Solution of the inverse heat conduction problem described by the Poisson equation for a cooled gas-turbine blade

The presented paper describes a method of solving the inverse problems of heat conduction, consisting in solving the Poisson equation for a simply connected region instead of the Laplace equation for a multiply connected one, like a gas-turbine blade provided with cooling channels. The considered method consists in determining unknown values of the source (heat sink) power in the cooling channels for a given external heat transfer situation to achieve as close as possible an isothermal outer surface. Afterwards the temperature and heat flux distributions at the cooling channel walls are determined. Since the unknown source power is sought, the problem is an inverse one. Taking into account the sought values the method is reckoned among the class of the fictitious source methods and presents an optimization scheme. Using an exemplary gas turbine blade cooling configuration, the results of the calculation obtained with this method have been compared to the results achieved with an inverse method using the boundary element method for a multiple connected region.