A 3-D Inverse Methodology Applied to the Design of Axisymmetric Ducts Free

An inverse inviscid potential fully 3-D methodology is introduced. The method is based on a potential function/stream function formulation where the physical space is mapped onto a computational one via a body-fitted coordinate transformation. Potential function and two orthogonal stream functions (vectors) are used as independent variables, whilst the velocity magnitude, the aspect ratio of the elementary streamtubes cross-section and density are the dependent ones. Differential geometry and generalized tensor analysis arguments are employed both to formulate the method and derive the governing differential equations. A reduced version of the general 3-D methodology is applied to the design of axisymmetric ducts. The main advantage of the proposed approach is that the flow and geometry solutions are entirely decoupled. The geometry is computed independently after the flow field has been determined. Results are compared to analytical and numerical solutions of a direct method.