Ruprecht-Karls-Universität Heidelberg

Multiphase Flows and Combustion

Head: Prof. Dr. E. Gutheil

Transported PDF Modeling of Turbulent Spray Flows

Turbulent spray flows are characterized through statistical fluctuations of the characteristic variables of the flow field. An excellent method to account for these processes is the use of a probability density function (PDF), which in the ideal case comprises all statistical variables as well as all moments of the probability density function. The classical methods using presumed PDFs typically use the first and second moments only; moreover, they assume statistical independence of these variables.


The shape of the PDF changes throughout the flow field, and it may be described though a transport equation of the PDF. The advantage of this approach is that both chemical reaction and evaporation terms appear in closed form, and no modeling is required. However, the molecular mixing term needs to be modeled which is achieved through the IEM model (interchange with the mean), which is extended to account for the spray vaporization.


PDFs are derived for the mixture fraction of the gas phase as well as two dimensional mixture fractions of the mixture fraction and the gas velocity for non reactive sprays as well as for the mixture fraction and enthalpy for spray combustion. Figure 1 shows the contour plot of the methanol vapor mass fraction with marked positions where shapes of PDFs are evaluated. It appears (c.f. Fig. 2) that the generally used ß function is not suitable to account for the bimodal structure of the transported PDF. A modified ß function with two additional parameters is able to properly predict the structure.


Figure 3 shows a comparison of the measured and computed gas temperature of an ethanol/air spray flame at atmospheric pressure. The transported PDF method greatly improves the prediction of the experiment.


The PDF method may be extended to account for further flow field characteristics, and it is a very promising method for future simulations.


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Abb. 1: Mass fraction of the methanol vapor


Abb. 2: Comparison of transported and ß function


Abb. 3: Comparison with experimental data