Optimizing thermal performance of pin-fin arrays using Bayesian methods for turbine cooling

Pin-fin arrays are crucial in the cooling of aerospace components. Specifically, pin-fins find extensive usage in the trailing edge of turbine blades, primarily due to the harsh operating conditions these blades experience. With the development of additive manufacturing, complex internal geometries that were previously too expensive to manufacture are now feasible. This advancement has created a new pin-fin design space to be explored. In this paper, Bayesian optimization (BO) is conducted to find the pin-fin array that optimizes the trade-off between heat transfer and pressure drop in a two-dimensional channel. The complexity of the pin-fin geometry varies, and is controlled by the number of connecting piece-wise cubic splines used to close the shape. Different designs are obtained using 3-, 4-, 5-, and 6-splines in a staggered pin-fin array orientation. The optimization objectives included the minimization of pressure drop, the maximization of heat transfer, and the maximization of efficiency. It is found that the pin-fins which utilize 4-splines outperform all others due to their symmetric characteristics. The performances of the pin-fin array plateaus after increasing the complexity beyond 5-splines. It is concluded that the optimization objective significantly influences the final shape characteristics and behavior. As expected, the pressure drop minimization finds aerodynamic shapes while heat transfer maximization increases the total surface area in the channel. The maximization of efficiency results in a balance of aerodynamic shapes and total surface area.