Development of a three-dimensional turbulent duct flow analysis

A method for computing three-dimensional turbulent subsonic flow in curved ducts is described. An approximate set of governing equations is given for viscous flows which have a primary flow direction. The derivation is coordinate invariant, and the resulting equations are expressed in terms of tensors. General tube-like coordinates were developed for a general class of geometries applicable to many internal flow problems. The coordinates are then particularized to pipes having superelliptic cross sections whose shape can vary continuously between a circle and a near rectangle. The analysis is applied to a series of relevant aerodynamic problems including transition from nearly square to round pipes and flow through a pipe with an S-shaped bend.