**Summary of the Master Thesis by Denis V. Efimov, presented on March 26, 2013**

**Supervisors: Prof. dr D.J.E.M. Roekaerts, Dr. M.K. Stoellinger, G. Sarras MSc**

Turbulent combustion processes are used in domestic and industrial energy conversion processes, e.g. electricity generation, heat generation and internal combustion engines. The increasing need for energy efficiency and pollutants emission reduction leads to a need for the development of numerical techniques for the modeling of turbulent combustion with high predictive capability.

Solving numerically the exact transport equations describing turbulent combustion for all time and length scales is not suitable for engineering applications due to the high computational expenses. On the other hand, the common approach of modeling of turbulent reacting flows based on the solution of the averaged transport equations encounters a major closure problem when the mean chemical source term has to be computed. The simple approach of evaluation of the mean chemical source term as a function of mean values of the chemical species concentrations and mean temperature can only handle simple cases and is not suited for handling the above mentioned applications. For a proper description of the mean chemical source term, including effects of turbulence chemistry interaction, the full joint statistics of the thermochemical quantities is required. This can be accomplished employing the stochastic approach for turbulent reacting flows used in this thesis. Within this approach the full one-point statistics of the flow and thermochemical quantities is represented by the joint velocity-scalar probability density function (PDF).

A transport equation for this PDF is solved by a Monte Carlo method estimating the joint PDF of the relevant variables by a large amount of Lagrangian notional particles each assigned a number of properties as the velocity and the thermochemical composition. The PDF method has the major advantage that it treats the chemical source term in an exact way, without closure problem, but the closure for the effects of the molecular diffusion on the smallest scales remains the main challenge in this approach. The quality of the closure model for this molecular diffusion fluxes, further called micromixing, has a high impact on the performance of the PDF method as the combustion can take place only after the reactants are mixed on the smallest scales.

This thesis examines a modeling approach for improvement of the existing closure models for the micro-mixing term in the PDF equation. In the standard joint velocity-scalar PDF approach the mixing of scalar quantities (species mass fractions, enthalpy) according a micromixing model proceeds without taking into account information on velocity statistics. The hypothesis tested in this work is that more accurate results are obtained if the mixing of scalar quantities takes into account the underlying velocity statistics. The investigation is accomplished by comparing the performance of the simplest existing model for the micromixing, the standard Interaction by Exchange with the Mean (IEM) model, with its velocity conditioned version, the Interaction by Exchange with the Conditional Mean (IECM) model.

The numerical technique for solving the PDF transport equation is a hybrid finite volume/ Monte Carlo algorithm, where the Monte Carlo model is combined with a Reynolds–averaged Navier–Stokes turbulence model. The chemistry model is based on a Flamelet Generated Manifold (FGM), which assumes that the local structures in a turbulent flame are identical to the structure of laminar flames. Utilizing this model the large set of thermochemical properties assigned to the Monte Carlo notional particles can be reduced to a set of two calculated variables, lowering the computation time. The reduced set of scalar variables consists of avariable describing the degree of mixedness and a variable describing the reaction progress.

The test case used for validation of the current computational models is known as "Delft flame III" (See figure). This is a laboratory scale piloted non-premixed co-flow flame burner with natural gas as the main fuel. The results of the performed simulations are compared with the available detailed experimental database of the Delft flame. It has found that the velocity conditioned IECM micro-mixing model yields an improved performance compared to that of the standard IEM model. The improvement can be described as follows, the variable describing the degree of mixedness is up to two times less overestimated at the peak values using the IECM model. The overestimation of the mean temperature obtained with the IECM simulation is, at some locations, two to three times lower than that of the IEM simulation, the same situation applies to the mean profiles of the variable describing the reaction progress. The simulation done with the IECM model gives accurate profiles of the mean reaction progress variable at the upstream locations.

The conclusion is drawn that, at least in the context of the IEM micro-mixing model, the effects of the velocity conditioning on micro-mixing are far from negligible, however a more sophisticated algorithm for implementation of these effects should be found to enable their use in practical applications. Also an assessment is made of different configurations for the IECM model algorithm.

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