A method is described for the inverse design of complex coolant flow passage shapes in internally cooled turbine blades. This method is a refinement and extension of a method developed by the authors for designing a single coolant hole in turbine blades. The new method allows the turbine designer to specify the number of holes the turbine blade is to have. In addition, the turbine designer may specify that certain portions of the interior coolant flow passage geometry are to remain fixed (eg. struts, surface coolant ejection channels, etc.). Like the original design method, the designer must specify the outer blade surface temperature and heat flux distribution and the desired interior coolant flow passage surface temperature distributions. This solution procedure involves satisfying the dual Dirichlet and Neumann specified boundary conditions of temperature and heat flux on the outer boundary of the airfoil while iteratively modifying the shapes of the coolant flow passages using a least squares optimization procedure that minimizes the error in satisfying the specified Dirichlet temperature boundary condition on the surface of each of the evolving interior holes. Portions of the inner geometry that are specified to be fixed are not modified. A first order panel method is used to solve Laplace's equation for the steady heat conduction within the solid portions of the hollow blade, making the inverse design procedure very efficient and applicable to realistic geometries. Results are presented for a realistic turbine blade design problem.
