Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-14T06:27:28.519Z Has data issue: false hasContentIssue false
  • English
  • Français

Reynolds number scaling of burning rates in spherical turbulent premixed flames

Published online by Cambridge University Press:  05 November 2020

Tejas Kulkarni Open the ORCID record for Tejas Kulkarni [Opens in a new window] ,
Romain Buttay ,
M. Houssem Kasbaoui Open the ORCID record for M. Houssem Kasbaoui [Opens in a new window] ,
Antonio Attili Open the ORCID record for Antonio Attili [Opens in a new window]  and
Fabrizio Bisetti Open the ORCID record for Fabrizio Bisetti [Opens in a new window]
Tejas Kulkarni*
Affiliation:
Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, TX78712, USA
Romain Buttay
Affiliation:
Clean Combustion Research Center (CCRC), King Abdullah University of Science and Technology (KAUST), Thuwal23955, Saudi Arabia
M. Houssem Kasbaoui
Affiliation:
Department of Aerospace and Mechanical Engineering, Arizona State University, Tempe, AZ85281, USA
Antonio Attili
Affiliation:
School of Engineering, University of Edinburgh, EdinburghEH9 3FD, UK
Fabrizio Bisetti
Affiliation:
Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, TX78712, USA
*
†Email address for correspondence: tukulkarni@utexas.edu
Get access Rights & Permissions [Opens in a new window]

Abstract

In the flamelet regime of turbulent premixed combustion the enhancement in the burning rates originates primarily from surface wrinkling. In this work we investigate the Reynolds number dependence of burning rates of spherical turbulent premixed methane/air flames in decaying isotropic turbulence with direct numerical simulations. Several simulations are performed by varying the Reynolds number, while keeping the Karlovitz number the same, and the temporal evolution of the flame surface is compared across cases by combining the probability density function of the radial distance of the flame surface from the origin with the surface density function formalism. Because the mean area of the wrinkled flame surface normalized by the area of a sphere with radius equal to the mean flame radius is proportional to the product of the turbulent flame brush thickness and peak surface density within the brush, the temporal evolution of the brush and peak surface density are investigated separately. The brush thickness is shown to scale with the integral scale of the flow, evolving due to decaying velocity fluctuations and stretch. When normalized by the integral scale, the wrinkling scale defined as the inverse of the peak surface density is shown to scale with Reynolds number across simulations and as turbulence decays. As a result, the area ratio and the burning rate are found to increase as ${Re}_{\lambda }^{1.13}$, in agreement with recent experiments on spherical turbulent premixed flames. We observe that the area ratio does not vary with turbulent intensity when holding the Reynolds number constant.

JFM classification

Reacting Flows: Turbulent reacting flows Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A2
Check for updates
Copyright
© The Author(s), 2020. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Abdel-Gayed, R. G. & Bradley, D. 1977 Dependence of turbulent burning velocity on turbulent Reynolds number and ratio of flaminar burning velocity to r.m.s. turbulent velocity. Symp. (Int.) Combust. 16 (1), 1725–1735.CrossRefGoogle Scholar
Abdel-Gayed, R. G., Bradley, D. & Gray, P. 1981 A two-eddy theory of premixed turbulent flame propagation. Phil. Trans. R. Soc. Lond. A 301 (1457), 1–25.Google Scholar
Ahmed, I. & Swaminathan, N. 2013 Simulation of spherically expanding turbulent premixed flames. Combust. Sci. Technol. 185 (10), 1509–1540.CrossRefGoogle Scholar
Ahmed, I. & Swaminathan, N. 2014 Simulation of turbulent explosion of hydrogen–air mixtures. Intl J. Hydrogen Energ. 39 (17), 9562–9572.CrossRefGoogle Scholar
Albin, E. 2010 Contribution to numerical modelling of turbulent flames: DNS-EEM comparisons. PhD thesis, Rouen, INSA.Google Scholar
Albin, E. & D'Angelo, Y. 2012 Assessment of the evolution equation modelling approach for three-dimensional expanding wrinkled premixed flames. Combust. Flame 159 (5), 1932–1948.CrossRefGoogle Scholar
Andrews, G. E., Bradley, D. & Lwakabamba, S. B. 1975 Measurement of turbulent burning velocity for large turbulent Reynolds numbers. Symp. (Int.) Combust. 15 (1), 655–664.CrossRefGoogle Scholar
Baines, W. D. & Peterson, E. G. 1951 An investigation of flow through screens. Trans. Am. Soc. Mech. Engrs 73, 467–480.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1948 a Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A 193 (1035), 539–558.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1948 b Decay of turbulence in the final period. Proc. R. Soc. Lond. A 194 (1039), 527–543.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1956 Turbulent diffusion. In Surveys in Mechanics (ed. Batchelor, G. K. & Davies, R. M.). Cambridge University Press.CrossRefGoogle Scholar
Bird, R. B., Stewart, W. E. & Lightfoot, E. N. 2006 Transport Phenomena, 2nd edn. John Wiley & Sons.Google Scholar
Borghi, R. 1985 On the Structure and Morphology of Turbulent Premixed Flames, pp. 117–138. Springer.Google Scholar
Bray, K. N. C. & Libby, P. A. 1986 Passage times and flamelet crossing frequencies in premixed turbulent combustion. Combust. Sci. Technol. 47 (5–6), 253–274.CrossRefGoogle Scholar
Bray, K. N. C., Libby, P. A. & Moss, J. B. 1984 Flamelet crossing frequencies and mean reaction rates in premixed turbulent combustion. Combust. Sci. Technol. 41 (3–4), 143–172.CrossRefGoogle Scholar
Bray, K. N. C. & Moss, J. B. 1977 A unified statistical model of the premixed turbulent flame. Acta Astronaut. 4 (3–4), 291–319.CrossRefGoogle Scholar
Cant, R. S. & Bray, K. N. C. 1989 Strained laminar flamelet calculations of premixed turbulent combustion in a closed vessel. Symp. (Int.) Combust. 22 (1), 791–799.CrossRefGoogle Scholar
Chakraborty, N. & Cant, R. S. 2005 Effects of strain rate and curvature on surface density function transport in turbulent premixed flames in the thin reaction zones regime. Phys. Fluids 17 (6), 065108.CrossRefGoogle Scholar
Chaudhuri, S., Akkerman, V. & Law, C. K. 2011 Spectral formulation of turbulent flame speed with consideration of hydrodynamic instability. Phys. Rev. E 84 (2), 026322.CrossRefGoogle ScholarPubMed
Chaudhuri, S., Wu, F. & Law, C. K. 2013 Scaling of turbulent flame speed for expanding flames with Markstein diffusion considerations. Phys. Rev. E 88, 033005.CrossRefGoogle ScholarPubMed
Chaudhuri, S., Wu, F., Zhu, D. & Law, C. K. 2012 Flame speed and self-similar propagation of expanding turbulent premixed flames. Phys. Rev. Lett. 108 (4), 044503.CrossRefGoogle ScholarPubMed
Chorin, A. J. 1968 Numerical solution of the Navier–Stokes equations. Math. Comput. 22, 745–762.CrossRefGoogle Scholar
Cifuentes, L., Dopazo, C., Martin, J. & Jimenez, C. 2014 Local flow topologies and scalar structures in a turbulent premixed flame. Phys. Fluids 26 (6), 065108.CrossRefGoogle Scholar
Comte-Bellot, G. & Corrsin, S. 1971 Simple Eulerian time correlation of full-and narrow-band velocity signals in grid-generated, isotropic turbulence. J. Fluid Mech. 48 (2), 273–337.CrossRefGoogle Scholar
Creta, F., Lamioni, R., Lapenna, P. E. & Troiani, G. 2016 Interplay of Darrieus–Landau instability and weak turbulence in premixed flame propagation. Phys. Rev. E 94, 053102.CrossRefGoogle ScholarPubMed
Damköhler, G. 1940 Der einflußder turbulenz auf die flammengeschwidigkeit in gasgemischen. Z. Elektrochem. 46, 601–652 (translation in NASA Tech. Memo. 1112 (1947)).Google Scholar
Darrieus, G. 1938 Propagation d'un front de flamme. La Technique Moderne 30, 18.Google Scholar
Deschamps, B., Boukhalfa, A., Chauveau, C., Gökalp, I., Shepherd, I. G. & Cheng, R. K. 1992 An experimental estimation of flame surface density and mean reaction rate in turbulent premixed flames. Symp. (Int.) Combust. 24 (1), 469–475.CrossRefGoogle Scholar
Desjardins, O., Blanquart, G., Balarac, G. & Pitsch, H. 2008 High order conservative finite difference scheme for variable density low Mach number turbulent flows. J. Comput. Phys. 227 (15), 7125–7159.CrossRefGoogle Scholar
Falgout, R. D., Jones, J. E. & Yang, U. M. 2006 The design and implementation of Hypre, a library of parallel high performance preconditioners. In Numerical Solution of Partial Differential Equations on Parallel Computers, pp. 267–294. Springer.CrossRefGoogle Scholar
Fogla, N., Creta, F. & Matalon, M. 2013 Influence of the Darrieus–Landau instability on the propagation of planar turbulent flames. Proc. Combust. Inst. 34 (1), 1509–1517.CrossRefGoogle Scholar
Fries, D., Ochs, B., Saha, A., Ranjan, D. & Menon, S. 2019 Flame speed characteristics of turbulent expanding flames in a rectangular channel. Combust. Flame 199, 1–13.CrossRefGoogle Scholar
Hindmarsh, A. C., Brown, P. N., Grant, K. E., Lee, S. L., Serban, R., Shumaker, D. E. & Woodward, C. S. 2005 SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. 31, 363–396.CrossRefGoogle Scholar
Hinze, J. O. 1975 Turbulence. McGraw-Hill.Google Scholar
Hirschfelder, J., Curtiss, C., Bird, R. & Mayer, M. 1954 Molecular Theory of Gases and Liquids. Wiley.Google Scholar
Huang, M. J. & Leonard, A. 1995 Velocity autocorrelations of decaying isotropic homogeneous turbulence. Phys. Fluids 7 (10), 2455–2464.CrossRefGoogle Scholar
Huh, K. Y., Kwon, J. & Lee, D. 2013 Relationships for maximum flame surface density and brush thickness through conditional analysis in turbulent premixed combustion. Phys. Fluids 25 (7), 075108.CrossRefGoogle Scholar
Jiang, L. J., Shy, S. S., Li, W. Y., Huang, H. M. & Nguyen, M. T. 2016 High-temperature, high-pressure burning velocities of expanding turbulent premixed flames and their comparison with bunsen-type flames. Combust. Flame 172, 173–182.CrossRefGoogle Scholar
Johnson, N. L., Kotz, S. & Balakrishnan, N. 1994 Continuous Univariate Distributions, 2nd edn. Wiley-Interscience.Google Scholar
Kim, J. & Moin, P. 1985 Application of a fractional-step method to incompressible Navier–Stokes equations. J. Comput. Phys. 59 (2), 308–323.CrossRefGoogle Scholar
Kobayashi, H., Seyama, K., Hagiwara, H. & Ogami, Y. 2005 Burning velocity correlation of methane/air turbulent premixed flames at high pressure and high temperature. Proc. Combust. Inst. 30 (1), 827–834.CrossRefGoogle Scholar
Kobayashi, H., Tamura, T., Maruta, K., Niioka, T. & Williams, F. A. 1996 Burning velocity of turbulent premixed flames in a high-pressure environment. Symp. (Int.) Combust. 26 (1), 389–396.CrossRefGoogle Scholar
Kolla, H., Rogerson, J. W. & Swaminathan, N. 2010 Validation of a turbulent flame speed model across combustion regimes. Combust. Sci. Technol. 182 (3), 284–308.CrossRefGoogle Scholar
Landau, L. D. 1944 On the theory of slow combustion. Acta Physicochim. USSR 19, 77–85.Google Scholar
Libby, P. A. & Bray, K. N. C. 1980 Implications of the laminar flamelet model in premixed turbulent combustion. Combust. Flame 39 (1), 33–41.CrossRefGoogle Scholar
Libby, P. A. & Williams, F. A. 1994 Turbulent Reacting Flows. Academic Press.Google Scholar
Lipatnikov, A. 2012 Fundamentals of Premixed Turbulent Combustion. CRC Press.CrossRefGoogle Scholar
Lipatnikov, A. N. & Chomiak, J. 2002 Turbulent flame speed and thickness: phenomenology, evaluation, and application in multi-dimensional simulations. Prog. Energy Combust. Sci. 28 (1), 1–74.CrossRefGoogle Scholar
Liu, C. C., Shy, S. S., Peng, M. W., Chiu, C. W. & Dong, Y. C. 2012 High-pressure burning velocities measurements for centrally-ignited premixed methane/air flames interacting with intense near-isotropic turbulence at constant Reynolds numbers. Combust. Flame 159, 2608–2619.CrossRefGoogle Scholar
Liu, X. D., Osher, S. & Chan, T. 1994 Weighted essentially non-oscillatory schemes. J. Comput. Phys. 115, 200–212.CrossRefGoogle Scholar
Luca, S., Al-Khateeb, A. N., Attili, A. & Bisetti, F. 2018 a Comprehensive validation of skeletal mechanism for turbulent premixed methane–air flame simulations. J. Propul. Power 34, 153–160.CrossRefGoogle Scholar
Luca, S., Attili, A., Lo Schiavo, E., Creta, F. & Bisetti, F. 2018 b On the statistics of flame stretch in turbulent premixed jet flames in the thin reaction zone regime at varying Reynolds number. Proc. Combust. Inst. 37 (2), 2451–2459.CrossRefGoogle Scholar
Mathur, S., Tondon, P. K. & Saxena, S. C. 1967 Thermal conductivity of binary, ternary and quaternary mixtures of rare gases. Mol. Phys. 12, 569–579.CrossRefGoogle Scholar
Maz'ya, V. 1985 Sobolev Spaces, chap. 1.2.4, p. 37. Springer.Google Scholar
McBride, B. J., Gordon, S. & Reno, M. A. 1993 Coefficients for calculating thermodynamic and transport properties of individual species. NASA Tech. Memo. 4513.Google Scholar
Mohamed, M. S. & Larue, J. C. 1990 The decay power law in grid-generated turbulence. J. Fluid Mech. 219, 195–214.CrossRefGoogle Scholar
Mueller, B. 1999 Low Mach number asymptotics of the Navier–Stokes equations and numerical implications. In Lecture Series, von Kármán Institute for Fluid Dynamics.CrossRefGoogle Scholar
Peaceman, D. W. & Rachford, H. H. 1955 The numerical solution of parabolic and elliptic differential equations. J. Soc. Ind. Appl. Maths 3, 28–41.CrossRefGoogle Scholar
Peters, N. 1988 Laminar flamelet concepts in turbulent combustion. Symp. (Int.) Combust. 21 (1), 1231–1250.CrossRefGoogle Scholar
Peters, N. 1992 A spectral closure for premixed turbulent combustion in the flamelet regime. J. Fluid Mech. 242, 611–629.CrossRefGoogle Scholar
Peters, N. 1999 The turbulent burning velocity for large-scale and small-scale turbulence. J. Fluid Mech. 384, 107–132.CrossRefGoogle Scholar
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.CrossRefGoogle Scholar
Pierce, C. D. 2001 Progress-variable approach for large-eddy simulation of turbulent combustion. PhD thesis, Stanford University.Google Scholar
Pocheau, A. 1992 Front propagation in a turbulent medium. Europhys. Lett. 20 (5), 401–406.CrossRefGoogle Scholar
Poinsot, T. & Veynante, D. 2012 Theoretical and Numerical Combustion, 3rd edn. Centre Européen de Recherche et de Formation Avancée en Calcul Scientifique.Google Scholar
Pope, S. B. 1988 The evolution of surfaces in turbulence. Intl J. Engng Sci. 26 (5), 445–469.CrossRefGoogle Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Renou, B., Mura, A., Samson, E. & Boukhalfa, A. 2002 Characterization of the local flame structure and the flame surface density for freely propagating premixed flames at various Lewis numbers. Combust. Sci. Technol. 174 (4), 143–179.CrossRefGoogle Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17 (9), 095106.CrossRefGoogle Scholar
Shy, S. S., Lee, E. I., Chang, N. W. & Yang, S. I. 2000 Direct and indirect measurements of flame surface density, orientation, and curvature for premixed turbulent combustion modeling in a cruciform burner. Proc. Combust. Inst. 28 (1), 383–390.CrossRefGoogle Scholar
Sinhuber, M., Bodenschatz, E. & Bewley, G. P. 2015 Decay of turbulence at high Reynolds numbers. Phys. Rev. Lett. 114, 034501.CrossRefGoogle ScholarPubMed
Smith, G. P., Golden, D. M., Frenklach, M., Moriarty, N. W., Eiteneer, B., Goldenberg, M., Bowman, C. T., Hanson, R. K, Song, S., Gardiner, W. C. Jr., et al. 1999 Gri-mech version 3.0. Available at: http://combustion.berkeley.edu/gri-mech/version30/text30.html.Google Scholar
Taylor, G. I. 1922 Diffusion by continuous movements. Proc. R. Soc. Lond. A 2 (1), 196–212.Google Scholar
Taylor, G. I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151 (873), 421–444.Google Scholar
Tomboulides, A. G., Lee, J. C. Y. & Orszag, S. A. 1997 Numerical simulation of low Mach number reactive flows. J. Sci. Comput. 12 (2), 139–167.CrossRefGoogle Scholar
Trouvé, A. & Poinsot, T. 1994 The evolution equation for the flame surface density in turbulent premixed combustion. J. Fluid Mech. 278, 1–31.CrossRefGoogle Scholar
Vervisch, L., Bidaux, E., Bray, K. & Kollmann, W. 1995 Surface density function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches. Phys. Fluids 7 (10), 2496–2503.CrossRefGoogle Scholar
Veynante, D., Duclos, J. M. & Piana, J. 1994 Experimental analysis of flamelet models for premixed turbulent combustion. Symp. (Int.) Combust. 25 (1), 1249–1256.CrossRefGoogle Scholar
Wilke, C. R. 1950 A viscosity equation for gas mixtures. J. Chem. Phys. 18, 517–519.CrossRefGoogle Scholar
Wu, F., Saha, A., Chaudhuri, S. & Law, C. K. 2015 Propagation speeds of expanding turbulent flames of $\textrm {C}_4$ to $\textrm {C}_8$ $n$-alkanes at elevated pressures: experimental determination, fuel similarity, and stretch-affected local extinction. Proc. Combust. Inst. 35 (2), 1501–1508.CrossRefGoogle Scholar
Yang, S., Saha, A., Liu, Z. & Law, C. K. 2018 Role of Darrieus–Landau instability in propagation of expanding turbulent flames. J. Fluid Mech. 850, 784–802.CrossRefGoogle Scholar
Zheng, T., You, J. & Yang, Y. 2017 Principal curvatures and area ratio of propagating surfaces in isotropic turbulence. Phys. Rev. Fluids 2 (10), 103201.CrossRefGoogle Scholar

Kulkarni et al. supplementary movie 1

Volume rendering of the outwardly propagating flame front for the simulation R1 (blue colour), along with a planar cut showing the normalized velocity magnitude │V│/SL (white - yellow - red colours).

Download Kulkarni et al. supplementary movie 1(Video)
Video 1.1 MB

Kulkarni et al. supplementary movie 2

Volume rendering of the outwardly propagating flame front for the simulation R2 (blue colour), along with a planar cut showing the normalized velocity magnitude │V│/SL (white - yellow - red colours).

Download Kulkarni et al. supplementary movie 2(Video)
Video 1.3 MB

Kulkarni et al. supplementary movie 3

Volume rendering of the outwardly propagating flame front for the simulation R3s (blue colour), along with a planar cut showing the normalized velocity magnitude │V│/SL (white - yellow - red colours).

Download Kulkarni et al. supplementary movie 3(Video)
Video 950.9 KB