통계학적 정상 상태의 난류 예혼합 화염의 내부 구조와 전파 특성와 관한 연구

Abstract

The turbulent burning velocity, ST represents the propagating characteristics of a turbulent flame brush to determine the mean reaction rate in turbulent premixed combustion. Since the pioneering work of Damköhler most experimental data and correlations involve strong scatters and arbitrary tuning constants for measured and predicted ST's. In this work, a general expression for ST is derived from the continuum form of the transport equation for the mean reaction progress variable, <c>, and shown to be valid in all turbulent premixed combustion regimes. New analytical relationships for the inverse scale, 1/Lw, are proposed in the laminar flamelet and the distributed reaction regime. They are combined to give new predictive relationships for the ST in the two limiting regimes and extended to be applicable in the intermediate regime as well. They involve flamelet thickness, mean curvature, molecular and turbulent diffusivities at the leading edge without any tuning constants. The proposed relationships are shown to be consistent with measurements in literature at varying pressures, laminar flame speeds, turbulent intensities and mixture compositions. Convincing agreement is achieved for ST and 1/Lw for different turbulence and laminar flame properties of stagnating compressible flames and in parametric study with respect to turbulent intensity, laminar flamelet thickness and integral length scale for freely propagating incompressible flames. 3D incompressible and fully compressible DNS's have been performed for freely propagating and stagnating flames respectively. Bending of ST from the linear behavior occurs due to either increase in the mean curvature by wrinkling or increase in the flamelet thickness by small scale turbulence. The effect of the mean strain rate is investigated on ST and internal structures of turbulent premixed flames. The mean strain rate may affect the ST through flamelet thickness and mean curvature or indirectly through turbulence at the leading edge. The mean curvature increased slightly with the mean strain rate, although with negligible influence on the resulting ST in the laminar flamelet regime. It is explained how a mean strain rate led to a thinner flame brush and a higher maximum flame surface density by checking the analytical expressions for the gradients of and flame surface density. Results show significant contribution of convective fluxes in the normal and the transverse direction to determine the axial profiles of <c> and flame surface density. Limiting behaviors are identified at the leading and trailing edge for conditional velocities in burned and unburned gas and on flame surfaces. Conditional statistics of relevant flow variables are also examined to show gradient diffusion at a higher mean strain rate through conditional momentum equations in burned and unburned gas. There is no gravity and the Lewis number is assumed unity for simplification.