Inverse design of multiholed internally cooled turbine blades

A methodology is described for the inverse design and/or analysis of coolant flow passage shapes in multiholed internally cooled turbine blades. The user of this technique may specify the temperature (or heat flux) distribution along the aerofoil outer surface. In addition, the temperature on the surface of each of interior coolant flow passages (holes) may be specified. The numerical solution of the outer hot gas flow field determines the remaining unspecified aerofoil outer surface quantity—surface heat flux if temperature was originally specified or vice versa. The position and shape of each turbine blade coolant hole is then found iteratively by solving the heat conduction problem within the solid portions of the blade. This solution procedure involves satisfying the dual Dirichlet and Neumann specified boundary conditions of temperature and heat flux on the outer boundary of the aerofoil. The inner hole geometry is then modified using an optimization procedure in such a way as to minimize the error in satisfying the specified Dirichlet temperature boundary condition on the surface of each of the evolving interior holes. Results are shown for single‐hole and double‐hole configurations that have analytic solutions and for a realistic turbine blade design problem.