3D numerical simulation of the flow of viscous newtonian and shear thinning fluids in a twin sigma blade mixer

Abstract

ABSTRACT:The flow and mixing in a 3D geometrically accurate representation of a twin sigma blade mixer is simulated using the finite element method (FEM) combined with the mesh superimposition technique as implemented by Polyflow (Fluent, Inc.) to calculate the velocity, velocity gradients, shear rates, and mixing index. The mixing conditions and material models are based on those used in the laser-Doppler anemometry (LDA) experiments of Prakash and Kokini. The simulation results are analyzed to determine the effect of increasing shear thinning on the flow and mixing, and are also compared with the experimental results of Prakash and Kokini for the This is publication no. NJAES D10544-3-05 of the New Jersey Agricultural Experiment Station.

Mixing simulation of a viscous Newtonian liquid in a twin sigma blade mixer

“…Connelly and Kokini 15 used this technique in 2-D with Polyflow to demonstrate the effect of single paddle vs. co-rotating twin paddle mixing on the mixer effectiveness using a viscous Bird-Carreau dough model. They also showed how increasingly shear thinning behavior changes the flow and mixing patterns in a 3-D geometrically accurate representation of a fully filled twin sigma blade Farinograph mixer in two-blade configurations, 12 in a way that coincided with the LDA results of Prakash and Kokini. 6,7,8,9 A similar technique introduced by Bertrand and Tanguy 16,17 superimposes the moving-part geometry on the meshed flow domain using Lagrangian multipliers with a velocity constrain.…”

“…The positions are given in meters using an origin centered between the two blades' axes of rotation, which is 0.0818 m from the top on the back face with positive x pointing left toward the fast blade, positive z pointing down and positive y pointing toward the front of the mixer. B1 is centered between the front and back of the mixer and slightly higher than the horizontal plane through the center of both blades, in the area shown in the simulations in Connelly and Kokini 12 to have consistently high-shear rates and mixing index values, that will lead to highly effective distributive and dispersive mixing. The positions of clusters B2 and B3 are initially outside the interblade region, but near one of the blades.…”

“…The mesh superposition technique 12,13,24 was used to account for the movement of the sigma blades. The final bowl mesh was chosen after a preliminary study with the corn syrup fluid model at the initial blade position that examined the problem size, solution time and convergence for a series of bowl meshes containing from 13,872 to 62,034 elements.…”

“…The points are generally located in the areas between the wide central section of the blades, and the curved sections of the blades that sweep the front and back of the bowl, which is also about the location where the cluster B3 was initially located. When compared with the velocity vectors, mixing index and shear rates mapped in Connelly and Kokini, 12 it can be seen that these points are in areas that have been shown to have poorer mixing potential.…”

“…It mainly involves the mechanisms of laminar shear, elongational flow and distributive mixing in order to reduce the scale of segregation, while molecular diffusion (which occurs very slowly) and dispersion act to reduce the intensity of segregation. 1,23 Connelly and Kokini 12 use numerical simulation to analyze the flow and mixing at two positions in the twin sigma blade mixer for viscous Newtonian, power-law and cross-fluid models by calculating mappings of the velocity profiles, shear rate and dispersive mixing index. However, in order to get a complete picture of the distributive mixing ability in a mixer, it is necessary to get an indication if all the material in the mixer will be able to distribute throughout the flow area over time and also experience the levels of stretch required for good laminar mixing.…”