Numerical Studies of Mixing in Pipes and Static Mixers

Sammanfattning: The objective of the present work was to investigate the mixing process in static mixers under laminar flow conditions, and in pipes during the displacement of dissimilar liquids. A numerical scheme and a method of characterizing static mixers were developed. The effects of changes in geometry, flow rate, viscosity ratio and volumetric flow rate ratio on the mixing process were investigated using computational fluid dynamics (CFD) and the methods developed. Eulerian and Lagrangian mixing analysis were used to evaluate the mixing process. A rate of striation thinning method was developed to characterize the static mixer. Using elliptic Fourier descriptors it was possible to determine the uncertainty in the particle tracking, and the number of particles and Fourier components needed to reproduce a desired level of detail. With the method developed the formation of vortices could be observed in the flow using the Z factor, the magnitude of helicity and the rate of striation thinning as measures. The Reynolds number at which vortices were observed depended on the length-to-diameter ratio of the mixer elements. The vortices increased the stretching of the striations, but some striations passed the mixer elements almost unaffected regardless of the flow rate. For the investigation of mixing of dissimilar liquids in a pipe a numerical scheme was developed and verified against experimental data for the velocity and concentration distribution during the displacement of yoghurt by water. The scheme reproduces the global velocity and concentration distribution of the two liquids flowing in different flow regimes. Using the scheme developed, the displacement process was found to be affected by the flow rate and the rheological properties of the yoghurt. When studying the mixing of two dissimilar liquids in a static mixer it was found that the viscosity ratio between the two liquids influences the mixing process: the greater the difference in viscosity, the lower the rate of striation thinning, i.e. the slower the mixing. This is due to a difference in elongation rate between the liquids, which exists until equilibrium in shear stress has been reached at the interface between the liquids.