Despite having the advantage of a secondary flow pattern in coiled tubes, a very high Dean number is required to induce significant mixing in helical coils, usually implying high shear rates. At very high shear rates, polymer fluids with long molecular chains can be damaged. Therefore, in this study, we investigate the enhancement of mixing of a viscoelastic fluid in a coiled tube at low Dean numbers using the concept of a coiled flow inverter (CFI). Viscoelastic flow simulations were performed for CFIs of different curvature ratios, by changing the coil diameter, for a range of Weissenberg numbers (Wi) 0-125. An analytical method using velocity streamlines to quantify mixing is presented. The pressure drop per unit length increases with increasing Wi number. A more efficient mixing is predicted in the CFI, when compared with a helix of the same curvature ratio for all flow conditions. The mixing in the CFI is improved with an increase in flow rates (Wi). The mixing is enhanced at every bend because of flow inversion in the CFI.

A novel approach to Multiphase-Particle-in-Cell (MP-PIC), called Continuum Particle Model (CPM), is developed for dense gas-particle flows. CPM has high computational speed, comparable to that of MP-PIC, but a robustness and accuracy closer to that of a Discrete Element Model (DEM). The gas phase is treated as a continuum phase and particles are tracked discretely, but particle collisions are modelled by considering the divergence of the continuum particle stress tensor. Details on efficient solution to the model are presented. For comparison, a parametric study is performed for quasi-2D fluidized beds. Comparison of CFD-CPM is made with MP-PIC and CFD-DEM. The particle stress models by Harris and Crighton, and by Srivastava and Sundaresan are tested in our CFD-CPM. Results from CFD-CPM based on the Srivastava and Sundaresan particle stress model show good agreement with CFD-DEM results. We validate our model by comparison with experimental benchmark results from Gopalan et. al. (2016).

In this paper, we present a number of key numerical methods that can be used to study elongated particles in fluid flows, with a specific emphasis on fluidised beds. Fluidised beds are frequently used for the production of biofuels, bioenergy, and other products from biomass particles, which often have an approximate elongated shape. This raises numerous issues in a numerical approach such as particle-particle contact detection and the accurate description of the various hydrodynamic forces, such as drag, lift, and torque, that elongated particles experience when moving in a fluid flow. The modelling is further complicated by a separation of length scales where industrial flow structures that can extend for many metres evolve subject to solid-solid and solid-fluid interactions at the millimetre scale. As a result, it is impossible to simulate both length scales using the same numerical approach, and a multiscale approach is necessary. First, we outline the direct numerical simulation (DNS) approach that may be employed to estimate hydrodynamic force closures for elongated particles in a fluid flow. We then describe the key aspects of a CFD-DEM approach, which can be used to simulate laboratory scale fluidisation processes, that must be addressed to study elongated particles. Finally, we briefly consider how current industrial-scale models, which concretely assume particle sphericity, could be adapted for the simulation of large collections of elongated particles subject to fluidisation.