A computational study of laminar and turbulent flows in rotating rectangular ducts

Rotating flow problems have long been of interest in fluid mechanics because they have a wide range of applications in engineering practice. The flow of fluid in the radial passageways of radial pumps or centrifugal compressors and the flow through the cooling passages of turbine blades are some of the examples of the rotating flow problems. Better understanding of the effect of the rotation on the flows mentioned above will help engineers to design more efficient rotary machines such as turbines and compressors.

This work is concerned with fully developed incompressible laminar and turbulent flows through rectangular straight ducts rotating in an orthogonal mode. The Navier-Stokes equations are solved by the finite-volume method for low to high rotation rates. The finite-volume equations are formulated in strong conservative form on a general, nonorthogonal grid system. The resulting equations are solved by an implicit, time marching, pressure correction based algorithm. Solutions are obtained for aspect ratios 1, 2, and 3. For laminar flow, predictions have been performed for Reynolds number of 2000 and for turbulent flow the computations were carried out for a Reynolds number of 20000. Values of the Rossby number ranged from 0.1 to 3500 for laminar flow and from 0.3 to 140 for turbulent flow. The standard k-e model is used to model the turbulence.

Low rotational speeds cause the formation of a pair of symmetric vortices on the cross-section. At higher rotational speeds, a more complex four-vortex structure develops. The transition point depends on the cross-sectional geometry. Moreover, over a range of Rossby number, either two- or four-vortex solutions are possible. The rotation leads to significant differences between the values of friction factor and Nusselt number on the suction and pressure sides of the duct. Some comparisons with available experimental and theoretical results were made.