Scalable Heat Transfer Characterization on Film Cooled Geometries Based on Discrete Green’s Functions

Abstract

The aerothermal characterization of film-cooled geometries is traditionally performed at reduced temperature conditions, which then requires a debatable procedure to scale the convective heat transfer performance to engine conditions. This paper describes an alternative engine-scalable approach, based on Discrete Green’s Functions (DGF) to evaluate the convective heat flux along film-cooled geometries. The DGF method relies on the determination of a sensitivity matrix that accounts for the convective heat transfer propagation across the different elements in the domain. To characterize a given test article, the surface is discretized in multiple elements that are independently exposed to perturbations in heat flux to retrieve the sensitivity of adjacent elements, exploiting the linearized superposition. The local heat transfer augmentation on each segment of the domain is normalized by the exposed thermal conditions and the given heat input. The resulting DGF matrix becomes independent from the thermal boundary conditions, and the heat flux measurements can be scaled to any conditions given that Reynolds number, Mach number, and temperature ratios are maintained. The procedure is applied to two different geometries, a cantilever flat plate and a film-cooled flat plate with a 30 degree 0.125 in. cylindrical injection orifice with length-to-diameter ratio of 6. First, a numerical procedure is applied based on conjugate 3D unsteady Reynolds-averaged Navier–Stokes (URANS) simulations to assess the applicability and accuracy of this approach. Finally, experiments performed on a flat plate geometry are described to validate the method and its applicability. Wall-mounted thermocouples are used to monitor the surface temperature evolution, while a 10 kHz burst-mode laser is used to generate heat flux addition on each of the discretized elements of the DGF sensitivity matrix.