Interactions between vortices and flexible walls

We give two fundamental solutions for the motion of a point vortex near a flexible wall, up to first order in wall deflection, using computational methods. For a point vortex near an infinite horizontal wall, the deformation of the wall intensifies the flow at the wall near the vortex, and increases the speed of the vortex. Near a circular wall there is a strong mutual amplification of the deflection of the wall and the pressure force induced by the deflection, as the point vortex approaches the wall. The total force on the wall diverges as the inverse cube of the distance to the point vortex, and the induced speed of the point vortex diverges as the inverse fourth power of distance to the wall.     

Adaptive panel representation for oblique collision of two vortex rings

In this article, we use a hierarchical panel method for representing vortex sheet surface motion in 3D flow to investigate the oblique collision of two vortex rings. The particles representing the sheet are advected by a regularized Biot-Savart integral with smoothed Rosenhead-Moore kernel. The particle velocities are evaluated by an adaptive treecode algorithm based on Taylor expansions in Cartesian coordinates. The method allowed us to consider late stages of a vortex rings collision, producing a funnel region. Vorticity iso-surfaces evolution is also investigated.     

Numerical investigations on vortical structures of viscous film flows along periodic rectangular corrugations

Two-dimensional gravity-driven film flows along a substrate with rectangular corrugations are studied numerically by using Finite Volume Method. The volume of fluid (VOF) method is utilized to capture the evolution of free surfaces. The film flows down an inclined plate are simulated to validate the numerical implementation of the present study. Results obtained indicate that the phase shift between the surface wave and the wall corrugation increases as the Reynolds number. The parametric studies on the interesting resonant phenomenon indicate that the peak Reynolds numbers increase as the raise of the wall depth or the decline of the inclination angle. The dependence of the flow fields is analyzed on the Reynolds numbers and wall depth in details. It is found that the vortical structures in the steady flows, either produced by the interaction between capillary wrinkling and inertia, or by the rectangular geometry, are closely related to the remarkable deformation of the free surfaces. This conclusion is also confirmed by the transient flow development of two typical simulations, i.e., flows in capillary–inertial regime and in inertial regime.     

The effect of air-water interface on the vortex shedding from a vertical circular cylinder

The flow past an interface piercing circular cylinder at the Reynolds number Re=2.7×10⁴ and the Froude numbers Fr=0.2 and 0.8 is investigated using large-eddy simulation. A Lagrangian dynamic subgrid-scale model and a level set based sharp interface method are used for the spatially filtered turbulence closure and the air-water interface treatment, respectively. The mean interface elevation and the rms of interface fluctuations from the simulation are in excellent agreement with the available experimental data. The organized periodic vortex shedding observed in the deep flow is attenuated and replaced by small-scale vortices at the interface. The streamwise vorticity and the outward transverse velocity generated near the edge of the separated region, which enforces the separated shear layers to deviate from each other and restrains their interaction, are primarily responsible for the devitalization of the periodic vortex shedding at the interface. The lateral gradient of the difference between the vertical and transverse Reynolds normal stresses, increasing with the Froude number, is the main source of the streamwise vorticity and the outward transverse velocity at the interface.     

Drag amplification of long flexible riser models undergoing multi-mode VIV in uniform currents

Measurement data of long flexible riser models are used to study the drag amplification due to multi-mode vortex induced vibration (VIV). The riser model was towed in a towing tank, and vibration along its length was measured indirectly at a set of discrete points using accelerometers, along with the total drag and lift forces on the model. These data were used to fit expressions for the drag amplification taking into account the spatial variation of the vibration amplitude along the riser length. The results were compared with the existing empirical expression used in the VIV analysis tool SHEAR7 as well as other test data. It was found that the expression in SHEAR7 agrees well with the test data. However, for larger vibration amplitudes, it appears to under-predict the drag amplification.     

Propagation of a pair of vortices through a tilted lens

The propagation of a pair of vortices nested in a Gaussian beam through a tilted lens is studied. It is shown that after passing through the tilted lens, the relation between the transverse position of vortices and the tilt coefficient is linear in the propagation for isopolar vortex pair and vortex dipole, and in the three-dimensional (3D) case the vortex trajectories are sometimes like U or X shapes. With increasing the orientation angle of the vortex pair, the trajectories of vortices are circles for the both cases. The overlap of vortices may take place for the isopolar vortex pair, while the annihilation and revival of vortices occur for the vortex dipole in the propagation.     

Flux trapping in a macroscopic cylinderical hole drilled in Bi-Sr-Ca-Cu-O

The flux dynamics in a polycrystalline sample of Bi_1.7Pb_0.3Sr₂Ca₂Cu₃O_x with a macroscopic cylindrical hole (CH) drilled was investigated by slow transport relaxation (V-t curves) and magnetovoltage measurements (V-H curves). It was monitored that there are several discontinuities in the time evolution of quenched state in V-t curves, which was attributed to the leaving of quantized flux lines trapped through CH together with surface superconducting effects. We observed that asymmetric V-H curves demonstrate unusual remarkable counter clockwise hysteresis effects upon cycling of field. This interesting result was correlated mainly to the flux trapping inside the CH that acts as a macroscopic attractive pinning center for flux lines. Further, the hysteresis effects in V-H curves for a fixed transport current provide a direct evidence that the number of flux lines, measured dissipation and relative decrease/increase in irreversibilities could be determined by sweeping rate of external magnetic field (dH/dt) which leads also to peculiar time effects.     

Treatment of vortex sheets for the transonic full-potential equation

This paper summarizes a combined analytical-computational technique which models vortex sheets in transonic potential-flow methods. In this approach, the inviscid nature of discontinuities across vortex sheets is preserved by employing the step function to remove singularities at these surfaces. The location and strength of the vortex sheets are determined by satisfying the flow-tangency boundary condition and the vorticity transport equation. The theory is formulated for the general three-dimensional case, but its application is confined to the problem of computing slipstreams behind propellers with free-vortex blading in axisymmetric flows.     

Hydrodynamics of a particle impact on a wall

The problem of a particle impacting on a wall, a common phenomenon in particle-laden flows in the minerals and process industries, is investigated computationally using a spectral-element method with the grid adjusting to the movement of the particle towards the wall. Remeshing is required at regular intervals to avoid problems associated with mesh distortion and the constantly reducing maximum time-step associated with integration of the non-linear convective terms of the Navier–Stokes equations. Accurate interpolation between meshes is achieved using the same high-order interpolation employed by the spectral-element flow solver. This approach allows the full flow evolution to be followed from the initial approach, through impact and afterwards as the flow relaxes. The method is applied to the generic two-dimensional and three-dimensional bluff body geometries, the circular cylinder and the sphere. The principal case reported here is that of a particle colliding normally with a wall and sticking. For the circular cylinder, non-normal collisions are also considered. The impacts are studied for moderate Reynolds numbers up to approximately 1200. A cylindrical body impacting on a wall produces two vortices from its wake that convect away from the cylinder along the wall before stalling while lifting induced wall vorticity into the main flow. The situation for a sphere impact is similar, except in this case a vortex ring is formed from the wake vorticity. Again, secondary vorticity from the wall and particle plays a role. At higher Reynolds number, the secondary vorticity tends to form a semi-annular structure encircling the primary vortex core. At even higher Reynolds numbers, the secondary annular structure fragments into semi-discrete structures, which again encircle and orbit the primary core. Vorticity fields and passive tracer particles are used to characterize the interaction of the vortical structures. The evolution of the pressure and viscous drag coefficients during a collision are provided for a typical sphere impact. For a Reynolds number greater than approximately 1000 for a sphere and 400 for a cylinder, the primary vortex core produced by the impacting body undergoes a short-wavelength instability in the azimuthal/spanwise direction. Experimental visualisation using dye carried out in water is presented to validate the predictions.