Film Cooling

Cooling air is ejected from inside the turbine blade onto the blade surface, forming a low-temperature "film" between it and the high-temperature main gas flow. This film acts as an insulating layer, reducing the heat flux to the blade surface. It's an essential technology in modern gas turbines where inlet temperatures exceed 1500°C.

The adiabatic film cooling effectiveness $\eta$ is the fundamental index.

Here $T_{\infty}$ is the mainstream temperature, $T_{aw}$ is the adiabatic wall temperature, and $T_c$ is the cooling air temperature. $\eta = 1$ means the wall is at the cooling air temperature, and $\eta = 0$ means no cooling effect.

It's not that simple. The blowing ratio $M$ is an important parameter.

If $M$ is too small, the cooling air gets swallowed by the mainstream and the effect is weak. If $M$ is too large, the cooling jet lifts off from the wall, actually reducing cooling efficiency. For circular holes, the optimal range is said to be around $M \approx 0.5$ to $1.0$.

Of course. Shaped holes (fan-shaped, laidback holes) have an expanded exit, which reduces the momentum of the cooling air, making lift-off less likely. Data shows that for the same $M$, $\eta$ can improve by 30-50% compared to circular holes. Engine manufacturers like GE and Rolls-Royce have even patented their own hole shapes.

RANS is the mainstream approach but has limitations. The standard k-ε model tends to overestimate lateral diffusion of the cooling jet, often overpredicting $\eta$. Realizable k-ε or SST k-ω models are recommended, but even they struggle to accurately capture jet reattachment after lift-off.

LES can physically and correctly reproduce the mixing of the cooling jet and mainstream, so the $\eta$ distribution is closer to experiments than RANS. However, computational cost becomes 100 to 1000 times that of RANS. In practice, a realistic approach is to use RANS in the design stage and LES for final verification. Recently, Hybrid RANS/LES (DES or SBES models) are used as a compromise.

Use the cooling hole diameter $D$ as a reference. Aim for at least 20 divisions around the hole circumference and about 20 divisions along the hole's internal length. The first wall layer should target $y^+ < 1$. Ideally, maintain a mesh density of $\Delta x / D \approx 0.1$ downstream of the hole exit for at least $x/D = 30$.

Exactly. In practice, there are three approaches. (1) Mesh only representative holes in detail and simulate others with mass flow boundary conditions. (2) Use a source term model to introduce cooling effects without individually meshing holes. (3) Use dedicated features like the Film Cooling Model in Ansys Fluent. STAR-CCM+ also has a Cooling Film function.

OpenFOAM doesn't have a standard dedicated film cooling function, but you can use codedFixedValue to prescribe velocity/temperature profiles at hole exits. Another method is to connect a separate region with fine mesh only around the holes using AMI (Arbitrary Mesh Interface).

Classics include Goldstein et al.'s single circular hole film cooling experiment (1968) and, more recently, shaped hole experimental data from the University of Michigan and Ohio State University. The standard validation procedure is to compare with 2D $\eta$ distributions obtained using temperature-sensitive paint (PSP/TSP) or IR thermography.

For RANS, $\eta$ on the centerline within 20% of experimental values, and laterally averaged $\eta$ within 15%, is often considered "reasonable." For LES, aim for within 10%. However, discrepancies tend to be larger in lift-off regions and at jet edges.

Let's organize the main parameters and their effects.