An inverse design method for viscous flow in turbomachinery blading using a wall virtual movement

Abstract

An inverse shape design method for turbomachinery blades based on a time-accurate solution of the viscous flow equations is presented. The design scheme is formulated such that either the blade pressure distributions on pressure and suction surfaces, or the blade pressure loading and its thickness distribution can be prescribed as design variables. The blade profile is modified using a virtual velocity distribution that would make the momentum flux on the blade surfaces equal to the design momentum flux. The flow is simulated by solving the Reynolds-averaged Navier–Stokes equations that are discretized using a cell vertex finite-volume method, where an arbitrary Lagrangian–Eulerian formulation is used to account for mesh movement. An algebraic Baldwin–Lomax model is used for turbulence closure. The inverse method is first validated for a transonic compressor cascade; it is then used to redesign a subsonic turbine and a transonic compressor. The results show that the design method is rather robust, flexible and useful in reshaping the blade geometry to achieve the prescribed design variables. They also indicate that by carefully tailoring the design target, significant improvement can be achieved in the blade aerodynamic performance.

Keywords:

• inverse method
• aerodynamic blade design
• viscous inverse design
• virtual wall movement
• arbitrary Lagrangian Eulerian formulation

Acknowledgements

The authors would like to thank Mr B. Roidl for his efforts in redesigning the midspan section of Rotor 67, under the guidance of the second author. The financial support of the National Sciences and Engineering Research Council (NSERC) of Canada, and the ENCS Faculty Support for Research Thesis at Concordia University, are gratefully acknowledged.