THREE-DIMENSIONAL TURBULENT COMPRESSIBLE SUBSONIC DUCT FLOW ANALYSIS FOR USE WITH CONSTRUCTED COORDINATE SYSTEMS.

An approximate analysis is presented for computation of three-dimensional subsonic flow in straight and curved diffusers. The development parallels that of Briley and McDonald for forward-marching solution of viscous primary and secondary flows, but differs in the coordinate formulation used and in details of the approximations. The present formulation is intended to facilitate the use of constructed coordinates in circumstances where it is difficult to maintain smooth behavior in higher derivatives. This analysis is applicable to nonorthogonal coordinate systems having a curved centerline and planar transverse coordinate surfaces normal to the centerline. The primary flow direction is taken to coincide with the local direction of the duct centerline and is hence normal to transverse coordinate planes. The formulation utilizes vector components (velocity, vorticity, transport equations) defined in terms of local Cartesian directions aligned with the centerline tangent, although the governing equations themselves are expressed in general nonorthogonal coordinates. For curved centerlines, these vector quantities are redefined in new local Cartesian directions at each streamwise location. The use of local Cartesian variables and fluxes leads to governing equations which require only first derivatives of the coordinate transformation, and this provides for the afore-mentioned ease in using constructed coordinates.