Large Eddy Simulation of Leading Edge Film Cooling: Part I — Computational Domain and Effect of Coolant Pipe Inlet Condition

A numerical investigation is conducted to study compound angle leading edge film cooling with Large Eddy Simulation. The leading edge has two rows of coolant holes located at ±15° of the stagnation line. Coolant jets are injected into the flow field at 30° (span-wise) and 90° (stream-wise). Mainstream Reynolds number is 100,000 based on the free stream velocity and cylinder diameter. Jet to mainstream velocity and density ratios are 0.4 and 1.0, respectively. It is found that during startup the stagnation line at the leading edge is not stationary but moves on a timescale much larger than the characteristic turbulent scales generated by the jet-mainstream interaction. To alleviate the long time integration necessitated by this feature, only half the domain is calculated (fixed stagnation) by showing that there is very little correlation in the flow structures generated by the jet-mainstream interaction on either side of stagnation. A comparison is made between a laminar uniform profile at the coolant pipe inlet with a time-dependent turbulent profile extracted from an auxiliary turbulent pipe flow calculation. The former over-predicts the span-wise averaged effectiveness, while the latter promotes better mixing in the outer region of jet-mainstream interaction and lowers the adiabatic effectiveness showing good agreement with measurements. In both cases, a characteristic low frequency interaction between the jet and the mainstream is identified at a non-dimensional frequency between 0.79 and 0.95 based on jet diameter and velocity. Even in the absence of any free-stream and jet turbulence, a turbulent boundary layer is established within a diameter downstream of the jet due to the strong lateral entrainment downstream of injection. The entrainment is primarily driven by an asymmetric counterrotating vortex pair in the immediate wake of the coolant jet. The driving mechanism for the formation of these vortices is a low pressure zone in the wake which entrains mainstream flow laterally into this region.