CFD Models of Non-Newtonian Power Law Fluids in a Baffled Stirred Tank

Mixing is a crucial role in the processing and manufacturing of products across industries such as pharmaceuticals, cosmetics and food production. Optimizing mixing requires careful modeling and simulation of fluid motion inside mixing tanks to maximize productivity. Computational fluid dynamics (CFD) is often used to visualize this fluid movement using vectors, streamlines and contours to illustrate the distributions of velocity, volume fraction, and other important parameters through the mixing tank. Once these values are plotted and shown over the entire tank, impeller speed and viscosity can be adjusted to compare differences and deviations. This project focused on modeling fluid flow within the transition regime, which is less understood than the classical laminar or turbulent regimes due to the Navier-Stokes equations and Reynolds number limits being less well defined.

The working fluid was Carbopol, a non-Newtonian shear thinning material whose viscosity is both concentration and pH dependent. To simulate fluid flow of Carbopol, a non-Newtonian model was used which incorporates the viscosities calculated at the impeller and wall as well as the flow consistency index and the flow behavior index to create a power law model that gives a physically consistent, spatially varying viscosity field. From this power law model, torque, power number and blend time can all be calculated. A multiphase transient simulation was performed after the tank reached steady state, so that the dyed Carbopol could be introduced.

Two different viscosities of Carbopol were simulated, 3350 cP and 7500 cP, with three distinct transition flow regimes for each viscosity, ranging from laminar-transition flow with lower Reynolds number to transition-turbulent flow with higher Reynolds number. To achieve these different flow regimes, the impeller speed was varied. Two turbulence models were tested which use the Reynolds Averaged Navier-Stokes equations, the Spalart-Allmaras and k-epsilon models. Spalart-Allmaras is a one equation model that solves for a modified eddy viscosity while k-epsilon solves two equations for turbulent kinetic energy and the dissipation rate.

When running the multiphase transient simulations, simulation times were kept constant across flow regimes to ensure an accurate comparison between models & viscosities. Simulation times were 165 seconds for the laminar-transition regime, 20 seconds for the transition regime & 15 seconds for the transition-turbulent regime.

To promote homogeneous mixing throughout the tank, baffles were created in the geometry with inflation added during meshing. The baffles in a mixing tank provide the necessary velocity gradients for the fluid to move axially and combined with the A320 axial impeller, induce vertical movement throughout the tank, ensuring a uniform mixture.

Experimental validation included laboratory mixing trials conducted under matching conditions, where videos were recorded to compare to the CFD simulations. Comparing volume fraction distribution of the dyed Carbopol, results obtained through simulations can be visualized and validated. When comparing between turbulence models, the dyed volume distribution contours for the Spalart-Allmaras model are tighter and show slightly less dye dispersion than the k-epsilon model. It is especially prominent in the laminar-transition regime, where the contours are very well defined and clear. There are also unmixed pockets present below the impeller in many of the higher impeller speed regimes in the Spalart-Allmaras model, which are not present in the k-epsilon model.