Heat Transfer

The primary zone of a gas turbine combustor contains gas at temperatures between 2000 K and 2500 K. The nickel-based superalloy liner surrounding that gas begins to lose creep strength above 1100 K and will oxidize rapidly above 1300 K. Without active cooling, a liner would fail within seconds.

This is the heat transfer problem: the gap between flame temperature and material limit is almost 1000 K, and the liner has no opportunity to conduct heat away — it is surrounded by hot gas on one side and slightly cooler (but still hot) compressor bypass air on the other.

Lefebvre's treatment of heat transfer is organized around quantifying the threat, then cataloguing the engineering responses.

The three heat transfer modes at the liner

1. Internal radiation

The combustion products — CO₂, H₂O, and especially soot particles — are significant radiators in the infrared. A sooty diffusion flame can have a luminosity that delivers radiative heat flux to the liner wall on the order of 0.3–0.8 MW/m². Soot particles are particularly effective blackbody-like radiators; this is why clean (low-soot) combustors actually reduce the thermal design challenge as a secondary benefit.

Radiative flux scales as $T_\text{flame}^4$, making it extremely sensitive to temperature. A 10% increase in flame temperature increases radiative load by ~46%.

2. Internal convection

The hot combustion gases scrubbing the inside of the liner transfer heat by convection. The convective flux is:

$\dot{q}_\text{conv, in} = h_\text{in} (T_g - T_w)$

where $h_\text{in}$ is the internal convection coefficient, $T_g$ is the bulk gas temperature, and $T_w$ is the liner wall temperature. In the primary zone, $T_g - T_w$ can be 1000 K or more, so even moderate $h_\text{in}$ values produce significant flux.

3. External convection (the defense)

Compressor bypass air flowing over the outside of the liner removes heat from the external surface:

$\dot{q}_\text{conv, out} = h_\text{out} (T_w - T_\text{cool})$

This is the primary natural cooling mechanism. Even without any active cooling scheme, the bypass air moderates the liner temperature. The challenge is that $T_\text{cool}$ is itself quite high (compressor exit temperature at high power is 700–900 K), so the temperature difference driving external convection is limited.

The energy balance at the liner wall in steady state:

$\dot{q}_\text{rad, in} + \dot{q}_\text{conv, in} = \dot{q}_\text{conv, out} + \dot{q}_\text{cond}$

Conduction through the liner wall is minimal (liners are thin metal sheets, ~1–2 mm). The dominant terms are internal heat load versus external convective cooling.

Cooling techniques: the evolution

Film cooling

The earliest systematic approach to liner cooling. A slot or row of holes at the leading edge of a liner panel injects cool compressor air tangentially along the inner surface. This "film" of cool air forms a thin insulating blanket between the hot gas and the metal.

The film effectiveness $\eta_f$ is defined as:

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

where $T_{aw}$ is the adiabatic wall temperature with film, $T_g$ is the hot gas temperature, and $T_c$ is the coolant temperature. Film effectiveness starts near 1.0 at the injection point and decays exponentially downstream as the film mixes with the hot gas.

The limitation: Because the film decays, periodic re-injection is required — every 30–50 mm of liner surface. Multiple slot rows consume significant air fractions (25–35% of total combustor air in some older designs), leaving less air for primary-zone combustion and dilution.

Transpiration cooling

In principle, the most efficient approach: the liner is made from a porous metal or ceramic material, and cooling air seeps uniformly through the entire surface, creating a distributed film.

The cooling air velocity through the pores is extremely low; it does not disrupt the internal flow field. Every part of the surface is protected continuously.

The reality: Porous liner materials are mechanically weak and difficult to manufacture to consistent quality. Thermal cycling causes fatigue in the thin pore walls. Combustion products (especially at off-stoichiometric conditions) can deposit carbon or oxidation products that gradually block the pores, reducing cooling uniformity. Transpiration cooling remains largely in research; it has not seen widespread production use.

Effusion cooling (the modern standard)

Effusion cooling is the engineering compromise that dominated production designs from the 1980s onward. The liner is laser-drilled with thousands of small, angled holes (diameter ~0.5–1.0 mm) in a dense array pattern. Air flows through these holes at low velocity, creating a quasi-uniform "transpiration-like" film, but without the structural and fouling problems of a truly porous wall.

The angled holes (typically 20–30° to the surface) are critically important: they produce a velocity component tangential to the wall, which improves film persistence and reduces the local turbulent mixing that erodes the film.

Modern effusion-cooled liners require 15–20% less cooling air than slot-cooled designs for equivalent wall temperature, which is a significant fuel burn and emissions benefit.

Thermal barrier coatings (TBCs)

A ceramic overcoat — typically Yttria-Stabilized Zirconia (YSZ), 100–300 μm thick — is applied to the hot-side surface of the liner. Zirconia has a thermal conductivity roughly 20× lower than nickel superalloy, providing significant temperature drop across the coating even at low thickness.

The thermal resistance added by the TBC:

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

For 150 μm of YSZ ($k \approx 2$ W/m·K), $R_\text{TBC} \approx 7.5 \times 10^{-5}$ m²·K/W. At a heat flux of 1 MW/m², this corresponds to a temperature drop of ~75 K across the coating — meaning the metal beneath it is 75 K cooler than it would be without the coating.

TBCs are now standard on liner panels and dome components in all modern aircraft combustors. The practical challenge is TBC spallation: thermal cycling causes differential thermal expansion between the ceramic coating and the metallic bond coat beneath it, eventually causing delamination. TBC durability is one of the active areas of materials research.

The cooling penalty

Every gram of cooling air is air that did not participate in combustion. This has cascading consequences:

1. Efficiency: Air used for cooling does not burn fuel; the combustor requires more fuel to achieve the same turbine inlet temperature.

2. Emissions: Film and effusion cooling inject relatively cold air adjacent to the liner wall. This creates locally cold, near-wall regions where CO oxidation is quenched. The thin boundary layer never reaches the temperature needed for complete CO burnout. This is a direct source of CO and UHC emissions at low power — and it compounds with the lean operation of modern combustors.

3. Exit temperature uniformity: Large amounts of cooling air mixing into the main flow can create cold streaks at the combustor exit, worsening Pattern Factor in the radial direction.

The modern design target is expressed as cooling effectiveness with minimum air. This drives the adoption of effusion cooling and TBCs: both reduce the air fraction required to maintain acceptable liner temperatures, releasing more air for combustion and dilution.

The numbers in context

At takeoff conditions on a modern turbofan:

• Primary zone gas temperature: ~2300 K
• Turbine inlet temperature: ~1900 K
• Maximum liner metal temperature (with cooling): ~1100 K
• Cooling air fraction of total combustor air: ~15–20%

These numbers define the boundary conditions of the thermal design problem. Every generation of engine pushes turbine inlet temperature higher (better specific work and efficiency), which pushes liner thermal loads higher, which demands improved cooling technology to avoid consuming the efficiency gains in cooling air penalties.

Lesson 9 addresses the question that has hovered over this entire course: with all of this combustion happening at such high temperatures, what pollutants are produced, where, and how do we reduce them?