Probability Density Function Modeling of Turbulent Spray Combustion

  • Rana M. Humza
  • Yong Hu
  • Eva GutheilEmail author
Conference paper
Part of the ERCOFTAC Series book series (ERCO, volume 19)


Spray processes play a crucial role in liquid fueled combustion devices such as Diesel or fueled rocket engines and industrial furnaces. The combustion occurs under turbulent conditions, and a wide dynamic range of length and time scales characterize these processes, where the scales of the flow field and chemical reactions typically differ considerably. Moreover, a strong interdependence of liquid breakup and atomization, turbulent dispersion, droplet evaporation, and fuel-air mixing makes the spray modeling a challenging task. In the present chapter, a one-point one-time Eulerian statistical description of a joint mixture fraction—enthalpy probability density function (pdf) model for the gas phase is derived and modeled. A Lagrangian Monte Carlo method is used to solve the high-dimensional joint pdf transport equation. Two different mixing models, the interaction-by-exchange-with-the-mean and an extended modified Curl model, are employed in order to evaluate molecular mixing in the context of two-phase reacting flows. Moreover, a modified β function for application in turbulent spray flames, which has been proposed in an earlier study of non-reacting spray flows, is discussed in comparison with the standard β function and the transported pdf method. The modified β function is defined through two additional parameters compared to the standard form, and the choice of these parameters is discussed in the present study. A steady, two-dimensional, axisymmetric, turbulent liquid fuel/air spray flame is investigated, where both methanol and ethanol are studied. The numerical results are compared and discussed in context with the experimental data.


Nozzle Exit Mixture Fraction Spray Flame Scalar Dissipation Rate Conditional Moment Closure 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors gratefully acknowledge the financial support of Heidelberg School of Mathematical and Computational Sciences for their financial support. YH acknowledges funding through the China Scholarship Council.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Interdisciplinary Center for Scientific ComputingUniversity of HeidelbergHeidelbergGermany

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