An Approximate Solution for the Flow Between a Rotating and a Stationary Disk

The linear Ekman-layer equations are solved for the case of a rotor-stator system with a superimposed radial outflow of fluid. For laminar flow, the predicted rotational speed of the core between the boundary layers on the rotor and stator agrees well with existing experimental measurements when the superimposed flow rate is zero, but the theoretical solutions underestimate the core rotation when the flow rate is nonzero. For turbulent flow, the linear theory underestimates the core rotation under all conditions. Solutions of the turbulent momentum-integral equations for the rotor are used to provide an approximation for the core rotation that agrees reasonably well with the measured values over a range of flow rates and rotational speeds. Despite the fact that the equations take no account of the presence of the peripheral shroud, the approximate solutions for the moment coefficients are in reasonable agreement with the available experimental data. It is shown that the core rotation is suppressed and the moment coefficient equals that of a free disk when the superimposed flow rate equals the free-disk entrainment rate.