Combustion and Reactions Chapter 3: Laminar Non-premixed flames
This chapter develops the physical and modeling framework for laminar non-premixed (diffusion) flames, where mixing, not chemistry, controls combustion. It introduces the mixture fraction as the central variable, explains flame structure under different kinetic assumptions, and connects theory to CFD modeling strategies and experimental observations. Additional insights from tutorials and classical studies highlight how real flames deviate from idealized models due to finite-rate chemistry, transport effects, and strain
1. Context and Motivation
Non-premixed combustion appears whenever fuel and oxidizer enter separately and mix during the process: jet flames, burners, furnaces, diesel engines.
The key shift compared to premixed combustion:
There is no pre-defined mixture
Reaction depends on how fast species mix
Physically, this means:
Chemistry can be very fast (especially at high temperature)
Mixing becomes the rate-limiting process
This is why these flames are often called diffusion flames.
From an engineering standpoint:
Easier to operate (no flashback risk)
Harder to control precisely (mixing-driven)
Often produce lower burning intensity but higher pollutant sensitivity
2. Main Concepts
Non-Premixed Flame Definition
Fuel and oxidizer:
Enter from separate streams
Only react after molecular mixing
In a jet flame:
Fuel diffuses outward
Oxidizer diffuses inward
Reaction occurs where they meet
Flame Structure
The flame is organized into three regions:
Fuel-rich zone → excess fuel, no oxidizer
Oxidizer-rich zone → excess oxidizer, no fuel
Reaction zone → where both meet and react
Physically, this means:
The flame is not volumetric everywhere
It is localized around a thin reaction layer
In the ideal limit:
This layer becomes a reaction surface (no thickness)
No Flame Propagation
Unlike premixed flames:
There is no flame speed
The flame does not “travel” into reactants
Instead:
The flame is anchored where mixing creates flammable conditions
Mixture Fraction (Core Variable)
The most important variable in non-premixed combustion.
Definition (physically):
Fraction of local mass originating from the fuel stream
Key properties:
Pure oxidizer → 0
Pure fuel → 1
Intermediate values → mixed fluid
Crucially:
It is a conserved scalar
It depends only on transport (convection + diffusion)
No chemical source term appears
This is a major simplification:
→ Instead of solving many species equations, we solve one transport equation
Stoichiometric Mixture Fraction
A special value:
Corresponds to perfect fuel–oxidizer proportion
Physically:
Location where combustion is most intense
Temperature reaches maximum
Interpretation:
If mixture fraction is lower → excess oxidizer
If higher → excess fuel
This creates a natural division of the flame structure
3. Modeling Framework / Formulations
Simple Chemically Reacting System (SCRS)
A simplified combustion model:
Single global reaction
Few variables needed
Key idea:
The entire thermochemical state can be described using:
Mixture fraction (mixing)
One reactive variable (or even none in simplified cases)
Infinitely Fast, Irreversible Reaction (Burke–Schumann Limit)
Assumptions:
Chemistry is infinitely fast
Reaction occurs instantly upon mixing
Implications:
Fuel and oxidizer cannot coexist locally
Reaction zone becomes a mathematical surface
Most important consequence:
No need to solve reaction rates
Everything depends on mixture fraction only
This leads to:
Simple mapping:
Mixture fraction → species → temperature
Physically:
“Mixed is burned” assumption
Limitation:
Ignores ignition limits, finite rates, dissociation
Infinitely Fast, Reversible (Equilibrium) Model
Instead of full conversion:
System reaches chemical equilibrium
Now:
Composition depends on mixture fraction through equilibrium chemistry
Advantage:
Predicts:
Intermediate species
Pollutants (CO, NO)
Limitation:
Assumes equilibrium everywhere → often unrealistic
Finite-Rate Chemistry
More realistic:
Reaction rates are finite
Fuel and oxidizer can coexist
Effects:
Finite flame thickness
Delayed reaction zones
Species “leakage” across the flame
This is necessary for:
Accurate pollutant prediction
Detailed flame structure
Flamelet Concept
Key modeling idea:
Complex flames can be decomposed into 1D laminar flame structures
Typically studied using:
Opposed-jet (strained) flames
Physically:
Represents balance between:
Diffusion (mixing)
Strain (stretching the flame)
This becomes the foundation for:
Turbulent combustion models
4. Numerical / CFD Aspects
Two Main Modeling Strategies
1. Mixture Fraction Models (Fast Chemistry)
Solve only mixture fraction
Use precomputed relationships
Pros:
Fast
Robust
Cons:
Limited accuracy (no kinetics detail)
2. Species Transport + Finite Rate Chemistry
Solve transport for each species
Include reaction mechanisms
Key requirements:
CHEMKIN mechanisms for chemistry
Stiff chemistry solvers (due to fast reactions)
Transport Modeling
Important effects:
Multicomponent diffusion
Thermal diffusion (Soret effect)
Physically:
Diffusion controls flame structure directly
Stiffness Problem
Chemical reactions:
Much faster than flow processes
Numerically:
Leads to stiff systems
Solution:
Specialized solvers (stiff chemistry solvers)
Acceleration methods like ISAT
Mesh Considerations
Critical region:
Reaction zone
Requirement:
High refinement near flame
Otherwise:
Flame thickness and gradients poorly captured
5. Physical Interpretation and Engineering Intuition
Mixing-Controlled Combustion
The dominant idea:
→ Mixing rate controls combustion
Implications:
Faster mixing → shorter, more intense flame
Poor mixing → long, weak flame
Role of Strain
In opposed-jet flames:
Increasing strain:
Thins the flame
Can extinguish it
Physically:
Mixing becomes too fast for chemistry to keep up
Péclet Number Effects
Represents:
Ratio of convection to diffusion
Low value:
Diffusion-dominated → wider flames
High value:
Convection-dominated → elongated flames
Partial Equilibrium Insight (Advanced)
From experimental studies:
Reaction zone is not fully equilibrium
Instead:
Some reactions equilibrate quickly
Others lag behind
Important observation:
Radical concentrations can exceed equilibrium values
→ Indicates non-equilibrium chemistry
This explains why simple equilibrium models can fail
6. Applications
Jet burners and industrial furnaces
Gas turbines (diffusion flame modes)
Diesel combustion
Laboratory flame studies (opposed-jet flames)
Fire modeling
7. Limitations and Assumptions
Fast Chemistry Models
Ignore finite-rate effects
Cannot capture ignition/extinction properly
Equilibrium Models
Overpredict completeness of combustion
Miss transient chemistry effects
Finite-Rate Models
Computationally expensive
Require detailed chemistry data
Mixture Fraction Approach
Assumes two-stream mixing
Less accurate with complex inlet conditions
Study Priorities
Focus especially on:
Mixture fraction concept
Stoichiometric mixture fraction and its meaning
Flame structure (fuel-rich / reaction / oxidizer-rich)
Fast chemistry vs finite-rate models
Why mixing controls combustion
Flamelet idea and strained flames
Key Takeaways
Non-premixed flames are mixing-controlled systems
The mixture fraction is the central variable
The stoichiometric surface defines the flame location
Fast chemistry simplifies modeling but reduces realism
Finite-rate chemistry introduces realistic flame structure
Flamelets connect laminar and turbulent combustion modeling
Real flames often exhibit partial equilibrium, not full equilibrium