Adjoint Method for Shape Optimization in Real Gas Flow Applications

Abstract

An adjointbased shape optimization approach for supersonic turbine cascades is proposed for application to organic Rankine cycle (ORC) turbines. The algorithm is based on an inviscid discrete adjoint method and encompasses a fast lookup table (LuT) approach to accurately deal with realgas flows. The turbine geometry is defined by adopting stateoftheart parameterization techniques (NURBS), enabling to handle both global and local control of the shape of interest. A preconditioned steepest descent method has been chosen as gradientbased optimization algorithm to efficiently search for the nearest minimum. The potential of the optimization approach is first verified by application on the redesign of an existing converging–diverging turbine nozzle operating in thermodynamic regions characterized by relevant realgas effects. A significant efficiency improvement and a more uniform flow at the blade outlet section are achieved, with expected beneficial effects on the aerodynamics of the downstream rotor. The optimized configuration is also assessed by means of highfidelity turbulent simulations, which point out the capability of the present inviscid approach in optimizing supersonic turbine cascades with very limited computational burdens. Finally, the newly developed realgas adjoint method is compared against adjoints based on ideal equations of state on the same design problem. Results show that the performance gain obtained by a fully realgas optimization strategy is by far higher than that achieved with simplified approaches in case of ORC turbines. This proves the relevance of including accurate thermodynamic models in all steps of ORC turbine design.