Abstract

An aerodynamic inverse shape design of turbomachinery blading in three-dimensional viscous flow is developed and implemented into a commercial CFD program, namely ANSYS-CFX.
The design method is based on specifying one blade parameter, the stacking condition that is a line from hub to tip, and two other flow parameters these can be a- a target pressure distribution over the blade suction surface (or a target pressure loading) and a blade thickness distribution, b- or target pressure distributions on pressure and suction surfaces. This inverse design approach is fully consistent with the viscous flow assumption and is independent of the CFD approach taken.
The blade walls are assumed to be moving with a virtual velocity that would asymptotically drive the blade to the shape that would correspond to the specified target pressure distribution. This virtual velocity distribution is computed from the difference between the computed and the target pressure distributions. The wall displacement is computed in a Junction Box Routine and communicated to ANSYS-CFX using CFX Expression Language and User Defined Functions at each design step.
In ANSYS-CFX, an element based finite volume formulation is used for space discretization. The Arbitrary Lagrangian-Eulerian formulation of the unsteady Reynolds-Averaged Navier Stokes (URANS) equations is solved in a time accurate fashion with the blade motion being the source of unsteadiness. At each time step, the blade shape is modified and dynamic meshing is used to remesh the fluid flow domain.
The implementation is first validated on a transonic rotor blade; the capability, robustness and accuracy of the method in satisfying the design target are then assessed on a single subsonic stator blade row, the rotor blade of an axial compressor stage and, the rotor and stator blades of an axial turbine stage where different choices of the design variables are used. The method is finally implemented to the redesign of a transonic compressor stage, a subsonic axial compressor stage and a turbine stage so as to improve their aerodynamic performance.