Modeling effusion cooling and conjugate heat transfer using local source method

Aerodynamic cooling of hot components/surfaces such as those encountered in gas turbine engines is needed to avoid premature failure of parts due to thermo-mechanical stresses. An effective way of achieving this cooling is through the exchange of heat via effusion/film cooling holes on the hot surfaces. The gases absorb heat as they flow through the cooling holes and also by forming a protective layer of relatively cool gases near the hot surface. Modeling these processes allow for durable design of components and computational simulations offer a complementary way to design new parts or enable performance assessment of the existing parts at new operating conditions. However, in order to perform numerical simulations of heat transfer through effusion holes, the heat conduction through the solid liner and the convection from the gas phase must be coupled considering all the relevant length and time scales. The time scale separation between the solid and the gas phase makes this prohibitively expensive for large scale computations. In applications involving hundreds of effusion holes, resolving the geometry of each effusion hole along with the primary flow (with typically larger length scales) is very challenging. In the current work, we overcome the difficulties associated with the resolution of cooling holes by employing a local source method (Andreini et al, J. Eng. Gas Turb. Power, 2014) to model the heat transfer to the walls. This method is assessed in a canonical configuration based on experiments performed by Gustafsson (Gustaffson, Ph.D. Thesis, 2001). Large Eddy Simulations (LES) coupled with conjugate heat transfer (CHT) models are used in this study. Simulations that resolve the flow passages explicitly using mesh both in the fluid and the solid domains, were used to validate the fidelity of grid resolution, turbulence models and other simulation parameters in predicting velocity fields and wall temperature data. Although, resolving all the effusions passages provides the most accurate results, it is not practical in real applications. Hence, a local source model is employed to model the heat transfer that happens in the cooling-hole passages. In this method, the effusion passage is not resolved (using a mesh) and the mass transfer across the cooling hole passage is prescribed as an injection-extraction boundary condition. The heat transfer at the fluid-solid interface of the cooling-hole passage is also modeled based on Nusselt number correlations available in the literature. This modeling procedure enables simulations with flexible mesh topologies that can be generated at a relatively low cost in comparison to the fully resolved mesh configurations. The local source method is assessed and validated using the available experimental data. The results show that the meshes which resolve the penetration depth in the solid and which conform at the solid-gas interface provide better prediction of the wall temperatures.