Hybrid design methods of cascade profile based on variational principles

Abstract

PurposeProvides two hybrid methods for the aerodynamic design of cascade profiles, of which the design constraints are the combination of aerodynamic and geometric conditions.Design/methodology/approachIn the first method, the design constrain is composed of the velocity (or pressure) distribution on part of the blade surface and the geometry of the rest part. In the second method, the aerodynamic load distribution, i.e. the pressure difference between the suction and pressure surfaces, and the blade thickness distribution are employed as the design constrain. These constraints, together with all the other boundary conditions, are involved in the stationary conditions of a variational principle. The solution domain, i.e. the blade‐to‐blade passage, is transformed into a square in the image plane, while the blade contour is projected to a straight line; thus, the difficulty caused by the unknown geometry of profile is avoided. Finite element method is employed to produce the calculation code.FindingsApplications show the accuracy and the flexibility of the two methods, which can satisfy the different needs from blade design. Finally, the possibility of combining the hybrid methods with the through‐flow method is discussed, which would develop the present methods to three‐dimensional design of cascades.Research limitations/implicationsThe design methods are limited to frictionless flow.Practical implicationsA design software of cascade profiles based on this method has been developed, and will be provided to the engineering users for cascade design.Originality/valueThe hybrid methods developed in this paper can satisfy the demands from different aspects of engineering designs: aerodynamics, strength, manufacture, etc.