The Inverse Design of Internally Cooled Turbine Blades

A methodology is developed for the inverse design and/or analysis of interior coolant flow passage shapes in internally cooled configurations with particular applications to turbine cascade blade design. The user of this technique may specify the temperature (or heat flux) distribution along the blade outer fixed surface shape and the unknown interior coolant/blade interface. The numerical solution of the outer gas flow field determines the remaining unspecified blade outer surface quantity—surface heat flux if temperature was originally specified or vice versa. Along the unknown coolant flow passage shape the designer has the freedom to specify the desired temperature distribution. The hollow blade wall thickness distribution is then found from the solution of Laplace’s equation governing the temperature field within the solid portion of the hollow blade, while satisfying both boundary conditions of temperature and heat flux at the fixed outer blade surface, and the specified temperature boundary condition on the evolving inner surface. A first order panel method, coupled with Newton’s N-dimensional interation scheme, is used for the iterative solution of the unknown coolant/blade interface shape. Results are shown for a simple eccentrical bore pipe cross section and a realistic turbine blade cross section. The inverse design procedure is shown to be efficient and stable for all configurations that have been tested.