A novel scalar tracking method for optimising film cooling systems

The purpose of this paper is to outline a novel passive-scalar tracking method for computational fluid dynamics optimisation studies. An example of its utility is in isolating the contributions of individual film cooling holes to overall cooling effectiveness on a heavily film cooled component. To isolate individual cooling contributions, passive (not a physical property of the flow, and therefore non-interacting) scalar variables are associated with the flow at each cooling hole outlet, with the scalar variable diffusivity set equal to the effective turbulent thermal diffusivity to replicate the mixing behaviour of the thermal field. The scalar tracking method is demonstrated by application to the optimisation of a nozzle guide vane endwall film cooling system, allowing a highly optimised system to be designed in three to five computational fluid dynamics simulations, orders of magnitude faster than optimisations performed using automated design space exploration. The test case for the method is an improved design of platform cooling system in which a relatively small quantity of high-momentum coolant is injected upstream of the vanes to reduce the total pressure deficit in near-wall region, followed by additional film cooling in low Mach number regions deeper into the passage. The optimised design uses half the coolant mass flow of a baseline design, while maintaining similar cooling effectiveness levels in critical regions.