Application of Internal Heat Transfer Inverse Problem Solution Method to Jet Array Impingement Cooling System

Abstract Detailed thermal performance estimation of real-hardware internally cooled gas-turbine components is challenging due to the lack of optical and instrumentation access to the internal surfaces. In scaled, laboratory conditions, such estimates can be obtained by solving an inverse heat conduction problem that links the desired internal heat load distribution to a set of measured external temperatures through the solution of a partial differential equation. If sufficiently reliable, the results provide cooling system designers with valuable insights into the effects of the combinations of different cooling techniques, of secondary flows, and of manufacturing methods. Without some form of regularization, however, such inverse problems are ill-posed in that the estimates are not uniquely defined by the temperature measurements and are highly sensitive to measurement noise. In this study, an adjoint-based deterministic optimization method is used to estimate high-dimensional internal heat transfer coefficient distributions produced by a jet-array impingement system with local extraction of post-impingement flow. A method for determining the optimum amount of regularization to apply is also adopted and validated using the experimental results. Tests were performed by applying the impingement system in steady conditions to a heated metal plate and measuring the temperature response on the opposite side with a scientific grade infra-red camera. The particular cooling system was chosen because it produces high spatial gradients of heat transfer coefficients which are difficult to reconstruct from the external temperature measurements due to the three-dimensional conduction effects through the wall of the plate. Variations of plate thickness and Reynolds number were used to test the robustness of the method, and the resulting estimates for all conditions were compared to corresponding reference results obtained in a previous, dedicated test campaign.