Velocity distributions in a stirred tank containing a yield stress fluid

Abstract

The radial distribution of tangential velocity around an impeller has been estimated using laminar flow around a rotating cylinder as a model. A yield stress model for the fluid rheology gave a boundary at which the fluid velocity fell to zero (cavern boundary) which moved outwards with increasing impeller tip speed. A power-law model for the fluid suggested that the fluid velocity only fell to zero at the outer wall of the vessel and the cavern boundary was taken to occur when the tangential velocity fell to 1% of the impeller tip speed. Increasing the impeller speed did not affect the cavern size for a power-law fluid. Laser-Doppler measurements of the velocity distribution in a 0.17% carbopol solution around a Rushton turbine and a pitched-blade impeller of identical diameter showed that the flow patterns were similar. Both impellers generated a largely tangential flow, with small radial-axial circulation loops above and below the blades. The absolute velocities around the Rushton turbine were greater than those around the pitched-blade impeller by a factor of approximately two. This difference had little effect on the cavern size as measured and as predicted. The measured distribution of tangential velocities on the centreline of each impeller was well predicted by the yield stress model, although a correction was required for the pitched-blade turbine to allow for the lower fluid velocity at the blade tip radius. The power-law model, with a similar correction, also predicted the measured velocity distribution for either impeller. The values of v rms obtained from non-shaft-encoded laser-Doppler measurements showed significant fluctuations in the measured velocity. By making shaft-encoded measurements and using these to estimate the periodic contribution to v rms, it was found that the fluctuations were almost entirely due to the periodic nature of the flow imposed by the blades of the impeller. There was no significant random fluctuations, confirming that the fluid was in laminar flow inside the cavern.