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Report on PDF Models for Turbulence Chemistry Interaction

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Technical Report

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The Aldanox Group Inc Manotick, Ontario Canada

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Many numerical solvers aimed at the solution of high speed chemically reacting flows employ methods that solve directly for both the change in thermal and mass diffusivity due to turbulence through the solution of a turbulent Prandtl and turbulent Schmidt number directly. In many cases, the solution of the turbulent Schmidt number requires a method of modelling the effects of species massfraction fluctuations on the source terms representing the chemical reactions occurring. One approach that has seen reasonable success is the use of Probability Density Functions PDFs to evaluate the time averaged values of fluctuating massfraction terms appearing in the governing equations. Both assumed forms for these PDFs as well as PDFs where their evolution itself is part of the solution procedure have been implemented. The assumed forms have generally been regarded as being the best combination of accuracy and computational efficiency. Indeed, the use of a multivariate Beta PDF for the species massfraction fluctuations reduces to an algebraic expression avoiding the need to numerically integrate the PDF as is required when using a Gaussian PDF. This report details the implementation of assumed, jointly uncorrelated PDFs for both temperature and species massfraction fluctuations. It shows that provided one is already using a variable Prandtl andor variable Schmidt number numerical solver, no additional conservation equations are required the use of a temperature PDF requires the variable Prandtl number solver, the use of a composition PDF requires the variable Schmidt number solver.

Subject Categories:

  • Statistics and Probability
  • Operations Research
  • Fluid Mechanics

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