Fuel and Combustion

Fuel and Combustion

Study of Mass Fraction Oscillation Effects on the Laminar Diffusion Flame Structure

Authors
Farhad Fathieh
Ali Khosousi
Mohammad Farshchi
Akbar Ghafourian Morshed
Scientific Center of Aerospace Systems, Faculty of Aerospace Engineering, Sharif University of Technology, Tehran, Iran
Abstract
In this work, the unsteady response of a laminar diffusion flame to harmonic mass fraction oscillations is investigated. Flame-sheet assumption is utilized to model the laminar unsteady two-dimensional co-flow diffusion flame. The flow is assumed to be subsonic, inviscid, and uniform. The convection-diffusion equation for conserved scalar with appropriate boundary conditions is solved. Considering the stoichiometric mass fraction surface to be the flame surface, it is possible to obtain the flame zone. Assuming that unburnt species cannot pass across the flame surface and that the diffusion coefficient is constant, heat release rate can be related to the flame area. To best of our knowledge, this is the first time this approach has been applied to a diffusion flame to calculate heat release rate. Flame response function is acquired as oscillations of heat release rate to fluctuations of fuel mass fraction. At each Peclet number, frequency domain is divided into three regions, namely diffusion-dominated region, convection-diffusion region, and convection-dominated region. Our results indicate that the magnitude of response function decreases as excitation frequency increases, while phase difference approaches a constant value. Also, as Peclet number increases, the amplitude of oscillations in heat release rate increases in diffusion-dominated and convection-diffusion regions, but it does not change significantly in convection-dominated region.
Keywords
Diffusion flame
Mass fraction
Flame structure
Heat release rate
Excitation frequency
1.     S. P. Burke and T. E. W. Schumann, “Diffusion Flames,” Industrial & Engineering Chemistry, 10, p. 998, 1928.
2.     J. A. Fay, “The Distributions of Concentration and Temperature in a Laminar Jet Diffusion Flame,” Journal of Aeronautical Sciences, 21, pp. 681-689, 1954.
3.     F. G. Roper, “The Prediction of Laminar Jet Diffusion Flame Sizes: Part I. Theoretical Model,” Combustion and Flame, 29, pp. 219-226, 1977.
4.     F. G. Roper, C. Smith and A. C. Cunningham, “The Prediction of Laminar Jet Diffusion Flame Sizes: Part II. Experimental Verification,” Combustion and Flame, 29, pp. 227-234, 1977.
5.     F. G. Roper, “Laminar Diffusion Flame Sizes for Curved Slot Burners Giving Fan-shaped Flames,” Combustion and Flame, 31, pp. 251-259, 1978.
6.     K. C. Smyth, J. H. Miller, R. C. Dorfman, W. G. Mallard and R. J. Santoro, “Soot Inception in a Methane/Air Diffusion Flame as Characterized by Detailed Species Profiles,” Combustion and Flame, 62, pp. 157-181, 1985.
7.     S. Khosid and J. B. Greenberg, “The Burke-Schumann Spray Diffusion Flame in a Nonuniform Flow Field,” Combustion and Flame, 118, pp. 13-24, 1999.
8.     J. Baker, K. Srireddy and R. Varagani, “Buoyancy-Controlled Laminar Diffusuion Slot Flame Heights,” Microgravity Sci. Technol., Vol. XIV/4, pp. 27-35, 2003.
9.     Y. Wang, Y. Lei, X. Zhang, W. Hu, J. Konig, O. Hinrichs, Chr. Eigenbrod and H. Rath., “Buoyancy Influence on Wrinkled,” Microgravity sci. technol., Vol. XIII/1, pp. 8-12, 2001.
10.  M. Tyagi, S. R. Chakravarthy and R. I. Sujith, “Unsteady Combustion Response of a Ducted Non-premixed Flame and Acoustic Coupling,” Combustion Theory Modeling, 11, No. 2, pp. 205-226, 2005.
11.  M. Tyagi, N. Jamadar and S. R. Chakravarthy, “Oscillatory Response of an Idealized Two-Dimensional Diffusion Flame: Analytical and Numerical Study,” Combustion and Flame, 149, pp. 271-285, 2007.
12.  N. Peters, Turbulent Combustion, Cambridge University, 2000.
13.  K. K. Kuo, Principles of Combustion, John Wiley & Sons, New York, 1986.
14.  M. Fleifel, A. M. Annaswamy, Z. A. Ghoniem and A. F. Ghoniem, “Response of a Laminar Premixed Flame to Flow Oscillations: A Kinematic Model and Thermoacoustic Instability Results,” Combustion and Flame, 106, pp. 487-510, 1996.