A Three-Dimensional Viscous Transonic Inverse Design Method

The development and application of a three-dimensional inverse methodology is presented for the design of turbomachinery blades. The method is based on the mass-averaged swirl, rV~θ distribution and computes the necessary blade changes directly from the discrepancies between the target and initial distributions. The flow solution and blade modification converge simultaneously giving the final blade geometry and the corresponding steady state flow solution. The flow analysis is performed using a cell-vertex finite volume time-marching algorithm employing the multistage Runge-Kutta integrator in conjunction with accelerating techniques (local time stepping and grid sequencing). To account for viscous effects, dissipative forces are included in the Euler solver using the log-law and mixing length models. The design method can be used with any existing solver solving the same flow equations without any modifications to the blade surface wall boundary condition. Validation of the method has been carried out using a transonic annular turbine nozzle and NASA rotor 67. Finally, the method is demonstrated on the re-design of the blades.