The lift force on a spherical bubble in a viscous linear shear flow

1998 ◽  
Vol 368 ◽  
pp. 81-126 ◽  
Author(s):  
DOMINIQUE LEGENDRE ◽  
JACQUES MAGNAUDET
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Lift Force ◽  
Lift Coefficient ◽  
Reynolds Numbers ◽  
Bubble Surface ◽  
Vorticity Field ◽  
Linear Shear ◽  
High Reynolds

The three-dimensional flow around a spherical bubble moving steadily in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations. The bubble surface is assumed to be clean so that the outer flow obeys a zero-shear-stress condition and does not induce any rotation of the bubble. The main goal of the present study is to provide a complete description of the lift force experienced by the bubble and of the mechanisms responsible for this force over a wide range of Reynolds number (0.1[les ]Re[les ]500, Re being based on the bubble diameter) and shear rate (0[les ]Sr[les ]1, Sr being the ratio between the velocity difference across the bubble and the relative velocity). For that purpose the structure of the flow field, the influence of the Reynolds number on the streamwise vorticity field and the distribution of the tangential velocities at the surface of the bubble are first studied in detail. It is shown that the latter distribution which plays a central role in the production of the lift force is dramatically dependent on viscous effects. The numerical results concerning the lift coefficient reveal very different behaviours at low and high Reynolds numbers. These two asymptotic regimes shed light on the respective roles played by the vorticity produced at the bubble surface and by that contained in the undisturbed flow. At low Reynolds number it is found that the lift coefficient depends strongly on both the Reynolds number and the shear rate. In contrast, for moderate to high Reynolds numbers these dependences are found to be very weak. The numerical values obtained for the lift coefficient agree very well with available asymptotic results in the low- and high-Reynolds-number limits. The range of validity of these asymptotic solutions is specified by varying the characteristic parameters of the problem and examining the corresponding evolution of the lift coefficient. The numerical results are also used for obtaining empirical correlations useful for practical calculations at finite Reynolds number. The transient behaviour of the lift force is then examined. It is found that, starting from the undisturbed flow, the value of the lift force at short time differs from its steady value, even when the Reynolds number is high, because the vorticity field needs a finite time to reach its steady distribution. This finding is confirmed by an analytical derivation of the initial value of the lift coefficient in an inviscid shear flow. Finally, a specific investigation of the evolution of the lift and drag coefficients with the shear rate at high Reynolds number is carried out. It is found that when the shear rate becomes large, i.e. Sr=O(1), a small but consistent decrease of the lift coefficient occurs while a very significant increase of the drag coefficient, essentially produced by the modifications of the pressure distribution, is observed. Some of the foregoing results are used to show that the well-known equality between the added mass coefficient and the lift coefficient holds only in the limit of weak shears and nearly steady flows.

scholarly journals Reversal of the lift force on an oblate bubble in a weakly viscous linear shear flow

2009 ◽  
Vol 628 ◽  
pp. 23-41 ◽  
Author(s):  
RICHARD ADOUA ◽  
DOMINIQUE LEGENDRE ◽  
JACQUES MAGNAUDET
Keyword(s):  
Shear Flow ◽  
Lift Force ◽  
Reynolds Numbers ◽  
Bubble Surface ◽  
Relative Shear ◽  
Linear Shear ◽  
Wake Instability ◽  
Reversal Mechanism ◽  
Bubble Rising ◽  
High Reynolds

We compute the flow about an oblate spheroidal bubble of prescribed shape set fixed in a viscous linear shear flow in the range of moderate to high Reynolds numbers. In contrast to predictions based on inviscid theory, the numerical results reveal that for weak enough shear rates, the lift force and torque change sign in an intermediate range of Reynolds numbers when the bubble oblateness exceeds a critical value that depends on the relative shear rate. This effect is found to be due to the vorticity generated at the bubble surface which, combined with the velocity gradient associated with the upstream shear, results in a system of two counter-rotating streamwise vortices whose sign is opposite to that induced by the classical inviscid tilting of the upstream vorticity around the bubble. We show that this lift reversal mechanism is closely related to the wake instability mechanism experienced by a spheroidal bubble rising in a stagnant liquid.

Shear versus vortex-induced lift force on a rigid sphere at moderate Re

2002 ◽  
Vol 473 ◽  
pp. 379-388 ◽  
Author(s):  
P. BAGCHI ◽  
S. BALACHANDAR
Keyword(s):  
Numerical Simulation ◽  
Reynolds Number ◽  
Shear Flow ◽  
Lift Force ◽  
Lift Coefficient ◽  
Rigid Sphere ◽  
Free Rotation ◽  
Rigid Spheres ◽  
Linear Shear ◽  
Strong Lift

The lift forces on rigid spheres entrained in a vortex and a linear shear flow are computed using a direct numerical simulation. The sphere Reynolds number is in the range 10 to 100. The lift coefficient in a vortex is shown to be nearly two orders of magnitude higher than that in a shear flow. The inviscid mechanism is shown to be inadequate to account for the enhanced lift force. The effect of free rotation of the sphere is also shown to be too small to account for the enhanced lift force. Flow structure around the sphere is studied to explain the generation of the strong lift force in a vortex.

The effect of confinement on the motion of a single clean bubble

2008 ◽  
Vol 616 ◽  
pp. 419-443 ◽  
Author(s):  
B. FIGUEROA-ESPINOZA ◽  
R. ZENIT ◽  
D. LEGENDRE
Keyword(s):  
Reynolds Number ◽  
Lift Force ◽  
Reasonable Agreement ◽  
Bubble Radius ◽  
Reynolds Numbers ◽  
Bubble Surface ◽  
Total Drag ◽  
High Reynolds ◽  
Main Effects ◽  
Gap Width

The effect of confining a gas bubble between two parallel walls was investigated for the inertia-dominated regime characterized by high Reynolds and low Weber numbers. Single bubble experiments were performed with non-polar liquids such that the bubble surface could be considered clean; hence, shear free. The drag coefficient was found to be the result of two main effects: the Reynolds number and the confinement. The total drag could be written as the product of the corresponding unconfined drag, which depended mainly on the Reynolds number, and a function F(s)=1 + κs3. The confinement parameter s was defined as the ratio of the bubble radius to the gap width. The value of the constant κ depended on the way in which the bubbles moved within the gap, which was found to be either in a rectilinear (κ≈8) or oscillatory trajectory (κ≈80). For Re < 70, and a range of values of the confinement parameter, the bubbles followed a rectilinear path. For this regime, numerical simulations were performed to obtain the drag force on the bubble directly; a reasonable agreement was found with experiments. Moreover, a comparison of these results with a potential-flow-based model indicated that the vorticity produced at the walls induced a significant part of the drag. For Re > 70, oscillations were observed in the bubble trajectory. In all cases, the oscillation occurred in a zigzag manner. Near the transition the bubbles oscillated but did not reach the walls; for larger Reynolds numbers, the bubbles collided repeatedly with the walls as they ascended. The instability, which is different from the well-known unconfined path instability, resulted from the reversal of sign of the wall-induced lift force: for low Reynolds number, the walls have a stabilizing effect because of the repulsive nature of the lift force between the walls and the bubble, while for high Reynolds number the lift is attractive and trajectories become unstable. Considering a model for the lift force of a bubble moving near a wall, the conditions for the transition were identified. A reasonable agreement between the model and experiments was found.

scholarly journals Drag and lift forces acting on a spherical gas bubble in homogeneous shear liquid flow

2009 ◽  
Vol 629 ◽  
pp. 173-193 ◽  
Author(s):  
KEN-ICHI SUGIOKA ◽  
SATORU KOMORI
Keyword(s):  
Shear Rate ◽  
Shear Flow ◽  
Lift Force ◽  
Lift Coefficient ◽  
Gas Bubble ◽  
Fluid Shear ◽  
Air Bubble ◽  
Linear Shear ◽  
Lift Forces ◽  
Drag And Lift

Drag and lift forces acting on a spherical gas bubble in a homogeneous linear shear flow were numerically investigated by means of a three-dimensional direct numerical simulation (DNS) based on a marker and cell (MAC) method. The effects of fluid shear rate and particle Reynolds number on drag and lift forces acting on a spherical gas bubble were compared with those on a spherical inviscid bubble. The results show that the drag force acting on a spherical air bubble in a linear shear flow increases with fluid shear rate of ambient flow. The behaviour of the lift force on a spherical air bubble is quite similar to that on a spherical inviscid bubble, but the effects of fluid shear rate on the lift force acting on an air bubble in the linear shear flow become bigger than that acting on an inviscid bubble in the particle Reynolds number region of 1≤Rep≤300. The lift coefficient on a spherical gas bubble approaches the lift coefficient on a spherical water droplet in the linear shear air-flow with increase in the internal gas viscosity.

On a Circular Cylinder in a Uniform Planar Shear Flow at Subcritical Reynolds Number

2002 ◽  
Author(s):  
D. Sumner ◽  
O. O. Akosile
Keyword(s):  
Reynolds Number ◽  
Circular Cylinder ◽  
Shear Flow ◽  
Lift Force ◽  
Experimental Studies ◽  
Reynolds Numbers ◽  
Low Velocity ◽  
Static Pressure Distribution ◽  
Planar Shear ◽  
The Mean

An experimental investigation was conducted of a circular cylinder immersed in a uniform planar shear flow, where the approach velocity varies across the diameter of the cylinder. The study was motivated by some apparent discrepancies between numerical and experimental studies of the flow, and the general lack of experimental data, particularly in the subcritical Reynolds number regime. Of interest was the direction and origin of the steady mean lift force experienced by the cylinder, which has been the subject of contradictory results in the literature, and for which measurements have rarely been reported. The circular cylinder was tested at Reynolds numbers from Re = 4.0×104 − 9.0×104, and the dimensionless shear parameter ranged from K = 0.02 − 0.07, which corresponded to a flow with low to moderate shear. The results showed that low to moderate shear has no appreciable influence on the Strouhal number, but has the effect of lowering the mean drag coefficient. The circular cylinder develops a small steady mean lift force directed towards the low-velocity side, which is attributed to an asymmetric mean static pressure distribution on its surface. The reduction in the mean drag force, however, cannot be attributed solely to this asymmetry.

Drag and lift forces on a rotating sphere in a linear shear flow

1999 ◽  
Vol 384 ◽  
pp. 183-206 ◽  
Author(s):  
RYOICHI KUROSE ◽  
SATORU KOMORI
Keyword(s):  
Shear Flow ◽  
Lift Force ◽  
Fluid Velocity ◽  
Reynolds Numbers ◽  
Fluid Shear ◽  
Rotating Sphere ◽  
High Particle ◽  
Linear Shear ◽  
Lift Forces ◽  
Drag And Lift

The drag and lift forces acting on a rotating rigid sphere in a homogeneous linear shear flow are numerically studied by means of a three-dimensional numerical simulation. The effects of both the fluid shear and rotational speed of the sphere on the drag and lift forces are estimated for particle Reynolds numbers of 1[les ]Rep[les ]500.The results show that the drag forces both on a stationary sphere in a linear shear flow and on a rotating sphere in a uniform unsheared flow increase with increasing the fluid shear and rotational speed. The lift force on a stationary sphere in a linear shear flow acts from the low-fluid-velocity side to the high-fluid-velocity side for low particle Reynolds numbers of Rep<60, whereas it acts from the high-velocity side to the low-velocity side for high particle Reynolds numbers of Rep>60. The change of the direction of the lift force can be explained well by considering the contributions of pressure and viscous forces to the total lift in terms of flow separation. The predicted direction of the lift force for high particle Reynolds numbers is also examined through a visualization experiment of an iron particle falling in a linear shear flow of a glycerin solution. On the other hand, the lift force on a rotating sphere in a uniform unsheared flow acts in the same direction independent of particle Reynolds numbers. Approximate expressions for the drag and lift coefficients for a rotating sphere in a linear shear flow are proposed over the wide range of 1[les ]Rep[les ]500.

Drag and lift forces acting on a spherical water droplet in homogeneous linear shear air flow

2007 ◽  
Vol 570 ◽  
pp. 155-175 ◽  
Author(s):  
KEN-ICHI SUGIOKA ◽  
SATORU KOMORI
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Shear Flow ◽  
Rigid Sphere ◽  
Fluid Shear ◽  
Spherical Droplet ◽  
Linear Shear ◽  
Lift Forces ◽  
Drag And Lift ◽  
Homogeneous Linear

Drag and lift forces acting on a spherical water droplet in a homogeneous linear shear air flow were studied by means of a three-dimensional direct numerical simulation based on a marker and cell (MAC) method. The effects of the fluid shear rate and the particle (droplet) Reynolds number on drag and lift forces acting on a spherical droplet were compared with those on a rigid sphere. The results show that the drag coefficient on a spherical droplet in a linear shear flow increases with increasing the fluid shear rate. The difference in the drag coefficient between a spherical droplet and a rigid sphere in a linear shear flow never exceeds 4%. The lift force acting on a spherical droplet changes its sign from a positive to a negative value at a particle Reynolds number of Rep ≃ 50 in a linear shear flow and it acts from the high-speed side to the low-speed side for Rep ≥ 50. The behaviour of the lift coefficient on a spherical droplet is similar to that on a stationary rigid sphere and the change of sign is caused by the decrease of the pressure lift. The viscous lift on a spherical droplet is smaller than that on a rigid sphere at the same Rep, whereas the pressure lift becomes larger. These quantitative differences are caused by the flow inside a spherical droplet.

The inertial lift on a spherical particle in a plane Poiseuille flow at large channel Reynolds number

1999 ◽  
Vol 381 ◽  
pp. 63-87 ◽  
Author(s):  
EVGENY S. ASMOLOV
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Reynolds Numbers ◽  
Thin Layers ◽  
Rigid Sphere ◽  
Outer Flow ◽  
Inertial Migration ◽  
Flow Past ◽  
Large Channel ◽  
Linear Shear

The inertial migration of a small rigid sphere translating parallel to the walls within a channel flow at large channel Reynolds numbers is investigated. The method of matched asymptotic expansions is used to solve the equations governing the disturbance flow past a particle at small particle Reynolds number and to evaluate the lift. Both neutrally and non-neutrally buoyant particles are considered. The wall-induced inertia is significant in the thin layers near the walls where the lift is close to that calculated for linear shear flow, bounded by a single wall. In the major portion of the flow, excluding near-wall layers, the wall effect can be neglected, and the outer flow past a sphere can be treated as unbounded parabolic shear flow. The effect of the curvature of the unperturbed velocity profile is significant, and the lift differs from the values corresponding to a linear shear flow even at large Reynolds numbers.

Inertial migration of a small sphere in linear shear flows

1991 ◽  
Vol 224 ◽  
pp. 261-274 ◽  
Author(s):  
John B. McLaughlin
Keyword(s):  
Reynolds Number ◽  
Shear Rate ◽  
Slip Velocity ◽  
Reynolds Numbers ◽  
Rigid Sphere ◽  
Square Root ◽  
Small Sphere ◽  
Inertial Migration ◽  
Particle Reynolds Number ◽  
Linear Shear

The motion of a small, rigid sphere in a linear shear flow is considered. Saffman's analysis is extended to other asymptotic cases in which the particle Reynolds number based on its slip velocity is comparable with or larger than the square root of the particle Reynolds number based on the velocity gradient. In all cases, both particle Reynolds numbers are assumed to be small compared to unity. It is shown that, as the Reynolds number based on particle slip velocity becomes larger than the square root of the Reynolds number based on particle shear rate, the magnitude of the inertial migration velocity rapidly decreases to very small values. The latter behaviour suggests that contributions that are higher order in the particle radius may become important in some situations of interest.

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