Hostname: page-component-f554764f5-8cg97 Total loading time: 0 Render date: 2025-04-22T00:31:23.617Z Has data issue: false hasContentIssue false
  • English
  • Français

Unsteady counterflowing strained diffusion flames: diffusion-limited frequency response

Published online by Cambridge University Press:  26 April 2006

Fokion N. Egolfopoulos  and
Charles S. Campbell
Fokion N. Egolfopoulos
Affiliation:
Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA
Charles S. Campbell
Affiliation:
Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A detailed numerical study has been conducted on the effect of unsteadiness on the dynamics of counterflowing strained diffusion methane/oxygen/nitrogen flames. The modelling included the solution of the unsteady conservation equations of mass, momentum, energy, and species along the stagnation streamline in an opposed jet using detailed descriptions of chemistry and transport. The unsteadiness was introduced by independently imposing sinusoidal variations of the reactant velocity, concentration and temperature at the exits of the nozzles. The results demonstrate that the flame's response is quasi-steady at low frequencies, while at higher frequencies the amplitudes of the induced oscillations are reduced and phase shifted with respect to the imposed signal. At still higher frequencies, the flame no longer responds to the oscillations in the external field. A rigorous physical explanation of the frequency response was provided from first principles by identifying that oscillations imposed at the nozzle exits result in reactant concentration and temperature oscillations at the outer edge of the preflame diffusive zones. The diffusion attenuates the oscillations in this zone in a manner analogous to the velocity attenuation in Stokes’ second problem. The validity of the analogy was confirmed by examining flames over a wide range of frequencies and initial conditions. The current analysis also provided a criterion for the cutoff frequency separating the quasi-steady and transient regimes – information which can be useful in the establishment of laminar flamelet libraries.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 318 , 10 July 1996 , pp. 1 - 29
Copyright
© 1996 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.)

Article purchase

Temporarily unavailable

References

Bracco, P. V. 1988 Structure of flames in premixed-charge IC engines. Combust. Sci. Tech. 58, 209.Google Scholar
Carrier, G. F., Fendell, F. E. & Marble, F. E. 1975 The effect of strain rate on diffusion flames. SIAM J. Appl. Maths 28, 463–499.Google Scholar
Cetegen, B. M. & Bogue, D. R. 1991 Combustion in a stretched fuel strip with finite rate chemistry. Combust. Flame 86, 359–370.Google Scholar
Cetegen, B. M. & Pines, D. S. 1992 Combustion of a stretched carbon monoxide ligament with radiative heat losses. Combust. Flame 91, 143–152.Google Scholar
Chelliah, H. K., Law, C. K., Ueda, T., Smooke, M. D. & Williams, F. A. 1990 An experimental and theoretical investigation of the dilution, pressure and flow-field effects on the extinction condition of methane—air—nitrogen diffusion flames. Twenty-Third Symp. (Intl) on Combustion, pp. 503–511. The Combustion Institute.
Clarke, J. F. & Stegen, G. R. 1968 Some unsteady motions of a diffusion flame sheet. J. Fluid Mech. 34, 343–358.Google Scholar
Darabiha, N. 1992 Transient behaviour of laminar counterflow hydrogen—air diffusion with complex chemistry. Combust. Sci. Tech. 86, 163–181.Google Scholar
Dixon-Lewis, G. 1990 Structure of laminar flames. Twenty-Third Symp. (Intl) on Combustion, pp. 305–324. The Combustion Institute.
Egolfopoulos, F. N., Cho, P. & Law, C. K. 1989 Laminar flame speeds of methane-air mixtures under reduced and elevated pressures. Combust. Flame 76, 375–391.Google Scholar
Egolfopoulos, F. N., Du, D. X. & Law, C. K. 1992 A comprehensive study of methanol kinetics in freely-propagating and burner-stabilized flames, flow and static reactors, and shock tubes. Combust. Sci. Tech. 83, 33–75.Google Scholar
Egolfopoulos, F. N. & Law, C. K. 1990 Chain mechanisms in the overall reaction orders in laminar flame propagation. Combust. Flame 80, 7–16.Google Scholar
Egolfopoulos, F. N. & Law, C. K. 1994 Further considerations on the methanol oxidation kinetics. In preparation.
Ghoniem, A. F., Soteriou, M. C., Cetegen, B. M. & Knio, O. M. 1992 Effect of steady and periodic strain on unsteady flamelet combustion. Twenty-Fourth Symp. (Intl) on Combustion, pp. 223–230. The Combustion Institute.
Haworth, D. C., Drake, M. C., Pope, S. B. & Blint, R. J. 1988 The importance of time-dependent flame structures in stretched laminar flamelet models for turbulent jet diffusion flames. Twenty-Second Symp. (Intl) on Combustion, pp. 589–597. The Combustion Institute.
Im, H. G. & Law, C. K. 1993 Response of counterflow diffusion flame to oscillating strain rates. Technical Meeting of the Eastern States Section of The Combustion Institute, Paper 99, Princeton University, Princeton, NJ.
Im, H. G., Law, C. K., Kim, J. S. & Williams, F. A. 1995 Response of counterflow diffusion flame to oscillating strain rates. Combust. Flame 100, 21–30.Google Scholar
Kee, R. J., Miller, J. A., Evans, G. H. & Dixon-Lewis, G. 1988 A computational model of the structure and extinction of stretched, opposed flow, premixed methane—air flames. Twenty-Second Symp. (Intl) on Combustion, pp. 1479–1494. The Combustion Institute.
Kee, R. J., Rupley, F. M. & Miller J. A. 1989 Chemkin-II: A Fortran chemical kinetics package for the analysis of gas-phase chemical kinetics. Sandia Rep. SAND89-8009.Google Scholar
Kee, R. J., Warnatz, J. & Miller J. A. 1983 A Fortran computer code package for the evaluation of gas-phase viscosities, conductivities, and diffusion coefficients. Sandia Rep. SAND83-8209.Google Scholar
Kim, J. S. & Williams, F. A. 1994 Contributions of strained diffusion flames to acoustic pressure response. Combust. Flame 98, 279–299.Google Scholar
Law, C. K. 1988 Dynamics of stretched flames. Twenty-Second Symp. (Intl) on Combustion, pp. 1381–1402. The Combustion Institute.
Libby, P. A. & Williams, F. A. 1982 Structure of laminar flamelets in premixed turbulent combustion. Combust. Flame 44, 287–303.Google Scholar
Libby, P. A. & Williams, F. A. 1984 Stretched premixed laminar flames with two reaction zones. Combust. Sci. Tech. 37, 221–252.Google Scholar
Linan, A. & Crespo, A. 1976 An asymptotic analysis of unsteady diffusion flames for large activation energies. Combust. Sci. Tech. 14, 95–117.Google Scholar
McIntosh, A. C., Batley, G. & Brindley J. 1993 Short length scale pressure pulse interactions with premixed flames. Combust. Sci. Tech. 91, 1–13.Google Scholar
Miller, J. A., Kee, R. J., Smooke, M. D. & Grcar, J. F. 1984 The computation of the structure and extinction limit of a methane-air stagnation point diffusion flame. Spring Meeting of the Western States Section of The Combustion Institute, Paper WSS/CI 84-10.
Peters, N. 1984 Laminar diffusion flamelet models in non-premixed turbulent combustion. Prog. Energy Combust. Sci. 10, 221–252.Google Scholar
Peters, N. 1986 Laminar flamelet concepts in turbulent combustion. Twenty-First Symp. (Intl) on Combustion, pp. 1231–1250. The Combustion Institute.
Rogg, B. 1989 Numerical analysis of strained premixed CH4—air flames with detailed chemistry. In Numerical and Applied Mathematics (ed. W. F. Ames.), pp. 159–167. J. C. Baltzer AG.
Rutland, C. J. & Ferziger, J. H. 1990 Unsteady strained premixed laminar flames. Combust. Sci. Tech. 73, 305–326.Google Scholar
Saitoh, T. & Otsuka, Y. 1976 Unsteady behavior of diffusion flames and premixed flames for counter flow geometry. Combust. Sci. Tech. 12, 135–146.Google Scholar
Smooke, M. D., Puri, I. K. & Seshadri, K. 1986 A comparison between numerical and experimental measurements of the structure of a counterflow diffusion flame burning diluted methane in diluted air. Twenty-First Symp. (Intl) on Combustion, pp. 1783–1792. The Combustion Institute.
Spalding, D. B. 1978 Counterflow Diffusion Flames. Seventeenth Symp. (Intl) on Combustion, pp. 431–440. The Combustion Institute.
Stahl, G. & Warnatz, J. 1991 Numerical investigation of time-dependent properties and extinction of strained methane— and propane—air flamelets. Combust. Flame 85, 285–299.Google Scholar
Strahle, W. C. 1965 Periodic solutions to a convective droplet burning problem: the stagnation point. Tenth Symp. (Intl) on Combustion, pp. 1315–1325. The Combustion Institute.
White, F. M. 1991 Viscous Fluid Flow, 2nd edn. McGraw-Hill.
Williams, F. A. 1985 Combustion Theory, 2nd edn. Benjamin/Cummings.
Wu, C. K. & Law, C. K. 1984 On the determination of laminar flame speeds from stretched flames. Twentieth Symp. (Intl) on Combustion, pp. 1941–1949. The Combustion Institute.
Yu, C., Law, C. K. & Wu, C. K. 1986 Laminar flame speeds of hydrocarbon + air mixtures with hydrogen addition. Combust. Flame 63, 339–347.Google Scholar
Zhu, D. L., Egolfopoulos, F. N. & Law, C. K. 1988 Experimental and numerical determination of laminar flame speeds of methane/(Ar, N2, CO2)—air mixtures as function of stoichiometry, pressure, and flame temperature. Twenty-Second Symp. (Intl) on Combustion, pp. 1537–1545. The Combustion Institute.