- Particle-laden turbulent flows, wherein a large number of small size particles are dispersed in a fluid, are widely encountered in environmental and industrial applications. Understanding their underlying physics, making predictions without performing expensive experiments, and ultimately optimizing the systems carrying such flows, require accurate and robust modelling tools. The Euler-Lagrange (EL) approach has received much attention in modeling such flows due to its simplicity, affordability and partial accuracy. In this approach, the fluid phase is solved using an Eulerian framework while particles are treated as Lagrangian point-particles (PP) in the flow and tracked following the Newton's second law of motion based on the available closures for the fluid forces acting on the particles.
For two-way coupled flows, the effect of particles on the fluid phase is modelled by applying the particle reaction force to the background flow through a momentum source term. Using such a simplified point force model, however, could result in inaccuracies in capturing the experimental observations or analytical solutions. One source of inaccuracy is that, the fluid phase equations in this approach are solved for the entire flow field including the volume occupied by the particles, and the mass displacement of the particles is not taken into account. The other source is that the accuracy of the fluid forces acting on the particles depends on the `undisturbed fluid velocity', that is by definition, the velocity that is not influenced by the presence of particles. However, in two-way coupled simulations, particles disturb the fluid phase at their location, and such an `undisturbed' fluid velocity is no longer available. The alternative and common use of the disturbed fluid velocity can produce erroneous predictions by as much as 100%.
In this dissertation, the spatio-temporal variations in the volume fraction of the fluid phase are taken into account to capture the mass displacement effect of particles. Large-eddy simulations (LES) coupled with PP approach performed for a particle-laden jet under a range of volume loadings show that the mass displacement effect tends to become important for particle volume loadings above $5\%$. Concerning the second issue, a general scheme is developed to correct the PP approach in order to recover the undisturbed fluid velocity at the location of particles. The model is accurate, cost-efficient and applicable for isotropic and anisotropic grids with high aspect ratio typically encountered in the turbulent channel flow simulations. The present scheme handles all types of particle-laden flows with and without no-slip walls. Tests performed on a settling particle in parallel and perpendicular motion to a no-slip wall shows the accuracy and robustness of the model in reducing the errors in predicting the particle settling velocity.
The present EL-PP approach is applied to a particle-laden turbulent channel flow to predict the interaction of particle and turbulence. It is observed that the uncorrected PP approach, wherein the disturbed fluid velocity is employed for the fluid force computations, fails in capturing the experimental observations. However, when the PP approach is corrected with the newly developed correction scheme, the recovery of the undisturbed fluid velocity at the location of particles produces accurate fluid forces and captures most of the experimental observations.
Finally, the effect of deforming particles, such as liquid droplets in liquid atomization, is briefly investigated. Different deformation models are tested against the experimental data to identify the best model for each breakup regime. It is observed that ignoring such an effect produces significant underprediction on the motion of droplets.