Report on PDF Models for Turbulence Chemistry Interaction

Abstract

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 and/or 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).

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Document Details

Document Type
Technical Report
Publication Date
Mar 01, 2014
Accession Number
AD1018031

Entities

People

  • J. Etele

Tags

Communities of Interest

  • Energy and Power Technologies
  • Weapons Technologies

DTIC Thesaurus Topics

  • Arrhenius Equation
  • Boltzmann Equation
  • Chemical Reactions
  • Combustion
  • Computational Fluid Dynamics
  • Computational Science
  • Delta Functions
  • Distribution Functions
  • Equations
  • Prandtl Number
  • Probability
  • Probability Density Functions
  • Probability Distributions
  • Random Variables
  • Thermal Conductivity
  • Turbulence
  • Turbulent Mixing

Readers

  • Computational Fluid Dynamics (CFD)
  • Fluid Dynamics.
  • Regression Analysis.