Drag and lift forces on bubbles in a rotating flow

2007 ◽  
Vol 571 ◽  
pp. 439-454 ◽  
Author(s):  
ERNST A. VAN NIEROP ◽  
STEFAN LUTHER ◽  
JOHANNA J. BLUEMINK ◽  
JACQUES MAGNAUDET ◽  
ANDREA PROSPERETTI ◽  
...  
Keyword(s):  
Solid Body ◽  
Slip Velocity ◽  
Strong Dependence ◽  
Bubble Diameter ◽  
Rotating Flow ◽  
Viscous Effects ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Lift Forces ◽  
Drag And Lift

The motion of small air bubbles in a horizontal solid-body rotating flow is investigated experimentally. Bubbles with a typical radius of 1 mm are released in a liquid-filled horizontally rotating cylinder. We measure the transient motion of the bubbles in solid-body rotation and their final equilibrium position from which we compute drag and lift coefficients for a wide range of dimensionless shear rates 0.1<Sr<2 (Sr is the velocity difference over one bubble diameter divided by the slip velocity of the bubble) and Reynolds numbers 0.01<Re<500 (Re is based on the slip velocity and bubble diameter). For large Sr, we find that the drag force is increased by the shear rate. The lift force shows strong dependence on viscous effects. In particular, for Re<5, we measure negative lift forces, in line with theoretical predictions.

scholarly journals Drag and lift forces on clean spherical and ellipsoidal bubbles in a solid-body rotating flow

2011 ◽  
Vol 682 ◽  
pp. 434-459 ◽  
Author(s):  
MARIE RASTELLO ◽  
JEAN-LOUIS MARIÉ ◽  
MICHEL LANCE
Keyword(s):  
Aspect Ratio ◽  
Drag Coefficient ◽  
Solid Body ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Uniform Flow ◽  
Rotating Flow ◽  
Wide Range ◽  
Spherical Bubbles ◽  
Drag And Lift

A single bubble is placed in a solid-body rotating flow of silicon oil. From the measurement of its equilibrium position, lift and drag forces are determined. Five different silicon oils have been used, providing five different viscosities and Morton numbers. Experiments have been performed over a wide range of bubble Reynolds numbers (0.7 ≤ Re ≤ 380), Rossby numbers (0.58 ≤ Ro ≤ 26) and bubble aspect ratios (1 ≤ χ ≤ 3). For spherical bubbles, the drag coefficient at the first order is the same as that of clean spherical bubbles in a uniform flow. It noticeably increases with the local shear S = Ro−1, following a Ro−5/2 power law. The lift coefficient tends to 0.5 for large Re numbers and rapidly decreases as Re tends to zero, in agreement with existing simulations. It becomes hardly measurable for Re approaching unity. When bubbles start to shrink with Re numbers decreasing slowly, drag and lift coefficients instantaneously follow their stationary curves versus Re. In the standard Eötvös–Reynolds diagram, the transitions from spherical to deformed shapes slightly differ from the uniform flow case, with asymmetric shapes appearing. The aspect ratio χ for deformed bubbles increases with the Weber number following a law which lies in between the two expressions derived from the potential flow theory by Moore (J. Fluid Mech., vol. 6, 1959, pp. 113–130) and Moore (J. Fluid Mech., vol. 23, 1965, pp. 749–766) at low- and moderate We, and the bubble orients with an angle between its minor axis and the direction of the flow that increases for low Ro. The drag coefficient increases with χ, to an extent which is well predicted by the Moore (1965) drag law at high Re and Ro. The lift coefficient is a function of both χ and Re. It increases linearly with (χ − 1) at high Re, in line with the inviscid theory, while in the intermediate range of Reynolds numbers, a decrease of lift with aspect ratio is observed. However, the deformation is not sufficient for a reversal of lift to occur.

Drag and lift forces on particles in a rotating flow

2009 ◽  
Vol 643 ◽  
pp. 1-31 ◽  
Author(s):  
J. J. BLUEMINK ◽  
D. LOHSE ◽  
A. PROSPERETTI ◽  
L. VAN WIJNGAARDEN
Keyword(s):  
Solid Body ◽  
Numerical Results ◽  
Rotating Flow ◽  
Cylinder Axis ◽  
Drag Coefficients ◽  
Rotating Sphere ◽  
Particle Spin ◽  
Wide Range ◽  
Drag And Lift ◽  
Lift And Drag

A freely rotating sphere in a solid-body rotating flow is experimentally investigated. When the sphere is buoyant, it reaches an equilibrium position from which drag and lift coefficients are determined over a wide range of particle Reynolds numbers (2 ≤ Re ≤ 1060). The wake behind the sphere is visualized and appears to deflect strongly when the sphere is close to the cylinder axis. The spin rate of the sphere is recorded. In fluids with low viscosity, spin rates more than twice as large as the angular velocity of the cylinder can be observed. By comparing numerical results for a fixed but freely spinning sphere with a fixed non-spinning sphere for Re ≤ 200, the effect of the sphere spin on the lift coefficient is determined. The experimentally and numerically determined lift and drag coefficients and particle spin rates all show excellent agreement for Re ≤ 200. The combination of the experimental and numerical results allows for a parameterization of the lift and drag coefficients of a freely rotating sphere as function of the Reynolds number, the particle spin and the location of the particle with respect to the cylinder axis. Although the effect of the flow rotation on the particle spin is different in shear flow and solid-body rotating flow, the effect of spin on lift is found to be comparable for both types of flow.

Bubble behaviour in a horizontal high-speed solid-body rotating flow

2021 ◽  
Vol 925 ◽  
Author(s):  
Majid Rodgar ◽  
Hélène Scolan ◽  
Jean-Louis Marié ◽  
Delphine Doppler ◽  
Jean-Philippe Matas
Keyword(s):  
Aspect Ratio ◽  
Solid Body ◽  
High Speed ◽  
Lift Coefficient ◽  
Rotating Flow ◽  
Axis Of Rotation ◽  
Large Fluctuations ◽  
The Mean ◽  
Drag And Lift ◽  
The Impact

We study experimentally the behaviour of a bubble injected into a horizontal liquid solid-body rotating flow, in a range of rotational velocities where the bubble is close to the axis of rotation. We first study the stretching of the bubble as a function of its size and of the rotation of the cell. We show that the bubble aspect ratio can be predicted as a function of the bubble Weber number by the model of Rosenthal (J. Fluid Mech., vol. 12, 1962, 358–366) provided an appropriate correction due to the impact of buoyancy is included. We next deduce the drag and lift coefficients from the mean bubble position. For large bubbles straddling the axis of rotation, we show that the drag coefficient $C_D$ is solely dependent on the Rossby number $Ro$, with $C_D \approx 1.5/Ro$. In the same limit of large bubbles, we show that the lift coefficient $C_L$ is controlled by the shear Reynolds number $Re_{shear}$ at the scale of the bubble. For $Re_{shear}$ larger than 3000 we observe a sharp transition, wherein large fluctuations in the bubble aspect ratio and mean position occur, and can lead to the break-up of the bubble. We interpret this regime as a resonance between the periodic forcing of the rotating cell and the eigenmodes of the stretched bubble.

On the Axial-Flexural-Torsional Coupling of Underwater Slender Cylinders

2012 ◽  
Author(s):  
Waldir T. Pinto ◽  
Carlos A. Levi
Keyword(s):  
Large Strains ◽  
Element Formulation ◽  
Algebraic Equations ◽  
Three Dimensional Model ◽  
Cylindrical Structures ◽  
Highly Nonlinear ◽  
Wide Range ◽  
Torsional Coupling ◽  
Lift Forces ◽  
Drag And Lift

This paper presents a numerical model for the simulation of the axial-flexural-torsional coupling of undewater cylindrical structures. Cylindrical structures are largely utilized in the marine environment in a wide range of applications as in risers, marine cables, flexible pipes, mooring systems and so on. They may exhibit complex axial-flexural-torsional coupling, which makes the structural analysis highly nonlinear. In addition, the fluid-structure interaction may include flow induced vibrations, frequency lock-in and internal flow effects. The proposed three-dimensional model assumes that the structure aspect ratio is very high, its cross section is circular, the cable is elastic and may experience large displacements and large strains, as long as the elastic regime holds. The steady state load on the cylinder consists of the self-weight and buoyancy, drag and lift forces, in addition to a distributed residual twist along the cylinder. The drag and lift forces are evaluated by Morison type formulation. The governing differential equations are derived from first principles, assuming Newtonian mechanics. Then, they are solved numerically by a finite element formulation based on nonlinear space frame elements. The resulting set of algebraic equations is solved by a minimization technique that uses the Newton-Raphson algorithm. Results show the ability of the model to predict the static configuration of equilibrium of the cylinder and to capture the coupling between axial, flexural and torsional responses of the cylinder.

scholarly journals Drag and lift forces on interface-contaminated bubbles spinning in a rotating flow

2009 ◽  
Vol 624 ◽  
pp. 159-178 ◽  
Author(s):  
MARIE RASTELLO ◽  
JEAN-LOUIS MARIÉ ◽  
NATHALIE GROSJEAN ◽  
MICHEL LANCE
Keyword(s):  
Reynolds Number ◽  
Solid Body ◽  
Equilibrium Position ◽  
Rotating Flow ◽  
Dimensionless Numbers ◽  
Air Bubble ◽  
Demineralized Water ◽  
Drag And Lift ◽  
Area Of Influence ◽  
Eotvos Number

The equilibrium position of a spherical air bubble in a solid body rotating flow around a horizontal axis is investigated experimentally. The flow without bubbles is checked to be solid body rotating. The area of influence of the bubble is characterized to determine for each bubble whether the incoming flow is perturbed or not. The demineralized water used is shown to Tbe contaminated, and spinning of the bubble's interface is observed and measured. From the measurement of the bubble's equilibrium position, drag and lift coefficients are determined. They appear to be dependent on two dimensionless numbers. Eo the Eötvös number and Rω the rotational Reynolds number (or Taylor number Ta) can be varied independently by changing the control parameters, and for that reason are the convenient choice for experiments. (Re, Ro) with Ro the Rossby number is an equivalent choice generally adopted in the literature for numerical simulations, and Re denotes the Reynolds number. When using this second representation, the Ro number appears to be an indicator of the influence on the force coefficients of the shear, of the curvature of the streamlines of the flow and of the bubble's spinning. The bubble's spinning effect on the lift force is far from trivial. Its contribution explains the important gap between lift values for a bubble (not spinning) in a clean fluid and for a bubble (spinning) in a contaminated fluid as present.

scholarly journals Clean versus contaminated bubbles in a solid-body rotating flow

2017 ◽  
Vol 831 ◽  
pp. 592-617 ◽  
Author(s):  
Marie Rastello ◽  
Jean-Louis Marié ◽  
Michel Lance
Keyword(s):  
Solid Body ◽  
Lift Force ◽  
Rotating Flows ◽  
Rotating Flow ◽  
Rossby Number ◽  
Dynamical Equations ◽  
Drag And Lift Coefficients ◽  
New Information ◽  
Rear Part ◽  
Drag And Lift

The behaviour of clean and contaminated bubbles in solid-body rotating flows is compared in terms of drag and lift forces. Both spherical and deformed bubbles are considered. For that comparison, we have completed the data published in Rastello et al. (J. Fluid Mech., vol. 624, 2009, pp. 159–178; J. Fluid Mech., vol. 682, 2011, pp. 434–459) by a new series of measurements. When they are contaminated, bubbles are subject to an additional lift force due to the spinning of their surfaces, while the clean ones are not. A detailed description of this spinning motion is presented and an expression for the Magnus-like lift it induces is given in the light of the new information. The component of the lift induced by flow rotation depends on the Rossby number $Ro$, contrary to the case of clean bubbles. Including the ‘spin’ induced lift component in the dynamical equations provides a better prediction of the bubble’s trajectory in contaminated fluid. The presence of contaminants immobilizes the rear part of the bubble and reduces significantly the deformation. The laws of deformation according to the nature of the surface are presented. The way deformation influences the drag and lift coefficients in pure and contaminated fluids is quantified and discussed. Expressions for these various coefficients are proposed.

Drag and lift forces on a bubble rising near a vertical wall in a viscous liquid

2002 ◽  
Vol 461 ◽  
pp. 277-300 ◽  
Author(s):  
FUMIO TAKEMURA ◽  
SHU TAKAGI ◽  
JACQUES MAGNAUDET ◽  
YOICHIRO MATSUMOTO
Keyword(s):  
Bubble Diameter ◽  
Bubble Radius ◽  
Vertical Wall ◽  
Ccd Camera ◽  
Reynolds Numbers ◽  
Experimental Results ◽  
Order Effects ◽  
Theoretical Predictions ◽  
Bubble Rising ◽  
Drag And Lift

The two components of the force acting on a clean almost spherical bubble rising near a plane vertical wall in a quiescent liquid are determined experimentally. This is achieved by using an apparatus in which a CCD camera and a microscope follow the rising bubble. This apparatus allows us to measure accurately the bubble radius, rise speed and distance between the bubble and the wall. Thereby the drag and lift components of the hydrodynamic force are determined for Reynolds numbers Re (based on bubble diameter, rise velocity U, and kinematic viscosity ν) less than 40. The results show the existence of two different regimes, according to the value of the dimensionless separation L* defined as the ratio between the distance from the bubble centre to the wall and the viscous length scale ν/U. When L* is O(1) or more, experimental results corresponding to Reynolds numbers up to unity are found to be in good agreement with an analytical solution obtained in the Oseen approximation by adapting the calculation of Vasseur & Cox (1977) to the case of an inviscid bubble. When L* is o(1), higher-order effects not taken into account in previous analytical investigations become important and measurements show that the deformation of the bubble is significant when the viscosity of the surrounding liquid is large enough. In this regime, experimental results for the drag force and shape of the bubble are found to agree well with recent theoretical predictions obtained by Magnaudet, Takagi & Legendre (2002) but the measured lift force tends to exceed the prediction as the separation decreases.

QCD at Fixed Order: Processes

2018 ◽  
Author(s):  
John Campbell ◽  
Joey Huston ◽  
Frank Krauss
Keyword(s):  
Hadron Collider ◽  
Detailed Comparison ◽  
Theoretical Description ◽  
Higgs Bosons ◽  
Final States ◽  
Collider Physics ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Fixed Order ◽  
The Subject

At the core of any theoretical description of hadron collider physics is a fixed-order perturbative treatment of a hard scattering process. This chapter is devoted to a survey of fixed-order predictions for a wide range of Standard Model processes. These range from high cross-section processes such as jet production to much more elusive reactions, such as the production of Higgs bosons. Process by process, these sections illustrate how the techniques developed in Chapter 3 are applied to more complex final states and provide a summary of the fixed-order state-of-the-art. In each case, key theoretical predictions and ideas are identified that will be the subject of a detailed comparison with data in Chapters 8 and 9.

Mass Transfer From a Bubble in a Vertical Pipe

2011 ◽  
Author(s):  
Shogo Hosoda ◽  
Ryosuke Sakata ◽  
Kosuke Hayashi ◽  
Akio Tomiyama
Keyword(s):  
Carbon Dioxide ◽  
Mass Transfer ◽  
Bubble Diameter ◽  
Vertical Pipe ◽  
Oblate Spheroidal ◽  
Wide Range ◽  
Bubble Sizes ◽  
Small Bubbles ◽  
Taylor Bubbles

Mass transfer from single carbon dioxide bubbles in a vertical pipe is measured using a stereoscopic image processing method to develop a mass transfer correlation applicable to a wide range of bubble and pipe diameters. The pipe diameters are 12.5, 18.2 and 25.0 mm and the bubble diameter ranges from 5 to 26 mm. The ratio, λ, of bubble diameter to pipe diameter is therefore varied from 0.2 to 1.8, which covers various bubble shapes such as spherical, oblate spheroidal, wobbling, cap, and Taylor bubbles. Measured Sherwood numbers, Sh, strongly depend on bubble shape, i.e., Sh of Taylor bubbles clearly differs from those of spheroidal and wobbling bubbles. Hence two Sherwood number correlations, which are functions of the Peclet number and the diameter ratio λ, are deduced from the experimental data: one is for small bubbles (λ < 0.6) and the other for Taylor bubbles (λ > 0.6). The applicability of the proposed correlations for the prediction of bubble dissolution process is examined through comparisons between measured and predicted long-term bubble dissolution processes. The predictions are carried out by taking into account the presence of all the gas components in the system of concern, i.e. nitrogen, oxygen and carbon dioxide. As a result, good agreements for the dissolution processes for various bubble sizes and pipe diameters are obtained. It is also demonstrated that it is possible to evaluate an equilibrium bubble diameter and instantaneous volume concentration of carbon dioxide in a bubble using a simple model based on a conservation of gas components.

SIMULATION OF AN AXISYMMETRIC RISING BUBBLE BY A MULTIPLE RELAXATION TIME LATTICE BOLTZMANN METHOD

2009 ◽  
Vol 23 (24) ◽  
pp. 4907-4932 ◽  
Author(s):  
ABBAS FAKHARI ◽  
MOHAMMAD HASSAN RAHIMIAN
Keyword(s):  
Free Surface ◽  
Lattice Boltzmann Method ◽  
Lattice Boltzmann ◽  
Rise Velocity ◽  
Rising Bubble ◽  
Wide Range ◽  
Theoretical Predictions ◽  
Multiple Relaxation Time ◽  
Bubble Rising ◽  
Boltzmann Method

In this paper, the lattice Boltzmann method is employed to simulate buoyancy-driven motion of a single bubble. First, an axisymmetric bubble motion under buoyancy force in an enclosed duct is investigated for some range of Eötvös number and a wide range of Archimedes and Morton numbers. Numerical results are compared with experimental data and theoretical predictions, and satisfactory agreement is shown. It is seen that increase of Eötvös or Archimedes number increases the rate of deformation of the bubble. At a high enough Archimedes value and low Morton numbers breakup of the bubble is observed. Then, a bubble rising and finally bursting at a free surface is simulated. It is seen that at higher Archimedes numbers the rise velocity of the bubble is greater and the center of the free interface rises further. On the other hand, at high Eötvös values the bubble deforms more and becomes more stretched in the radial direction, which in turn results in lower rise velocity and, hence, lower elevations for the center of the free surface.

Sign in / Sign up

Export Citation Format

Share Document