Gas Turbine CombustionA First-Principles Course

How this course works

Each lesson opens with one question and builds the intuition to answer it before formalising anything. Along the way you will find:

• Live explorables. More than two dozen interactive simulations, from swirling recirculation zones and stability loops to singing combustors and hydrogen flashback. They are not decoration: each is a small physical model you can push until it breaks. Predict first, then drag.
• Pause and ponder. Questions worth a minute of thought before you reveal the answer.
• Check your intuition. Short quizzes whose explanations are often the best part.
• Watch the idea. Many simulations have a narrated tour that moves the sliders for you, like a short animated lecture. Press it, then take the controls.
• Challenges. Small goals under the simulations ("can you keep it lit at 100 m/s?") that tick themselves off when you succeed.
• Estimate first. Before a big number is revealed, you guess it on a logarithmic scale — the way Feynman taught estimation.
• Going deeper. The equations engineers actually use, colour-coded to match the pictures: $\cfuel{\phi}$ is always fuel gold, $\cflame{T}$ always flame red.
• Dotted words are defined on hover — the full glossary is at the bottom of this page.

Throughout the course, colours mean the same thing everywhere:

• The Design Studio. The course ends with a capstone: pick a mission and design a combustor that passes eleven certification tests at once.

What you will be able to do

• Explain why each major combustor design decision exists, not just what it is
• Derive the stability loop from a single ratio, and see why altitude relight is so hard
• Reason about the trade-offs between stability, efficiency, emissions, noise and durability
• Understand how NOₓ, CO and soot form, and how lean premixed, RQL and staged combustors fight them
• See why sustainable fuels are nearly drop-in, and why hydrogen is a whole new combustion problem

Prerequisites

Comfort with undergraduate thermodynamics and fluid mechanics helps. Chemical kinetics is introduced from scratch. The mathematics is kept at the level of understanding, not derivation for its own sake.

A note on the approach

The hardest thing about learning combustion is not any single concept. It is holding the whole system in your head while going deep on each piece. So every lesson starts from why this matters to the combustor as a whole, and the course keeps returning to three threads: temperature is the master variable, time is the currency, and air is the budget.

The structure follows Arthur Lefebvre and Dilip Ballal's Gas Turbine Combustion (3rd edition), which remains the definitive reference in the field. The simulations are reduced-order models chosen to reproduce the right shapes and magnitudes. They are built for intuition, not for design.

Glossary

Equivalence ratio φLesson 2

Actual fuel–air ratio divided by the stoichiometric one. Below 1 is lean (spare air), above 1 is rich (spare fuel).

StoichiometricLesson 2

The exact mixture in which every fuel molecule finds just enough oxygen to burn completely — about 1 kg of kerosene per 14.7 kg of air.

Adiabatic flame temperatureLesson 2

The temperature a mixture reaches if it burns completely with no heat lost. A bell-shaped function of φ, peaking slightly rich.

Arrhenius lawLesson 2

Reaction rate ∝ exp(−Eₐ/RT): only molecules in the energetic tail can react, so rates grow exponentially with temperature.

Activation energy EₐLesson 2

The energy barrier a collision must overcome for a reaction to happen.

Laminar flame speed S_LLesson 2

The speed at which a flame front travels into fresh premixed gas — about 0.4 m/s for kerosene, ~2–3 m/s for hydrogen.

Premixed flameLesson 2

Fuel and air are mixed before burning; the flame is a travelling wave whose temperature you choose via φ.

Diffusion flameLesson 2

Fuel and air meet in the flame and burn where they reach stoichiometric proportions — robust, but always at the hottest surface.

FlashbackLesson 2

A flame propagating upstream, against the flow, into hardware not designed to contain it.

Pressure recovery CₚLesson 3

The fraction of the inlet dynamic pressure a diffuser turns into static pressure.

Flow separationLesson 3

When slow near-wall fluid cannot push into rising pressure, stops, and turns back — detaching the flow from the wall.

Dump diffuserLesson 3

A short pre-diffuser followed by a sudden step. It accepts a fixed, stable separation in exchange for shortness and robustness.

Swirl number SₙLesson 4

Ratio of the axial flux of angular momentum to that of axial momentum. Above ~0.6 the flow on the axis reverses.

Central recirculation zoneLesson 4

A bubble of reversed flow on the combustor axis, created by vortex breakdown, that returns hot products to ignite fresh mixture.

Vortex breakdownLesson 4

The abrupt reversal of flow on the axis of a strongly swirling jet as its swirl decays and axial pressure rises.

Momentum-flux ratio JLesson 4

ρⱼVⱼ² / ρₘVₘ² — the jet-to-crossflow momentum ratio that sets how deep a liner jet penetrates.

Pattern factorLesson 4

(T_max − T_mean)/(T_mean − T_inlet) at the combustor exit: how much hotter the worst hot streak is than average.

Damköhler numberLesson 5

Da = τ_flow / τ_chem, residence time over chemical time. Above 1 the flame survives; below 1 it blows out.

Lean blowoutLesson 5

Flame-out caused by too little fuel: the chemistry slows until it can no longer keep up with the flow.

Loading parameter θLesson 5

Lefebvre’s P^1.75·A·D^0.75·e^(T₃/300)/ṁ: bundles pressure, temperature, size and airflow into one predictor of efficiency.

Sauter mean diameterLesson 6

D₃₂ = Σd³/Σd²: the droplet size with the same volume-to-surface ratio as the whole spray — the right average for evaporation.

d² lawLesson 6

A droplet’s surface area shrinks at a constant rate, so its lifetime grows with the square of its initial diameter.

Airblast atomizerLesson 6

An injector that spreads fuel into a thin film and shatters it with fast air, rather than with fuel pressure.

Rayleigh criterionLesson 7

A heat source drives a sound wave when heat is released in phase with the pressure oscillation.

Helmholtz resonatorLesson 7

A cavity connected through a neck that absorbs acoustic energy strongly near its tuned frequency.

Film coolingLesson 8

A layer of cool air injected along the liner wall to shield it from the hot gas; its effectiveness decays downstream.

Effusion coolingLesson 8

Thousands of small angled holes that bleed coolant through the liner, building a continuous protective film.

Thermal barrier coatingLesson 8

A thin ceramic layer (usually yttria-stabilised zirconia) on the hot side of the liner that insulates the metal.

Zeldovich mechanismLesson 9

The chain O + N₂ → NO + N, N + O₂ → NO + O that makes thermal NO; its rate ∝ exp(−69 090/T).

RQLLesson 9

Rich-burn, Quick-quench, Lean-burn: a low-NOₓ strategy that jumps across the stoichiometric band as fast as possible.

Lean premixedLesson 9

Premixing fuel and air lean before burning so no gas ever sees stoichiometric temperatures.

Sustainable aviation fuelLesson 10

Kerosene-like fuels from non-fossil feedstocks (e.g. HEFA, Fischer–Tropsch), certified as blends with Jet-A.

MicromixLesson 10

A hydrogen combustor concept using thousands of tiny, fast jets and compact flames to avoid flashback.