Presented in this paper are two case studies on the application of the adjoint method to turbine blading aerodynamic design optimization. One case involves the use of the adjoint method in a direct design, where the blade geometry is changed to reduce the entropy generation rate of a power turbine subject to mass flow rate and pressure ratio constraints. The other case investigates the use of the adjoint method in an inverse design, where the blade geometry is changed to approach a target static pressure loading on a blade surface, also subject to mass flow rate and pressure ratio constraints. Promising results are obtained for the two cases. Also examined in the two case studies is the application of the adjoint method to flow field with big separations, which can be detrimental to the convergence of an adjoint solution due to its linearity.
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