CFD Analysis of Mixing in the Transition Regime: User-Defined Functions and Viscosity Variations

Mixing is a common process used in the manufacturing and processing industry. To optimize the mixing efficiency, it is critical to understand what is going on inside the tank. In a physical mixing tank, several flow regimes exist simultaneously. At the impeller, turbulent flow is likely to exist. In the bulk and the surface of the tank, the fluid can be in laminar flow. Between the two extremes, there will be a wide range of Reynolds Numbers, all falling into the transitional flow regime. The process for industrial mixing is typically modeled in the laminar or turbulent regimes, as the equations governing these regimes are well understood. ^1-2 Due to the complexity of transition mixing, there is minimal modeling done in the regime despite it being a common working regime for many industries. The lack of accurate transition mixing models hinders these industries in fully understanding their processes. ¹ Computational Fluid Dynamics (CFD) is used in modeling various physical systems to analyze velocity profiles, streamlines, volume fraction distribution, and numerous other fluid and flow properties.

A user-defined function is a C program function that can be dynamically loaded into CFD software packages, such as ANSYS Fluent. A UDF serves to enhance the standard features of code already apparent inside the ANSYS fluent solver code. In this case, a UDF was written to redescribe the shear-thinning viscosity behavior of the fluid, Carbopol, in the transition regime based off the Carreau-Yasuda model for non-Newtonian fluids. Carbopol is a non-Newtonian, shear-thinning fluid whose viscosity profile can be altered with change in pH and/or concentration. Two different viscosities, 7500 cP and 3350 cP, were used to investigate their dependence on flow patterns. The UDF was incorporated into the two different viscosities with two different ANSYS fluent models: The Spallart-Allmaras Model and The Transition Shear-Stress Turbulence Model. Different mixing regimes were achieved by changing the speed of the impeller. Without the UDF, both RANS models struggled to characterize the flow and shear-thinning viscosity behavior for Reynold’s numbers that existed within the transition regime. The UDF worked to better represent the dispersion of dye and the shear-thinning of the Carbopol throughout the entire mixing tank.

References

[1] Oldshue, J.Y. “A Guide to Fluid Mixing.”, 2003.

[2] Kresta, Suzanne M. Advances in Industrial Mixing: A Companion to the Handbook of

Industrial Mixing. Wiley, 2016.