Shear-induced incipient motion of a single sphere on uniform substrates at low particle Reynolds numbers

2017 ◽  
Vol 825 ◽  
pp. 284-314 ◽  
Author(s):  
J. R. Agudo ◽  
C. Illigmann ◽  
G. Luzi ◽  
A. Laukart ◽  
A. Delgado ◽  
...  
Keyword(s):  
Shear Flow ◽  
Numerical Study ◽  
Reynolds Numbers ◽  
Angle Of Repose ◽  
External Parameter ◽  
Incipient Motion ◽  
Substrate Topography ◽  
Linear Shear ◽  
Effective Level ◽  
Single Sphere

We study the incipient motion of single spheres in steady shear flow on regular substrates at low particle Reynolds numbers. The substrate consists of a monolayer of regularly arranged fixed beads, in which the spacing between beads is varied resulting in different angles of repose and exposures of the particle to the main flow. The flow-induced forces and the level of flow penetration into the substrate are determined numerically. Since experiments in this range had shown that the critical Shields number is independent of inertia but strongly dependent on the substrate geometry, the particle Reynolds number was fixed to 0.01 in the numerical study. Numerics indicates that rolling motion is always preferred to sliding and that the flow penetration is linearly dependent on the spacing between the substrate particles. Besides, we propose an analytical model for the incipient motion. The model is an extension of Goldman’s classical result for a single sphere near a plain surface taking into account the angle of repose, flow orientation with respect to substrate topography and shielding of the sphere to the linear shear flow. The effective level of flow penetration is the only external parameter. The model, applied to triangular and quadratic arrangements with different spacings, is able to predict the dependence of the critical Shields number on the geometry and on the orientation of the substrate. The model is in very good agreement with numerical results. For well-exposed particles, we observed that the minimum critical Shields number for a certain angle of repose does not depend sensitively on the considered arrangement. At large angles of repose, as expected in fully armoured beds, the model is consistent with experimental results for erodible beds at saturated conditions.

scholarly journals Fluid-Structure Energy Transfer of a Tensioned Beam Subject to Vortex-Induced Vibrations in Shear Flow

2011 ◽  
Author(s):  
Remi Bourguet ◽  
Michael S. Triantafyllou ◽  
Michael Tognarelli ◽  
Pierre Beynet
Keyword(s):  
Energy Transfer ◽  
Shear Flow ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Structural Vibrations ◽  
Fluid Structure ◽  
Vortex Induced Vibrations ◽  
Linear Shear ◽  
Structural Responses ◽  
Lock In

The fluid-structure energy transfer of a tensioned beam of length to diameter ratio 200, subject to vortex-induced vibrations in linear shear flow, is investigated by means of direct numerical simulation at three Reynolds numbers, from 110 to 1,100. In both the in-line and cross-flow directions, the high-wavenumber structural responses are characterized by mixed standing-traveling wave patterns. The spanwise zones where the flow provides energy to excite the structural vibrations are located mainly within the region of high current where the lock-in condition is established, i.e. where vortex shedding and cross-flow vibration frequencies coincide. However, the energy input is not uniform across the entire lock-in region. This can be related to observed changes from counterclockwise to clockwise structural orbits. The energy transfer is also impacted by the possible occurrence of multi-frequency vibrations.

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.

Numerical study on uniform-shear flow over a circular disk at low Reynolds numbers

2018 ◽  
Vol 30 (8) ◽  
pp. 083605 ◽  
Author(s):  
Jianzhi Yang ◽  
Minghou Liu ◽  
Changjian Wang ◽  
Xiaowei Zhu ◽  
Aifeng Zhang
Keyword(s):  
Shear Flow ◽  
Numerical Study ◽  
Circular Disk ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Uniform Shear ◽  
Uniform Shear Flow ◽  
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.

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.

Numerical study of the deformation and rheology characteristics of the emulsion droplets using the boundary element method

2014 ◽  
Vol 10 ◽  
pp. 7-12
Author(s):  
O.A. Abramova ◽  
Yu.A. Itkulova ◽  
N.A. Gumerov ◽  
I.Sh. Ahatov
Keyword(s):  
Boundary Element Method ◽  
Shear Flow ◽  
Boundary Element ◽  
Numerical Study ◽  
Numerical Technique ◽  
Reynolds Numbers ◽  
Low Reynolds Numbers ◽  
Emulsion Droplets ◽  
Cuda Technology ◽  
Element Method

The present paper is dedicated to the investigation of the 3D dynamics of two viscous immiscible liquids in an unbounded domain at low Reynolds numbers. The numerical technique is based on the boundary element method. To accelerate the calculations and increase the problem scale the parallelization of computations on graphic processors (GPU) using CUDA technology is used. The inclination angle and the deformation of droplets in a shear flow at various parameters are studied. The obtained results are compared with the experimental data represented in the literature, numerical results and the small deformations theory. The calculation of rheological characteristics for dilute emulsions in shear flow is carried out for different viscosity ratios of internal and external liquids.

A note on the rate of heat or mass transfer from a small particle freely suspended in a linear shear field

1980 ◽  
Vol 98 (2) ◽  
pp. 299-304 ◽  
Author(s):  
Andreas Acrivos
Keyword(s):  
Mass Transfer ◽  
Nusselt Number ◽  
Shear Flow ◽  
Small Particle ◽  
Arbitrary Shape ◽  
Reynolds Numbers ◽  
Small Sphere ◽  
Linear Shear ◽  
Small Reynolds Numbers ◽  
Freely Suspended

It is shown that for a small sphere freely suspended in a linear shear flow at small Reynolds numbers, the Nusselt number N is given by $N = \{1 - \alpha P^{\frac{1}{2}} + o(P^{\frac{3}{2}})\}^{-1}$, where P is the Péclet number. For any given type of shear flow, the numerical value of the constant α can be obtained from a general expression derived by Batchelor (1979). The corresponding result for a particle of arbitrary shape is N/N0 = {1 − αN0P½ + O(P3/2)}−1, where N0 is the Nusselt number for pure conduction.

Sign in / Sign up

Export Citation Format

Share Document