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

References:

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)