(192b) CFD Simulations to Address Mixing in the Transition Region

Mixing is a common practice used in the manufacturing and processing industry and is typically modeled in the laminar or the turbulent regime because the equations governing these regimes are well understood.^1-5 Due to the complexity of mixing in the transition regime, minimal modeling exists despite this type of mixing being a common working regime in many industrial processes.⁶ Certain industries, including agrochemicals, pharmaceuticals, cosmetics, food and mining, naturally find themselves operating in and around the transition regime. The limited ability to fully understand these processes hampers accurate predictions of optimized configurations that typically involve complex non-Newtonian fluids.

This project utilizes computational fluid dynamics (CFD) as a tool to enable the modeling of various physical systems to analyze velocity profiles, streamlines, and numerous other fluid and flow parameters. Our approach will discretize the governing equations of fluid flow using finite volume methods that solve the Navier Stokes equations numerically via iterative procedures. Using CFD, we will model and analyze properties of fluid domains, such as velocity profiles, pressure contours, and volume fractions. Inaccuracies of transition mixing models may arise from the inability of CFD to predict large scale instabilities in the flow domain. We will circumvent this limitation by incorporating multiphase transient simulations of the mixing of Carbopol, a high molecular weight, crosslinked polyacrylic acid polymer, to study the transient mixing region with high accuracy.

Work in our lab thus far has confirmed that the laminar viscous model is sufficiently accurate when used with fluids in the transition regime using mid to low Reynolds Numbers.⁷ The Reynolds Stress Model and Shear Stress Turbulence Model behave well for mid to high Reynolds Numbers as they better capture turbulence within the flow.⁷

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 goal of the work was to use CFD simulations to find the best fit model that most accurately represents mixing in all flow regimes in a tank and verify the percentage mixed by extracting the torque data from the simulation to calculate the power number. The power number is a dimensionless number that relates resistance forces to inertial forces and can ultimately be used to calculate the blend time to ensure the tank simulations are fully mixed with 95 percent homogeneity.²

Our work includes laboratory mixing videos that were used to compare to the CFD simulation results. In this case, we work to model the volume fraction distribution of dye that is released in the tank while being mixed at various speeds. By following the dye distribution, flow patterns become easier to visualize as well as analyze. Changes of impeller velocity and fluid viscosity enable changes in the Reynolds number. After using a series of equations to find shear rate, shear stress, and viscosity, the necessary impeller speeds were determined to achieve five regimes: laminar, laminar-transition, transition, transition-turbulent, and turbulent regimes. Other than the impeller speed, identical conditions for these regimes were used across the laminar viscous, Reynolds Stress, and k-kl-omega models to select the most accurate scenario.

In the laminar viscous model, the transition between each of the five regimes was clear and smooth while the other two models either yielded no mixing patterns or images that were indistinguishable between regimes. After compiling images of the simulated tanks at various stages of mixing, the Laminar Viscous model was determined to show the best mixing patterns throughout the entire tank.

The result of this work is a more complete understanding of the transition flow regime that is important in the understanding of many industrial mixing processes and the simulation of the various flow regimes that occur simultaneously in various areas of a mixing tank.

References

(1) Oldshue, J. Y.; Herbst, N. R. A Guide To Fluid Mixing; Mixing Equipment Corporation, 1990.

(2) Paul, E. L.; Atiemo0Obeng, V.; Kresta, S. M. Handbook of Industrial Mixing; Wiley-Interscience, 2004.

(3) Kresta, S. M.; Etchells, A. W.; Dickey, D. S.; Atiemo-Obeng, V. A. Advances in Industrial Mixing; John Wiley and Sons: Hoboken, NJ, 2016.

(4) Zhang, Y.; Gao, Z.; Li, Z.; Derksen, J. J. Transitional flow in a Rushton turbine stirred tank. AIChE Journal 2017, 63 (8), 3610.

(5) Machado, M. B.; Bittorf, K. J.; Roussinova, V. T.; Kresta, S. M. Transition from turbulent to transitional flow in the top half of a stirred tank. Chemical Engineering Science 2013, 98, 218.

(6) Mendoza, F.; Bañales, A. L.; Cid, E.; Xuereb, C.; Poux, M.; Fletcher, D. F.; Aubin, J. Hydrodynamics in a stirred tank in the transitional flow regime. Chemical Engineering Research and Design 2018, 132, 865.

(7) Baker, H. J.; Yu, W.; Flower, R. D.; Foster, D. G. In AICHE National Conference Boston, Mass, 2021.