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)