CFD Modeling of Non-Newtonian Power Law Fluids in the Transition Regime

Mixing is an essential operation used in the manufacturing and processing industries, and modeling the flow it creates throughout the tank is crucial to gain the level of understanding needed to optimize its efficiency. Flow regimes are characterized by their Reynolds number, a dimensionless quantity expressing the ratio of the inertial force to viscous force in the flow. For stirred mixing tanks, Reynolds numbers below 30 indicate the laminar regime and Reynolds numbers above 1000 suggest the turbulent regime. Governing equations exist to model flow in the laminar and turbulent regimes; however, this is not the case for the range of Reynolds numbers falling between these regimes, called the transition regime. In real mixing tanks, all flow regimes occur simultaneously. Turbulent-like flow tends to exist closer to the impeller while laminar-like flow tends to exist closer to the baffles; between these exists the complex transition flow. This project aims to create one model that can accurately model flow throughout all regimes using Carbopol, a non-Newtonian fluid that exists in many shampoos, dishwashing liquids and laundry detergents as the test fluid. Carbopol at viscosities of 3,355 cP, 7,500 cP, and 10,000 cP were modeled and compared in both a labatory mixing tank and using ANSYS Fluent, a commercial Computational Fluid Dynamic (CFD) software package. To model the mixing patterns in ANSYS, multiphase transient simulations that show the volume fraction distribution of dye released into the mixing tank were analyzed using different viscous models under the laminar-transition, transition, and transition-turbulent regimes for each starting viscosity. Blend times for the transition, transition-turbulent, and turbulent regimes were also calculated for the 10,000 cP Carbopol simulations using torque data from mixing Carbopol in the laboratory. The viscous models tested were the Scale-Adaptive Simulation (SAS) model, the Spalart-Allmaras Model (SAM), and the Detached Eddy Simulation (DES) model. The results suggest that the CFD simulations match well with the laboratory results and contribute to the further understanding of mixing in the transition region.