Scalar dissipation rate based flamelet modelling of turbulent premixed flames

Abstract

Lean premixed combustion has potential for reducing emissions from combustion devices without compromising fuel efficiency, but it is prone to instabilities which presents design difficulties. From emissions point of view reliable predictions of species formation rates in the flame zone are required while from the point of view of thermo--acoustics the prediction of spatial variation of heat release rate is crucial; both tasks are challenging but imperative in CFD based design of combustion systems. In this thesis a computational model for turbulent premixed combustion is proposed in the RANS framework and its predictive ability is studied.

The model is based on the flamelet concept and employs strained laminar flamelets in reactant--to--product opposed flow configuration. The flamelets are parametrised by scalar dissipation rate of progress variable which is a suitable quantity to describe the flamelet structure since it is governed by convection--diffusion--reaction balance and represents the flame front dynamics. This paramaterisation is new. The mean reaction rate and mean species concentrations are obtained by integrating the corresponding flamelets quantity weighted by the joint pdf of the progress variable and its dissipation rate. The marginal pdf of the progress variable is obtained using $\beta$--pdf and the pdf of the conditional dissipation rate is presumed to be log--normal. The conditional mean dissipation rate is obtained from unconditional mean dissipation rate which is a modelling parameter. An algebraic model for the unconditional mean scalar dissipation rate is proposed based on the relevant physics of reactive scalar mixing in turbulent premixed flames. This algebraic model is validated directly using DNS data. An indirect validation is performed by deriving a turbulent flame speed expression using the Kolmogorov--Petrovskii--Piskunov analysis and comparing its predictions with experimental data from a wide range of flame and flow conditions.

The mean reaction rate closure of the strained flamelets model is assessed using RANS calculations of statistically planar one--dimensional flames in corrugated flamelets and thin reaction zones regimes. The flame speeds predicted by this closure were close to experimental data in both the regimes. On the other hand, an unstrained flamelets closure predicts flame speed close to the experimental data in the corrugated flamelets regime, but overpredicts in the thin reaction zones regime indicating an overprediction of the mean reaction rate.

The overall predictive ability of the strained flamelets model is assessed via calculations of laboratory flames of two different configurations: a rod stabilised V--flame and pilot stabilised Bunsen flames. For the V--flame, whose conditions correspond to the corrugated flamelets regime, the strained and unstrained flamelets models yield similar predictions which are in good agreement with experimental measurements. For the Bunsen flames which are in the thin reaction zones regime, the unstrained flamelet model predicts a smaller flame brush while the predictions of the strained flamelets model are in good agreement with the experimental data. The major and minor species concentrations are also reasonably well predicted by the strained flamelets model, although the minor species predictions seem sensitive to the product stream composition of the laminar flamelets.

The fluid dynamics induced attenuation of the reaction rate is captured by the strained flamelets model enabling it to give better predictions than the unstrained flamelets model in the thin reaction zones regime. The planar flames and laboratory flames calculations illustrate the importance of appropriately accounting for fluid dynamic effects on flamelet structure and the scalar dissipation rate based strained flamelet model seems promising in this respect. Furthermore, this model seems to have a wide range of applicability with a fixed set of model parameters.