Numerical investigation of the mixing of highly viscous liquids with Cowles impellers

This work is aimed at investigating the mixing process of highly viscous paints, used to colour leathers in the tanning industry, through Computational Fluid Dynamics (CFD). In particular, a mixing tank is fed with a master liquid and different liquid pigments and then stirred by Cowles impellers in order to obtain a paint of a uniform colour. The typical dynamic viscosity of the liquids in this process is μ ~ O(0.1-10) Pa·s, while the Cowles rotational speed is usually very high, i.e. 3000-5000 rpm. The numerical model is based on the solution of the unsteady Reynolds-Averaged Navier–Stokes (RANS) equations for continuity, momentum and species mass fractions, the latter being used to describe the different components. The impeller motion is modelled through the Sliding Deforming Mesh (SDM) approach, using rotating (unstructured) meshes in the impeller region and a static (structured) mesh in the remainder of the tank. The master liquid and coloured pigments are assumed to stratify within the tank at initial time and the steady rotational speed is then imposed abruptly to the impellers. The level of homogeneity in the stirred tank is evaluated through the analysis of component concentration fields over time. In particular, such local concentrations can be used to determine the mixture colour in different regions of the tank, and hence predict the degree of homogeneity at different times; this is accomplished by defining a proper homogeneity indicator based on the spatial variance of the estimated colour. The proposed numerical model provides an efficient method to investigate the colour of the mixture and to evaluate an appropriate mixing time. The methodology gives also important indications for the tank design, especially useful in the case of non-conventional impellers, high rotation rates and viscous fluids.