Breakup of a leaky dielectric drop in a uniform electric field.

Electrohydrodynamic (EHD) breakup phenomena for a leaky dielectric drop suspended in another immiscible viscous dielectric and subjected to a uniform electric field are examined using the leaky dielectric theory and the explicit forcing lattice Boltzmann method, by taking into account full nonlinear inertia effects. The breakup modes are first computed for varied conductivity of the drop fluid, as the viscosity ratio λ (=µ_{in}/µ_{out}) is momentarily set to unity, that is, for the slightly conducting (R=σ_{in}/σ_{out}<10), moderately conducting (10≤R≤20), and highly conducting (R>20) cases. For slightly conducting drops (R=5) only one breakup mode via two symmetrical necks persists for permittivity ratios 0.05Ca_{E,critical} (ratio of electric and surface tension forces), despite significant length-scale variation of mother and daughter drops. At higher Q (for increased drop permittivity) two necks move closer to the bulbous midpart of the extended droplet, which helps enlarge two daughter drops. However, in the case of moderately conducting drops (10≤R≤20) the number of necks increased to four for increased Ca_{E}. Accordingly two pairs of symmetrical daughter drops are created because of recurrent fluctuations of the electrical shear stress and centerline momentum flux. For highly conducting cases of R>20, depending on Ca_{E}, three distinctly elongated droplet states are formed prior to breakup, which results in the onset of three different breakup modes, namely, via formations of lobed ends (Ca_{E}≤0.264), pointed ends (Ca_{E}≤0.68), and nonpointed ends (Ca_{E}>0.83). While being consistent with past measurements, here we precisely characterize the associated breakup mechanisms and physics in terms of the interactive electric pressure, electric shear stress, and hydrodynamic pressure plus velocity gradients. Since the EHD drop breakup is a dynamic process, on an elongated slender drop the activated locally distinct driving forces, i.e., electric pressure at the end regions and tangential electric stress in the midsection, effectively lead to neck formations by virtue of the created high centerline velocity gradient. Accordingly, resulting variations of local extension rate and net mass flux toward drop ends or into intermediate bulbous regions facilitate the multiple-mode drop breakup via the inertia effect, whereas the developed negative curvature around a neck encourages capillary breakup. We also explicitly reveal the effect of the viscosity contrast λ, which particularly influences the breakup characteristics over a broader range of conductivity ratios.

Asymmetry and bifurcations in three-dimensional sudden-contraction channel flows.

This study reports the presence of two different stable modes of bifurcation in the near field of a three-dimensional sudden contraction. To be precise, flow downstream of a symmetric sudden contraction undergoes a transition from a symmetric state to an asymmetric state through a symmetry-breaking pitchfork bifurcation following an increase in the channel aspect ratio or the Reynolds number. In addition, the oncoming (upstream) symmetry-plane flow exhibits spanwise bifurcations along the topological core lines of each of the salient roof and floor eddies. Small aspect-ratio (contraction) channels are noted to facilitate interesting splitting of the salient roof and floor eddies into multicore forms with accompanying spanwise flow bifurcations along the respective vortical core lines. Herein extensive three-dimensional simulations performed with various aspect and contraction ratios and Reynolds numbers clearly suggest that flow transition in the sudden-contraction channels should indeed occur primarily through these two generically distinct modes of bifurcation.

Three-dimensional simulation of square jets in cross-flow.

Direct numerical simulations are performed to predict the three-dimensional unsteady flow interactions in the near-field of a square jet issuing normal to a cross-flow. The simulated flow features reveal the formation of an upstream horseshoe vortex system, which is the result of an interaction between the oncoming channel floor shear layer and the transverse jet; the growth of a sequence of Kelvin-Helmholtz instability-induced vortical rollers in the mixing layer between the jet and the cross-flow, which wrap around the front side of the jet; and the inception process of the counter-rotating vortex pair (CVP), which is initiated through the folding of the lateral jet shear layers. It has been observed that for a square jet in cross-flow, the developed Kelvin-Helmholtz instability induced shear layer rollers do not form closed circumferential vortex rings. Along the downstream side of the jet, the extended tails of such rollers gradually join the locally evolving CVP. The very inception of the CVP is, however, observed to take place within the cross-flow-induced skewed lateral jet shear layers, and such inception was seen to occur slightly below the jet orifice. The simulated results also reveal the growth of the upright wake vortices from the topological singular points that developed on the cross-flow floor boundary layer. The accumulated floor vortices are seen to spiral around the critical points and subsequently leave the channel floor uprightly. During upward motion these vortices eventually get entrained into the CVP core. It has been made clear topologically that the unstable local surface excitations are the seeds from which upright vortices grow. Interestingly, such findings remain quite consistent with the existing experimental predictions for a round jet. Simulations were performed for two moderate values of the Reynolds number 225 and 300, based on the jet width and the average cross-flow inlet velocity, and for two different values of the jet to cross-stream velocity ratio, 2.5 and 3.5.

Generation of streamwise vortices in square sudden-expansion flows.

The intent of the present work is to investigate the nature of jet spreading and the process of evolution of the associated embedded streamwise vortices for the steady flow through a two-step square sudden expansion. Simulations are performed to review the flow physics within a square channel which undergoes a first expansion with an uniform step height 0.75h ( h being the inlet channel width); and at a streamwise distance 8h from the plane of first expansion the channel goes through another expansion with the second step height being half of the first step height. Unlike asymmetric jets, the square jet is observed to experience relatively faster nonuniform azimuthal perturbations during its streamwise evolution and at some downstream location the jet expands in such a way that it looks as if it has locally rotated by 45 degrees. The developed four pairs of outflow type streamwise vortices (with each pair occupying their position at the end of a jet diagonal), which dominated over the first expansion zone, seems to control the azimuthal jet deformation process through their induced outward velocity. Another important aspect of the present investigation is that here we have established a unique pressure analysis which efficiently predicts the presence of all the streamwise vortices in the setup and also their nature of dynamics without any ambiguity. Moreover, the presented pressure analysis suggests that nonuniform lateral flow acceleration within the channel, as induced by the developed transverse pressure gradient skewing, influences the generation of the streamwise vortices. The pressure analysis also successfully predicts every local change in the dynamics of the embedded streamwise vortices, during the downstream evolution of the jet.

Interaction of trailing vortices in the wake of a wall-mounted rectangular cylinder.

Numerical simulations are performed to investigate three-dimensional unsteady vortex-vortex and vortex-surface interactions in the near field of a wall-mounted rectangular cylinder placed inside a channel. The generation mechanism of the upstream and the trailing vortices from the topologically important critical points and their near-wall evolution pattern have been examined in detail. In the upstream region, a laminar necklace vortex system formed around the junction between the rectangular block (cylinder) and the flat channel floor. A sequence of streamwise vortical rollers dominated the downstream interaction region, and they exhibited strong unsteady vortex-surface interaction. Streamwise vortices which formed upstream of the obstacle exhibited quadrupole structure with the dominant pair being central downwash, whereas those lifting the flow behind the obstacle were of predominantly central upwash. Notably, at some downstream location, the near-wall wake structure was observed to locally disappear due to mutual interaction and annihilation by opposite strength vortices on either side of the wake centerline. During the entire course of unsteady flow evolution, such a disappearance of the wake remained closely associated with local contraction of the limiting streamlines on the channel floor, the development of a pair of topologically important floor critical points (saddles), and the presence of a near-wall node on the vertical symmetry plane. The dominance of inward transverse flow toward these saddles together with flow evolution from the downstream node on the vertical symmetry plane were found to be particularly responsible for facilitating the local interaction of various vortices of opposite strength, leading to significant vorticity cancellation in the region. Moreover, the basic source of the wake vortices and their nature of evolution behind the cylinder were also investigated here, and they were found to be fundamentally different from what one usually observes in the near-wake of a transverse jet. However, the growth of a pair of vertically lifting vortices from the spiraling shear layer nodes just behind the downstream edge of the cylinder base was detected in this flow configuration also.