On the validity of Damköhler’s second hypothesis in statistically planar turbulent premixed flames in the thin reaction zones regime

Abstract The validity of Damkohler's second hypothesis, which was originally proposed for premixed combustion for conditions where the large scale turbulent timescale remains smaller than the chemical timescale and the integral length scale remains smaller than the flame thickness, has been assessed for a range of Damkohler and Karlovitz numbers (i.e. 0.2 ≤ D a ≤ 3.0 and 0.58 ≤ K a ≤ 33.34 ) using a three-dimensional DNS database of statistically planar turbulent premixed flames subjected to forced unburned gas turbulence. It has been found that Damkohler's first hypothesis remains valid for all cases considered in this work irrespective of the combustion regime. By contrast, Damkohler's second hypothesis does not hold in the strict sense for the thin reaction zones regime flames with small values of Damkohler number. However, the ratio of the turbulent flame speed normalised by laminar burning velocity and the square root of the ratio of turbulent diffusivity to mass diffusivity converges to a value of the order of unity for the flames with high turbulence intensity and low Damkohler number in the thin reaction zones regime. Under this condition, Damkohler's second hypothesis, in an order of magnitude sense, can be considered to be valid alongside Damkohler's first hypothesis. A scaling analysis has been carried out using the equilibrium of the tangential strain rate and curvature terms in the Flame Surface Density transport equation to demonstrate that Damkohler's second hypothesis can be expected to be valid only in an order of magnitude sense for the thin reaction zones regime flames with small values of Damkohler number.