Aerodynamic design method of cascade profiles based on load and blade thickness distribution

A cascade profile design method was proposed using the aerodynamic load and blade thickness distribution as the design constraints, which were correspondent to the demands from the aerodynamic characteristics and the blade strength. These constraints, together with all the other boundary conditions , were involved in the stationary conditions of a variational principle , in which the angle-function was employed as the unknown function. The angle-function ( i. e. , the circumferential angular coordinate) was defined in the image plane composed of the stream function coordinate ( circumferential direction ) and streamline coordinate. The solution domain, i.e., the blade-to-blade passage, was transformed into a square in the image plane, while the blade contour was projected to a straight line ; thus, the difficulty of the unknown blade geometry was avoided. The finite element method was employed to establish the calculation code. Applications show that this method can satisfy the design requests on the blade profile from both aerodynamic and strength respects. In addition, quite different from the most inverse-problem approaches that often encounter difficulties in the convergence of iteration, the present method shows a stable and fast convergence tendency. This will be significant for engineering applications.