Computational method for the design of ducts

This paper describes an inverse method that applies to two-dimensional, irrotational and incompressible flow, based on a transformation of variables from the physical plane defined by (x, y), to a computational plane defined by the stream function ψ, and the velocity potential, ?. In this new plane, the resulting differential equation describing the flow is relatively simple, and should be solved in a domain that presents always a rectangular shape, facilitating the generation of a numerical grid appropriate to the problem. The solution of this equation gives the distribution of the x coordinate throughout the flow field, while the values of the y coordinate are calculated by integration of the previous result. Some of the numerical details of the procedure will be discussed, with special emphasis on the numerical treatment of the boundary conditions. The application of the described method to the design of a curved duct with an overall deflection of around 90° will be presented, with the aim of showing the potentialities of the method, which is computationally quite simple.