ICS2019

Combustion Modeling - Iran First International Combustion School (ICS2019)

Lessons on Combustion Modeling

Lesson 1: Governing equations, thermodynamics, kinetics, and transport properties (~1.5 h)

• Presentation of the course, learning objectives, organization
• Transport equations
  • Continuity and momentum equations
  • Conservation of species; diffusion fluxes (Stefan-Maxwell theory, Fick diffusion, Soret effect)
  • Energy equation: enthalpy and temperature formulations
• Basics of thermodynamics, kinetics, and transport properties
  • Enthalpy and specific heats, NASA polynomial formalism
  • Kinetic parameters, reaction rate, reversible reactions, equilibrium constant, examples of kinetic mechanisms in CHEMKIN format, pressure-dependent reactions (third-body, fall-off reaction, Chebyshev formalism, PLOG formalism)
  • Kinetic theory of gases (viscosity, mass diffusion coefficients, thermal conductivity, Lewis number)
• Introduction to the CHEMKIN formalism

Lesson 2: Numerical algorithms for reactive flows (~2 h)

• Introduction: complexity of reacting flows and combustion
  • Detailed kinetics and combustion
  • Non-linearity, coupling, stiffness
• The 0D reacting system model
  • Governing equations
  • Numerical solution of ODE systems
  • The Jacobian matrix and the sparsity of kinetic mechanisms
• Ideal reacting systems in combustion
  • Batch Reactor
  • Shock Tube Reactor
  • Perfectly Stirred Reactor
  • Plug Flow Reactor

Lessons 3: Numerical methods for 1D and multi-dimensional flames (~2 h)

• Introduction: Combustion and transport phenomena & laminar flames
• Numerical solution of 1D flames
  • Premixed laminar flames
    • Burner stabilized unstretched (or flat) flame
      • Governing equations and modeling aspects
      • Numerical solution
    • Freely-propagating unstretched (or flat) flame
      • Governing equations and modeling aspects
  • Counterflow diffusion flames
    • Governing equations and modeling aspects
• Multidimensional flames
  • Introduction and examples
  • Governing equations
  • Numerical algorithms for multidimensional flames
  • The operator-splitting method

Lesson 4: Advanced techniques for reacting flows with detailed kinetics (~1.5 h)

• Acceleration of simulations by reduction of specie
  • Skeletal reduction
  • Quasi Steady-State Approximation (QSSA)
  • Dynamic Stiffness Removal (DSR)
  • Dynamic Adaptive Chemistry (DAC)
• Acceleration of simulation by reduction of reacting environments
  • Reaction Network Analysis (RNA) and Kinetic Post-Processor (KPP)
  • Dynamic Adaptive Clustering
  • ISAT (In Situ Adaptive Tabulation)
• Species bundling for diffusion coefficient reduction
• Computation Cost Minimization
• Numerical tools for analysis of kinetic mechanisms
  • Sensitivity Analysis
  • Rate of Production and Reaction Path Analyses

Lesson 5: Introduction to numerical modeling of turbulent reacting flows (~1.5 h)

• Introduction to turbulent flows
• Statistical description of turbulent flows
  • Reynolds and Favre average
  • 2-point correlations
  • Turbulent eddies and energy cascade
• Kolmogorov’s Theory
  • Kolmogorov’s similarity hypotheses
  • Kolmogorov’s scales
  • Energy spectrum
• Transport equations for mean variables
  • Need of mean/filtered equations
  • Averaged transport equations for continuity and momentum
  • Closure models for turbulent flows: 𝜅−𝜀 model
  • Favre’s averaged transport equations for passive scalars and species

Lesson 6: Turbulent combustion modeling (~2 h)

• Introduction to turbulent combustion modeling
  • Fluid dynamic and chemical time scales
  • Effects of turbulent fluctuations on chemical reactions
  • Need of turbulent combustion models
• Non-premixed combustion
  • Eddy Dissipation models: ED, ED-FR, EDC
  • Steady Laminar Flamelet model
    • Mixture fraction
    • Flamelet equations
    • Presumed PDF approach
• Premixed combustion
  • Eddy Break-Up (EBU) model
  • Bray-Libby-Moss (BLM) model
  • G-Equation