Combustion and Reactions Chapter 5: Turbulent NON-PREMIXED Combustion
This chapter develops the modeling of turbulent non-premixed combustion, where fuel and oxidizer enter separately and react only after mixing. The core idea is that mixing governs combustion, enabling simplifications through the mixture fraction framework and PDF methods. The chapter integrates theory (regimes, models) with practical CFD workflows (Fluent) and a realistic application (BERL combustor), showing how different models trade accuracy, cost, and physical fidelity
Context and Motivation
Non-premixed combustion is the dominant configuration in:
Gas turbines (diffusion flames)
Diesel engines
Industrial burners
Furnaces
Key feature:
→ Fuel and oxidizer are not pre-mixed
Instead:
They meet → mix → react
In turbulent flows:
Mixing is strongly enhanced by eddies
Reaction rates are often mixing-limited, not chemistry-limited
Physically, this means:
Chemistry is often “fast enough”
The bottleneck is bringing reactants together
Main Concepts
1. What Defines a Non-Premixed Turbulent Flame
Separate fuel and oxidizer streams
Reaction occurs in a thin mixing layer (flame sheet)
Turbulence:
Stretches and folds scalar fields
Increases interfacial area → faster diffusion
Time for mixing >> time for chemistry
→ Justifies simplifying chemistry
2. Sensitivity to Strain and Extinction
Unlike premixed flames:
Non-premixed flames are highly sensitive to strain
Turbulence can:
Stretch flame → thin it
Over-stretch → local extinction
Important insight:
→ Turbulence does not always enhance combustion
→ It can also destroy it
3. Combustion Regimes (Non-Premixed)
Key parameters:
Turbulent Reynolds number
Turbulent Damköhler number
Regimes:
1. Laminar-like flames
Weak turbulence
2. Steady flamelets
Fast chemistry
Thin flame sheets
Chemistry adapts instantly
3. Unsteady flamelets
Moderate turbulence
Flame responds dynamically
4. Extinction regime
Strong turbulence
Flame locally quenched
Key Interpretation
Increasing turbulence:
→ Wrinkles flame → enhances mixing
→ Eventually destroys flameTransition governed by:
→ Competition between mixing time and chemistry time
Modeling Framework / Formulations
1. Mixture Fraction Concept (Core Idea)
The central simplification:
→ Replace many species equations with one scalar: mixture fraction (f)
Definition:
Fraction of material originating from the fuel stream
Key properties:
Conserved (no reaction source term)
Fully determines composition under ideal conditions
Physical Interpretation
f = 1 → pure fuel
f = 0 → pure oxidizer
f = f_st → stoichiometric mixture → flame location
2. Two-Step Problem Decomposition
Solve mixing problem → obtain f field
Use chemistry model → map f → species, temperature
This is extremely powerful:
→ Decouples flow from chemistry
3. Turbulence Effect: Need for PDFs
In turbulence:
f fluctuates
So:
You don’t know instantaneous f
Only mean and variance
Solution:
→ Use Probability Density Function (PDF)
Mean quantities obtained by integrating over PDF
Interpretation
Instead of:
→ “What is f here?”
We ask:
→ “What distribution of f exists here?”
Modeling Approaches
1. Chemical Equilibrium Model
Idea
Chemistry is infinitely fast
System always at equilibrium
Thus:
→ Thermochemical state depends only on f (and possibly enthalpy)
Implementation Insight (Fluent)
Precompute equilibrium chemistry
Store in tables (PDF tables)
During simulation → lookup values
PDF tables reduce computational cost significantly
Advantages
Very efficient
Captures dissociation effects
Robust
Limitations
Requires very high Damköhler number
Cannot capture:
Ignition
Extinction
Slow chemistry
2. Eddy Dissipation Model (EDM / EBU)
Core Idea
→ Reaction rate controlled by turbulent mixing
Chemistry assumed fast
Reaction rate proportional to turbulence time scale
Based on eddy turnover time
Uses simple global reactions
Physical Meaning
Eddies bring reactants together
Reaction occurs instantly after mixing
Advantages
Very simple
Cheap
Works well for many industrial flames
Limitations
No temperature dependence
Cannot capture detailed chemistry
Overpredicts temperature
Needs tuning
3. Finite Rate / Eddy Dissipation Model
Hybrid model:
→ Reaction rate = minimum of:
Chemical rate (kinetics)
Mixing rate
Combines chemistry + turbulence
4. Flamelet Models
Idea
→ Turbulent flame = ensemble of laminar flamelets
Flame structure solved separately
Stored in tables
Coupled with turbulence via PDF
Types
Steady Flamelet
Assumes fast chemistry
Limited ability for extinction/ignition
Unsteady Flamelet
Captures:
Ignition
Extinction
Slow species
Physical Insight
Turbulence wrinkles flame
But locally, flame behaves like laminar
5. Primitive Variable vs Reaction Rate Approach
Primitive Variable
Solve for f + PDF
Use tables for chemistry
Reaction Rate
Directly model reaction source terms
Numerical / CFD Aspects
1. Fluent Workflow (Non-Premixed Model)
Enable turbulence + energy
Select non-premixed model
Choose:
Equilibrium
Flamelet
Define:
Fuel / oxidizer streams
Mixture fraction
Generate PDF table
Solve flow
Key idea:
→ Heavy chemistry handled offline via tables
2. BERL Combustor Case
A realistic industrial flame:
300 kW combustor
Swirling air + fuel injection
PDF mixture fraction model
Important Physics
Swirl creates recirculation zone
Recirculation traps hot gases
→ Provides ignition source
→ Stabilizes flame
Engineering Interpretation
Flame stabilization is not just chemistry
→ It is flow-driven
3. Boundary Conditions Matter
From workflow:
Turbulence intensity
Inlet profiles
Temperature
Strong influence on:
→ Mixing → combustion
Physical Interpretation and Engineering Intuition
1. Mixing Controls Combustion
In non-premixed turbulent flames:
→ No mixing = no combustion
This is the central idea.
2. Flame Location
Flame sits at:
→ Stoichiometric mixture fraction surface
This surface:
Moves with flow
Is distorted by turbulence
3. Flame Structure
Not a smooth front
Instead:
Wrinkled
Intermittent
Strained
4. Role of Turbulence
Turbulence:
Enhances mixing → increases reaction
But:
Excessive strain → extinction
5. Recirculation = Flame Stabilization
From BERL combustor:
Swirl → recirculation
Recirculation:
Traps hot gases
Re-ignites fresh mixture
This is a key design mechanism.
Applications
Gas turbine combustors
Diesel engines
Industrial burners
Flares
Rocket injectors
Limitations and Assumptions
Mixture Fraction Approach
Assumes conserved scalar
Requires equal diffusivities
Equilibrium Model
Only valid for fast chemistry
EDM
Ignores chemistry details
Temperature-independent
Flamelet Models
May fail in:
Strong extinction
Low Damköhler regimes
General
PDF assumptions introduce uncertainty
Model selection is critical
Study Priorities
If short on time:
Mixture fraction concept (most important)
Mixing-controlled combustion idea
PDF role in turbulence
Equilibrium vs EDM vs Flamelet differences
Combustion regimes diagram
Flame stabilization via recirculation
Key Takeaways
Non-premixed combustion is fundamentally a mixing-controlled process
The mixture fraction reduces complex chemistry to a scalar problem
Turbulence introduces fluctuations → handled via PDF methods
Equilibrium models are fast but limited
EDM is simple and widely used but crude
Flamelet models provide the best balance for realistic flames
Recirculation zones are critical for flame stability in real systems