Harish N. Dixit

Capillary effects on floating cylindrical particles

In this study, we develop a systematic perturbation procedure in the small parameter, B1/2, where B is the Bond number, to study capillary effects on small cylindrical particles at interfaces. Such a framework allows us to address many problems involving particles on flat and curved interfaces. In particular, we address four specific problems: (i) capillary attraction between cylinders on flat interface, in which we recover the classical approximate result of Nicolson [“The interaction between floating particles,” Proc. Cambridge Philos. Soc. 45, 288–295 (1949)10.1017/S0305004100024841], thus putting it on a rational basis; (ii) capillary attraction and aggregation for an infinite array of cylinders arranged on a periodic lattice, where we show that the resulting Gibbs elasticity obtained for an array can be significantly larger than the two cylinder case; (iii) capillary force on a cylinder floating on an arbitrary curved interface, where we show that in the absence of gravity, the cylinder experiences a lateral force which is proportional to the gradient of curvature; and (iv) capillary attraction between two cylinders floating on an arbitrary curved interface. The present perturbation procedure does not require any restrictions on the nature of curvature of the background interface and can be extended to other geometries.In this study, we develop a systematic perturbation procedure in the small parameter, B1/2, where B is the Bond number, to study capillary effects on small cylindrical particles at interfaces. Such a framework allows us to address many problems involving particles on flat and curved interfaces. In particular, we address four specific problems: (i) capillary attraction between cylinders on flat interface, in which we recover the classical approximate result of Nicolson [“The interaction between floating particles,” Proc. Cambridge Philos. Soc. 45, 288–295 (1949)10.1017/S0305004100024841], thus putting it on a rational basis; (ii) capillary attraction and aggregation for an infinite array of cylinders arranged on a periodic lattice, where we show that the resulting Gibbs elasticity obtained for an array can be significantly larger than the two cylinder case; (iii) capillary force on a cylinder floating on an arbitrary curved interface, where we show that in the absence of gravity, the cylinder experiences a...

Vortex shedding patterns, their competition, and chaos in flow past inline oscillating rectangular cylinders

The flow past inline oscillating rectangular cylinders is studied numerically at a Reynolds number representative of two-dimensional flow. A symmetric mode, known as S-II, consisting of a pair of oppositely signed vortices on each side, observed recently in experiments, is obtained computationally. A new symmetric mode, named here as S-III, is also found. At low oscillation amplitudes, the vortex shedding pattern transitions from antisymmetric to symmetric smoothly via a regime of intermediate phase. At higher amplitudes, this intermediate regime is chaotic. The finding of chaos extends and complements the recent work of Perdikaris et al. [Phys. Fluids 21(10), 101705 (2009)]. Moreover, it shows that the chaos results from a competition between antisymmetric and symmetric shedding modes. For smaller amplitude oscillations, rectangular cylinders rather than square are seen to facilitate these observations. A global, and very reliable, measure is used to establish the existence of chaos.

Vortex-induced instabilities and accelerated collapse due to inertial effects of density stratification

A vortex placed at a density interface winds it into an ever-tighter spiral. We show that this results in a combination of a centrifugal Rayleigh-Taylor (CRT) instability and a spiral Kelvin-Helmholtz (SKH) type of instability. The SKH instability arises because the density interface is not exactly circular, and dominates at large times. Our analytical study of an inviscid idealized problem illustrates the origin and nature of the instabilities. In particular, the SKH is shown to grow slightly faster than exponentially. The predicted form lends itself for checking by a large computation. From a viscous stability analysis using a finite-cored vortex, it is found that the dominant azimuthal wavenumber is smaller for lower Reynolds number. At higher Reynolds numbers, disturbances subject to the combined CRT and SKH instabilities grow rapidly, on the inertial time scale, while the flow stabilizes at low Reynolds numbers. Our direct numerical simulations are in good agreement with these studies in the initial stages, after which nonlinearities take over. At Atwood numbers of 0.1 or more, and a Reynolds number of 6000 or greater, both stability analysis and simulations show a rapid destabilization. The result is an erosion of the core, and breakdown into a turbulence-like state. In studies at low Atwood numbers, the effect of density on the inertial terms is often ignored, and the density field behaves like a passive scalar in the absence of gravity. The present study shows that such treatment is unjustified in the vicinity of a vortex, even for small changes in density when the density stratification is across a thin layer. The study would have relevance to any high-Peclet-number flow where a vortex is in the vicinity of a density-stratified interface.

Effect of density stratification on vortex merger

We study the effect of density stratification in the plane on the merging of two equal vortices. Direct numerical simulations are performed for a wide range of parameters. Boussinesq and non-Boussinesq effects are considered separately. With the Boussinesq approximation, moderate to high Prandtl number and Froude number close to unity, there is a monotonic drifting away of the vortices from each other, and merger is completely prevented. Among non-Boussinesq effects, the inertial effects of density stratification are highlighted. These give rise to a breaking of symmetry, and consequently, the vorticity centroid is found to drift significantly from its initial position. Using an idealized model, we explore the role of baroclinic vorticity in determining these features of the merger process.

Dynamics of Cross-Flow Heat Exchanger Tubes With Multiple Loose Supports

Dynamics of cross-flow heat exchanger tubes with two loose supports has been studied. An analytical model of a cantilever beam that includes time-delayed displacement term along with two restrained spring forces has been used to model the flexible tube. The model consists of one loose support placed at the free end of the tube and the other at the midspan of the tube. The critical fluid flow velocity at which the Hopf bifurcation occurs has been obtained after solving a free vibration problem. The beam equation is discretized to five second-order delay differential equations (DDEs) using Galerkin approximation and solved numerically. It has been found that for flow velocity less than the critical flow velocity, the system shows a positive damping leading to a stable response. Beyond the critical velocity, the system becomes unstable, but a further increase in the velocity leads to the formation of a positive damping which stabilizes the system at an amplified oscillatory state. For a sufficiently high flow velocity, the tube impacts on the loose supports and generates complex and chaotic vibrations. The impact loading on the loose support is modeled either as a cubic spring or a trilinear spring. The effect of spring constants and free-gap of the loose support on the dynamics of the tube has been studied.

Instabilities due a vortex at a density interface: gravitational and centrifugal effects

A vortex placed at an initially straight density interface winds it into an ever-tightening spiral. This flow then displays rich dynamics, due to inertial effects caused by density stratification (non-Boussinesq effects), and gravitational effects. In the absence of gravity we showed recently that the flow is subject to centrifugal Rayleigh-Taylor and spiral Kelvin-Helmholtz instabilities. The latter grows slightly faster than exponentially. In this paper we present computations including gravity with and without and with inertial effects. Gravity modifies the spiralling process and contributes to the breakdown of the vortex. When both effects are allowed to operate together, the resulting flow has a complex radial character, with small-scale structures near the vortex core attributed to non-Boussinesq effects, and large scale roll-up due to gravity followed by breakdown.