A self-contained progress variable space solution method for thermochemical variables and flame speed in freely-propagating premixed flamelets

Abstract

Flamelet models for premixed combustion, which are based on equations formulated and solved in progress variable space, have been proposed in the past, but have not been adopted for chemistry reduction methods. This is due to one limitation of these models: they need a closure for both the magnitude and the shape of the gradient (or scalar dissipation rate) of the progress variable, which is essential for an accurate prediction of the flame displacement speed. So far, solution methods for the aforementioned models require gradient information as an input, which is either modelled and non-generic, or extracted from a previous physical space flame solution for the analogous problem. The objective of this work is to provide a self-contained solution method for freely-propagating premixed flamelets in progress variable space, by solving an additional flamelet equation for the gradient of the progress variable. With this, the novel method provides both magnitude and shape of the gradient. Studying hydrogen-air and methane-air configurations, it is demonstrated that an accurate prediction of the laminar flame speed without the necessity for further input parameters can be obtained.

Derivation and analysis of two-dimensional composition space equations for multi-regime combustion using orthogonal coordinates

“…( 12)) [28] and no generic analytical closure exists. In our previous works [28,29], a separate equation for the progress variable gradient has been utilized and it is likely that this approach can be extended to complement the composition space equations presented here. This aspect should be explored in future work.…”

“…A worthwhile extension of the present composition space theory is the consistent represen-tation of differential diffusion (non-unity Lewis numbers). Previous works on one-dimensional composition space modeling for premixed [28,29,34] and non-premixed combustion [39,40] have shown that this can be realized conditioning on either mixture fraction or progress variable. The extension of the two-dimensional composition space equations for differential diffusion requires a careful incorporation of detailed diffusion modeling leading to additional terms and transport effects, such as curvature-induced differential diffusion [41].…”

“…(23) the transient terms compensate each other and vanish. It has been shown in previous works [28,29] that composition space models can accurately recover characteristics of transient combustion processes (e.g. auto-ignition, spherical expanding flames) based on this approximation.…”

“…In composition space, the Eqs. ( 26) and ( 27) consistently simplify to the 1D premixed flamelet equations [28,34,37]:…”

“…This has several reasons: first, 2D composition space models rely on closure strategies for the scalar dissipation rates (or gradients) of the conditioning variables and the so-called cross-terms which additionally appear in the equations. Only recently it has been shown that a closure for the progress variable gradient (or its scalar dissipation rate) requires an additional equation to be solved [28,29], since no general model exists for this quantity. Second, while the classical flamelet equations are simple to solve and implement, 2D composition space models are significantly more complex.…”