Fluid and suspension hydrodynamics in the impeller discharge flow of stirred tanks

Abstract: The hydrodynamics of an agitated tank have been studied byphase-Doppler anemometry. The focus is on the impeller anddischarge region of a 45o pitched blade turbine (PBT). Thestudy includes agitation of pure water as well as of a dilutesuspension of process particles. A three-dimensionalphase-Doppler anemometer is used to measure local,instantaneous, three-dimensional velocities of the fluid and ofthe suspended particles. A shaft encoding technique is used toresolve the turbulent fluctuations from the periodic velocityfluctuation due to the impeller blades, and to provide moredetailed information about the variations relative to theimpeller blade. Velocity bias is corrected for by the total3-dimensional velocity.The mean flow field, the fluctuating velocities, and thecomplete Reynolds stress tensor, are reported for the liquidphase flow. The periodic fluctuations in the flow that aregenerated by the impeller blades are eliminated in theexamination of the turbulence. The anisotropy of the turbulenceis assessed by the invariants of the anisotropy tensor. Thetrailing vortex structure is demonstrated to be associated withhigh kinetic energy and strong anisotropy of the turbulence.The vortex is still observable 130-140 degrees behind theblade. It gradually moves down from the impeller blade but thelocation in radial direction remains essentially unchanged. Theinfluence of the periodic fluctuations is examined and it isshown that the turbulence appears more isotropic when theperiodic fluctuations are not eliminated.The solid particle concentration is low below the impellerand is high above the impeller tip. The particles diverge fromthe liquid flow mean direction, especially below the agitatorclose to the tip where the strongest turbulence is found.Periodic fluctuations in the particle concentration relate tothe variations found in the angle-resolved mean velocity andfluctuating velocity. The ratio of the maximum to the minimumconcentration is about 2.0 in the present study.The baffles influence on the conditions in the impellerregion, and this influence can be observed on the fluid meanvelocity field, the angle-resolved velocities, the kineticenergy, and on the behavior of larger process particles. In theimpeller region the highest kinetic energies are about 15%higher upstream of the baffle than at the middle plane betweenthe baffles. The highest energy level in the middle plane isactually the lowest value and is therefore not representativewhen rotation symmetry is assumed.Local energy dissipation rates have been investigated, andthe integration of the local energy dissipation rates overdifferent control volumes has been compared with macroscopicenergy balance calculations. The discrepancy is significant.Different reasons have been analyzed and recommendations forfurther investigation are given. In the outflow region there is a significant variation alsoin the direction of the instantaneous velocity, which may leadto direction bias in the case of non-spherical measurementvolume. In order to account for this direction bias, amathematical model is developed to estimate the projected areaof the measurement volume in LDA or PDA. It is shown that theprojected area variation can lead to a significant directionbias in determination of time averaged values and localparticle concentration in a highly turbulent stirred tank flow.This bias is however negligible for an orthogonal optical setup, as is used in the present study.Keywords:Hydrodynamics, phase-Doppler anemometer,suspension, pitched-blade turbine, anisotropy, turbulence,Reynolds stresses, trailing vortex, kinetic energy, stirredtank