Asymptotic expressions for turbulent burning velocity at the leading edge of a premixed flame brush and their validation by published measurement data
Authors: Lee Jaeseo , Lee Gwang G. , Huh Kang Y. 
Published: December 2014

This paper presents validation of new analytical expressions for the turbulent burning velocity, ST, based on asymptotic behavior at the leading edge (LE) in turbulent premixed combustion. Reaction and density variation are assumed to be negligible at the LE to avoid the cold boundary difficulty in the statistically steady state. Good agreement is shown for the slopes, dST/du′, with respect to Lc/δf at low turbulence, with both normalized by those of the reference cases. δf is the inverse of the maximum gradient of reaction progress variable through an unstretched laminar flame, and Lc is the characteristic length scale given as burner diameter or measured integral length scale. Comparison is made for thirty-five datasets involving different fuels, equivalence ratios, H2 fractions in fuel, pressures, and integral length scales from eight references [R. C. Aldredge et al., “Premixed-flame propagation in turbulent Taylor–Couette flow,” Combust. Flame 115, 395 (1998); M. Lawes et al., “The turbulent burning velocity of iso-octane/air mixtures,” Combust. Flame 159, 1949 (2012); H. Kido et al., “Influence of local flame displacement velocity on turbulent burning velocity,” Proc. Combust. Inst. 29, 1855 (2002); J. Wang et al., “Correlation of turbulent burning velocity for syngas/air mixtures at high pressure up to 1.0 MPa,” Exp. Therm. Fluid Sci. 50, 90 (2013); H. Kobayashi et al., “Experimental study on general correlation of turbulent burning velocity at high pressure,” Proc. Combust. Inst. 27, 941 (1998); C. W. Chiu et al., “High-pressure hydrogen/carbon monoxide syngas turbulent burning velocities measured at constant turbulent Reynolds numbers,” Int. J. Hydrogen Energy 37, 10935 (2012); P. Venkateswaran et al., “Pressure and fuel effects on turbulent consumption speeds of H2/CO blends,” Proc. Combust. Inst. 34, 1527 (2013); M. Fairweather et al., “Turbulent burning rates of methane and methane–hydrogen mixtures,” Combust. Flame 156, 780 (2009)]. The turbulent burning velocity is shown to increase as the flamelet thickness, δf, decreases at a high pressure, for an equivalence ratio slightly rich or close to stoichiometric and for mixture of a high H2 fraction. Two constants involved are C to scale turbulent diffusivity as a product of turbulent intensity and characteristic length scale and Cs to relate δf with the mean effective Lm. Lm=Dmu/SLu0 is the scale of exponential decay at the LE of an unstretched laminar flame. The combined constant, KC/Cs, is adjusted to match measured turbulent burning velocities at low turbulence in each of the eight different experimental setups. All measured ST/SLu0 values follow the line, KDtu/Dmu + 1, at low turbulent intensities and show bending below the line due to positive mean curvature and broadened flamelet thickness at high turbulent intensities. Further work is required to determine the constants, Cs and K, and the factor, Lm/Lm*−Lm∇⋅nf, that is responsible for bending in different conditions of laminar flamelet and incoming turbulence.