Bruce Kakimpa

We report the construction and use of a vortex reactor which uses a rapidly rotating cylinder to generate Taylor vortices for continuous flow thermal and photochemical reactions. The reactor is designed to operate under conditions required for vortex generation. The flow pattern of the vortices has been represented using computational fluid dynamics, and the presence of the vortices can be easily visualized by observing streams of bubbles within the reactor. This approach presents certain advantages for reactions with added gases. For reactions with oxygen, the reactor offers an alternative to traditional setups as it efficiently draws in air from the lab without the need specifically to pressurize with oxygen. The rapid mixing generated by the vortices enables rapid mass transfer between the gas and the liquid phases allowing for a high efficiency dissolution of gases. The reactor has been applied to several photochemical reactions involving singlet oxygen (¹O₂) including the photo-oxidations of α-terpinene and furfuryl alcohol and the photodeborylation of phenyl boronic acid. The rotation speed of the cylinder proved to be key for reaction efficiency, and in the operation we found that the uptake of air was highest at 4000 rpm. The reactor has also been successfully applied to the synthesis of artemisinin, a potent antimalarial compound; and this three-step synthesis involving a Schenk-ene reaction with ¹O₂, Hock cleavage with H⁺, and an oxidative cyclization cascade with triplet oxygen (³O₂), from dihydroartemisinic acid was carried out as a single process in the vortex reactor.

This paper presents a coupled ETFM-VOF framework for the numerical simulation of multi-scale thin liquid films. A depth-averaged Eulerian thin-film model (ETFM) is used to simulate the oil flow in very thin-film regions where film thicknesses are below the grid resolution while elsewhere in the domain where grid resolution is sufficient to resolve the film, a traditional Volume-of-Fluid (VOF) approach is retained. The two approaches are coupled through momentum and mass conserving source terms and a transition criterion is introduced where the total liquid volume fraction in each cell is evaluated and either the ETFM or VOF approach used depending on the sufficiency of the local grid resolution. Using this approach, thin-film flows characterised by multiple film thickness scales may be reliably simulated at a relatively lower computational cost. The model builds upon currently available ETFM and VOF approaches to thin-film modelling and represents a novel approach to the numerical simulation of multiphase flows involving a varying range of film thickness scales in space and time. A numerical test case of the 3D rimming flow inside an idealised aero-engine bearing chamber has been used to demonstrate the approach and comparisons made against high resolution VOF solutions.

Thin-film flows encountered in engineering systems such as aero-engine bearing chambers often exhibit capillary waves and occur within a moderate to high Weber number range. Although the depth-averaged simulation of these thin-film flows is computationally efficient relative to traditional volume-of-fluid (VOF) methods, numerical challenges remain particularly for solutions involving capillary waves and in the higher Weber number, low surface tension range. A depth-averaged approximation of the Navier–Stokes equations has been used to explore the effect of surface tension, grid resolution, and inertia on thin-film rimming solution accuracy and numerical stability. In shock and pooling solutions where capillary ripples are present, solution stability, and accuracy are shown to be highly sensitive to surface tension. The common practice in analytical studies of enforcing unphysical low Weber number stability constraints is shown to stabilize the solution by artificially damping capillary oscillations. This approach, however, although providing stable solutions is shown to adversely affect solution accuracy. An alternative grid resolution-based stability criterion is demonstrated and used to obtain numerically stable shock and pooling solutions without recourse to unphysical surface tension values. This allows for the accurate simulation of thin-film flows with capillary waves within the constrained parameter space corresponding to physical material and flow properties. Results obtained using the proposed formulation and solution strategy show good agreement with available experimental data from literature for low Re coating flows and moderate to high Re falling wavy film flows.

This paper explores the role of surface tension, grid resolution, inertia term representation and temporal discretisation scheme in the numerical simulation of shear-driven thin-film rimming flows. An ideal film formulation and solution strategy, suitable for the simulation of smooth, shock and pool solutions is presented. Shock and pool solution stability is shown to be dependent on the provision of sufficient grid refinement to resolve key flow features present in the solution such as steep fronts and small wavelength capillary waves. A minimum grid refinement criterion is proposed based on the findings from a parametric study. A previously established dependence of solution stability on surface tension is shown to be linked to the sensitivity of the wavelengths of disturbances in the capillary zone on the surface tension coefficient. Solution strategies utilising un-physically high surface tension values to guarantee stability, are explored and shown to enhance stability by modifying the solution in the capillary zone to one that is resolvable on the available grid. The role of inertia in solution stability is also investigated and simplified inertia representations are shown to primarily affect accuracy but not stability.

An isothermal thin-film flow over a rotating plate has been simulated using the depth-averaged Eulerian Thin-Film modelling (ETFM) approach. The model setup is based on published experimental and numerical Volume of Fluid (VOF) CFD studies of the same problem to allow for model validation. A range of controlled film inlet heights and mass flow rates are explored together with varied plate rotational speeds ranging from a stationary plate (50rpm) to 200 rpm. While the VOF model has previously been shown to accurately reproduce film thickness, the Eulerian thin-film model is shown to provide predictions of comparable accuracy at a much lower computational cost. The model is also shown to be able to reproduce the film solution’s sensitivity to variations in fluid properties due to changes in inlet temperature. A full 3D domain has been used in this study and the ETFM model is also shown to be able to reproduce azimuthal film thickness variations and surface features similar to those previously observed in experiments.