Flow and Heat Transfer in a Smooth U-Duct with and without Rotation

This study shows that when computing a compressible flow in a rotating duct of a given geometry and radial distance from the axis of rotation, the inlet Mach number must be specified in addition to the inlet Reynolds number, inlet rotation number, coolant-to-wall temperature ratio, and Prandtl number. This is because the inlet Mach number and other dimensionless parameters collectively fix the rotational speed, which strongly influences centrifugal buoyancy. This study also shows the nature of the three-dimensional flow induced by Coriolis force, centrifugal buoyancy, and a 180-deg bend in a U-shaped square duct with smooth walls for three rotation numbers (0, 0.24, and 0.48), and two Reynolds numbers (2.5 x 104 and 5 X 104). Key flow mechanisms that affect heat transfer are identified. The computed heat transfer coefficient on the leading and trailing faces of the rotating duct compares well with available experimental data. This computational study is based on the ensemble-averaged conservation equations of mass, mo-mentum (compressible Navier- Stokes), and energy closed by a -o/shear stress transport model of tur-bulence that can be integrated to the wall; i.e., wall functions were not used. Solutions were generated by using a cell-centered finite volume method on a structured grid based on second-order accurate Roe differencing, and on a diagonalized alternating-direction implicit scheme with local time-stepping and V-cycle multigrid. Nomenclature Dh = hydraulic diameter of duct h = heat transfer coefficient, qwl(Tw — Tb) k = turbulent kinetic energy