Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-05T08:41:52.315Z Has data issue: false hasContentIssue false

Dynamical behaviour of a premixed turbulent open V-flame

Published online by Cambridge University Press:  26 April 2006

C. W. Rhee
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA Current address: Samsung Heavy Industries Co. Ltd., Daeduk R & D Center, PO Box 43, Daeduk Science Town, Taejon, Korea 305-600.
L. Talbot
Affiliation:
Department of Mechanical Engineering, University of California, Berkeley, CA 94720, USA
J. A. Sethian
Affiliation:
Department of Mathematics, University of California, Berkeley, CA 94720, USA

Abstract

The level-set approach of Osher & Sethian to tracking interfaces is successfully adapted to the simulation of a premixed turbulent open V-flame including the effects of exothermicity and baroclinicity. In accord with experimental observations this algorithm, along with a flame anchoring scheme, predicts flame cusping for a case in which a strong vortex pair interacts with the flame front. The computed velocity and scalar statistics obtained for the turbulent V-flame compare reasonably well with experimental results by Cheng & Shepherd, and demonstrate the importance of flame-generated vorticity in the determination of flame dynamics and product velocity characteristics.

Type
Research Article
Copyright
© 1995 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

Ashurst, W. T. 1987 Vortex simulation of unsteady wrinkled laminar flames. Combust. Sci. Technol. 52, 325351.Google Scholar
Batchelor, G. K. & Townsend, A. A. 1948 Decay of isotropic turbulence in the initial period. Proc. R. Soc. Lond. A 193, 539558.Google Scholar
Blake, W. K. 1986 Mechanics of Flow-Induced Sound and Vibration, vol. I, chapter 5. Academic.
Bray, K. N. C., Libby, P. A. & Moss, J. B. 1986 Flamelet crossing frequencies and mean reaction rates in premixed turbulent combustion. Combust. Sci. Technol. 41, 143172.Google Scholar
Bray, K. N. C. & Moss, J. B. 1977 A unified statistical model of the premixed turbulent flame. Acta Astronautica 4, 291319.Google Scholar
Cheng, R. K. 1984 Conditional sampling of turbulence intensities and Reynolds stress in premixed turbulent flames. Combust. Sci. Technol. 41, 109142.Google Scholar
Cheng, R. K. & Shepherd, I. G. 1986 Interpretation of conditional statistics in open oblique premixed turbulent flames. Combust. Sci. Technol. 49, 1740.Google Scholar
Cheng, R. K., Shepherd, I. G. & Talbot, L. 1988 Reaction rates in premixed turbulent flames and their relevance to the turbulent burning speed. Twenty-Second Symp. (Intl) on Combustion, pp. 771780. The Combustion Institute.
Chopp, D. 1993 Computating minimal surfaces via level set curvature flow. J. Comput. Phys. 106, 7791.Google Scholar
Chopp, D. & Sethian, J. A. 1994 Curvature flow and singularity development. J. Exp. Maths 2, 235255.Google Scholar
Chorin, A. J. 1973 Numerical study of slightly viscous flow. J. Fluid Mech. 57, 159.Google Scholar
Clavin, P. 1985 Dynamic behavior of premixed flame fronts in laminar and turbulent flows. Energy Combust. Sci. 11, 109142.Google Scholar
Darrieus, G. 1938 Propagation d'un front de flamme: assai de théorie des vitesses anomales de déflagration par developpement spontané de la turbulence. Presented at the 6th Intl Congress Appl. Mech., Paris, 1946 (Unpublished).
Evans, L. C. & Sprunk, J. 1991 Motion of level sets by mean curvature, I. J. Diffl Geom. 33, 635681.Google Scholar
Garcia-Ybarra, P., Nicoli, C. & Clavin, P. 1984 Soret and dilution effects on premixed flames. Combust. Sci. Technol. 42, 87109.Google Scholar
Ghoniem, A. F., Chorin, A. J. & Oppenheim, A. K. 1982 Numerical modeling of turbulent flow in a combustion tunnel. Phil. Trans. R. Soc. Lond. A 304, 303325.Google Scholar
Hayes, W. D. 1959 The vorticity jump across a gasdynamic discontinuity. J. Fluid Mech. 2, 595600.Google Scholar
Hertzberg, J. R., Namazian, M. & Talbot, L. 1984 A laser tomographic study of a laminar flame in a Kármán vortex street. Combust. Sci. Technol. 38, 205216.Google Scholar
Hyman, J. A. 1984 Numerical methods for tracking interfaces. Physica 12D, 396407.Google Scholar
Kerstein, A. R., Ashurst, W. T. & Williams, F. A. 1988 Field equation for interface propagation in an unsteady homogeneous flow field. Phys. Rev. A 37, 27282731.Google Scholar
Landau, L. 1944 A contribution to the theory of slow combustion. J. Exp. Theor. Phys. 14, 240.Google Scholar
Leonard, A. 1980 Vortex methods for flow simulation. J. Comput. Phys. 37, 289335.Google Scholar
Liñán, A. & Williams, F. A. 1993 Fundamental Aspects of Combustion, Chap. 5. Oxford University Press.
Malladi, R., Vemuri, B. & Sethian, J. A. 1993 A shape detection scheme using level sets. Submitted for publication. IEEE J. Image Analysis, June.Google Scholar
Markstein, G. H. 1964 Nonsteady Flame Propagation Pergamon.
Mulder, W., Osher, S. J. & Sethian, J. A. 1992 Computing interface motion in compressible gas dynamics. J. Comput. Phys. 100, 209228.Google Scholar
Namer, I., Bill, R. G., Talbot, L. & Robben, F. 1984 Density fluctuations in a Karman vortex street. AIAA J. 22, 647654.Google Scholar
Osher, S. J. & Sethian, J. A. 1988 Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 1249.Google Scholar
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. Twenty-First Symp. (Intl) on Combustion, pp. 12311250. The Combustion Institute.
Pindera, M.-Z. & Talbot, L. 1986 Flame induced vorticity: The effects of stretch. Twenty-First Symp. (Intl) on Combustion, pp. 13571366. The Combustion Institute.
Pindera, M.-Z. & Talbot, L. 1988 Some fluid dynamic considerations in the modeling of flames. Combust. Flame 73, 111125.Google Scholar
Poinsot, T., Vegnante, D. & Candel, S. 1991 Quenching process and premixed turbulent combustion diagrams. J. Fluid Mech. 228, 561606.Google Scholar
Pope, S. B. 1976 The probability approach to the modeling of turbulent reacting flows. Combust. Flame 27, 299312.Google Scholar
Rhee, C. W. 1992 Dynamical behavior of a premixed open v-flame with exothermicity and baroclinicity. PhD thesis, Mechanical Engineering, University of California, Berkeley.
Roberts, W. L. & Driscoll, J. F. 1991 A laminar vortex interacting with a premixed flame. Combust. Flame 87, 245256.Google Scholar
Sethian, J. A. 1984 Curvature and the evolution of fronts. Commun. Math. Phys. 101, 487499.Google Scholar
Sethian, J. A. 1989 A review of recent numerical algorithms for hypersurfaces moving with curvature-dependent speed. J. Diffl Geom. 31, 131161.Google Scholar
Sethian, J. A. & Ghoniem, A. F. 1988 Validation study for vortex methods. J. Comput. Phys. 74, 283.Google Scholar
Sethian, J. A. & Strain, J. 1992 Crystal growth and dendrite formation. J. Comput. Phys. 98, 231253.Google Scholar
Shepherd, I. G. & Ashurst, W. T. 1992 Flame front geometry in premixed turbulent flames. Twenty-Fourth Symposium (Intl) on Combustion, pp. 485491. The Combustion Institute.
Shepherd, I. G., Cheng, R. K. & Goix, P. J. 1990 The spatial scalar structure of premixed turbulent stagnation point flames. Twenty-Third Symposium (Intl) on Combustion, pp. 781787. The Combustion Institute.
Swarztrauber, P. N. 1974 A direct method for the discrete solution of separable elliptic equations. SIAM J. Numer. Anal. 11, 11361150.Google Scholar
Trouvé, A. & Poinsot, T. 1993 The evolution equation for the flame surface density in turbulent premixed combustion. Center for Turbulence Research Manuscript 140, Stanford University, Stanford, CA.
Wu, M.-S. & Driscoll, J. F. 1992 A numerical simulation of a vortex convected through a laminar premixed flame. Combust. Flame 91, 310322.Google Scholar
Zhu, J. & Sethian, J. A. 1992 Projection methods coupled to level set interface techniques. J. Comput. Phys. 102, 128138.Google Scholar