Hydrodynamic interaction of two particles in confined linear shear flow at finite Reynolds number

2007 ◽  
Vol 19 (11) ◽  
pp. 113305 ◽  
Author(s):  
Yiguang Yan ◽  
Jeffrey F. Morris ◽  
Joel Koplik
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Hydrodynamic Interaction ◽  
Linear Shear

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.

Linear shear flow over a square cylinder at low Reynolds number

2005 ◽  
Vol 17 (7) ◽  
pp. 078103 ◽  
Author(s):  
M. Cheng ◽  
S. H. N. Tan ◽  
K. C. Hung
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Low Reynolds Number ◽  
Square Cylinder ◽  
Linear Shear ◽  
Low Reynolds

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.

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.

Drag and lift forces on a spherical particle moving on a wall in a shear flow at finite Re

2010 ◽  
Vol 657 ◽  
pp. 89-125 ◽  
Author(s):  
HYUNGOO LEE ◽  
S. BALACHANDAR
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Hydrodynamic Forces ◽  
Immersed Boundary ◽  
Bounded Linear ◽  
Number Range ◽  
Linear Shear ◽  
Present Composite ◽  
Lift Forces ◽  
Drag And Lift

Recent research (Zeng, PhD thesis, 2007; Zeng et al., Phys. Fluids, vol. 21, 2009, art. no. 033302) has shown that both the shear- and wall-induced lift contributions on a particle sharply increase as the gap between the wall and the particle is decreased. Explicit expressions that are valid over a range of finite Re were obtained for the drag and lift forces in the limiting cases of a stationary particle in wall-bounded linear flow and of a particle translating parallel to a wall in a quiescent ambient. Here we consider the more general case of a translating and rotating particle in a wall-bounded linear shear flow where shear, translational and rotational effects superpose. We have considered a modest Reynolds number range of 1–100. Direct numerical simulations using immersed boundary method were performed to systematically figure out the characteristics of hydrodynamic forces on a finite-sized particle moving while almost in contact with a wall. We present composite correlation for the hydrodynamic forces which are in agreement with all the available low-Reynolds-number theories.

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