Heat Transfer

The liner as a thermal circuit

The liner wall sits between two gases: the hot combustion products inside and the cooler compressor air flowing through the annulus outside (which is itself at 700–900 K at high power). In steady state, heat in equals heat out:

$\underbrace{R_1 + C_1}_{\text{in: radiation + convection}} \;=\; \underbrace{K_{1-2}}_{\text{conduction through wall}} \;=\; \underbrace{R_2 + C_2}_{\text{out: to annulus air}}$

Two ways in, one way through, two ways out. The wall temperature is simply wherever these balance.

Radiation in ($R_1$) comes from the hot CO₂ and H₂O, and above all from soot. Glowing soot particles radiate almost like a black body, so a sooty, luminous flame can pour several times more radiation onto the wall than a clean, blue one. Radiation scales as $\cflame{T}^4$: a 10% hotter flame means about 46% more radiant heat.

Convection in ($C_1$) comes from hot gas scrubbing the wall: $\dot q = h_\text{in}(T_g - T_w)$, with a driving temperature difference of a thousand kelvin or more.

Out, the annulus air removes heat by convection ($C_2$), but the coolant is itself hot, so the driving temperature difference is limited.

Play with the circuit. Start with no protection at all.

With nothing but the bare wall, the metal sits hundreds of kelvin over its limit. Notice where the temperature drops: most of the fall happens in the gas boundary layers either side of the metal, not in the metal itself. A thin nickel wall is a good conductor, so it can't protect itself; it just takes whatever temperature the balance of inflows and outflows dictates. So there are only a few ways to cool it:

1. Shield it from convection: put a layer of cool air between the hot gas and the wall (film cooling).
2. Shield it from radiation: burn with less soot.
3. Add insulation on the hot side: a thermal barrier coating.
4. Pull more heat out the back: more vigorous cooling of the cold side.

The evolution of liner cooling

Film cooling

The classic answer is to inject a thin layer of relatively cool air through slots along the inside of the liner, so the wall sees a "blanket" instead of the flame. Its quality is measured by the film effectivenessFilm coolingA layer of cool air injected along the liner wall to shield it from the hot gas; its effectiveness decays downstream.:

$\eta_f = \frac{\cflame{T_g} - T_{aw}}{\cflame{T_g} - \ccool{T_c}}$

where $T_{aw}$ is the temperature of the gas actually touching the wall. Right at the slot, $\eta_f \approx 1$ and the wall sees pure coolant. Downstream, turbulence mixes the film into the hot gas and $\eta_f$ decays, so a fresh slot is needed every few centimetres, and the wall temperature becomes a sawtooth.

Transpiration cooling

The ideal limit is a porous wall with coolant seeping uniformly through its whole surface: perfect, continuous protection. In practice porous materials are weak, hard to manufacture consistently, and their tiny pores clog with oxide and carbon. It remains largely a research topic.

Effusion cooling

Effusion coolingEffusion coolingThousands of small angled holes that bleed coolant through the liner, building a continuous protective film. is the modern workhorse.

The practical approximation to transpiration: a solid liner laser-drilled with thousands of tiny holes (~0.5 mm), angled shallowly (~20–30°) along the surface. Each jet is weak, but together they build up a continuous film, and the air flowing through the holes also cools the wall from inside the holes on its way through.

The comparison is the whole argument for effusion: a steadier, cooler wall for less air.

Thermal barrier coatings

A thermal barrier coatingThermal barrier coatingA thin ceramic layer (usually yttria-stabilised zirconia) on the hot side of the liner that insulates the metal. attacks the problem from the other side.

A ceramic layer, typically yttria-stabilised zirconia (YSZ), 100–500 μm thick, sprayed on the hot side. Its thermal conductivity is about a tenth of the metal's, so it adds a thermal resistance

$R_\text{TBC} = \frac{t_\text{TBC}}{k_\text{TBC}}$

For 150 μm of YSZ ($k \approx 1.5$–$2$ W/m·K), $R \approx 10^{-4}$ m²K/W. At a heat flux of 1 MW/m², that is a ~75–100 K drop across a coating thinner than a credit card. Add a TBC in the widget above and watch the metal fall under its limit while the ceramic surface runs hotter. The ceramic's own limits (sintering, and spallation caused by thermal-expansion mismatch over thousands of cycles) cap how thick and how hot it can go.

The cooling penalty

Every gram of cooling air is a gram that never meets the fuel in the primary zone and never helps the dilution jets. That has consequences all over the combustor:

• Less air for combustion and dilution. Fewer, weaker dilution jets mean a worse pattern factor (Lesson 4); a richer, hotter primary zone means more NOₓ (Lesson 9).
• Cold walls quench chemistry. The near-wall film is too cool for CO to finish oxidising to CO₂, which makes it a direct source of CO and unburned hydrocarbons, especially at low power.
• The cycle keeps getting hotter. Each engine generation raises pressure ratio and turbine entry temperature. That raises the heat load and makes the compressor air, the coolant, hotter, squeezing the problem from both sides.

We have now built, fed, stabilised and protected the combustor. Time to read the bill: what comes out of the exhaust, how it forms, and the strategies that keep it within the law.