Effect of wall oscillation on dispersion in axi‐symmetric flows between two coaxial cylinders

Abstract

AbstractLongitudinal dispersion of solute released in an unsteady flow between two coaxial cylinders is studied by employing the method of moments. The flow unsteadiness is caused by the oscillation of the outer cylinder in its own plane around the inner. A finite difference implicit scheme is adopted to solve the Aris integral moment equations arising from the unsteady convective‐diffusion equation for all time period. The behaviour of dispersion coefficient due to periodic flow with the variation of radius ratio, absorption parameter and frequency parameter has been examined. Assuming that the distribution of concentration is initially uniform over the cross‐section of the annulus, it is shown that, like the case of oscillatory flow caused by periodic pressure gradient, dispersion coefficient can be diminished by increasing absorption at the boundary. The radius ratio of the annular tube is found to have variable effect on the dispersion coefficient depending on the position (inner or outer) of the oscillatory tube. The axial distributions of mean concentration are approximated using Hermite polynomial representation from the first four central moments for a range of different radius ratios, absorption parameters, and frequencies of the wall oscillation. It has been found that the peak of the concentration distribution increases with increase in frequency parameter and radius ratio but opposite trend follows for the absorption parameter.