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Iso-surface mass flow density and its implications for turbulent mixing and combustion

Published online by Cambridge University Press:  15 October 2007

SEUNG HYUN KIM  and
ROBERT W. BILGER
SEUNG HYUN KIM
Affiliation:
Center for Turbulence Research, Stanford University, Stanford CA 94305-3035, USA
ROBERT W. BILGER
Affiliation:
School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2003, Australia
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Abstract

A new result is derived for the mass flow rate per unit volume through a scalar iso-surface – called here the ‘iso-surface mass flow density’. The relationship of the surface mass flow density to the local entrainment rate per unit volume in scalar mixing and to the local reaction rate in turbulent premixed combustion is considered. In inhomogeneous flows, integration of the surface mass flow density across the layer in the direction of the mean scalar inhomogeneity yields the mean entrainment velocity in scalar mixing and the turbulent burning velocity in premixed combustion. For non-premixed turbulent reacting flow, this new result is shown to be consistent with the classical result of Bilger (Combust. Sci. Technol. vol. 13, 1976, p. 155) for fast one-step irreversible chemical reactions. Direct numerical simulation data for conserved scalar mixing, isothermal reaction front propagation and turbulent premixed flames are analysed. It is found that the entrainment velocity in the conserved scalar mixing case is sensitive to a threshold value. This suggests that the entrainment velocity is not a well-defined concept in temporally developing mixing layers and that scaling laws for the viscous superlayer warrant further investigation. In the isothermal reaction fronts problem, the characteristics of iso-surface propagation in a low Damköhler number regime are investigated. In premixed flames, the effects of non-stationarity on the turbulent burning velocity are addressed. The difference from the existing methods for determining turbulent burning velocity, and the implications of the present results for flames with multi-dimensional complex geometry are discussed. It is also shown that the surface mass flow density is related to the turbulent scalar flux in statistically stationary one-dimensional premixed flames. Variations of the local propagation characteristics due to departure from an unstretched laminar flame structure are shown to decrease the tendency to counter-gradient transport in turbulent premixed flames.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 590 , 10 November 2007 , pp. 381 - 409
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Bilger, R. W. 1976 The structure of diffusion flames. Combust. Sci. Technol. 13, 155–170.CrossRefGoogle Scholar
Bilger, R. W. 2004 Marker fields for turbulent premixed combustion. Combust. Flame 138, 188–194.CrossRefGoogle Scholar
Bilger, R. W., Antonia, R. A. & Srinivasan, K. R. 1976 The determination of intermittency from the probability density function of a passive scalar. Phys. Fluids 19, 1471.Google Scholar
Bilger, R. W., Pope, S. B., Bray, K. N. C. & Driscoll, J. M. 2005 Paradigms in turbulent combustion research. Proc. Combust. Inst. 30, 21–42.Google Scholar
Bray, K. N. C. 1991 Studies of the turbulent burning velocity. Proc. R. Soc. Lond. A 431, 315–335.Google Scholar
de Bruyn Kops, S. M. & Mortensen, M. 2005 Conditional mixing statistics in a self-similar scalar mixing layer. Phys. Fluids 17, 095107.Google Scholar
Candel, S. M. & Poinsot, T. J. 1990 Flame stretch and the balance equation for flame area. Combust. Sci. Technol. 70, 1–15.CrossRefGoogle Scholar
Chakraborty, N. & Cant, R. S. 2005 Influence of Lewis number on curvature effects in turbulent premixed flame propagation in the thin reaction zones regime. Phys. Fluids 17, 105105.Google Scholar
Cheng, R. K. & Ng, T. T. 1984 On defining the turbulent burning velocity in premixed V-shaped turbulent flames. Combust. Flame 57, 155–167.CrossRefGoogle Scholar
Cheng, R. K. & Shepherd, I. G. 1991 The influence of burner geometry on premixed turbulent flame propagation. Combust. Flame 85, 7–26.Google Scholar
Ching, E. C. S. 1996 General formula for stationary or statistically homogeneous probability density functions. Phys. Rev. E 53, 5899–5903.Google Scholar
Damköhler, G. 1940 Der einflußder Turbulenz auf die Flammengeschwidigkeit in Gasgemischen. Z. Electrochem. 46, 601–652.Google Scholar
Gibson, C. H. 1968 Fine structure of scalar fields mixed by turbulence. I. Zero-gradient points and minimal gradient surfaces. Phys. Fluids 11, 2305–2315.Google Scholar
de Goey, L. P. H. & Boonkkamp, J. H. M. 1999 A flamelet description of premixed laminar flames and the relation with flame stretch. Combust. Flame 119, 253–271.CrossRefGoogle Scholar
Gouldin, F. C. 1996 Combustion intensity and buring rate integral of premixed flames. Proc. Combust. Inst. 26, 381–388.CrossRefGoogle Scholar
Kennedy, C. A., Carpenter, M. H. & Lewis, R. M. 2000 Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations. Appl. Numer. Maths. 35, 177–219.CrossRefGoogle Scholar
Klimenko, A. Y. & Bilger, R. W. 1999 Conditional moment closure for turbulent combustion. Prog. Energy Combust. Sci. 25, 595–687.CrossRefGoogle Scholar
Kolmogorov, A. N., Petrovskii, I. G. & Piskunov, N. S. 1937 A study of the diffusion equation with a source term for application to a biological problem. Bull. Moscow State Univ. A 1, 1.Google Scholar
Kortschik, C., Plessing, T. & Peters, N. 2004 Laser optical investigation of turbulent transport of temperature ahead of the preheat zone in a premixed flame. Combust. Flame 236, 43–50.CrossRefGoogle Scholar
Lele, S. K. 1992 Compact finite difference schemes with spectral-like resolution. J. Comput. Phys. 103, 16–42.Google Scholar
Lipatnikov, A. N. & Chomiak, J. 2002 Turbulent burning velocity and speed of developing, curved, and strained flames.. Proc. Combust. Inst. 29, 2113–2121.CrossRefGoogle Scholar
Lipatnikov, A. N. & Chomiak, J. 2005 Self-similarly developing, premixed, turbulent flames: A theoretical study.. Phys. Fluids 17, 065105.CrossRefGoogle Scholar
Lundgren, T. 2003 Linearly forced isotropic trubulence. Annu. Res. Briefs, pp. 461–473, Stanford University/NASA Ames.Google Scholar
Peters, N. 2000 Turbulent Combustion. Cambridge University Press.CrossRefGoogle Scholar
Poinsot, T. J. & Lele, S. K. 1992 Boundary conditions for direct numerical simulations of compressible viscous flows. J. Comput. Phys. 101, 104–129.CrossRefGoogle Scholar
Pope, S. B. 1988 The evolution of surfaces in turbulence. Intl J. Engng Sci. 28, 445–469.CrossRefGoogle Scholar
Pope, S. B. 1990 Computation of turbulent combustion: progress and challenges. Proc. Combust. Inst. 23, 591–612.Google Scholar
Pope, S. B. 2000 Turbulent Flows. Cambridge University Press.Google Scholar
Pope, S. B. & Ching, E. S. C. 1993 Stationary probability density functions: an exact result. Phys. Fluids A 5, 1529–1531.Google Scholar
Rosales, C. & Meneveau, C. 2005 Linear forcing in numerical simulations of isotropic turbulence: physical space implementations and convergence properties. Phys. Fluids 17, 095106.CrossRefGoogle Scholar
Shepherd, I. G. & Kostiuk, L. W. 1994 The burning rate of premixed turbulent flames in divergent flows. Combust. Flame 96, 371–380.CrossRefGoogle Scholar
Swaminathan, N., Bilger, R. W. & Ruetsch, G. R. 1997 Interdependence of the instantaneous flame front structure and the overall scalar flux in turbulent premixed flames. Combust. Sci. Tech. 128, 73–97.CrossRefGoogle Scholar
Swaminathan, N., Bilger, R. W. & Cuenot, B. 2001 Relationship between turbulent scalar flux and conditional dilatation in premixed flames with complex chemistry. Combust. Flame 126, 1764–1779.Google Scholar
Thévenin, A. 2005 Three-dimensional direct simulations and structure of expanding turbulent methane flames. Proc. Combust. Inst. 30, 629–637.Google Scholar
Trouve, A. & Poinsot, T. J. 1994 The evolution for the flame surface density. J. Fluid Mech. 278, 1–26.CrossRefGoogle Scholar
Vervisch, L., Bidaux, E., Bray, K. N. C. & Kollmann, W. 1995 Surface density function in premixed turbulent combustion modeling, similarities between probability density function and flame surface approaches. Phys. Fluids 7, 2496–2503.CrossRefGoogle Scholar
Veynante, D. & Poinsot, T. J. 1997 Effects of pressure gradients on turbulent premixed flames. J. Fluid Mech. 353, 83–114.Google Scholar
Zimont, V. L. 1979 Theory of turbulent combustion of a homogeneous fuel mixture at high Reynolds numbers.. Combust. Explos. Shock Waves 15, 305–311.Google Scholar