Fuel Injection

Everything in the previous four lessons assumed that fuel was already in the gas phase, mixing with air, and reacting. In reality, the fuel enters the combustor as a liquid — Jet-A at room temperature is about as viscous as water — and must be converted into a fine spray of microscopic droplets before it can evaporate and react.

This conversion process is atomization, and it is the responsibility of the fuel injector. A poorly performing injector can undermine every other aspect of the combustor design: large droplets evaporate slowly, burn incompletely, and produce soot; non-uniform spray distributions create local rich zones that generate both soot and NOₓ; mismatched cone angles send burning fuel into liner walls.

Why droplet size matters

A liquid droplet must first reach its boiling point and then fully evaporate before the vapor can mix with air and react. The time required scales with the square of the droplet diameter (the $d^2$ evaporation law):

$t_\text{evap} \propto d_0^2$

A droplet of 100 μm takes 100 times longer to evaporate than a 10 μm droplet. In a combustor with residence times on the order of milliseconds, the injector must consistently produce droplets in the 10–50 μm range to ensure complete evaporation and burnout before the dilution zone.

Sauter Mean Diameter

A real spray contains droplets of many sizes. The standard summary statistic is the Sauter Mean Diameter (SMD), defined as the diameter of a hypothetical single droplet that has the same volume-to-surface-area ratio as the entire spray:

$\text{SMD} = D_{32} = \frac{\sum_i n_i d_i^3}{\sum_i n_i d_i^2}$

SMD is the correct metric because evaporation rate is proportional to surface area while the energy content (mass) is proportional to volume. A larger SMD means disproportionately more fuel locked in large, slowly evaporating droplets.

For modern airblast atomizers at operating conditions, SMD values of 15–40 μm are typical. For comparison, a human hair is ~70 μm.

The three injector families

Pressure-swirl (simplex) atomizers

The original gas turbine fuel injector. Fuel is supplied at high pressure (20–40 bar above combustor pressure) through a tangential inlet into a swirl chamber. The swirling liquid exits the orifice as a hollow conical sheet, which then breaks up into droplets under aerodynamic instabilities.

The breakup process: the thin liquid sheet oscillates due to Kelvin-Helmholtz instability at the fuel-air interface, breaks into ligaments, which then pinch off into droplets.

SMD correlation (Lefebvre):

$\text{SMD} \propto \frac{\mu_L^{0.16} \sigma^{0.12}}{\rho_A^{0.5} \Delta P_L^{0.43}}$

where $\mu_L$ is liquid viscosity, $\sigma$ is surface tension, $\rho_A$ is air density, and $\Delta P_L$ is the fuel pressure drop across the nozzle.

The idle problem: At low power, fuel flow rate drops by a factor of 5–10 relative to takeoff. To maintain reasonable SMD, you would need proportionally lower $\Delta P_L$ — but the relationship is a 0.43 power, so the SMD degrades significantly. Simplex nozzles produce coarse, poorly atomized spray at idle, leading to high CO and UHC at low power.

Duplex and dual-orifice atomizers

A pragmatic solution to the idle problem: two fuel circuits, a primary (small) orifice active at low power, and a secondary (large) orifice that opens at higher power settings. The primary circuit is sized to maintain good $\Delta P_L$ and SMD across the idle range. The secondary circuit handles the high-flow takeoff and cruise conditions.

The transition between primary-only and combined flow must be managed carefully — fuel staging instabilities can cause momentary pressure oscillations during the transition.

Airblast atomizers

Instead of relying on fuel pressure to break up the liquid, airblast atomizers use the kinetic energy of high-velocity airflow. A thin fuel sheet is formed and then exposed to high-velocity compressor air on both sides. The aerodynamic forces (proportional to the air-fuel velocity difference) shred the sheet into fine droplets.

$\text{SMD} \propto \frac{\sigma}{\rho_A V_\text{rel}^2 d} \left(1 + \frac{\dot{m}_L}{\dot{m}_A}\right)$

At high-power conditions, compressor air velocities are high, $V_\text{rel}$ is large, and SMD is excellent — often below 20 μm. More importantly, because the fuel is introduced as a thin sheet into the airstream, fuel-air mixing begins immediately, even before evaporation is complete. This pre-mixing reduces locally rich zones and produces dramatically lower soot compared to pressure-swirl designs.

Why airblast won for aircraft:

• Excellent SMD and mixing at operating conditions
• Low smoke — the pre-mixing suppresses fuel-rich zones
• Lower fuel supply pressures required (30–40 bar vs. 100+ bar for pressure-swirl)

The starting problem: At engine start, airflow is very low and $V_\text{rel}$ is small. Airblast atomizers are poor atomizers at start. Production engines address this by adding a separate simplex pilot circuit that activates during starting and low-power operation, with the main airblast circuits phasing in above a threshold power level.

Spray characteristics beyond SMD

A complete injector characterization includes:

Cone angle: The half-angle of the spray cone. Too narrow and the spray does not distribute evenly across the primary zone; too wide and droplets impinge on the liner walls before evaporating. Typical design targets: 60–90° full cone angle.

Penetration: How far the spray penetrates into the crossflow before the droplets are aerodynamically redirected. Large, high-inertia droplets penetrate farther; small droplets follow the gas streamlines almost immediately.

Circumferential uniformity: Non-uniformity (azimuthal variation in spray density) directly translates into Pattern Factor — hot and cold streaks at the combustor exit. Injector manufacturing tolerances and deposits from thermal degradation both affect this.

Viscosity: the hidden enemy

Lefebvre repeatedly emphasizes that fuel viscosity is the primary degrader of atomization quality. Viscosity resists the internal circulation that forms the swirl in a pressure-swirl nozzle, and it resists the breakup of the liquid sheet. Cold fuel (low temperature, potentially waxy) is more viscous and atomizes poorly.

This is why cold-soak conditions at high altitude are a specific concern: if the fuel temperature drops significantly during cruise, fuel viscosity rises, SMD increases, and combustion efficiency drops. In some engine designs, fuel is routed through heat exchangers to ensure adequate temperature before injection.

The injector as an emissions device

The fuel injector is not just a fluid mechanics component — it is directly responsible for the initial conditions of the combustion chemistry. An injector that produces fine, uniform spray with early fuel-air mixing will produce lower soot and lower NOₓ than one producing coarse, poorly mixed spray, even if both combustors have identical aerodynamic design downstream.

This makes injector development one of the most leverage-rich activities in modern combustor engineering: small improvements in spray quality propagate through the entire combustion process.

Lesson 7 looks at what happens when that combustion process couples with the acoustic modes of the combustor — and the destructive resonance phenomenon called combustion instability.