Introduction to Turbulence, review of turbulence models: RANS, LES, DNS, simple closure of chemical source terms, mixture fraction based modeling of turbulent nonpremixed combustion: flamelet model and CMC method, PDF and Monte Carlo methods, scalar mixing models, turbulent premixed flames, droplet and spray combustion.

Lecture­wise breakup (considering the duration of each lecture is 50 minutes)

I. Introduction (6 lectures):

  • Objectives and outline of the course

  • Review of thermodynamics

  • Review of chemical kinetics: elementary and overall reactions, reaction rate, combustion of hydrocarbons, reaction mechanisms

  • Turbulence theory: Characteristics of turbulence, examples of turbulent flows

  • Complexities associated with turbulent combustion, statistical description of turbulent flows

II. Review of Turbulence Models (6 lectures):

  • Derivation of the Reynolds and Favre averaging of Navier­Stokes equations

  • Turbulence models, length/time scales of turbulent flows, Kolmogorov hypotheses

  • Turbulence closure: zero equation, one equation and two­equation models

  • Transport equation for kinetic energy and dissipation rate

  • Large eddy simulation, models for the subgrid stress tensor, examples

  • Transport equation for reactive scalars, closure issues for the chemical source terms

  • Simple closure for the chemical source terms: EBU, EDC models

III. Turbulent non­premixed combustion (9 lectures):

  • Introduction: flame structure, definition of conserved scalar, mixture fraction

  • Characteristics of turbulent nonpremixed flame, functional dependencies of reactive scalars with mixture fraction: infinite fast chemistry, equilibrium chemistry, frozen chemistry, shape of the PDF for nonpremixed combustion

  • Derivation of transport equations for mean and variance of mixture fraction

  • Closure models for the unclosed terms, model for the scalar dissipation rate

  • Flamelet concept, derivation of the flamelet equations

  • Functional dependence of the reactive scalars with mixture fraction and scalar dissipation rate

  • Estimation of the averaged quantities, overall solution algorithm, some applications of the flamelet models

  • Conditional moments and its usefulness, introduction to conditional moment closure (CMC) method

  • Some examples of CMC method and its short­comings

IV. Probability Density Function based approaches for turbulent combustion (6 lectures):

  • Introduction to statistics: probability, mean, variance, skewness and flatness of a random variable, probability density function, cumulative distribution function, Bayes theorem, joint PDF, marginal PDF, conditional PDF, conditional expectation

  • Derivation of the transport equation for the PDF

  • Closure of various unclosed terms: chemical source terms, conditional velocity

  • Mixing models: IEM, CURL

V. Turbulent premixed combustion (7 lectures):

  • Introduction: turbulent premixed flames, turbulent flame speed, structure and characteristics of turbulent premixed flame, different regimes of turbulent premixed flame

  • Modeling of turbulent premixed flames: BML model

  • G equation / level­set approach and closure models

VI. Droplet evaporation and spray combustion (6 lectures):

  • Applications, simple model of droplet evaporation

  • Simple model for burning droplet, burning rate constant and droplet lifetime

  • Droplet burning in convective environments

  • Real­world effects on droplet burning rate

  • Spray phenomena

  • Modeling of turbulent sprays


  1. Turbulent Combustion, N. Peters, Cambridge University Press

  2. Computational models for turbulent reacting flows, R. O. Fox, Cambridge University Press

  3. An Introduction to Combustion: Concepts and Applications by S. R. Turns, McGraw­Hill Science/Engineering/Math; 3 edition (January 24, 2011)

  4. Combustion by I. Glassman, Academic Press; 4 edition (September 8, 2008)

  5. Combustion: Physical and Chemical Fundamentals, Modeling and Simulation, Experiments, Pollutant Formation by J. Warnatz, U. Mass and R. W. Dibble, Springer;  4th edition (November 9, 2010)