A Simple Method for Estimating Velocity Distributions in Swirling Flows

Abstract

We describe the important structural features of swirling recirculating flows induced by a rotating boundary. A knowledge of this structure has allowed us to match the core flow to the boundary layer using a momentum-integral technique. In particular, we derive a single integral-differential equation, valid for any shape of container, which predicts the distribution of swirl, secondary recirculation, and wall shear stress. This momentum-integral approach has been applied to three cases: flow between parallel disks; flow in a cone; and flow in a hemisphere. The results compare favorably with published experimental data, and with computed numerical results. Our momentum-integral approach complements numerical solution methods. For simple geometries all the important information can, in principle, be derived using the momentum-integral approach, and this is particularly useful for establishing the scaling laws. In more complex geometries a numerical approach may be more appropriate. However, even in such cases, the scaling laws derived using the momentum-integral analysis are still useful as they allow extrapolation of a single computation to a wide range of high Reynolds number flows.