This study focuses on the effects of flame stretch on the mass burning rate, for flames with nonunit Lewis numbers. The extended flame stretch model of de Goey and ten Thije Boonkkamp Combust. Flame ...119 (1999) 253–271, which was derived for multiple-species transport and chemistry, is used as a starting point. This model is adjusted to be able to predict the mass burning rate at the inner reaction layer of the flame. The accuracy of the theory is analyzed step by step using numerical results incorporating detailed chemistry and multispecies transport models. The adjusted model proves to be an accurate predictor of the mass burning rate. Furthermore, it is shown that not only the lean species Lewis number plays a role but also a number of other Lewis numbers have a significant influence on preferential diffusion. Preferential diffusion for methane/air mixtures is more difficult to predict accurately than for ethane/air and propane/air mixtures. Different contributions to the total preferential diffusion effect in methane/air mixtures partly cancel, which corresponds to an effective Lewis number being close to one. For fuels with Lewis numbers further away from one, no cancelation takes place and the accuracy of the predicted mass burning rate increases. Results show that the extended theory forms the basis for the first quantitative model to predict mass burning rates of premixed, laminar, stretched flames with nonunit Lewis numbers.
We present a model of a polluted groundwater site. The model consists of a coupled system of advection-diffusion-reaction equations for the groundwater level and the concentration of the pollutant. ...We use the complete flux scheme for the space discretization in combination with the ϑ -method for time integration and we prove a new stability result for the scheme. Numerical results are computed for the Guarani Aquifer in South America and they show good agreement with results in literature.
Liouville’s equation on phase space in geometrical optics describes the evolution of an energy distribution through an optical system, which is discontinuous across optical interfaces. The ...discontinuous Galerkin spectral element method is conservative and can achieve higher order of convergence locally, making it a suitable method for this equation. When dealing with optical interfaces in phase space, non-local boundary conditions arise. Besides being a difficulty in itself, these non-local boundary conditions must also satisfy energy conservation constraints. To this end, we introduce an energy conservative treatment of optical interfaces. Numerical experiments are performed to prove that the method obeys energy conservation. Furthermore, the method is compared to the industry standard ray tracing. The numerical experiments show that the discontinuous Galerkin spectral element method outperforms ray tracing by reducing the computation time by up to three orders of magnitude for an error of
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Two different curvilinear, flame coordinate systems are introduced. These form the basis for either the Intrinsic Disturbed Flame Equations (IDFE) or the Strongly Stretched Flamelet Equations (SSFE), ...which are quasi-one-dimensional systems of differential equations describing the inner structure and propagation velocity of stretched, premixed flames. Integral analysis is applied to derive relations for the mass burning rate, and for the IDFE, to derive jump conditions. The feasibility of both descriptions has been demonstrated. Finally, an efficient solution strategy for premixed flames is proposed, that combines both formalisms.
New expressions for the mass burning rate are derived from a recently introduced flamelet model using integral analysis. The results are compared with well-known expressions, based on ...large-activation-energy asymptotics. There is no restriction on Lewis numbers and the expressions reduce to the same results as found earlier with asymptotic techniques for Lewis numbers close to 1. From our analysis it appears that the burned edge of a stretched flamelet is most appropriate to determine the mass burning rate. The consequences for experimental and numerical studies are investigated.
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