Quick answer A turbine blade's film cooling effectiveness is η = (T_g − T_w)/(T_g − T_c) (T_g = gas temperature, T_w = wall temperature, T_c = coolant temperature), giving an effective gas temperature T_g,eff = T_g − η(T_g − T_c). Treating gas-side convection, wall conduction and coolant-side convection in series yields T_m ≈ (h_g·T_g,eff + h_c·T_c)/(h_g + h_c).
Adjust the combustion gas temperature, cooling air temperature, coolant-side heat transfer coefficient, film-cooling hole rows and allowable metal temperature to calculate the blade metal temperature, film-cooling effectiveness, overall cooling effectiveness and margin to allowable in real time.
Operating Conditions
Combustion gas temperature Tg1450 ℃
Cooling air temperature Tc550 ℃
Coolant-side heat transfer h_c2500 W/m²K
Film-cooling hole rows3 rows
Allowable metal temperature T_limit980 ℃
Animation
Live Values (cooling performance)
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Metal temperature Tm (℃)
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Film-cooling effectiveness η
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Overall cooling effectiveness Φ
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Margin to allowable (℃)
Blade Cross-Section Cooling Animation
Theory & Key Formulas
Film-cooling effectiveness: $\eta=\dfrac{T_g-T_w}{T_g-T_c}$, effective gas temperature $T_{g,\mathrm{eff}}=T_g-\eta\,(T_g-T_c)$
1-D wall heat balance (gas-side convection $h_g$, wall conduction $t/k$ and coolant-side convection $h_c$ in series): $T_m\approx\dfrac{h_g\,T_{g,\mathrm{eff}}+h_c\,T_c}{h_g+h_c}$
Known-solution check: …
What Is Turbine Blade Cooling Analysis?
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Do gas-turbine blades really have to be cooled with air? They sit behind the combustor, so aren't they a bit cooler already?
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No — they are extremely hot. In the latest engines the combustion gas reaches nearly 1500°C, but the melting point of the nickel superalloy the blades are made of is around 1300°C, so left alone they would melt. That is why part of the air compressed by the compressor is passed through the inside of the blades to cool them forcibly. Set the "Combustion gas temperature Tg" slider in this simulator to 1600°C and you will see how severe the conditions are.
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Really! So what is "film-cooling effectiveness η"? Is it separate from the cooling that passes through the inside of the blade?
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Good catch. Internal cooling alone is not enough — the surface has to be protected too. Film cooling is a technique in which countless tiny holes are drilled in the blade surface and cooling air is blown out of them. The air covers the surface with a thin film that blocks the direct heat from the hot gas. An η of 0.5 means the effective gas temperature is lowered by half the difference between the gas and cooling-air temperatures. In this tool, η rises with the "Film-cooling hole rows" (0 for 0 rows, 0.52 for 3, 0.66 for 6). Move the rows from 0 to 6 and watch the metal temperature fall from 858°C to 654°C.
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I see! But wouldn't it be safe to just make the cooling air colder and colder, or use more of it? Is there a problem with that?
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Sharp question. Cooling air is compressor air that is used without being burnt, so the more you use, the lower the engine's efficiency. And the thing that is easy to overlook is "thermal stress". When there is a temperature difference (ΔT) between the surface and the interior of the blade, or between the leading and trailing edges, the material tries to expand by different amounts, pulling against itself and generating large stresses. These cause fatigue failure. This tool does not calculate thermal stress, but if you lower the cooling-air temperature Tc from 550°C to 300°C, the metal temperature falls from 699°C to 491°C while the temperature difference across the wall widens from about 45°C to 58°C. Treat the "margin to allowable" as a safe-side guide based on temperature alone.
Frequently Asked Questions
This tool uses the saturating approximation η = 0.72×(1 − e^(−0.42n)), where n is the number of rows: 0 for 0 rows, 0.25 for 1, 0.52 for 3 and 0.66 for 6. The real η depends strongly on hole shape, angle and blowing ratio, so this relation is only a guide to the diminishing returns of adding rows.
Film cooling is disabled (η = 0) and the effective gas temperature equals the combustion gas temperature. Under the default conditions the metal temperature rises from 699°C to 858°C, the overall cooling effectiveness falls from 0.83 to 0.66, and the margin to the 980°C allowable temperature shrinks to 122°C. It shows how important film cooling is in real cooling design.
This simulator is a one-dimensional thermal-resistance network with a fixed gas-side heat transfer coefficient of 1200 W/m²K, wall thickness of 2 mm and thermal conductivity of 14 W/mK, and the metal temperature shown is the average of the two wall surfaces. It is intended for grasping qualitative trends; real design needs three-dimensional thermal and structural analysis that includes the local heat loads at the leading and trailing edges.
The metal temperature falls, but the temperature differences across the wall and between regions grow, which can increase thermal stress (this tool does not calculate thermal stress). In a real engine, preparing colder or more cooling air also increases the bleed flow and lowers engine efficiency, which must be taken into account.
Real-World Applications
Higher-efficiency aircraft engines:Advances in cooling technology have allowed the turbine inlet temperature (TIT) to rise, dramatically improving the thrust and fuel economy of jet engines. Trying parameter adjustments that raise the cooling effectiveness Φ in the simulator is engine design itself.
Durability of power-generation gas turbines:Power plants require continuous operation, and blade cracks caused by thermal fatigue are a major cause of failure. Analyses like this are performed routinely to understand how thermal stress arises and to optimise wall thickness and cooling-air flow.
Film-cooling hole layout design:Where on the blade, at what angle and how many cooling holes to drill is critically important. The value of η depends strongly on the hole layout, and detailed CFD (computational fluid dynamics) analysis is used in combination with simple network calculations like this one.
Evaluation of new materials and cooling methods:Used as a first step for comparing quantitatively the effect of new technologies such as ceramic matrix composites (CMC), impingement cooling and delta-wing film holes, and for examining the trade-offs against conventional methods (weight saving versus cooling performance, and so on).
Common Misconceptions and Points to Note
There are a few pitfalls when you start using this simulator. First, it is tempting to think that "the cooling-air temperature Tc is better the lower it is". The metal temperature certainly falls, but the "thermal stress" mentioned above actually gets worse. For example, lowering Tc from 550°C to 300°C brings the metal temperature down from 699°C to 491°C, but the temperature difference across the wall widens from about 45°C to 58°C and in a real blade the thermal stress increases. If the allowable stress of the material is exceeded, cracks follow. The golden rule of cooling design is "cool evenly, to the right temperature".
Next,the misconception that "adding film-hole rows to raise η keeps you safe". Raising η means blowing more cooling air out of the holes in the blade surface. For the engine as a whole this means that a large amount of the precious air compressed by the compressor cannot go to combustion — a trade-off that worsens thrust and fuel economy. In practice, designers usually aim for η ≈ 0.4–0.6 achieved with the minimum necessary air.
Finally, understand the simulator's limits. This tool is aone-dimensional, averaged evaluation using the thermal-resistance network method. A real blade has completely different heat loads at the leading edge, suction side and trailing edge, and the cooling effectiveness is locally high just downstream of each film hole. Even if the tool says "looks safe", the real design flow checks for hot spots and stress concentrations with detailed 3-D CFD and FEM structural analysis.
Set the "Combustion gas temperature Tg" (900–1700°C) and the "Cooling air temperature Tc" (300–700°C). The gas-side heat transfer coefficient is fixed at 1200 W/m²K, the wall thickness at 2 mm and the thermal conductivity at 14 W/mK
Set the strength of the internal cooling with "Coolant-side heat transfer h_c" (200–8000 W/m²K)
The "Film-cooling hole rows" (0–6) determine the film-cooling effectiveness η and lower the effective gas temperature T_g,eff
Set the "Allowable metal temperature T_limit" (800–1200°C) for the material; the difference from the metal temperature is shown as the margin to allowable, and the blade in the figure glows red when it is exceeded
Read the metal temperature Tm, film-cooling effectiveness η, overall cooling effectiveness Φ and the margin, and change the conditions to get a feel for the sensitivity of the cooling design
Worked Example
With the defaults (combustion gas temperature Tg = 1450°C, cooling air temperature Tc = 550°C, coolant side h_c = 2500 W/m²K, 3 film rows, allowable temperature 980°C): η = 0.72×(1 − e^(−1.26)) ≈ 0.52 and the effective gas temperature T_g,eff = 1450 − 0.52×900 ≈ 986°C. With the thermal resistances 1/1200 (gas side), 0.002/14 (wall) and 1/2500 (coolant side) in series, the heat flux is q ≈ 317 kW/m², the wall surfaces are at 722°C and 677°C, the (average) metal temperature Tm ≈ 699°C, the overall cooling effectiveness Φ = (1450 − 699)/900 ≈ 0.83 and the margin to the allowable temperature is 281°C. With 6 rows, η ≈ 0.66, Tm ≈ 654°C and Φ ≈ 0.88; with 0 rows it worsens to Tm ≈ 858°C, Φ ≈ 0.66 and a margin of 122°C.
Practical Notes
Relation between cooling-air pressure loss and flow: the more turbine stages there are, the higher the bleed pressure needed for the upstream stages and the lower the effective cooling performance in the downstream stages, so the trade-off must be evaluated stage by stage
Film-cooling holes are fine holes about 1 mm in diameter, and their shape, angle and manufacturing tolerances directly affect η. The rows–η relation in this tool is a guide; confirm the real η by tests or CFD
Thermal stress and fatigue life: the steeper the temperature gradient in the wall, the higher the thermal stress, and micro-cracks can grow with repeated start–stop cycles. This tool handles steady temperatures only, so verify transient temperature changes and thermal stress with separate thermal and structural analyses
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