A Novel 3D inverse method for the design of turbomachinery blades in rotational viscous flow: theory and applications

The development and application of a three-dimensional (3D) inverse methodology is presented for the design of turbomachinery blades. The design method is based on the specification of the blade loading distribution and the corresponding blade shape is systematically sought using directly the difference between the target and initial values. The design procedure comprises mainly of a CFD solver code and the blade-update algorithm to calculate the desired blade geometry as well as the corresponding 3D flow. The CFD code is a well-validated three-dimensional flow solver and has shock capturing ability to cope in both subsonic and high transonic-shocked, viscous flow. Fundamentally, it is a cell-vertex, finite volume, time-marching solver employing the multistage Runge-Kutta integrator in conjunction with accelerating techniques (local time stepping and grid sequencing). To account for viscosity, viscous forces are included in the solution using the log-law and mixing length models. The effects of rotating blades as well as tip clearance flow are also included in the flow prediction. The capabilities of the present method are demonstrated in the redesign of a transonic fan blade, the NASA Rotor 67. The redesign focuses on the shocked flow near the tip, where the effects of shock-boundary interaction and leakage flow are examined. The result shows conclusively that the shock-formation and its intensity in such a high-speed turbomachinery flow are well defined on the loading distributions. Simple guidelines to change the loading distribution can be followed using the proposed inverse methodology to improve the blade shape.