Optimal geometric representation of turbomachinery cascades using nurbs

Simulation-based shape optimization is getting a lot of attention at present. The geometric representation of the shape plays an important role in the optimization process; it affects the number of design variables as well as the smoothness of the final profile. This work is on finding an optimum representation of gas turbine blade profiles in two-dimensions using nonuniform rational B-splines (NURBS). This parameterization involves the solution of an inverse problem for the control points and weights, where the error in the representation is minimized using Simulated Annealing (SA), the latter gives the control points and weights that would approximate a given blade shape with minimum error, yet without loosing its smoothness. The optimum parameterization involves the minimum number of control points, their position and weight for a given error tolerance, and is identified for generic as well as real compressor and turbine blade cascades. The effect of this parameterization on the blades' aerodynamic performance is then discussed.