ALBERT

Description: Vorticity distributions in axisymmetric vortex rings produced by a piston-pipe apparatus are numerically studied over a range of Reynolds numbers, Re, and stroke-to-diameter ratios, L=D. It is found that a state of advective balance, such that ς=ω/φ/r≈F(Ψ,t).is achieved within the region (called the vortex ring bubble) enclosed by the dividing streamline. Here ς=ω/φ/r is the ratio of azimuthal vorticity to cylindrical radius, and Ψ is the Stokes streamfunction in the frame of the ring. Some, but not all, of the Re dependence in the time evolution of F.(Ψ,t) can be captured by introducing a scaled time t, where v is the kinematic viscosity. When vt=D2 〉∼ 0:02, the shape of F. Ψ is dominated by the linear-in-Ψ component, the coefficient of the quadratic term being an order of magnitude smaller. An important feature is that, as the dividing streamline (Ψ=0) is approached, F.(Ψ) tends to a non-zero intercept which exhibits an extra Re dependence. This and other features are explained by a simple toy model consisting of the one-dimensional cylindrical diffusion equation. The key ingredient in the model responsible for the extra Re dependence is a Robin-type boundary condition, similar to Newton's law of cooling, that accounts for the edge layer at the dividing streamline. © 2017 Cambridge University Press.

Description: The canonical case of a vortex ring interacting with a solid surface orthogonal to its symmetry axis exhibits a variety of intricate behaviours, including stretching of the primary vortex ring and generation of secondary vorticity, which illustrate key features of vortex interactions with boundaries. Replacing the solid boundary with a permeable screen allows for new behaviour by relaxing the no-through-flow condition, and can provide a useful analogue for the interaction of large-scale vortices with permeable structures or closely spaced obstructions. The present investigation considers the interaction of experimentally generated vortex rings with a thin permeable screen. The vortex rings were generated using a piston-in-cylinder mechanism using piston stroketo-diameter ratios (L/D) of 1.0 and 3.0 (nominal) with jet Reynolds numbers (Rej) of 3000 and 6000 (nominal). Planar laser-induced fluorescence and digital particle image velocimetry (DPIV) were used to study the interaction with wire-mesh screens having surface open-area ratios (φ) in the range 0.44-0.79. Solid surfaces (φ = 0) and free vortex rings (φ = 1) were also included as special cases. Measurement of the vortex trajectories showed expansion of the vortex ring diameter as it approached the boundary and generation of secondary vorticity similar to the case of a solid boundary, but the primary vortex diameter then began to contract towards the symmetry axis as the flow permeated the screen and reorganized into a transmitted vortex downstream. The trajectories were highly dependent on φ, with little change in the incident ring trajectory for φ = 0.79. Measurement of the hydrodynamic impulse and kinetic energy using DPIV showed that the change between the average upstream and downstream values of these quantities also depended primarily on φ, with a slight decrease in the relative change as L=D and/or Rej were increased. The kinetic energy dissipation (δE) was much more sensitive to φ, with a strongly nonlinear dependence, while the decrease in impulse (δI) was nearly linear in φ. A simple model is proposed to relate δE and δI in terms of bulk flow parameters. The model incorporates the decrease in flow velocity during the interaction due to the drag force exerted by the screen on the flow. © Copyright 2012 Cambridge University Press.

Description: The effect of turbulence on the mass transfer between a fluid and embedded small heavy inertial particles that experience surface reactions is studied. For simplicity, the surface reaction, which takes place when a gas phase reactant is converted to a gas phase product at the external surface of the particles, is unimolar and isothermal. Two effects are identified. The first effect is due to the relative velocity between the fluid and the particles, and a model for the relative velocity is presented. The second effect is due to the clustering of particles, where the mass transfer rate is inhibited due to the rapid depletion of the consumed species inside the dense particle clusters. This last effect is relevant for large Damköhler numbers, where the Damköhler number is defined as the ratio of the turbulent and chemical time scales, and it may totally control the mass transfer rate for Damköhler numbers larger than unity. A model that describes how this effect should be incorporated into existing simulation tools that utilize the Reynolds averaged Navier-Stokes approach is presented. © 2017 Cambridge University Press.