Numerical Simulation and Analysis of Power Consumption and Metzner-Otto Constant for Impeller of 6PBT

Majority of non-Newtonian fluids are pseudoplastic with shear-thinning property, which means that the viscosity will be different in different parts of the stirred tank. In such mixing process, it is difficult to predict accurately the power consumption and mean shear rate for designing novel impeller. Metzner-Otto method is a widely accepted method to solve these questions in mixing non-Newtonian fluids. As a result, Metzner-Otto constant will become a key factor to achieve an optimum way of economical mixing. In this paper, taking glycerine and xanthan gum solutions as research system, the power consumption, stirred by the impeller composed of perturbed six-bent-bladed turbine （6PBT） with differently geometrical characteristics in a cylindrical vessel, is studied by means of computational fluid dynamics （CFD）. The flow is modeled as laminar and a multiple reference frame （MRF） approach is used to solve the discretized equations of motion. In order to determine the capability of CFD to forecast the flow process, the torque test experiment is used to measure the glycerine solution power consumption. The theological properties of the xanthan gum solutions are determined by a Brookfleld rheometer. It is observed that the power consumption predicted by numerical simulation agrees well with those measured using torque experiment method in stirring glycerine solution, which validate the numerical model. Metzner-Otto constant is almost not correlated with the flow behavior index of pseudoplastic fluids. This paper establishes the complete correlations of power constant and Metzner-Otto constant with impeller geometrical characteristics through linear regression analysis, which provides the valuable instructions and references for accurately predicting the power consumption and mean shear rate of pseudoplastic fluids in laminar flow, comparatively.

Investigation of the Viscoelastic Effect on the Metzner and Otto Coefficient Through LDA Velocity Measurements

The Metzner and Otto correlation is the single practical method for incorporating non-Newtonian effects in the mixing process. In this article, the Metzner and Otto' s idea, the role of viscoelasticity on the Metzner and Otto coefficient, ks, effects of flow regime on ks and the determination of fc3 for Rushton turbine impeller have been studied using the direct method of the laser Doppler anemometry (LDA) velocity measurement for the case of viscoelastic liquids. The normalized mean tangential velocity profiles are independent of Rushton turbine impeller speeds. Contrary to literature findings, it is shown that the variation of local shear rate against the impeller speed is better correlated by the power equation, i.e. y= k'a Nb' , in the transition region, i. e. - 30 < Re <- 2000. Also, a correlation between improved coefficient, ks', and the elasticity number of viscoelastic liquids is given which is very helpful in designing of the mixing of both viscoelastic and inelastic non-Newtonian fluids through relating rheological properties to kinematical and dynamical parameters of the mixing process.