Combustion Performance

Lessons 1 through 4 established how a combustor is built. Lesson 5 is about how we know if it works — and, more precisely, when it stops working.

Lefebvre frames combustion performance around three questions that a designer must answer for every operating condition in the flight envelope:

1. How much of the fuel energy was actually released? (Efficiency)
2. Will the flame stay lit? (Stability)
3. If the flame goes out, can it re-light? (Ignition and relight)

Combustion efficiency

Combustion efficiency $\eta_c$ is the ratio of the actual temperature rise across the combustor to the ideal temperature rise if all fuel were burned completely:

$\eta_c = \frac{\Delta T_\text{actual}}{\Delta T_\text{ideal}} = 1 - \frac{\dot{m}_\text{UHC} \cdot H_{UHC} + \dot{m}_\text{CO} \cdot H_\text{CO}}{\dot{m}_f \cdot H_f}$

At sea-level takeoff, modern combustors achieve $\eta_c > 99.9\%$. The losses come from two sources: unburned hydrocarbons (UHC) that escaped the primary zone without reacting, and carbon monoxide (CO) that oxidized partway but not all the way to CO₂.

Efficiency and power: Efficiency is not a fixed number — it varies across the operating envelope. At maximum power, the combustor runs at high pressure and temperature; reaction rates are fast, and residence time is adequate. At idle, pressure is low, temperature is low, and fuel droplets are larger (the atomizer is less effective). Efficiency can drop to 97–98% at idle, which is significant from an emissions standpoint.

Combustion stability

A flame can be blown out in two ways:

Lean blowout (LBO): Too little fuel. The equivalence ratio drops below the lean flammability limit of the primary zone, the reaction slows, the temperature drops, and the flame cannot sustain itself.

Rich blowout: Too much fuel. In extremely rich conditions, the oxygen concentration in the primary zone falls so low that the reaction is suppressed.

In practice, LBO is the operationally important limit. Rich blowout in normal operation would require fuel system failure.

The stability loop

Lefebvre's signature contribution to stability characterization is the stability loop (sometimes called the "peaked hat" diagram). It plots the fuel-air ratio (FAR) against the air velocity through the combustor, and shows the boundary within which a stable flame exists.

The loop has this shape: at low air velocity, the flame is stable over a wide range of FAR. As velocity increases, the stable FAR range narrows — the loop pinches in. At some critical velocity (the blow-off velocity), only a single FAR will sustain a flame, and above that velocity the flame cannot be maintained at any fuel-air ratio.

What determines the blow-off velocity? The chemistry time scale must be shorter than the aerodynamic time scale (the residence time of the gases in the primary zone). If the gas flows through faster than the reaction can complete, the chain reactions cannot sustain themselves. Formally:

$\text{Da} = \frac{\tau_\text{flow}}{\tau_\text{chem}} > 1 \text{ (required for combustion)}$

The Damköhler number $\text{Da}$ captures this. When $\text{Da} < 1$, the flame blows out regardless of FAR.

Implications for design:

• Higher pressure widens the stability loop (faster chemistry, shorter $\tau_\text{chem}$)
• Larger combustor volume increases residence time (longer $\tau_\text{flow}$), helping stability
• Better swirler design improves recirculation (extends effective $\tau_\text{flow}$ in the primary zone)

Lean blowout and operational margins

The LBO equivalence ratio $\phi_\text{LBO}$ is not a single fixed number — it depends on inlet temperature, pressure, and air velocity. A practically important rule: the closer the combustor operates to $\phi_\text{LBO}$ in order to reduce NOₓ (lean operation), the smaller the margin against blowout when the engine is throttled or encounters a disturbance.

Modern lean-burning combustors operate with smaller stability margins than traditional diffusion flame designs. This is a known engineering trade. It is managed through:

• Pilot flames (a small, rich, stable pilot diffusion flame that re-ignites the main lean zone if it blows out)
• Closed-loop control of fuel-staging based on combustion sensor feedback
• Conservative LBO margins at certification

Ignition and altitude relight

Ground ignition

Starting the engine on the ground is straightforward by comparison: air is dense, fuel temperature is reasonable, and the igniter can deliver energy repeatedly. The igniter (typically a high-energy surface discharge plug, not a conventional spark plug) must be positioned within the CRZ where the hot recirculating products will help sustain the initial kernel.

Three phases of ignition:

1. Kernel formation: The spark produces a small, hot plasma that initiates reaction in the local fuel-air mixture. If the local mixture is outside the flammability limits, or the spark is in a high-velocity region that sweeps the kernel away before it grows, ignition fails.
2. Kernel growth: The kernel must grow large enough that its heat release exceeds its heat loss to the surrounding cold mixture. Below a critical kernel size, the flame dies.
3. Propagation: Once the primary zone is lit, the flame must propagate around the annulus (in annular combustors) or jump between cans via interconnectors (in can-annular designs).

Altitude relight

At altitude — low pressure, low temperature, low air density — all three ignition phases become more difficult simultaneously. The minimum ignition energy increases, the fuel atomization quality decreases (higher viscosity, lower fuel temperature), and the available air density to form a combustible mixture drops.

The altitude relight envelope is one of the most demanding requirements in combustor certification. The engine must demonstrate reliable relight across a range of Mach numbers and altitudes after a deliberate flameout. Meeting this envelope while also meeting emissions targets is a genuine design challenge — the fuel staging and primary zone conditions optimized for low NOₓ at cruise are often suboptimal for ignition at altitude.

The combustor loading parameter

Lefebvre introduces a fundamental sizing tool — the Combustion Intensity or Loading Parameter $\Psi$:

$\Psi = \frac{\dot{m}_\text{air}}{V_c \cdot P^n \cdot \exp(T_\text{in}/300)}$

where $\dot{m}_\text{air}$ is the air mass flow, $V_c$ is the combustor volume, $P$ is the pressure, $T_\text{in}$ is the inlet temperature, and $n \approx 1.8$.

The parameter captures how heavily loaded the combustor is relative to its size and inlet conditions. Above a critical value of $\Psi$, efficiency drops sharply because there is insufficient volume (residence time) to complete combustion at the given conditions.

This is the sizing equation: if you double the air mass flow and do not change $V_c$, $\Psi$ doubles and efficiency plummets. The combustor must grow in proportion to the engine. In modern high-bypass turbofans, the combustor volume is carefully sized to maintain acceptable $\Psi$ across the entire flight envelope.

The report card in practice

Performance is not measured in isolation. An efficient combustor that produces high NOₓ fails certification. A stable combustor that cannot relight at altitude fails safety requirements. The combustor design is successful only when efficiency, stability, and ignition are all satisfactory simultaneously — across every combination of altitude, Mach number, and power setting in the flight envelope.

Lesson 6 goes upstream in the combustion process: before any of this aerodynamics and performance discussion is relevant, the fuel must actually be introduced into the air stream in a useful form. That is the job of the fuel injector — and the physics of atomization that govern its success.