Inverse design of turbomachinery blades in rotational flow

This thesis describes the development of two inverse design methods, suitable for designing two- and fully three-dimensional turbomachinery blades. Integral to both methods is a finite volume, time-marching solver of the unsteady Euler equations. The solver was developed with an accurate shock capturing technique and improved with viscous modelling. Extensive verification of the flow solution was carried out on both subsonic and transonic test cases, which include the NASA-designed transonic fan, rotor 67. Good correlation was obtained between the computation and the experiment. The first design method developed is based on the mass-averaged swirl velocity distribution and computes the required blade shape directly from the discrepancies between the target and initial distributions. The method designs blades/blade sections with finite thickness and the only assumptions are those of the flow solver, which is used in its original form without modification. The method was validated and applied to the design of both two- and three-dimensional turbomachinery cascades in transonic flow, where it was demonstrated that the design parameter can be used to control the development of high speed flow and shock formation. The second method is based on the surface static pressure loading distribution. The basic concept of this method is to modify the original blade wall condition in the flow solver and impose the target specification explicitly on the surfaces of the blade or blade section, which are modelled as permeable. The permeable wall allows transpiring flow normal to the surfaces, which is used to update the blade shape. This method is also not restricted to blades with zero thickness and was validated and applied to the design of both two- and three-dimensional turbomachinery cascades in high transonic flow. The NASA Lewis rotor 67 was redesigned using this method, concentrating on eliminating undesirable flow characteristics, one of which was the strong shock formation at the tip of the blade. An overall qualitative improvement was observed in the new blade.