General three-dimensional viscous primary/secondary flow analysis

Generalized primary/secondary flow equations are derived as an approximation to the Navier-Stokes equations for three-dimensional viscous flows with a dominant flow direction. The primary/secondary flow equations are well posed for solution by spatial marching and can be solved one to two orders of magnitude faster than the Navier-Stokes equations. A key element in the approximations, which is a distinguishing feature of the present approach, is that accuracy is related to curvature terms obtained from a local primary flow direction rather than the coordinate system used to describe geometry of the flowfield. Potential flow streamlines for the flow geometry under consideration are a suitable choice for the primary flow direction. A sequentially decoupled implicit algorithm has been developed that exploits the form of the primary/secondary flow equations to obtain decoupled subsets of equations through choices for dependent variables, the sequence of equations, and the linearization scheme. Each of the equation subsets is solved by efficient and appropriate implicit numerical procedures. Computed solutions for flow in 90-deg bends agree very well with experimental data and Navier-Stokes solutions. The combined efficiency and accuracy of the approximate equations and solution algorithm make this approach attractive for problems in which a suitable primary flow direction can be identified.