The effect of radial impeller geometry on the link between power and flow numbers

Abstract

Impellers in stirred vessels are often characterized by dimensionless numbers such as the power and flow numbers. These are often crucial in determining mixing performance. Previous studies for high‐shear mixers have yielded correlations between the power, flow, and mixer geometries, since in these mixers the flow can be independently varied. For stirred vessels, dimensional analysis is typically used to develop such correlations, leading to less accurate predictive models. Here, we combine an analysis based on a balance of angular momentum balance with computational fluid dynamics simulations to comprehensively study the effect of impeller geometry on the relationship between power and flow. The results allow for the prediction of the flow generated by the impeller based on the easily measurable impeller power consumption and the geometrical dimensions of the impeller. The models are accurate over a wide range of geometries. Furthermore, we are able to predict both the primary and total flows.

The effect of axial impeller geometry on the link between power and flow numbers

“…This trend is almost identical to the trend observed for β ∂ΩQ in radial impellers. 39 Similarly to the observed results for radial impellers, there also appears to be no obvious effect of the impeller diameter on β ∂Ω2 for axial impellers. β ∂Ω2 can therefore be modeled as a function of W=D using the following…”

“…In the study for radial impellers by John et al, 39 the radius of ∂Ω Q was set in all cases to be equal to D=2 ð Þþ0:003m. The height of ∂Ω Q was set to be practically identical to the width of the impeller blades so that Z ≈ W. For this study on down-pumping axial impellers, we investigate two different locations for the measurement surface ∂Ω Q .…”

“…However, since all Reynolds-averaged Navier-Stokes (RANS) turbulence models somewhat under-predict the turbulent kinetic energy dissipation rate, for reasons discussed in Pope, 43 this method often yields power consumptions that are slightly lower than those computed from the impeller torque, even for proper grid refinement and higher order numerical schemes. 46 Since the power consumption computed from the impeller torque has been validated previously for RANS turbulence models, 39,46 it was decided in this study to compute the impeller power consumption using the torque method.…”

“…Jakobsen 38 showed how an angular momentum balance can be used to relate the power consumption to the generated flow rate for radial impellers under certain ideal assumptions. John et al 39 expanded this angular momentum balance for radial impellers by decomposing the velocity according to the Reynolds decomposition, and showed that the angular momentum balance yields an equation…”

Study of hydrodynamics and flow characteristics in a twin‐blade planetary mixer with non‐Newtonian fluids

“…[38][39][40][41] Rudolph et al 42 employed CFD to simulate the flow field in a coaxial mixer and obtained a single master power curve. John et al 43 investigated the influence of the radial impeller geometry on the relationship of flow and power in stirred vessels, and their results allowed for predicting the primary and total flows generated by the impellers with a wide range of geometries. Jamshidzadeh et al 44 assessed the power consumption for gas dispersion in a coaxial mixer with carboxymethyl cellulose (CMC) solutions and successfully developed two novel correlations for power and Reynolds numbers.…”