Taylor bubble moving in a flowing liquid in vertical channel: transition from symmetric to asymmetric shape

The velocity and shape of Taylor bubbles moving in a vertical channel in a Poiseuille liquid flow were studied for the inertial regime, characterized by large Reynolds numbers. Numerical experiments were carried out for positive (upward) and negative (downward) liquid mean velocity. Previous investigations in tube have reported that for upward flow the bubble is symmetric and its velocity follows the law of Nicklin whereas for certain downward flow conditions the symmetry is broken and the bubble rises appreciably faster. To study the bubble motion and to identify the existence of a transition, a 2D numerical code that solves the Navier-Stokes equations (through a VoF implementation) was used to obtain the bubble shape and the rise velocity for different liquid mean velocity. A reference frame located at the bubble tip as well as an irregular grid were implemented to allow for long simulation times without an excessively large numerical domain. It was observed that whenever the mean liquid velocity exceeded some critical value, bubbles adopted a symmetric final shape even though their initial shape was asymmetric. Conversely, if the mean liquid velocity was smaller than that critical value, a transition to a non-symmetric shape occurred, along with a correspondingly faster velocity. It was also found that surface tension has a stabilizing effect on the transition

Taylor bubble rising in a vertical pipe against laminar or turbulent downward flow: symmetric to asymmetric shape transition

The symmetry of Taylor bubbles moving in a vertical pipe is likely to break when the liquid flows downward at a velocity greater than some critical value. The present experiments performed in the inertial regime for Reynolds numbers in the range 100<Re <10000 show that bifurcation to an eccentric motion occurs, with a noticeable increase of the bubble velocity. The influence of the surface tension parameter (an inverse Eötvös number) has been investigated in the range [0.0045,0.067]. It appears that the motion of an asymmetric bubble is much more sensitive to surface tension than that of a symmetric bubble. For any given surface tension parameter, the symmetry-breaking bifurcation occurs in both laminar and turbulent flow at the same vorticity to radius ratio on the axis of the carrier fluid. This conclusion also applies to results obtained previously from numerical experiments in plane flows

A note on the onset of recirculation in a 2D Couette flow over a wavy bottom

Laminar Couette flow over a fixed wavy surface was studied with direct numerical simulation in a 2D periodic numerical domain. The mesh was generated by a conformal transformation that sets horizontal flow at the top of the domain, where a constant velocity boundary condition is given. The bottom of the domain is a wavy sinusoidal surface of wave slope 2πa/λ. The combined effect of bottom shape, inertia, and viscosity was explored using different Reynolds numbers (Re) and two dimen- sionless parameters in terms of channel width h, wavelength λ, and the amplitude of the wavy bottom a. Even if the Reynolds number was large, the simulations were not perturbed so the regime was always laminar. However, a recirculation appeared at the vicinity of the trough. The horizontal location of the eddy center was reported as a function of 2πa/λ and Reλ/h. The conditions for the onset of this recirculation were studied and compared with results from the literature. Two regimes can be clearly identified from the numerical results; a viscous regime with a weak dependence between 2πa/λ and Reλ/h for small Reynolds numbers and an inertial regime with an exponential dependence between 2πa/λ and Reλ/h for large Reynolds numbers, which presents an approximate slope of −1/3. Almost all results collapse in one single curve that characterizes the phenomenon (with the exception of some points where the flow is confined due to a large λ/h ratio)

The effect of column tilt on flow homogeneity and particle agitation in a liquid fluidized bed

The motion of particles in a solid-liquid fluidized bed was experimentally studied by video tracking of marked particles in a matched refractive index medium. In this study, two fluidized states are compared, one carefully aligned in the vertical direction ensuring a homogeneous fluidisation and another one with a non-homogeneous fluidisation regime that results from a slight tilt of the fluidisation column of 0.3° with respect to the vertical. As a result of the misalignment, large recirculation loops develop within the bed in a well-defined spatial region. It is found that in that range of solid fraction (between 0.3 and 0.4), the inhomogeneous motion of the particles leads to significant differences in velocity fluctuations as well as in self-diffusion coefficient of the particles in the vertical direction, whereas the fluidisation height remains unaffected. At lower (less than 0.2) or higher (higher than 0.5) concentration, particle agitation characteristics are almost unchanged in the vertical direction

Numerical Study of an Oscillating-Wing Wingmill for Ocean Current Energy Harvesting: Fluid-Solid-Body Interaction with Feedback Control

The performance and flow around an oscillating foil device for current energy extraction (a wingmill) was studied through numerical simulations. OpenFOAM was used in order to study the two-dimensional (2D) flow around a wingmill. A closed loop control law was coded in order to follow a reference angle of attack. The objective of this control law is to modify the angle of attack in order to enhance the lift force (and increase power extraction). Dimensional analysis suggests a compromise between the generator (or damper) stiffness and actuator/control gains, so a parametric study was carried out while using a new dimensionless number, called B, which represents this compromise. It was found that there is a maximum on the efficiency curve in terms of the aforementioned dimensionless parameter. The lessons that are learned from this fluid-structure and feedback coupling are discussed; this interaction, combined with the feedback dynamics, may trigger dynamic stall, thus decreasing the performance. Moreover, if the control strategy is not carefully selected, then the energy spent on the actuator may affect efficiency considerably. This type of simulation could allow for the system identification, control synthesis, and optimization of energy harvesting devices in future studies

A Mechanical Picture of Fractal Darcy’s Law

The main goal of this manuscript is to generalize Darcy’s law from conventional calculus to fractal calculus in order to quantify the fluid flow in subterranean heterogeneous reservoirs. For this purpose, the inherent features of fractal sets are scrutinized. A set of fractal dimensions is incorporated to describe the geometry, morphology, and fractal topology of the domain under study. These characteristics are known through their Hausdorff, chemical, shortest path, and elastic backbone dimensions. Afterward, fractal continuum Darcy’s law is suggested based on the mapping of the fractal reservoir domain given in Cartesian coordinates xi into the corresponding fractal continuum domain expressed in fractal coordinates ξi by applying the relationship ξi=ϵ0(xi/ϵ0)αi−1, which possesses local fractional differential operators used in the fractal continuum calculus framework. This generalized version of Darcy’s law describes the relationship between the hydraulic gradient and flow velocity in fractal porous media at any scale including their geometry and fractal topology using the αi-parameter as the Hausdorff dimension in the fractal directions ξi, so the model captures the fractal heterogeneity and anisotropy. The equation can easily collapse to the classical Darcy’s law once we select the value of 1 for the alpha parameter. Several flow velocities are plotted to show the nonlinearity of the flow when the generalized Darcy’s law is used. These results are compared with the experimental data documented in the literature that show a good agreement in both high-velocity and low-velocity fractal Darcian flow with values of alpha equal to 0α11 and 1α12, respectively, whereas α1=1 represents the standard Darcy’s law. In that way, the alpha parameter describes the expected flow behavior which depends on two fractal dimensions: the Hausdorff dimension of a porous matrix and the fractal dimension of a cross-section area given by the intersection between the fractal matrix and a two-dimensional Cartesian plane. Also, some physical implications are discussed

Transpiration of a Tropical Dry Deciduous Forest in Yucatan, Mexico

The study of forest hydrology and its relationships with climate requires accurate estimates of water inputs, outputs, and changes in reservoirs. Evapotranspiration is frequently the least studied component when addressing the water cycle; thus, it is important to obtain direct measurements of evaporation and transpiration. This study measured transpiration in a tropical dry deciduous forest in Yucatán (Mexico) using the thermal dissipation method (Granier-type sensors) in representative species of this vegetation type. We estimated stand transpiration and its relationship with allometry, diameter-at-breast-height categories, and previously published equations. We found that transpiration changes over time, being higher in the rainy season. Estimated daily transpiration ranged from 0.562 to 0.690 kg m–2 d–1 in the late dry season (April–May) and from 0.686 to 1.29 kg m–2 d–1 in the late rainy season (September–October), accounting for up to 51% of total evapotranspiration in the rainy season. These daily estimates are consistent with previous reports for tropical dry forests and other vegetation types. We found that transpiration was not species-specific; diameter at breast height (DBH) was a reliable way of estimating transpiration because water use was directly related to allometry. Direct measurement of transpiration would increase our ability to accurately estimate water availability and assess the responses of vegetation to climate change

Transpiration of a Tropical Dry Deciduous Forest in Yucatan, Mexico

The study of forest hydrology and its relationships with climate requires accurate estimates of water inputs, outputs, and changes in reservoirs. Evapotranspiration is frequently the least studied component when addressing the water cycle; thus, it is important to obtain direct measurements of evaporation and transpiration. This study measured transpiration in a tropical dry deciduous forest in Yucat&aacute;n (Mexico) using the thermal dissipation method (Granier-type sensors) in representative species of this vegetation type. We estimated stand transpiration and its relationship with allometry, diameter-at-breast-height categories, and previously published equations. We found that transpiration changes over time, being higher in the rainy season. Estimated daily transpiration ranged from 0.562 to 0.690 kg m&ndash;2 d&ndash;1 in the late dry season (April&ndash;May) and from 0.686 to 1.29 kg m&ndash;2 d&ndash;1 in the late rainy season (September&ndash;October), accounting for up to 51% of total evapotranspiration in the rainy season. These daily estimates are consistent with previous reports for tropical dry forests and other vegetation types. We found that transpiration was not species-specific; diameter at breast height (DBH) was a reliable way of estimating transpiration because water use was directly related to allometry. Direct measurement of transpiration would increase our ability to accurately estimate water availability and assess the responses of vegetation to climate change