Transport equation for premixed flame curvature conditioned to reaction zone in turbulent flow

Journal article, 2026

A compact transport equation is obtained for modeling evolution of flame curvature field in a turbulent flow. While known curvature transport equations are reduced to the newly derived one, the latter contains significantly fewer terms. The newly derived equation is also conditioned to flame reaction zone of a finite thickness and various terms in the conditioned transport equation are analyzed by processing two Direct Numerical Simulation (DNS) databases by Dave and Chaudhuri (Evolution of local flame displacement speeds in turbulence, J. Fluid Mech. 884 (2020) A46) and by Yuvraj et al. (How ‘‘mixing’’ affects propagation and structure of intensely turbulent, lean, hydrogen-air premixed flames, Combust. Flame 273 (2025) 113,903). Both DNS sets deal with complex-chemistry hydrogen-air flames. In one case, the equivalence ratio ϕ is equal to 0.81, diffusional-thermal effects are weakly pronounced, and turbulence is moderately intense (Karlovitz number Ka =13). In another case, ϕ = 0.4, diffusional-thermal effects play an important role, and turbulence is more intense (Ka = 115). Nevertheless, major qualitative trends found by analyzing the DNS data are similar in both cases. First, the data show that evolution of conditioned curvature is primarily controlled by two terms, which describe (i) curvature production by non-uniform velocity field and (ii) curvature reduction due to flame propagation. Second, application of Helmholtz-Hodge decomposition to the DNS velocity fields shows that the former term is controlled by rotational motions, contrary to the local flame strain rate, which is generated by irrotational motions in both flames. This fundamental difference between the effects of turbulent velocity field on flame strain rate and curvature should be considered when modeling such effects.