Finite‐element simulation of mixing: 1. Two‐dimensional flow in periodic geometry

The influence of cam geometry and operating conditions on chaotic mixing of viscous fluids in a twin cam mixer

“…The predictions were validated against published experimental 4 and numerical simulations. 3,4 The two impellers of the Twin Cam mixer are each in a separate, but connected, cylindrical barrel. These are shown diagrammatically in Figure 2.…”

“…An experimental and computational study of a Twin Cam mixer using equilateral triangular cams was performed by Avalosse and Crochet. 4 Bertand et al 3 also simulated an identical Twin Cam mixer using a finite element simulation combined with a Lagrange multiplier based fictitious domain method to model the moving cam geometry. Both of these studies looked at a single cam geometry and operating conditions (co-rotating cams with equal angular velocity) whereas this study aims to explore the mixing under a variety of cam geometries and operating conditions.…”

“…For time varying flow fields such as the Twin Cam mixer, this also eliminates the need to store large amounts of time-resolved velocity data. The SPH approach for modeling this system has been validated against finite element solutions 3,4 in the earlier article. 2 Flows that exhibit chaotic trajectories can be divided into regions that exhibit different mixing characteristics.…”

“…In particular, it is comparable to a 2D cross-section of the popular Twin Screw Extruder. As the flow within this 3D mixer is predominantly cross-wise, 3 the use of a 2D model is a useful approximation to the 3D case. However, the aim of the article is not to optimize this specific 2D mixer, but to establish a base of understanding to support the use of this methodology for more complex 3D flows.…”

Mixing of viscous immiscible liquids. Part 1: Computational models for strong–weak and continuous flow systems

“…The shear rate and residence time in the weak zone are estimated aṡ weak = 2 R ; weak = V weak q ; (6.4,6.5) where R is the average radial distance from the center to the edge of the rotor, is the average gap between the wall and the rotor, is the rotation rate of the rotor, q is the ow rate through the strong zone, and V weak is the where R is the distance from the center to the tip of the rotor, is the gap between the rotor tip and wall, and V strong is the volume of the strong zone. The stretching rate in the strong zone is based on stretching calculations of Avalosse and Crochet (1997). They analyzed mixing in three 2D mixers: "three di erent systems-" single cam, corotating twin cam, and counter rotating twin cam.…”