Blade cross-section & cooling channels
Through-wall temperature distribution
Theory & Key Formulas
Effective gas temperature: \(T_{g,eff}=T_g-\eta_f(T_g-T_c)\)
Cooling effectiveness: \(\phi=\dfrac{T_g-T_{wall}}{T_g-T_c}\)
Heat flux: \(q=(T_{g,eff}-T_c)/(1/h_g+t/k+1/h_c)\)
Thermal stress: \(\sigma=\dfrac{E\,\alpha\,\Delta T}{1-\nu}\)
Material: nickel superalloy (E = 200 GPa, α = 15×10−6/K, ν = 0.3, IN738-class)
What is turbine blade cooling?
🤩Why do gas-turbine blades have to be actively cooled?
🎓In modern engines the combustion gas reaches almost 1500 °C, but nickel-superalloy blades melt around 1300 °C. Compressed air is bled from the compressor and routed through the blade to keep the metal below its limit. Push the Tg slider up to 1600 °C and you can see why this matters.
🤩What does film cooling effectiveness ηf actually mean?
🎓Film cooling blows coolant out through small holes so it forms a protective film over the blade surface. ηf = 0.5 effectively shields half of the gas-to-wall temperature difference. Sweep the slider from 0 to 0.7 and watch the wall temperature drop.
🤩Why not just cool everything as cold as possible?
🎓Because the through-wall temperature gradient creates thermal stress. Drop Tc too low and the ΔT across the wall explodes — you'll see the stress card flash red. The design rule is: cool uniformly to a sensible temperature, not as cold as possible.
Physical model
The simulator models the wall as three thermal resistances in series: gas-side convection $1/h_g$, conduction through the wall $t/k$, and coolant-side convection $1/h_c$. With film cooling the driving temperature on the hot side is reduced from $T_g$ to $T_{g,eff}=T_g-\eta_f(T_g-T_c)$.
Heat flux $q$ is constant in steady state; the through-wall profile is linear because the conductivity is taken constant. Thermal stress is computed from the temperature drop $\Delta T = T_{hot}-T_{cool}$ across the wall using the constrained-plate formula $\sigma = E\alpha\Delta T/(1-\nu)$.
Real-world applications
Aero engines: raising the turbine inlet temperature is the single biggest lever for thrust and fuel burn. Better cooling has driven decades of TIT increases.
Power-generation gas turbines: continuous-duty operation means thermal fatigue cracks dominate failures. Engineers use exactly this kind of resistance network as a screening tool.
Cooling-hole layout: ηf depends strongly on film-hole geometry. CFD provides the local distribution, but a fast 1-D model like this is used to size mass-flow budgets.
Common misconceptions
"Lower Tc is always better" — no. The wall metal cools, but the through-wall ΔT grows and thermal stress can crack the blade.
"Maximise ηf for safety" — more film cooling means more compressor bleed, which directly hurts engine efficiency. Real designs target ηf = 0.4–0.6 with the minimum mass flow.
"This 1-D answer is the design" — the leading edge, suction surface and trailing edge all see different loads. Use this tool for screening, then verify hot spots and stress concentrations with 3-D CFD/FEA.
Worked Example
Gas turbine blade operating at Tg=1300°C with film cooling. Set η=0.7, Tc=400°C, k=12 W/m·K, T=2.0 mm, Hg=1000 W/m²·K, Hc=700 W/m²·K. The simulator calculates cooling effectiveness φ≈0.68, hot wall temperature ~950°C, heat flux ~320 kW/m², and thermal stress ~180 MPa. Reducing wall thickness to 1.5 mm increases stress to ~240 MPa, requiring higher-strength alloy or improved cooling design.