Path Oscillations Research Articles

WITHDRAWN: An experimental study of the dynamics and mass transfer of a rising bubble

In this work, the rise characteristics of shrinking CO2 and non-shrinking N2 bubbles in distilled water for a wide range of bubble sizes in ellipsoidal and wobbly regime (deq = 1.5 mm to 6.5 mm) have been investigated. For these bubbles, their size, trajectory, and rise velocity have been measured using a moving camera system, while the dissolved CO2 is qualitatively studied using a planar laser-induced fluorescence (P-LIF) technique. We explore the interplay between hydrodynamics and mass transfer using well-studied regimes in bubble behaviour. Our results show that the interrelation between mass transfer and bubble rise dynamics is quasi-steady in nature and strongly dependent on wake-induced effects: shape and path oscillations. Based on an analogy of the two phenomena, we conclude that the behaviour of smaller bubbles (<2 mm) as immobile spheres from a mass transfer perspective is not related to the mobility of the interface, but a lack of surface renewal of dissolved gas at the interface. We propose a mechanistic correlation for calculating the mass transfer coefficient, kL, in this regime of bubble size, using the knowledge of the drag coefficient.

Reducing Oscillations for Obstacle Avoidance in a Dense Environment Using Deep Reinforcement Learning and Time-Derivative of an Artificial Potential Field

Obstacle avoidance plays a crucial role in ensuring the safe path planning of quadrotor unmanned aerial vehicles (QUAVs). In this study, we propose a hierarchical framework for obstacle avoidance, which combines the use of artificial potential field (APF) and deep reinforcement learning (DRL) for training low-level motion controllers. Unlike traditional potential field methods, our approach modifies the state information received by the motion controllers using the outputs of the APF path planner. Specifically, the assumed target position is pushed away from obstacles, resulting in adjustments to the perceived position errors. Additionally, we address path oscillations by incorporating the target’s velocity information, which is calculated based on the time-derivative of the repulsive force. Experimental results have validated the effectiveness of our proposed framework in avoiding collisions with obstacles and reducing oscillations.

Global path guided vehicle obstacle avoidance path planning with artificial potential field method

AbstractAn artificial potential field method based on global path guidance (G‐APF) is proposed for target unreachability and local minima problems of the conventional artificial potential field (APF) method in complex environments with dynamic obstacles. First, for the target unreachability problem, the global path attraction is added to the APF; second, an obstacle detection optimisation method is proposed and the optimal virtual target point is selected by setting the evaluation function to improve the local minima problem; finally, based on the obstacle detection optimisation method, the gravitational and repulsive processes are improved so that the path can pass through the narrow channel smoothly and remain collision‐free. Experiments show that the method optimises 40.8% of the total path corners, reduces 81.8% of the number of path oscillations, and shortens 4.3% of the path length in Map 1. It can be applied to the vehicle obstacle avoidance path planning problem in complex environments with dynamic obstacles.

OSCILLATING BUBBLES RISING IN A DOUBLY CONFINED CELL

The motion of bubbles rising in confined geometries has gained interest due to its applications in mixing and mass transfer processes, ranging from bubble column reactors in the chemical industry to solar photobioreactors for algae cultivation. In this work we performed an experimental investigation of the behavior of air bubbles freely rising at high Reynolds numbers in a planar thin-gap cell of thicknessh=2.8 mm filled with distilled water. The in-plane width of the cell W is varied from 2.4 cm to 21 cm. We focus on the influence of lateral confinement on the motion of bubbles in the regimes with regular path and shape oscillations of large amplitude, that occur for the size range 0.6 cm&lt;d&lt;1.2cm. In addition, a rise regime that consists of a vertical rise path with regular shape oscillations, that does not appear in the laterally unconfined case, is uncovered. In the presence of lateral walls, the mean rise velocity of the bubble Vb becomes lower than the velocity of a laterally unconfined bubble of the same size beyond a critical bubble diameterdcVthat decreases as the confinement increases(i.e. as W decreases). The influence of the lateral confinement on the bubble mean shape can be determined from the change in the mean aspect ratio χ of the ellipse that best fits the bubble contour at each instant. It is observed that bubbles become closer to circular (χ closer to 1) as the confinement increases. The departure from the values ofχof the laterally unconfined case occur at a critical diameterdcχthat is lower for greater confinement and also greaterthandcVfor each confinement, thus indicating that the effect of the lateral confinement is seen earlier (i.e. on smaller bubbles) on the velocity than on the aspect ratio. Assuming that the wall effect is related to the strength of the downward flow generated by the bubble, we introduce the mean flow velocity in the space let free for the liquid between the walls and the bubble, Uf, that can be estimated by mass conservation asUf=dVb/(W−d). We further introduce the relative velocity between the bubble and the downward fluid in its vicinityUrel=Vb+Uf=Vb/ξ, whereξ=1−d/Wis the confinement ratio of the bubble. We found that, for a given bubble size in the oscillatory regime, Urel is approximately constant for all the studied values of W, and matches closely the value in the absence of lateral confinement. This provides an estimation, at leading order, of the bubble velocity that generalizes the expression proposed by Filella et al. (JFM, 2015) and accounts for the additional drag experienced by the bubble due to the lateral walls. We then show that, for givendandξ, the frequency and amplitudes of the oscillatory motion can be predicted using the characteristic length and velocity scales d and Urel.

OSCILLATING BUBBLES RISING IN A DOUBLY CONFINED CELL

The motion of bubbles rising in confined geometries has gained interest due to its applications in mixing and mass transfer processes, ranging from bubble column reactors in the chemical industry to solar photobioreactors for algae cultivation. In this work we performed an experimental investigation of the behavior of air bubbles freely rising at high Reynolds numbers in a planar thin-gap cell of thicknessh=2.8 mm filled with distilled water. The in-plane width of the cell W is varied from 2.4 cm to 21 cm. We focus on the influence of lateral confinement on the motion of bubbles in the regimes with regular path and shape oscillations of large amplitude, that occur for the size range 0.6 cm&lt;d&lt;1.2cm. In addition, a rise regime that consists of a vertical rise path with regular shape oscillations, that does not appear in the laterally unconfined case, is uncovered. In the presence of lateral walls, the mean rise velocity of the bubble Vb becomes lower than the velocity of a laterally unconfined bubble of the same size beyond a critical bubble diameterdcVthat decreases as the confinement increases(i.e. as W decreases). The influence of the lateral confinement on the bubble mean shape can be determined from the change in the mean aspect ratio χ of the ellipse that best fits the bubble contour at each instant. It is observed that bubbles become closer to circular (χcloser to 1) as the confinement increases. The departure from the values of χ of the laterally unconfined case occur at a critical diameter dcχ that is lower for greater confinement and also greater than dcV for each confinement, thus indicating that the effect of the lateral confinement is seen earlier (i.e. on smaller bubbles) on the velocity than on the aspect ratio. Assuming that the wall effect is related to the strength of the downward flow generated by the bubble, we introduce the mean flow velocity in the space let free for the liquid between the walls and the bubble, Uf, that can be estimated by mass conservation as Uf=dVb/(W−d). We further introduce the relative velocity between the bubble and the downward fluid in its vicinity Urel=Vb+Uf=Vb/ξ, whereξ=1−d/Wis the confinement ratio of the bubble. We found that, for a given bubble size in the oscillatory regime, Urel is approximately constant for all the studied values of W, and matches closely the value in the absence of lateral confinement. This provides an estimation, at leading order, of the bubble velocity that generalizes the expression proposed by Filella et al. (JFM, 2015) and accounts for the additional drag experienced by the bubble due to the lateral walls. We then show that, for givendandξ, the frequency and amplitudes of the oscillatory motion can be predicted using the characteristic length and velocity scalesdandUrel.

Wireless ultraviolet light MIMO assisted UAV direction perception and collision avoidance method

In order to solve the problem of UAV’s direction perception and collision prevention in the limited radio communication environment, we use wireless ultraviolet (UV) communication as an auxiliary communication method in UAVs. We improve the traditional artificial potential field (APF) method, design a UV- MIMO model installed on the UAV, and propose the improved artificial potential field (IAPF) method. On this basis, the determination of the threat source direction in IAPF algorithm is further simplified, and the improved artificial potential field based on ultraviolet MIMO (IAPF-UVMIMO) algorithm is proposed. Experimental results show that IAPF effectively solves the problems of unreachable targets, path oscillations and local minimums that exist in the traditional artificial potential field method. In addition, IAPF-UVMIMO also improves the tolerance of the threat source direction. Compared with IAPF, the number of collisions with actual collision threats is reduced by 22.6%.

Oscillatory Signatures in the Raindrop Motion Relative to the Air Medium with Terminal Velocity

This paper aims to study the path oscillations of single, spherical water droplets levitated in a wind tunnel to better comprehend the mechanical motion of small raindrops. The observations were carried out in the Mainz vertical wind tunnel. The discrete, fast Fourier transform was used to determine the oscillatory frequencies of the droplet paths, and the Hilbert transform was applied to analyze their instantaneous frequency stability. Both transversal and streamwise components of the path oscillations are described with typical frequencies of several tens of Hertz. The studied oscillations elongate the paths, reduce the terminal velocity of the smallest droplets, and make the rain droplet fall in a non-uniform motion even after reaching terminal velocity. The terminal velocity can be considered as physically having been reached if our proposed practical criterion is satisfied. From a fluid mechanics perspective, the paper fills an experimental gap in the studies of the paths oscillations of single, liquid spheres of microscopic sizes at low Bond numbers &lt;1 and relatively low Reynolds numbers ~102.

Experimental investigation of single helium bubbles rising in FLiNaK molten salt

An experimental investigation of single helium bubbles rising in a stagnant molten fluoride salt mixture was conducted in a 25.4 mm quartz tube at 600 °C and atmospheric pressure. The fluoride salt chosen for this research was the eutectic mixture of LiF-NaF-KF (46.5–11.5–42%), also known as FLiNaK. The images obtained using a high-speed camera were processed to estimate the bubble size, rising velocity, trajectory and shape. The shape of the bubble showed typical characteristics of wobbling bubble corresponding to published classifications. The trajectory of the rising bubble showed complex path oscillations and combinations of rectilinear, zig-zag and helical motion. The projected area-equivalent diameter and experimental terminal velocity varied from 5.26 to 6.23 mm and 232.35–259.57 mm/s, respectively. Several important dimensionless numbers were calculated and reported based on the experimental results, which are closely related to the phenomena involving a gas bubble rising in liquid. The measured terminal velocity was compared with the predictions of existing correlations that include the dimensionless numbers and showed reasonable agreement. The Particle Image Velocimetry (PIV) technique was applied to complement the experimental data set with high-fidelity measurements of the velocity field of the liquid molten salt surrounding the bubble. The paper presents a unique set of PIV and two-phase experimental data capturing the behavior of rising helium bubbles in molten FLiNaK and its surrounding flow field.

Dynamics of freely rising spheres: the effect of moment of inertia

The goal of this study is to elucidate the effect the particle moment of inertia (MOI) has on the dynamics of spherical particles rising in a quiescent and turbulent fluid. To this end, we performed experiments with varying density ratios $\varGamma$ , the ratio of the particle density and fluid density, ranging from $0.37$ up to $0.97$ . At each $\varGamma$ the MOI was varied by shifting mass between the shell and the centre of the particle to vary $I^*$ (the particle MOI normalised by the MOI of a particle with the same weight and a uniform mass distribution). Helical paths are observed for low, and ‘three-dimensional (3-D) chaotic’ trajectories at higher values of $\varGamma$ . The present data suggest no influence of $I^*$ on the critical value for this transition $0.42&lt;\varGamma _{{crit}}&lt;0.52$ . For the ‘3-D chaotic’ rise mode, we identify trends of decreasing particle drag coefficient ( $C_d$ ) and amplitude of oscillation with increasing $I^*$ . Due to limited data it remains unclear if a similar dependence exists in the helical regime as well. Path oscillations remain finite for all cases studied and no ‘rectilinear’ mode is encountered, which may be the consequence of allowing for a longer transient distance in the present compared with earlier work. Rotational dynamics did not vary significantly between quiescent and turbulent surroundings, indicating that for the present configuration these are predominantly wake driven.

Trajectory Analysis of Rising Spheroidal Bubbles in a Rolling Column

The rise of spheroidal bubbles is emulated using a hexapod with periodic angular perturbations to mimic bubble paths in columns onboard seagoing vessels. Bubble trajectories are determined using high-speed camera imaging/ultrasound Doppler velocimetry in vertical, inclined, and rolling columns. The performances of the measurement techniques are compared based on the bubble rise velocity time series and frequency spectra. A hierarchy of reference frames is developed to relate the bubble velocity/acceleration components in the (non-)Galilean frames and to infer from trajectography the lift and drag forces applying to the bubble in the moving-bubble frame. Wall disruption during bubble flights in the rolling column is scrutinized using various geometric/dynamic metrics to underline the dissimilarities between near-wall and centerline bubble path oscillations. Although Coriolis, centrifugal, and Euler accelerations play roles neither on the bubble streamwise rise nor the bubble accelerations, the time-varying character of the buoyancy force brings in dynamic features to the bubble rise in a rolling column that are distinct from those observed in static inclined columns.

Are Static and Dynamic Postural Balance Assessments Two Sides of the Same Coin? A Cross-Sectional Study in the Older Adults

The aim of this study was to investigate if the combination of static and dynamic postural balance assessments gives more accurate indications on balance performance among healthy older adults. We also aimed at studying the effect of a dual-task condition on static and dynamic postural balance control. Fifty-seven healthy older adults (age = 73.2 ± 5.0 year, height = 1.66 ± 0.08 m, and body mass = 72.8 ± 13.8 kg) completed the study. Static and dynamic balance were assessed both in single-task and dual-task conditions through a force plate and an oscillating platform. The dominant handgrip strength was also measured with a dynamometer. Pearson’s correlation revealed non-statistically significant correlations between static and dynamic balance performance. The dual-task worsened the balance performance more in the dynamic (+147.8%) than in the static (+25.10%, +43.45%, and +72.93% for ellipse area, sway path, and AP oscillations, respectively) condition (p < 0.001). A weak correlation was found between dynamic balance performance and handgrip strength both in the single (p < 0.05; r = −0.264) and dual (p < 0.05; r = −0.302) task condition. The absence of correlations between static and dynamic balance performance suggests including both static and dynamic balance tests in the assessment of postural balance alterations among older adults. Since cognitive-interference tasks exacerbated the degradation of the postural control performance, dual-task condition should also be considered in the postural balance assessment.

An experimental study of two identical air bubbles rising side-by-side in water

We experimentally study the dynamics of two identical air bubbles rising side-by-side in water by varying two parameters, namely, the radius of the bubble and center to center distance between them. The bubbles follow a three-dimensional spiraling motion, and their path and shape oscillations are observed in both the front and top views by using a high speed camera with a back-lit illumination and a mirror arrangement. Bubbles of different sizes are created by using a dumping cup mechanism, and the center to center distance between the two bubbles is varied by using telescopic joints. The dynamics of the two side-by-side bubbles is compared and contrasted with that of a single rising bubble. We found that the bubbles act independent of each other, like a single bubble, when the center to center distance is greater than seven times the radius of the bubbles. For similar separation distances, increasing the size of the bubbles results in a smaller terminal velocity and also lesser deviation from a spiral path due to high inertia.

Simulation of a bubble rising at high Reynolds number with mass-conserving finite element lattice Boltzmann method

A mass-conserving finite element lattice Boltzmann equation (FE-LBE) method for the simulation of a bubble rising in viscous fluid at high Reynolds number with large material property contrast is presented in this work. The presented model consists of the conservative phase-field equation for interface capturing and the pressure-velocity formulation of lattice Boltzmann equation (LBE) for recovering the hydrodynamic properties. In this computational framework, LBE is regarded as a special space time discretization of the discrete Boltzmann equation in the characteristic direction and the streaming step is carried out by solving a linear advection equation in an Eulerian framework. We conduct extensive investigations for numerical accuracy and stability through performing multiple benchmark simulations for single bubble rising in a viscous fluid in different flow regimes. The complex dynamics of a high Reynolds number bubble rising with path and shape oscillations are studied and compared to available experimental results. The simulated evolution of the bubble mean shape with Archimedes number, path and shape oscillations in different oscillation regimes, and wake dynamics of the bubble show a good agreement with available experimental data. The current model offers a remarkable improvement in mass conservation compared to the Cahn-Hilliard based FE-LBE model.

Boundary rod elements for modeling the railway at the bridge crossing under the action of the speed railway load

New rod boundary elements on an elastic foundation (finite elements of large length, when approximating the displacements by a set of linear and trigonometric functions) are proposed for calculating the path oscillations outside the bridge and on the bridge, combined with a double-track beam bridge connected through a layer with a high-speed rolling stock movement. The selection of interlayer material is related to the dynamics of the bridge. To build the methodology, the articles published earlier by the author are used: a step-by-step procedure for solving the problems of unsteady dynamics of structures and the method of “nodal accelerations” to take into account the action on the structures of a moving inertial load.

Numerical methods for conservation laws with rough flux

Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with flux functions driven by low-regularity paths. For a convex flux, it is demonstrated that driving path oscillations may lead to “cancellations” in the solution. Making use of this property, we show that for $$\alpha $$-Holder continuous paths the convergence rate of the numerical methods can improve from $$\mathcal {O}(\text {COST}^{-\gamma })$$, for some $$\gamma \in \left[ \alpha /(12-8\alpha ), \alpha /(10-6\alpha )\right] $$, with $$\alpha \in (0, 1)$$, to $$\mathcal {O}(\text {COST}^{-\min (1/4,\alpha /2)})$$. Numerical examples support the theoretical results.

Numerical study of rising bubbles with path instability using conservative level-set and adaptive mesh refinement

This paper focuses on three-dimensional direct numerical simulations of rising bubbles in the wobbling regime, and the study of its dynamical behavior for Eötvös number 1 ≤ Eo ≤ 10 and Morton number 1e−11 ≤ M ≤ 1e−9. The computational methodology is based on a mass Conservative Level-Set method, whereas the spatial discretization of the computational domain employs an Adaptive Mesh Refinement strategy for the reduction of computational resources. The Navier–Stokes equations are discretized using the finite-volume approach on a collocated unstructured mesh; the pressure-velocity coupling is solved using a classical fractional-step projection method. This methodology is applied to a series of verification and validation tests, which are compared with experiments and numerical results from the literature. Finally, buoyancy bubbles rising in the wobbling regime are researched at moderate to high Reynolds numbers (100 < Re < 3000). Terminal Reynolds number, drag coefficient and frequency of path oscillations are compared with empirical correlations and numerical studies from the literature. Results show the discharge of alternate oppositely-oriented hairpin vortex structures. Moreover, depending on the characteristics numbers of the system, different path features, bubble shape, and vortical structures in the wake are reported.

Path oscillations and enhanced drag of light rising spheres

The dynamics of light spheres rising freely under buoyancy in a large expanse of viscous fluid at rest at infinity is investigated numerically. For this purpose, the computational approach developed by Mougin &amp; Magnaudet (Intl J. Multiphase Flow, vol. 28, 2002, pp. 1837–1851) is improved to account for the instantaneous viscous loads induced by the translational and rotational sphere accelerations, which play a crucial role in the dynamics of very light spheres. A comprehensive map of the rise regimes encountered up to Reynolds numbers (based on the sphere diameter and mean rise velocity) of the order of $10^{3}$ is set up by varying independently the body-to-fluid density ratio and the relative magnitude of inertial and viscous effects in approximately 250 distinct combinations. These computations confirm or reveal the presence of several distinct periodic regions on the route to chaos, most of which only exist within a finite range of the sphere relative density and Reynolds number. The wake structure is analysed in these various regimes, evidencing the existence of markedly different shedding modes according to the style of path. The variation of the drag force with the flow parameters is also examined, revealing that only one of the styles of path specific to very light spheres yields a non-standard drag behaviour, with drag coefficients significantly larger than those measured on a fixed sphere under equivalent conditions. The outcomes of this investigation are compared with available experimental and numerical results, evidencing points of consensus and disagreement.

Nonspherical liquid droplet falling in air.

The dynamics of an initially nonspherical liquid droplet falling in air under the action of gravity is investigated via three-dimensional numerical simulations of the Navier-Stokes and continuity equations in the inertial regime. The surface tension is considered to be high enough so that a droplet does not undergo breakup. Vertically symmetric oscillations which decay with time are observed for low inertia. The amplitude of these oscillations increases for high Gallilei numbers and the shape asymmetry in the vertical direction becomes prominent. The reason for this asymmetry has been attributed to the higher aerodynamic inertia. Moreover, even for large inertia, no path deviations or oscillations are observed.

On Path Oscillations Analysis of Mechanical Multi-body and Hydrostatical Driving Units Coupled System

This research deals with the path dynamics of the multi-body systems embedding hydrostatically actuating units. The main purpose of this analysis consists by an optimal dynamic response of the mechanic and hydraulic coupled ensemble, taking into account the characteristic requirements for the final path of the working tool. Theoretical background contains elements both for the multi-body dynamics of mechanical parts, and for the hydraulic driving systems. The forward analysis in terms of command – action connection, and the reverse analysis in terms of system response evaluation and actuating system control frame the main research problem of this study. A computational application developed within Matlab-SimScape software was provided, and a comparative analysis between simulation data and experimental test results was presented. A practical example was developed based on the excavating equipment with a single bucket.

Weakly nonlinear model with exact coefficients for the fluttering and spiraling motion of buoyancy-driven bodies.

Gravity- or buoyancy-driven bodies moving in a slightly viscous fluid frequently follow fluttering or helical paths. Current models of such systems are largely empirical and fail to predict several of the key features of their evolution, especially close to the onset of path instability. Here, using a weakly nonlinear expansion of the full set of governing equations, we present a new generic reduced-order model based on a pair of amplitude equations with exact coefficients that drive the evolution of the first pair of unstable modes. We show that the predictions of this model for the style (e.g., fluttering or spiraling) and characteristics (e.g., frequency and maximum inclination angle) of path oscillations compare well with various recent data for both solid disks and air bubbles.