Objective
The objectives of the project are to formulate and validate new statistical computational models of micro mixing and diffusion in turbulent reacting flows, to develop the closure at the level of the joint probability density function (JPDF) of scalar, its gradient and velocity fluctuations and at the level of two-point PDF of a passive scalar.
The starting point for deriving the closed equation for the JPDF will be the unclosed equation that has been developed by one of the teams [15]. The closure problem is related to the calculation of coefficients, which are the conditional averages of a velocity gradient tensor and the tensor of gradient of a scalar gradient. All these coefficients should be calculated under the prescribed values of a scalar and scalar gradient. This task will be done by an approximation of the multidimensional JPDF of the mentioned values through a Gram-Charlier series expansion taking into account statistical moments of different order of the acceleration field and a scalar field with its first and second spatial derivatives together with the skewness and excess of multidimensional JPDFs. This work though rather cumbersome, once done, will enable to represent all the coefficients in the equation for the JPDF through ordinary (non-conditional) statistics of velocity and scalar fields. Then the closure of the equation for the JPDF is achieved by a combination of judicious truncation of a series expansion, known non-conditional statistics, DNS results, and laser diagnostic measurements. Throughout this study, use will be made of available databases both experimental and from direct numerical simulations.
The development of the model of turbulent reacting flows on the basis of two-point probability distributions actually represents a new approach to turbulent combustion modelling. Investigation in the frame of the proposed project will enable to compare the results of this new approach to those of the other methods and to diminish the number of hypotheses needed. The proposed two-point approach will permit to describe by one and the same theory combustion in fully developed turbulence, ignition and combustion at weak turbulence. The two-point description, in spite of being more complex due to the increase in the number of independent variables, can be the base for testing and refining other approaches to the problem of turbulent reacting flows. This approach could also help to represent the micro mixing in two phase-flow, especially near the liquid surface.
Numerical solution of these equations will be obtained by using the methodology for solving ill-posed problems, Monte Carlo simulation methods and also by the results on the joint movement of two fluid particles in turbulent reacting flow.
Applications will be made in studies on the prediction of completeness of combustion and ignition in combustion chambers and on the appearance of nitric oxides during turbulent combustion of hydrocarbons in air. All results, both theoretical and applied will be presented at conferences and published in international scientific journals.
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Programme(s)
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Topic(s)
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Funding Scheme
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Coordinator
2628 CJ Delft
Netherlands
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