Combustion and Reactions Chapter 6: Turbulent PREMIXED Combustion
This chapter develops the physical and numerical framework for turbulent premixed combustion, where fuel and oxidizer are mixed before ignition while turbulence strongly modifies flame propagation. The central challenge is modeling the interaction between turbulent eddies and flame structure across multiple scales. The chapter introduces turbulent combustion regimes, turbulent flame speed, progress-variable methods, G-equation models, flame surface density approaches, and partially premixed flamelet methods used in practical CFD simulations.
The chapter also connects theory with realistic engineering applications such as spark-ignition combustion and swirl-stabilized gas turbine combustors.
Context and Motivation
Premixed turbulent combustion appears in:
Spark-ignition engines
Lean-premixed gas turbines
Industrial burners
Explosion and safety studies
In these systems:
Fuel and oxidizer are mixed before ignition
Combustion occurs through a propagating flame front
Unlike laminar premixed flames, turbulence continuously interacts with the flame:
Wrinkling it
Stretching it
Thickening it
Sometimes extinguishing it
This interaction fundamentally changes:
Flame propagation speed
Flame thickness
Heat release rate
Stability
The entire modeling problem becomes a balance between:
Turbulent mixing scales
Chemical reaction scales
Structure of Turbulent Premixed Flames
Laminar Flame Structure Reminder
A premixed flame contains:
Preheat zone
Reaction zone
Burned gases
Heat and radicals diffuse upstream from products into reactants, allowing the flame to propagate.
The flame propagates normal to itself at the:
Laminar flame speed
Effect of Turbulence on the Flame
Turbulence changes flame geometry dramatically.
Large eddies:
Wrinkle and corrugate the flame front
Small eddies:
Can penetrate into the flame structure
Disturb transport processes
Modify flame thickness
Physically:
Turbulence increases total flame surface area
More flame surface → larger total burning rate
This produces the:
Turbulent flame speed
Turbulent Flame Speed
The turbulent flame speed represents the effective propagation speed of the wrinkled turbulent flame front.
It depends on:
Laminar flame speed
Turbulence intensity
Turbulence length scales
Local thermochemical state
Physically:
The flame still burns locally as a laminar flame
But turbulence increases the total flame area
The increase in burning area directly increases the effective propagation speed.
Turbulent Premixed Combustion Regimes
The interaction between turbulence and flame structure is classified using the Borghi–Peters diagram.
This is one of the most important conceptual frameworks in turbulent combustion.
Characteristic Scales
The classification uses:
Flame Scales
Laminar flame speed
Flame thickness
Chemical time scale
Turbulence Scales
Turbulence intensity
Integral eddy size
Kolmogorov scale
Eddy turnover times
The relative magnitude of these scales determines how turbulence interacts with the flame.
Key Dimensionless Numbers
Turbulent Reynolds Number
Measures turbulence intensity relative to viscous diffusion.
Large values:
Fully turbulent flow
Damköhler Number
Ratio:
Turbulent time scale
toChemical time scale
Interpretation:
Large Da → chemistry faster than turbulence
Small Da → turbulence dominates chemistry
This is the central combustion-regime parameter.
Karlovitz Number
Measures whether small turbulent eddies can penetrate the flame structure.
Interpretation:
Small Ka → flame structure survives
Large Ka → flame internal structure disrupted
Main Combustion Regimes
Wrinkled Flamelets Regime
Characteristics:
Turbulence wrinkles flame surface
Inner flame structure remains laminar
Small eddies cannot enter flame
Physically:
Flame behaves like many corrugated laminar flames
This is one of the most common engineering regimes.
Thickened Flame Regime
Small turbulent eddies begin entering the preheat zone.
Effects:
Flame thickens
Heat diffusion modified
Flame speed altered
However:
Reaction zone still survives
Broken Reaction Zones
Very intense turbulence.
Effects:
Small eddies penetrate reaction zone
Flame structure destroyed
Local extinction possible
In this regime:
Chemistry becomes rate-limiting
Combustion resembles distributed reaction
Engineering Interpretation
The Borghi diagram is essentially asking:
“Can turbulence penetrate the flame faster than chemistry restores it?”
This single question drives:
Flame stability
Model choice
Numerical requirements
Progress Variable Concept
One of the most important ideas in premixed combustion modeling.
Definition
A scalar variable describes combustion progress:
0 → fresh reactants
1 → fully burned products
The flame front is represented by the transition region between these values.
Physical Interpretation
The progress variable does not represent:
Partial chemistry
Instead:
It statistically represents the fraction of time spent in burned or unburned states within the turbulent flame brush.
This distinction is very important.
Why It Is Useful
Instead of solving:
Many species equations
We solve:
One transport equation
This greatly reduces computational cost.
The c-Equation Model
The most common premixed turbulent combustion model.
Core Idea
The model solves a transport equation for the progress variable.
The equation contains:
Convection
Diffusion
Turbulent transport
Flame propagation source term
The source term ensures:
Correct turbulent flame propagation speed
Flame Brush Concept
The actual flame front is too thin to resolve directly on engineering meshes.
Instead:
CFD resolves a thicker “flame brush”
Inside this region:
Progress variable varies between 0 and 1
The flame brush propagates at:
Turbulent flame speed
Zimont Model
Widely used turbulent flame speed correlation.
Most valid in:
Corrugated and thin reaction-zone regimes
The model relates flame speed to:
Turbulence intensity
Turbulence scales
Laminar flame speed
Engineering Interpretation
The c-equation model assumes:
Thin flame sheets
Turbulence mainly wrinkles flames
This works well for:
Gas turbines
Industrial premixed burners
Many practical combustion devices
The G-Equation Model
Another major flame-front tracking method.
Core Idea
Instead of transporting reaction progress:
The model tracks flame-front position geometrically
The G-variable defines:
Flame location in space
The flame front is represented by:
A level surface of G
Physical Meaning
The flame behaves like:
A moving interface propagating normal to itself
Propagation speed depends on:
Turbulent flame speed
Advantages
Good for:
Flame-front tracking
Spark ignition
Moving flames
Transient combustion
Widely used in:
Engine simulations
Limitations
Cannot fully resolve:
Detailed chemistry
Finite-rate effects
Thick reaction zones
Most accurate in:
Flamelet regimes
Flame Surface Density Models
These models directly represent the increase of flame area caused by turbulence.
Main Idea
Turbulence wrinkles the flame:
→ Flame surface increases
Combustion rate becomes proportional to:
Flame surface density
Local consumption speed
Coherent Flame Model / ECFM
One of the most important industrial models.
Tracks:
Flame surface density
Turbulent flame structure
Common in:
Engine combustion simulations
Physical Interpretation
Instead of:
Tracking chemistry directly
We track:
How much flame area exists locally
This connects turbulence geometry directly to burning rate.
Flamelet Generated Manifolds (FGM)
A very important practical combustion model.
Especially common in:
Partially premixed combustion
Gas turbines
Core Philosophy
Complex chemistry is precomputed using laminar flamelets.
Results stored in:
Lookup tables
During CFD:
Solver interpolates from tables
Instead of solving chemistry directly
Variables Typically Used
State often described using:
Mixture fraction
Progress variable
Their variances
This creates:
Efficient reduced-order chemistry models
Advantages
Captures detailed chemistry
Computationally affordable
Good balance of accuracy and cost
Limitations
Assumes:
Flamelet structure still exists
May fail for:
Strong extinction
Highly distributed combustion
Partially Premixed Combustion
Real combustors are rarely perfectly premixed.
Often:
Some mixing occurs before combustion
Additional mixing occurs inside combustor
This creates:
Hybrid combustion behavior
Important Features
Requires:
Premixed flame propagation
Non-premixed mixing effects
Turbulence–chemistry interaction
FGM models are especially useful here.
Flame Stabilization and Swirl
One of the most important engineering concepts.
Swirl-Stabilized Flames
Swirl creates:
Central recirculation zones
These zones:
Trap hot products
Continuously ignite incoming reactants
This stabilizes the flame.
Without recirculation:
Flame blowoff becomes likely
Can Combustor Physics
In practical combustors:
Turbulence enhances mixing
Swirl stabilizes flame
Recirculation maintains ignition
The entire combustor design revolves around controlling:
Residence time
Mixing
Flame position
Heat release distribution
Spark Ignition and Flame Propagation
The Hamamoto-type spark ignition problem illustrates several important ideas.
Observed Experimental Behavior
Increasing turbulence:
Increases turbulent flame speed
Thickens flame brush
Accelerates flame propagation
However:
Excessive turbulence may destabilize the flame
Important Physical Insight
Turbulence in burned gases decays faster because:
Temperature increases viscosity
Viscous dissipation becomes stronger
Combustion therefore modifies turbulence itself.
This is a strong example of:
Two-way turbulence–combustion coupling
Numerical and CFD Aspects
Pressure-Based Solvers
Premixed combustion models are generally used with:
Pressure-based solvers
Valid for:
Subsonic deflagrations
Not intended for:
Detonations
Strong compressibility
Mesh Requirements
Important regions:
Flame fronts
Recirculation zones
Shear layers
Premixed flames are often too thin to fully resolve.
Therefore:
Flame models represent subgrid flame behavior
Model Sensitivity
Strongly affected by:
Turbulence model
Turbulent flame speed correlation
Mesh resolution
Ignition model
Boundary conditions
Chemistry Handling
Practical simulations often use:
Reduced chemistry
Flamelets
PDF tables
Equilibrium approximations
Direct detailed chemistry remains expensive.
Physical Interpretation and Engineering Intuition
The Flame Is an Interface Problem
Premixed turbulent combustion is largely about:
Tracking moving reaction surfaces
Most models differ mainly in:
How they represent the flame front
Turbulence Increases Burning Rate Geometrically
The dominant mechanism is often:
→ Increased flame surface area
Not necessarily faster local chemistry.
Small Scales Matter Most
Large eddies:
Move the flame
Small eddies:
Determine whether flame structure survives
This is why the Karlovitz number is so important.
Recirculation Zones Are Essential
Modern combustors rely heavily on:
Flow stabilization mechanisms
Combustion is often stabilized aerodynamically rather than chemically.
Applications
Spark-ignition engines
Lean-premixed gas turbines
Industrial premixed burners
Explosion safety simulations
Swirl combustors
Hydrogen combustion systems
Limitations and Assumptions
Progress Variable Models
Assume thin flame fronts
Less accurate in distributed combustion
G-Equation Models
Geometric representation only
Limited chemistry detail
Flamelet Models
Assume flamelet structure survives
May fail in strong extinction regimes
General Challenges
Strong turbulence–chemistry coupling
Multiscale physics
Numerical stiffness
Model calibration dependence
Study Priorities
If short on time:
Borghi/Peters combustion regimes
Physical meaning of Karlovitz and Damköhler numbers
Turbulent flame speed concept
Progress variable and c-equation
G-equation concept
Flame surface density interpretation
FGM philosophy
Swirl stabilization mechanism
Key Takeaways
Turbulent premixed combustion is governed by turbulence–flame interaction.
Turbulence mainly increases combustion through flame wrinkling and increased surface area.
The Borghi diagram classifies combustion regimes using turbulence and flame scales.
The c-equation and G-equation are the main flame-front tracking approaches.
Flame surface density models directly connect turbulence to burning rate.
Flamelet Generated Manifolds provide efficient reduced-order chemistry modeling.
Swirl-induced recirculation is essential for practical flame stabilization.
Model validity strongly depends on combustion regime.