Development of a Reduced Order Model for Turbine Blade Cooling Design

Rotating detonation engines (RDEs) are expected to have higher specific work and efficiency, but the high-temperature transonic flow delivered by the combustor poses relevant design and technological difficulties. This work proposes a 1D model for turbine internal cooling design which can be used to explore multiple design options during the preliminary design of the cooling system. Being based on an energy balance applied to an infinitesimal control volume, the model is general and can be adapted to other applications. The model is applied to design a cooling system for a pre-existing stator blade geometry. Both the inputs and the outputs of the 1D simulation are in good agreement with the values found in the literature. Subsequently, 1D results are compared to a full conjugate heat transfer (CHT) simulation. The agreement on the internal heat transfer coefficient is excellent and is entirely within the uncertainty of the correlation. Despite some criticality in finding agreement with the thermal power distribution, the Mach number, the total pressure drop, and the coolant temperature increase in the cooling channels are accurately predicted by the 1D code, thus confirming its value as a preliminary design tool. To guarantee the integrity of the blade at the extremities, a cooling solution with coolant injection at the leading and trailing edge is studied. A finite element analysis of the cooled blade ensures the structural feasibility of the cooling system. The computational economy of the 1D code is then exploited to perform a global sensitivity analysis using a polynomial chaos expansion (PCE) surrogate model to compute Sobol' indices.