Immersogeometric analysis of moving objects in incompressible flows

We deploy the immersogeometric approach for tracking moving objects. The method immerses objects into non-boundary-fitted meshes and weakly enforces Dirichlet boundary conditions on the object boundaries. The object motion is driven by the integrated surface force and external body forces. A residual-based variational multiscale method is employed to stabilize the finite element formulation for incompressible flows. Adaptively refined quadrature rules are used to better capture the geometry of the immersed boundaries by accurately integrating the intersected background elements. Treatment for the freshly-cleared nodes (i.e. background mesh nodes that are inside the object at one time step, but are in the fluid domain at the next time step) is considered. We assess the accuracy of the method by analyzing object motion in different flow structures including objects freely dropping in viscous fluids and particle focusing in unobstructed and obstructed micro-channels. We show that key quantities of interest are in very good agreements with analytical, numerical and experimental solutions. We also show a much better computational efficiency of this framework than current commercial codes using adaptive boundary-fitted approaches. We anticipate deploying this framework for applications of particle inertial migration in microfluidic channels

The FDF or LES/PDF method for turbulent two-phase flows

In this paper, a new formalism for the filtered density function (FDF) approach is developed for the treatment of turbulent polydispersed two-phase flows in LES simulations. Contrary to the FDF used for turbulent reactive single-phase flows, the present formalislm is based on Lagrangian quantities and, in particular, on the Lagrangian filtered mass density function (LFMDF) as the central concept. This framework allows modeling and simulation of particle flows for LES to be set in a rigorous context and various links with other approaches to be made. In particular, the relation between LES for particle simulations of single-phase flows and Smoothed Particle Hydrodynamics (SPH) is put forward. Then, the discussion and derivation of possible subgrid stochastic models used for Lagrangian models in two-phase flows can set in a clear probabilistic equivalence with the corresponding LFMDF.Comment: 11 pages, proceedings of the 13 europena turbulence conference, submitted to JPC

Critical Stokes number for the capture of inertial particles by recirculation cells in 2D quasi-steady flows

Inertial particles are often observed to be trapped, temporarily or permanently, by recirculation cells which are ubiquitous in natural or industrial flows. In the limit of small particle inertia, determining the conditions of trapping is a challenging task, as it requires a large number of numerical simulations or experiments to test various particle sizes or densities. Here, we investigate this phenomenon analytically and numerically in the case of heavy particles (e.g. aerosols) at low Reynolds number, to derive a trapping criterion that can be used both in analytical and numerical velocity fields. The resulting criterion allows to predict the characteristics of trapped particles as soon as single-phase simulations of the flow are performed. Our analysis is valid for two-dimensional particle-laden flows in the vertical plane, in the limit where the particle inertia, the free-fall terminal velocity, and the flow unsteadiness can be treated as perturbations. The weak unsteadiness of the flow generally induces a chaotic tangle near heteroclinic or homoclinic cycles if any, leading to the apparent diffusion of fluid elements through the boundary of the cell. The critical particle Stokes number Stc below which aerosols also enter and exit the cell in a complex manner has been derived analytically, in terms of the flow characteristics. It involves the non-dimensional curvature-weighted integral of the squared velocity of the steady fluid flow along the dividing streamline of the recirculation cell. When the flow is unsteady and St > Stc, a regular motion takes place due to gravity and centrifugal effects, like in the steady case. Particles driven towards the interior of the cell are trapped permanently. In contrast, when the flow is unsteady and St < Stc, particles wander in a chaotic manner in the vicinity of the border of the cell, and can escape the cell