. Proc. Combust. Inst. 4, 645658.
Towery, C. A. Z., Poludnenko, A. Y., Urzay, J., O’Brien, J., Ihme, M. & Hamlington, P. E. 2016 Spectral kinetic energy transfer in turbulent premixed reacting flows. Phys. Rev. E 93, 053115.
Townsend, A. A. 1976 The Structure of Turbulent Shear Flow, 2nd edn. Cambridge University Press.
Tsinober, A. 2009 An Informal Conceptual Introduction to Turbulence. Springer.
Uranakara, H. A., Chaudhuri, S., Dave, H. L., Arias, P. G. & Im, H. G. 2016 A flame particle tracking analysis of turbulence–chemistry interaction in hydrogen–air premixed flames. Combust. Flame 163, 220240.
Videto, B. D. & Santavicca, D. A. 1990 Flame–turbulence interactions in a freely-propagating, premixed flame. Combust. Sci. Technol. 70, 4773.
Wabel, T. M., Skiba, A. W. & Driscoll, J. F. 2018 Evolution of turbulence through a broadened preheat zone in a premixed piloted Bunsen flame from conditionally-averaged velocity measurements. Combust. Flame 188, 1327.
Wang, H., Hawkes, E. R., Chen, J. H., Zhou, B., Li, Z. & Aldén, M. 2017 Direct numerical simulations of a high Karlovitz number laboratory premixed jet flame – an analysis of flame stretch and flame thickening. J. Fluid Mech. 815, 511536.
Whitman, S. H. R., Towery, C. A. Z., Poludnenko, A. Y. & Hamlington, P. E. 2019 Scaling and collapse of conditional velocity structure functions in turbulent premixed flames. Proc. Combust. Inst. 37, 25272535.
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Investigation of the influence of combustion-induced thermal expansion on two-point turbulence statistics using conditioned structure functions

  • V. A. Sabelnikov (a1) (a2), A. N. Lipatnikov (a3), S. Nishiki (a4) and T. Hasegawa (a5)

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