Vincent Robin

A multi-dirac presumed PDF model for turbulent reactive flows with variable equivalence ratio

The present paper is devoted to the numerical modeling of turbulent reactive flows in situations where reactants are not ideally premixed. In this case, the description of the local thermochemistry requires at least two variables. Here, we chose the mixture fraction ξ to describe the local composition of fresh mixture and the fuel mass fraction Y f to evaluate the progress of the chemical reaction. The numerical model is based on the earlier analysis made by Libby and Williams (2000), an analysis that led eventually to the LW-P model (Ribert et al. 2004) based on a two-scalar (Y f , ξ) Probability Density Function (PDF) involving two Dirac delta functions. In the present contribution, a generalization of the LW-P model to four delta function PDF is proposed, one which allows the cross-correlation between the two scalars to behave as predicted by the experiments. The model is applied to the calculation of a turbulent reactive flow of propane and air stabilized by a sudden expansion of a 2-D channel (Besson et al. 2001). Results obtained using either a two Dirac delta function PDF or a four Dirac delta function PDF are compared with available experimental data. The closure problem raised by the mean scalar dissipation term is also discussed.

Modeling the Effects of Thermal Expansion on Scalar Turbulent Fluxes in Turbulent Premixed Flames

The thermal expansion induced by the chemical reactions taking place in a turbulent reactive flow affects the velocity field so strongly that velocity fluctuations and velocity gradients can be governed by chemistry rather than by turbulence. Moreover, thermal expansion is well known to be responsible for counter-gradient turbulent diffusion and flame-generated turbulence phenomena. In the present paper, a specific description of the velocity field is used, which allows to separate the influence of thermal expansion from the effects related only to the turbulent motion. Using this description, all the usual turbulent quantities are expressed in terms of two contributions: one due to thermal expansion and one due to turbulence. The theoretical analysis shows that only the contributions due to turbulence should be resolved by transport equations in which unclosed terms do not depend on thermal expansion. Deduced from this analysis, a relatively simple closure modelis proposed and successfully validated through comparison with Direct Numerical Simulation data. Results show the ability of this model to represent the counter-gradient diffusion region of the flame as well as the region controlled by gradient transport, crucial to the propagation mechanism of the flame brush.

A Second-Order Model for Turbulent Reactive Flows with Variable Equivalence Ratio

A new theory for Reynolds stresses and turbulent scalar flux of both passive and reactive scalar is developed to describe turbulent reactive flows with partially premixed reactants. Starting points of the present study are based on i) an earlier analysis of the joint scalar PDF in partially premixed situations made by Libby and Williams (2000), and ii) a recent work carried out by Domingo and Bray (2000) dealing with the modeling of pressure fluctuating terms. Concerning the first point, the LW-P approach using a discrete PDF, made of four Dirac delta functions, is used in conjunction with the recent scalar dissipation closure proposed by Mura et al. (2007). Concerning the second point, special attention is paid to the closure of pressure fluctuating terms responsible for counter-gradient diffusion and flame generated turbulence effects. A new model for these terms valid in the case of partially premixed situations is proposed. This model takes different contributions into account, namely (i) a nonreactive part representing density changes closed by using conditional mean equations of motion, (ii) a reactive part, directly related to the mean chemical rate and (iii) an isotropization part which is a generalization of the “return-to-isotropy” model for constant density flows. Using this new closure, calculations are performed in the case of a confined turbulent partially premixed flame stabilized behind the plane sudden expansion of a 2-D channel.

A New Analysis of the Modeling of Pressure Fluctuations Effects in Premixed Turbulent Flames and its Validation Based on DNS Data

The modeling of transport in premixed turbulent flames is considered. In this context of second order modeling of momentum and scalar turbulent fluxes, special attention is paid to the closure of pressure fluctuating terms responsible for counter-gradient diffusion and flame generated turbulence effects. Based on a relatively general form of the PDF made of a series of delta functions, a new modeling proposal for these terms is introduced. The resulting model for the pressure terms takes into account (i) a nonreactive part that represents density changes, (ii) a reactive part directly related to mean chemical rate and (iii) an isotropization part which is a generalisation of the “return-to-isotropy” model for constant density flows. The model is tested using a three-dimensional compressible Direct Numerical Simulation database of a statistically steady planar turbulent premixed flame. A good agreement is found between the model expressions and the pressure fluctuating terms evaluated from DNS.