Experimental and Theoretical Studies of Flame-Front Stability

Abstract

ABSTRACT Rich hydrocarbon flames burning in tubes were found to assume a cellular structure in the absence of turbulence in the approach stream. The effects of type of fuel, mixture composition, and pressure on the phenomenon have been studied. A first-order perturbation treatment of flame-front stability gave results in qualitative agreement with experiments when the dependence of burning velocity on flame-front curvature was taken into account. NOTATION a = acceleration A1…A4 = constants cp = specific heat at constant pressure d = average cell size of cellular flames Di = diffusion coefficient of ith species F = aL/(Su0)2 f(x). g(y. t) = functions h = 2π/λ = wave number i = − 1 k = thermal conductivity L = characteristic length of order of flame front thickness m = ρu0Su = mass flow M = molecular weight of fuel Mi = molecular weight of ith species ni = concentration of ith species Nij = Mi(νij/ρDi) ρ = pressure Qi = heat released in jth reaction r = radial coordinate R = radius of curvature of flame front Su = burning velocity t = time T = absolute temperature u, v = velocity components wi = rate of jth reaction x, y = coordinates X = x/L Y0 = T Yi = ni, i = 1, …, n α = δ/ub0h βi = k/cpρDi γ = a/h(Su0)z δ = stability parameter ∈ = ρ u 0 / ρ b 0 φ = angle between tangent of flame front and y- axis χ = Lh = 2πL/λ νij = number of molecules of ith species generated in the jth reaction (νij is negative for those consumed) μ = parameter that determines curvature dependence of burning velocity λ = wave length λmax. = wave length for maximum instability ρ = density σ = μLh τ = parameter that determines curvature dependence of temperature of burned gas ξ , η = coordinates of an element of flame front ∝ = proportional to Subscripts u = unburned b = burned Superscripts 0 = zero order 1 = first order Presented at the 1950 Heat Transfer and Fluid Mechanics Institute, Los Angeles, June 28–30, 1950. Received August 24, 1950.