In the present work, we investigate the dynamics of a droplet of ferrofluid placed in a shear flow field subjected to the additional action produced by the application of a magnetic field in a direction perpendicular to the flow. The problem is solved in the framework of a moving-boundary method based on the solution of the Navier-Stokes equations complemented with the additional equations required for the determination of the magnetic force. The results reveal interesting changes in the trends displayed by the droplet deformation and inclination angle as a function of the capillary number when the intensity of the magnetic field is varied while maintaining flow conditions corresponding to the Stokes regime. The mechanism of droplet relaxation from equilibrium when the magnetic force is suddenly removed is also investigated. According to our numerical experiments the deformation evolves in time following a harmonic decaying process, which, in the limit of small capillary number, i.e. for very small deformations, can be fairly well represented by the temporal evolution of a simple damped harmonic oscillator.

The emergence of Particle Accumulation Structures (PAS) in non-cylindrical liquid bridges (LB) is studied numerically for a high Prandtl number liquid considering microgravity conditions. Simulations are conducted in the framework of a finite-volume (Eulerian) approach with non-isodense particles being tracked using a Lagrangian, one-way coupling scheme. First, the threshold of the Marangoni-flow instability is determined as a function of the aspect ratio and the volume of liquid held between the supporting disks, thereafter, PAS formation is investigated for supercritical conditions. The overall approach is specifically conceived to provide details about the morphological evolution of these structures as the main control parameters are varied. For this reason a set of new notions and definitions (such as the linear extension of the PAS, its inner core radius and the area of the "petals" or "blades") are introduced to allow a precise quantification of a series of purely geometrical effects. Though the analysis is deliberately limited to illustrating the macroscopic patterning behavior and its relationship with the overarching factors, a new model is proposed to interpret the increased ability of slender (concave) liquid bridges to support the formation of PAS over extended ranges of values of the particle Stokes number. This model yet relies on essentially geometrical arguments, that is, the triadic relationship among the curvature of the free surface, the topology of fluid streamlines and particle mass effects.

Abstract

Systems of solid particles in suspension driven by a time-periodic flow tend to create structures in the carrier fluid that are reminiscent of highly regular geometrical items. Within such a line of inquiry, the present study provides numerical results in support of the space experiments JEREMI (Japanese and European Research Experiment on Marangoni flow Instabilities) planned for execution onboard the International Space Station. The problem is tackled by solving the unsteady non-linear governing equations for the same conditions that will be established in space (microgravity, 5 cSt silicone oil and different aspect ratios of the liquid bridge). The results reveal that for a fixed supporting disk radius, the dynamics are deeply influenced by the height of the liquid column. In addition to its expected link with the critical threshold for the onset of instability (which makes Marangoni flow time-periodic), this geometrical parameter can have a significant impact on the emerging waveform and therefore the topology of particle structures. While for shallow liquid bridges, pulsating flows are the preferred mode of convection, for tall floating columns the dominant outcome is represented by rotating fluid-dynamic disturbance. In the former situation, particles self-organize in circular sectors bounded internally by regions of particle depletion, whereas in the latter case, particles are forced to accumulate in a spiral-like structure. The properties of some of these particle attractors have rarely been observed in earlier studies concerned with fluids characterized by smaller values of the Prandtl number.

The two-phase flow in a geometry representing the final portion of the internal cooling channels of a gas turbine blade is here presented and discussed. In the configuration under scrutiny, the coolant flows inside the duct in radial direction and it leaves the blade through the trailing edge after a 90 deg turning. An unsteady Reynolds Averaged Navier-Stokes (URANS) simulation of the flow inside such channel was carried out. An original non-linear version of the well-established ζ-f elliptic relaxation model was developed and applied here. The new model was implemented in the well-validated T-FlowS code currently developed by the authors’ group at Sapienza Università di Roma. The predictions demonstrated a good accuracy of the non-linear URANS model, clearly improving the results of the baseline linear ζ-f model and of the Launder Sharma k-ε model used as reference. The obtained unsteady flow field was adopted to track a large number of solid particles released from several selected sections at the inlet and representing the powders usually dispersed (sand, volcanic ashes) in the air spilled from the compressor and used as cooling fluid. The well-validated particle-tracking algorithm here adopted for determining the trajectories demonstrated to be very sensitive to the flow unsteadiness. Finally, the fouling of the solid surfaces was estimated by adopting a model based on the coefficient of restitution approach.