Conjugate Heat Transfer Analysis for Turbomachinery
Theory: the heat path from gas to coolant
Overview
Why must fluid and solid be solved together to predict turbine blade temperature?
Blade metal faces combustion gas outside and coolant inside. Its temperature is set by the balance of heat entering from the gas, conducting through the metal and removed by coolant. A fluid-only calculation must assume wall temperature or heat transfer coefficient, but these themselves depend on metal temperature. Blade life is so sensitive to metal temperature that errors of tens of kelvin are unacceptable, so conjugate heat transfer (CHT) solves fluid and solid in one calculation. First, let's see with 1D thermal resistances where the temperature drops occur.
Series thermal-resistance model
h_g and h_c are gas- and coolant-side heat transfer coefficients; t and k the thickness and conductivity of the thermal barrier coating (TBC) and metal; T_m the gas-side metal surface temperature; φ cooling effectiveness. Conditions: gas 1,700 K, coolant 800 K, h_g 3,000 W/m²K, h_c 2,000 W/m²K, metal (nickel superalloy) 1.5 mm at 25 W/mK, TBC 0.3 mm at 1.0 W/mK.
Blades working in gas above their melting point
Gas-turbine efficiency rises with turbine inlet temperature, so in modern large gas turbines inlet temperatures often exceed the melting point of nickel superalloys (around 1,600 K). Blades survive through internal cooling passages, film cooling that bleeds coolant over the surface, and ceramic thermal barrier coatings. Since the 1990s, CHT analysis solving fluid and solid together has been used to evaluate such cooling designs.
Worked examples
Example 1: with and without a thermal barrier coating
| Item | No TBC | With TBC |
|---|---|---|
| Heat flux | 1,007 kW/m² | 754 kW/m² |
| Gas-side surface | 1,364 K | 1,449 K |
| Metal gas-side surface | 1,364 K | 1,222 K |
| Metal coolant-side surface | 1,304 K | 1,177 K |
| Drop across TBC | — | 226 K |
| Drop across metal | 60 K | 45 K |
| Cooling effectiveness φ | 0.37 | 0.53 |
Example 2: heat-transfer-coefficient error and metal temperature (with TBC)
| Gas side h_g | Coolant 1,600 | Coolant 2,000 | Coolant 2,400 |
|---|---|---|---|
| 2,400 | 1,240 K | 1,195 K | 1,159 K |
| 3,000 | 1,268 K | 1,222 K | 1,186 K |
| 3,600 | 1,288 K | 1,243 K | 1,207 K |
Units W/m²K; values are metal gas-side surface temperatures. Varying each ±20% from the baseline (3,000, 2,000) shifts metal temperature by −27 to +21 K for the gas side and +46 to −36 K for the coolant side.
Example 3: comparison with a fixed wall temperature
Assuming a 1,400 K TBC surface and solving only the gas side gives 3,000 × (1,700 − 1,400) = 900 kW/m². The coupled solution has a 1,449 K surface and 754 kW/m². An assumed wall temperature only 49 K too low overestimated heat flux by 19%.
The coolant-side coefficient affects metal temperature more.
Here the coolant-side resistance (5.0×10⁻⁴) exceeds the gas side (3.3×10⁻⁴), so coolant-side errors matter more. Internal passages have turbulators such as ribs and pins, making heat transfer as hard to predict as outside. Solving the gas side precisely while using correlations for the coolant still leaves metal-temperature error. CHT solves coolant-passage flow simultaneously, automatically including distributions on both sides and heat spreading within the metal. Turbulence-model choice can still shift heat transfer coefficients by 20–30%, so validation against experiments is essential.
CHT workflow
- Use 1D thermal resistances to see which layers carry the drops.
- Build one model of gas and coolant flow plus metal and TBC solids.
- Use y⁺ ≈ 1 near walls rather than relying on wall functions for heat transfer.
- Give solid conductivity as a function of temperature.
- Validate against measured blade surface temperatures (thermocouples, thermal paints).
“The average temperature matched”
Post-service inspection of a turbine blade found oxidation damage only near part of the leading edge. The design had passed averaged heat transfer coefficients from fluid analysis to structural thermal analysis, and average blade temperature matched measurement. A CHT recalculation showed flow separating at a bend in the leading-edge cooling passage, sharply reducing coolant-side heat transfer locally and running the metal about 40 K hotter than its surroundings. Passing averages misses such local hot spots.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Assuming wall temperature | Wrong heat flux | Couple with CHT |
| Passing averaged coefficients | Local hot spots missed | Couple full distributions |
| Heat transfer via wall functions | Large coefficient errors | y⁺ ≈ 1 |
| Omitting the TBC | Metal temperature too high | Model as a thin layer |
| Correlations for coolant side | Residual metal error | Solve the passages too |
I'd like to learn related topics.
Related pages include CHT methodology, the solid–fluid interface, the partitioned approach, the monolithic approach and near-wall CHT.
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