[Show abstract][Hide abstract] ABSTRACT: The axisymmetric collapse of a cylindrical air cavity in water follows a
universal power law with logarithmic corrections. Nonetheless, it has
been suggested that the introduction of a small azimuthal disturbance
induces a long term memory effect, reflecting in oscillations which are
no longer universal but remember the initial condition. In this work, we
create non-axisymmetric air cavities by driving a metal disc through an
initially-quiescent water surface and observe their subsequent
gravity-induced collapse. The cavities are characterized by azimuthal
harmonic disturbances with a single mode number $m$ and amplitude $a_m$.
For small initial distortion amplitude (1 or 2% of the mean disc
radius), the cavity walls oscillate linearly during collapse, with
nearly constant amplitude and increasing frequency. As the amplitude is
increased, higher harmonics are triggered in the oscillations and we
observe more complex pinch-off modes. For small amplitude disturbances
we compare our experimental results with the model for the amplitude of
the oscillations by Schmidt et al. (2009) and the model for the collapse
of an axisymmetric impact-created cavity previously proposed by Bergmann
et al. (2009b). By combining these two models we can reconstruct the
three-dimensional shape of the cavity at any time before pinch-off.
[Show abstract][Hide abstract] ABSTRACT: Previous numerical studies have shown that the "ultimate regime of thermal
convection" can be attained in a Rayleigh-Benard cell when the kinetic and
thermal boundary layers are eliminated by replacing the walls with periodic
boundary conditions (homogeneous Rayleigh-Benard convection). Then, the heat
transfer scales like Nu ~ Ra^{1/2} and turbulence intensity as Re ~ Ra^{1/2},
where the Rayleigh number Ra indicates the strength of the driving force.
However, experiments never operate in unbounded domains and it is important to
understand how confinement might alter the approach to this ultimate regime.
Here we consider homogeneous Rayleigh-Benard convection in a laterally confined
geometry - a small aspect-ratio vertical cylindrical cell - and show evidence
of the ultimate regime as Ra is increased: In spite of the confinement and the
resulting kinetic boundary layers, we still find Nu ~ Re ~ Ra^{1/2}. The system
supports exact solutions composed of modes of exponentially growing vertical
velocity and temperature fields, with Ra as the critical parameter determining
the properties of these modes. Counterintuitively, in the low Ra regime, or for
very narrow cylinders, the numerical simulations are susceptible to these
solutions which can dominate the dynamics and lead to very high and unsteady
heat transfer. As Ra is increased, interaction between modes stabilizes the
system, evidenced by the increasing homogeneity and reduced fluctuations in the
r.m.s. velocity and temperature fields. We also test that physical results
become independent of the periodicity length of the cylinder, a purely
numerical parameter, as the aspect ratio is increased.
[Show abstract][Hide abstract] ABSTRACT: The pressure-driven inertial collapse of a cylindrical void in an inviscid
liquid is an integrable, Hamiltonian system that forms a finite-time
singularity as the radius of the void collapses to zero. Here it is shown that
when the natural cylindrical symmetry of the void is perturbed azimuthally, the
perturbation modes neither grow nor decay, but instead cause constant amplitude
vibrations about the leading-order symmetric collapse. Though the amplitudes
are frozen in time, they grow relative to the mean radius which is collapsing
to zero, eventually overtaking the leading-order symmetric implosion. Including
weak viscous dissipation destroys the integrability of the underlying symmetric
implosion, and the effect on the stability spectrum is that short-wavelength
disturbances are now erased as the implosion proceeds. Introducing a weak
rotational flow component to the symmetric implosion dynamics causes the
vibrating shapes to spin as the mean radius collapses. The above theoretical
scenario is compared to a closely related experimental realization of void
implosion: the disconnection of an air bubble from an underwater nozzle. There,
the thin neck connecting the bubble to the nozzle implodes primarily radially
inward and disconnects. Recent experiments were able to induce vibrations of
the neck shape by releasing the bubble from a slot-shaped nozzle. The frequency
and amplitude of the observed vibrations are consistent with the theoretical
prediction once surface tension effects are taken into account.
[Show abstract][Hide abstract] ABSTRACT: The axisymmetric collapse of a cylindrical air cavity in water follows a
universal power law with logarithmic corrections. Nonetheless, it has been
suggested that the introduction of a small azimuthal disturbance induces a long
term memory effect, reflecting in oscillations which are no longer universal
but remember the initial condition. In this work, we create non-axisymmetric
air cavities by driving a metal disc through an initially-quiescent water
surface and observe their subsequent gravity-induced collapse. The cavities are
characterized by azimuthal harmonic disturbances with a single mode number $m$
and amplitude $a_m$. For small initial distortion amplitude (1 or 2% of the
mean disc radius), the cavity walls oscillate linearly during collapse, with
nearly constant amplitude and increasing frequency. As the amplitude is
increased, higher harmonics are triggered in the oscillations and we observe
more complex pinch-off modes. For small amplitude disturbances we compare our
experimental results with the model for the amplitude of the oscillations by
Schmidt et al. (2009) and the model for the collapse of an axisymmetric
impact-created cavity previously proposed by Bergmann et al. (2009b). By
combining these two models we can reconstruct the three-dimensional shape of
the cavity at any time before pinch-off.
[Show abstract][Hide abstract] ABSTRACT: Numerical results for kinetic and thermal energy dissipation rates in bubbly Rayleigh-Bénard convection are reported. Bubbles have a twofold effect on the flow: on the one hand, they absorb or release heat to the surrounding liquid phase, thus tending to decrease the temperature differences responsible for the convective motion; but on the other hand, the absorbed heat causes the bubbles to grow, thus increasing their buoyancy and enhancing turbulence (or, more properly, pseudoturbulence) by generating velocity fluctuations. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.
[Show abstract][Hide abstract] ABSTRACT: Heavy or light particles introduced into a liquid trigger motion due to their buoyancy, with the potential to drive flow to a turbulent state. In the case of vapor bubbles present in a liquid near its boiling point, thermal coupling between the liquid and vapor can moderate this additional motion by reducing temperature gradients in the liquid. Whether the destabilizing mechanical feedback or stabilizing thermal feedback will dominate the system response depends on the number of bubbles present and the properties of the phase change. Here we study thermal convection with phase change in a cylindrical Rayleigh–Bénard cell to examine this competition. Using the Reynolds number of the flow as a signature of turbulence and the intensity of the flow, we show that in general the rising vapor bubbles destabilize the system and lead to higher velocities. The exception is a limited regime corresponding to phase change with a high latent heat of vaporization (corresponding to low Jakob number), where the vapor bubbles can eliminate the convective flow by smoothing temperature differences of the fluid.
New Journal of Physics 02/2011; 13(2):025002. DOI:10.1088/1367-2630/13/2/025002 · 3.56 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Numerical simulations of Rayleigh-B'enard convection in an infinite cylindrical cell show that despite the restriction of velocity and temperature fluctuations due to the side walls, the system approaches the ultimate regime of thermal convection as the Rayleigh number (Ra) is increased. Here, Ra is defined based on the underlying linear temperature gradient which is driving the convection. This periodic system has exact solutions composed of modes of exponentially growing vertical velocity and temperature fields. In the low Ra regime these solutions dominate the dynamics and lead to very high and unsteady heat transfer. As Ra is increased, interaction between these modes stabilizes the system, evidenced by the increasing homogeneity and reduced fluctuations in the r.m.s. velocity and temperature fields.
[Show abstract][Hide abstract] ABSTRACT: We report numerical results for thermal and kinetic energy dissipation rates in bubbly Rayleigh-B'enard convection. The bubbles always homogenize the temperature field by absorbing heat from surrounding fluid and attenuate the thermal energy dissipation. A small number of non-growing bubbles can even halt convection by smoothing the temperature fluctuations which drive the convection. Growing bubbles imply additional forcing on the fluid and thus increase the fluctuations and hence the kinetic energy dissipation. This enhancement depends on the ratio of the sensible heat to the latent heat of the phase change, given by the Jakob number, which determines the dynamics of the bubble growth.
[Show abstract][Hide abstract] ABSTRACT: A round disk with a harmonic disturbance impacts on a water surface and creates a non-axisymmetric cavity which collapses under the influence of hydrostatic pressure. We use disks deformed with mode m=2 to m=6. For all mode numbers we find clear evidence for a phase inversion of the cavity wall during the collapse. We present a fluid dynamics video showing high speed imaging of different modes, pointing out the characteristic features during collapse.
Physics of Fluids 09/2010; 22(9). DOI:10.1063/1.3481432 · 2.03 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: A round disk with a harmonic disturbance impacts on a water surface and creates a non-axisymmetric cavity which collapses under the influence of hydrostatic pressure. We use disks deformed with mode m=2 to m=6. For all mode numbers we find clear evidence for a phase inversion of the cavity wall during the collapse. We present a fluid dynamics video showing high speed imaging of different modes, pointing out the characteristic features during collapse.
[Show abstract][Hide abstract] ABSTRACT: Upon the impact of a circular disk on a water surface an expanding cylindrical cavity is created which collapses under the influence of the hydrostatic pressure. We experimentally observe small disturbances in the azimuthal direction that tend to grow towards the pinch-off. To quantitatively investigate the growth of specific mode-numbers, we use disks with a harmonic disturbance applied to their round shapes and study the collapse of the disturbed cavity using high-speed imaging. We performed experiments using disturbances up to mode number m=6, with varying strength from 1% to 25% of the radius of the undisturbed circular disk. For the smallest disturbances we compare the experimental results to a linear stability analysis, following Schmidt et al., Nat. Phys. 5, 343-346 (2009). Larger disturbances become non-linear in an early stage, showing a wealth of complex phenomena like secondary collapses and jets, during which the initial symmetry corresponding to the mode number m always remains preserved.