Pattern Transition on Inertial Focusing of Neutrally Buoyant Particles Suspended in Rectangular Duct Flows

The continuous separation and filtration of particles immersed in fluid flows are important interests in various applications. Although the inertial focusing of particles suspended in a duct flow is promising in microfluidics, predicting the focusing positions depending on the parameters, such as the shape of the duct cross-section and the Reynolds number (Re) has not been achieved owing to the diversity of the inertial-focusing phenomena. In this study, we aimed to elucidate the variation of the inertial focusing depending on Re in rectangular duct flows. We performed a numerical simulation of the lift force exerted on a spherical particle flowing in a rectangular duct and determined the lift-force map within the duct cross-section over a wide range of Re. We estimated the particle trajectories based on the lift map and Stokes drag, and identified the particle-focusing points appeared in the cross-section. For an aspect ratio of the duct cross-section of 2, we found that the blockage ratio changes transition structure of particle focusing. For blockage ratios smaller than 0.3, particles focus near the centres of the long sides of the cross-section at low Re and near the centres of both the long and short sides at relatively higher Re. This transition is expressed as a subcritical pitchfork bifurcation. For blockage ratio larger than 0.3, another focusing pattern appears between these two focusing regimes, where particles are focused on the centres of the long sides and at intermediate positions near the corners. Thus, there are three regimes; the transition between adjacent regimes at lower Re is found to be expressed as a saddle-node bifurcation and the other transition as a supercritical pitchfork bifurcation.

RANS-VOF Simulations of Fully Developed Density-Stratified Air-Water Flow in a 3D Rectangular Duct

We perform RANS-VOF simulation of turbulent, fully developed, density-stratified air-water flow in a 3D rectangular duct cross section of height twice the width. Flow through an open or partially-filled duct is characterized by the presence of an air-water interface interacting with a solid wall, forming a mixed-boundary corner. A novel feature of the mixed-boundary corner for turbulent flow is the interaction of wall turbulence with the air-water interface. In the current study, the RANS-VOF equations (for fully developed flow) are solved in a rectangular duct, using periodic inlet/outlet boundary conditions. The flow is completely specified by the (common) driving pressure gradient down the duct and by the fill factor (relative height of the heavier phase to the total height of the duct). Varying the pressure gradient and fill factor results in different flow combinations, namely, laminar air/laminar water, turbulent air/laminar water, turbulent air/turbulent water, laminar air/turbulent water. Since RANS-VOF simulations are computationally less expensive compared to LES and DNS, we systematically investigated a range of flow combinations. The Reynolds stresses are tracked near the mixed-boundary corner for the different flow combinations. The structure of the secondary vortices near the mixed-boundary corner differs from that in the corner formed by the solid vertical and horizontal duct walls.