Multipoint inverse design of an infinite cascade of airfoils

This paper describes a method for the design of an infinite cascade in incompressible flow. The method is based on conformal mapping and does allow for multipoint design. The cascade blade to be determined is divided into a desired number of segments. Over each segment, the velocity distribution is prescribed together with an inlet or outlet flow angle at which this velocity distribution is to be achieved. In this way multipoint design requirements can be met. It is necessary to satisfy several conditions that arise to guarantee compatibility with the inlet and outlet flow as well as closure of the cascade blade. Satisfaction of these conditions does not necessarily result in a cascade with all of the desired characteristics. For example, the cascade blades may be bulbous or crossed. Through Newton iteration, however, the desired characteristics may be prescribed directly. Four examples will be illustrated to demonstrate the capability of the method.