(267c) The Transition to Aeration in Turbulent Two-Phase Mixing in Stirred Vessels

Flow mixing inside stirred vessels occurs in a large array of industrial applications and produces complex dynamical structures. These structures, such as those seen in [1] for single-phase flow, exert a strong influence on the mixing efficiency. Many fast-moving consumer goods involve the manufacturing of so-called structured products (e.g., foods, creams, detergents), which are mass-produced via complex multiphase mixing processes of several base products, commonly carried out in agitated tanks. Some viscous products require rapid mixing, but the appearance of bubbles can lead to undesirable partial bottle-filling and process inefficiencies. In contrast, for other processes, such as those used in ice cream manufacturing (involving non-Newtonian fluids and emulsifiers [2,3] and those that deploy bioreactors, the promotion of ‘aeration’ is essential. Thus, it is crucial to predict the mixing patterns in stirred vessels, and to demarcate the aeration threshold as a function of relevant system parameters, such as fluid properties, and impeller geometry and rotational speed.

Mixing that induces aeration in a stirred vessel is perhaps one of the most challenging configurations to predict via accurate computational methods. This difficulty is due firstly to the high-density gap between the two phases (air-liquid mixing), which makes solvers difficult to converge. Moreover, the presence of a myriad interfacial singularities, such us interfacial breakup and coalescence, produces high velocity gradient, reduces consequently the computational time-step. Therefore, the time consuming for the computation is very long. Furthermore, an accurate calculation, with almost any assumption, it requires many computational skills that is not easy to combine together such as multiphase flows, fluid-structure interaction, turbulence modelling.... Finally, the multiscale dynamical (shear-layers and vortical structures) also requires important resolution. Consequently, it becomes very challenging and very costly in term of computational method to predict accurate mixing inducing aeration, despite the enormous industrial applications.

The combination of innovative numerical algorithms in a single numerical framework, able to accurately handle coupled physics in fluid mechanics such as multiphase interface motion, fluid-structure interaction and turbulence modelling, is essential for predicting complex mixing flow in stirred vessels. Moreover, a robust high-performance computing architecture enables in-depth understanding of previously inaccessible physics for such extreme flow regimes. In the context of aeration due to mixing in a stirred vessel, where the density ratio between the air and the liquid is O(10³), it is crucial to provide a robust and reliable numerical framework able to encompass all the techniques listed above.

We consider the mixing of a viscous fluid by the rotation of a pitched blade turbine inside an open, cylindrical tank, with air as the lighter fluid above. To examine the flow and interfacial dynamics, we utilise a highly-parallelised implementation of a hybrid front-tracking/level-set method that employs a domain-decomposition parallelisation strategy. Our numerical technique is designed to capture faithfully complex interfacial deformation, and changes of topology, including interface rupture and dispersed phase coalescence. As shown via transient, three-dimensional direct numerical simulations, the impeller induces the formation of primary vortices that arise in many idealised rotating flows as well as several secondary vortical structures resembling Kelvin-Helmholtz, vortex breakdown, blade tip vortices, and end-wall corner vortices. As the rotation rate increases, a transition to aeration is observed when the interface reaches the rotating blades leading to the entrainment of air bubbles into the viscous fluid and the creation of a bubbly, rotating, free surface flow. The mechanisms underlying the aeration transition are probed as are the routes leading to it, which are shown to exhibit a strong dependence on flow history.

Before reaching the challenging bubbly aeration regime, there are many attempts of computing mixing flow with many assumptions, For example, Ciofalo et al.[4] performed a three-dimensional turbulent flow simulation, where the flow equations are in the rotating reference frame of the impeller with the addition of a conventional linear logarithmic “wall function" as in [5]). The work presented in [6] compared alternative computational methods: the

first replaced the impeller by suitable boundary conditions, and the second consisted of dividing the computational domain into two concentric and partially-overlapping parts; the inner region, containing the impeller, where the flow is simulated in the impeller rotating reference frame, while in the outer region, simulations are conducted in the laboratory reference frame. This technique requires information exchange between the two regions. More recently, the work presented in [7] used the lattice Boltzmann method to simulate the flow in aerated bioreactors, and [8] coupled a volume-of-fluid method to a Reynolds stress model to capture the gas-liquid interface and
turbulent flow agitated by pitched blade turbines where the interface deflection reached the impeller hub.

To the best of our knowledge, studies involving unsteady, turbulent, and high deformable free surface
flows have been restricted to situations wherein the interface deflection does not descend beyond
the impeller blades. As a result, these studies are unable to analyse, in detail, the rich and complex
vortical structures accompanying such flows. Furthermore, the phenomenon of aeration has not yet been
studied in detail via numerical simulations despite its obvious importance to industrial applications as
highlighted above. Aeration involves the development of sufficiently large interfacial deformations that
lead to the interaction of the free surface with the rotating impeller. This, in turn, brings about the
entrainment and dispersion of the lighter phase into the underlying denser phase; for gas (air)-liquid
systems, the dispersed phase corresponds to bubbles (of air).

Our aim in this work is to present the intricacies of two-phase mixing flows in a stirred vessel via a standard LES (Large Eddy Simulation) Smagorinsky-Lilly turbulence model coupled with a Direct-Forcing Method for the motion of the impeller [9,10]. Moreover, our numerical framework is formulated in the context of a high-fidelity front-tracking technique for the interface [11,12] which is able to handle complex interfacial deformation, pinchoff and coalescence. Applying this new numerical scheme for stirred vessels, our results elucidate, for the first time, the challenging transition to aeration and its dependence on flow history (e.g., ramping up impulsively from a stationary state vs. increasing the impeller rotational speed following the achievement of a steady-state at lower speeds). A crucial metric for mixing-induced aeration that a numerical framework should be capable of furnishing is the gas/air holdup which corresponds to the relative amount of gas/air held in the liquid phase. We provide results for the temporal variation of the holdup from our simulation data.

REFERENCES

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