A SIMPLE METHOD FOR ESTIMATING VELOCITY DISTRIBUTIONS IN SWIRLING FLOWS

We describe the important structural features of swirling recirculatin g 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 mo mentum-integral technique. In particular, we derive a single integro-d ifferential equation, valid for any shape of container, which predicts the distribution of swirl, secondary recirculation, and wall shear st ress. 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 comple ments numerical solution methods. For simple geometries all the import ant information can, in principle, be derived using the momentum-integ ral approach, and this is particularly useful for establishing the sca ling laws. In more complex geometries a numerical approach may be more appropriate. However, even in such cases, the scaling laws derived us ing the momentum-integral analysis are still useful as they allow extr apolation of a single computation to a wide range of high Reynolds num ber flows.