Stokes’ paradox: creeping flow past a two-dimensional cylinder in an infinite domain

2017 ◽  
Vol 817 ◽  
pp. 374-387 ◽  
Author(s):  
Arzhang Khalili ◽  
Bo Liu
Keyword(s):  
Drag Coefficient ◽  
Creeping Flow ◽  
Infinite Cylinder ◽  
Ambient Fluid ◽  
Infinite Domain ◽  
Pressure Fields ◽  
Correct Calculation ◽  
Infinite Extent ◽  
Artificial Boundaries ◽  
Stable Numerical Method

Finite container sizes in experiments and computer simulations impose artificial boundaries which do not exist when they are meant to mimic ambient fluid of infinite extent. We show here that this is the case with flows past an infinite cylinder placed in an infinite ambient fluid (Stokes’ paradox). Using a highly efficient and stable numerical method that is capable of handling computational domains several orders of magnitude larger than in previous studies, we provide a criterion for the minimum necessary extent around an object in order to provide accurate velocity and pressure fields, which are prerequisites for correct calculation of secondary quantities such as drag coefficient. The careful and extensive simulations performed suggest an improved relation for the drag coefficient as a function of Reynolds number, and identify the most suitable experimental data available in the literature.

scholarly journals Study of hydraulic resistance of tangential swirlers

2021 ◽  
Vol 2094 (5) ◽  
pp. 052029
Author(s):  
N A Voinov ◽  
D A Zemtsov ◽  
A V Bogatkova ◽  
N V Deryagina
Keyword(s):  
Drag Coefficient ◽  
Hydraulic Resistance ◽  
Experimental Research ◽  
Process Parameters ◽  
Simulation Modelling ◽  
Hydraulic Drag ◽  
Comsol Multiphysics ◽  
Circular Channel ◽  
Pressure Fields ◽  
Wide Range

Abstract This article presents the results of experimental research and simulation of the hydraulic drag of tangential swirlers. Three types of swirler devices made with straight, profiled, and circular channel walls were studied within a wide range of design and process parameters. Simulation modelling on the Comsol Multiphysics platform was used to calculate hydraulic drag and determine the velocity and pressure fields. This allowed obtaining a dependence of the hydraulic drag coefficient of the investigated swirlers and identifying parameters affecting their hydraulic drag.

scholarly journals A finite-element algorithm for Stokes flow through oil and gas production tubing of uniform diameter

2020 ◽  
Vol 75 ◽  
pp. 79
Author(s):  
Lateef T. Akanji ◽  
Joao Chidamoio
Keyword(s):  
Finite Element ◽  
Stokes Flow ◽  
Computer Aided Design ◽  
Oil And Gas ◽  
Gas Production ◽  
Creeping Flow ◽  
Oil And Gas Production ◽  
Pressure Fields ◽  
Uniform Diameter ◽  
Production Tubing

Stokes flow of a Newtonian fluid through oil and gas production tubing of uniform diameter is studied. Using a direct simulation on computer-aided design of discretised conduits, velocity profiles with gravitational effect and pressure fields are obtained for production tubing of different inner but uniform diameter. The results obtained with this new technique are compared with the integrated form of the Hagen–Poiseuille equation (i.e., lubrication approximation) and data obtained from experimental and numerical studies for flow in vertical pipes. Good agreement is found in the creeping flow regime between the computed and measured pressure fields with a coefficient of correlation of 0.97. Further, computed velocity field was benchmarked against ANSYS Fluent; a finite element commercial software package, in a single-phase flow simulation using the axial velocity profile computed at predefined locations along the geometric domains. This method offers an improved solution approach over other existing methods both in terms of computational speed and accuracy.

Particle Collisions in a Lumped Particle Model

2011 ◽  
Vol 10 (4) ◽  
pp. 823-843 ◽  
Author(s):  
Omar al-Khayat ◽  
Are Magnus Bruaset ◽  
Hans Petter Langtangen
Keyword(s):  
Drag Coefficient ◽  
Volume Fraction ◽  
High Energy ◽  
Creeping Flow ◽  
Particle Model ◽  
Particle Collisions ◽  
Hindered Settling ◽  
Effective Work ◽  
Physical Experiments ◽  
Work Done

AbstractThis paper presents an extension of the lumped particle model in [1] to include the effects of particle collisions. The lumped particle model is a flexible framework for the modeling of particle laden flows, that takes into account fundamental features, including advection, diffusion and dispersion of the particles. In this paper, we transform a binary collision model and concepts from kinetic theory into a collision procedure for the lumped particle framework. We apply this new collision procedure to investigate numerically the role of particle collisions in the hindered settling effect. The hindered settling effect is characterized by an increase in the effective drag coefficient CD that influences each particle in the flow. This coefficient is given by , where ϕ is the volume fraction of particles, is the drag coefficient for a single particle, and n ≃ 4.67 for creeping flow. We obtain an approximation for CD/CD by calculating the effective work done by collisions, and comparing that to the work done by the drag force. In our numerical experiments, we observe a minimal value of n = 3.0. Moreover, by allowing high energy dissipation, an approximation for the classical value for creeping flow, n = 4.7, is reproduced. We also obtain high values for n, up to n = 6.5, which is consistent with recent physical experiments on the sedimentation of sand grains.

scholarly journals Existence theorems for trapped modes

1994 ◽  
Vol 261 ◽  
pp. 21-31 ◽  
Author(s):  
D. V. Evans ◽  
M. Levitin ◽  
D. Vassiliev
Keyword(s):  
Existence Theorems ◽  
Trapped Modes ◽  
Infinite Domain ◽  
General Shape ◽  
Trapped Mode ◽  
Local Oscillation ◽  
Parallel Lines ◽  
Infinite Extent ◽  
The Laplace Operator ◽  
Lowest Eigenvalue

A two-dimensional acoustic waveguide of infinite extent described by two parallel lines contains an obstruction of fairly general shape which is symmetric about the centreline of the waveguide. It is proved that there exists at least one mode of oscillation, antisymmetric about the centreline, that corresponds to a local oscillation at a particular frequency, in the absence of excitation, which decays with distance down the waveguide away from the obstruction. Mathematically, this trapped mode is related to an eigenvalue of the Laplace operator in the waveguide. The proof makes use of an extension of the idea of the Rayleight quotient to characterize the lowest eigenvalue of a differential operator on an infinite domain.

scholarly journals Review and comparison of different support loss models for micro-electro-mechanical systems resonators undergoing in-plane vibration

2011 ◽  
Vol 226 (1) ◽  
pp. 283-295 ◽  
Author(s):  
B Chouvion ◽  
S McWilliam ◽  
A A Popov ◽  
C H J Fox
Keyword(s):  
Micro Electro Mechanical System ◽  
Finite Domain ◽  
Test Cases ◽  
Simple Test ◽  
Infinite Domain ◽  
Micro Electro Mechanical Systems ◽  
Plane Vibration ◽  
Infinite Elements ◽  
Layer Method ◽  
Artificial Boundaries

Several approaches for calculating support loss in micro-electro-mechanical system resonators undergoing in-plane vibration are reviewed. In each of them, the support is approximated as a semi-infinite domain. The first approach is analytical and models the support as a semi-infinite thin plate. This is compared with two different finite element approaches that introduce artificial boundaries to their finite domain. In order to absorb outgoing waves and model the infinite support, a perfectly matched layer method and the use of infinite elements are considered. Simple test cases are studied and the results for the support losses predicted by the different methods are compared. It is shown that each of the methods yields similar trends. Using the developed analytical model, a parametric study is performed on the support losses of a ring-based resonator. General strategies for improving the quality factor by reducing support losses are provided.

scholarly journals The Role of Surface Infiltration in Hydromechanical Coupling Effects in an Unsaturated Porous Medium of Semi-Infinite Extent

Geofluids ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
L. Z. Wu ◽  
A. P. S. Selvadurai ◽  
J. Yang
Keyword(s):  
Porous Medium ◽  
Coupling Effect ◽  
Characteristic Curve ◽  
Numerical Procedure ◽  
Water Infiltration ◽  
Natural Phenomenon ◽  
Infinite Domain ◽  
Unsaturated Porous Medium ◽  
Infinite Extent ◽  
Van Genuchten Model

Rainfall infiltration into an unsaturated region of the earth’s surface is a pervasive natural phenomenon. During the rainfall-induced seepage process, the soil skeleton can deform and the permeability can change with the water content in the unsaturated porous medium. A coupled water infiltration and deformation formulation is used to examine a problem related to the mechanics of a two-dimensional region of semi-infinite extent. The van Genuchten model is used to represent the soil-water characteristic curve. The model, incorporating coupled infiltration and deformation, was developed to resolve the coupled problem in a semi-infinite domain based on numerical methods. The numerical solution is verified by the analytical solution when the coupled effects in an unsaturated medium of semi-infinite extent are considered. The computational results show that a numerical procedure can be employed to examine the semi-infinite unsaturated seepage incorporating coupled water infiltration and deformation. The analysis indicates that the coupling effect is significantly influenced by the boundary conditions of the problem and varies with the duration of water infiltration.

scholarly journals Drag and pressure fields for the MHD flow around a circular cylinder at intermediate Reynolds numbers

2005 ◽  
Vol 2005 (3) ◽  
pp. 183-203 ◽  
Author(s):  
T. V. S. Sekhar ◽  
R. Sivakumar ◽  
T. V. R. Ravi Kumar
Keyword(s):  
Circular Cylinder ◽  
Drag Coefficient ◽  
Stagnation Point ◽  
Stokes Equations ◽  
Separation Bubble ◽  
Flow Direction ◽  
Boundary Layer Separation ◽  
Pressure Fields ◽  
Correction Technique ◽  
Rear Stagnation Point

Steady incompressible flow around a circular cylinder in an external magnetic field that is aligned with fluid flow direction is studied forRe(Reynolds number) up to 40 and the interaction parameter in the range0≤N≤15(or0≤M≤30), whereMis the Hartmann number related toNby the relationM=2NRe, using finite difference method. The pressure-Poisson equation is solved to find pressure fields in the flow region. The multigrid method with defect correction technique is used to achieve the second-order accurate solution of complete nonlinear Navier-Stokes equations. It is found that the boundary layer separation at rear stagnation point forRe=10is suppressed completely whenN<1and it started growing again whenN≥9. ForRe=20and 40, the suppression is not complete and in addition to that the rear separation bubble started increasing whenN≥3. The drag coefficient decreases for low values ofN(<0.1)and then increases with increase ofN. The pressure drag coefficient, total drag coefficient, and pressure at rear stagnation point vary withN. It is also found that the upstream and downstream pressures on the surface of the cylinder increase for low values ofN(<0.1)and rear pressure inversion occurs with further increase ofN. These results are in agreement with experimental findings.

The Rayleigh–Taylor instability of a viscous liquid layer resting on a plane wall

1990 ◽  
Vol 217 ◽  
pp. 615-638 ◽  
Author(s):  
Lori A. Newhouse ◽  
C. Pozrikidis
Keyword(s):  
Surface Tension ◽  
Liquid Layer ◽  
Viscosity Ratio ◽  
Taylor Instability ◽  
Creeping Flow ◽  
Plane Wall ◽  
Ambient Fluid ◽  
Initial Thickness ◽  
Two Fluids ◽  
Rayleigh Taylor Instability

The nonlinear Rayleigh–Taylor instability of a liquid layer resting on a plane wall below a second liquid of higher density is considered. Under the assumption of creeping flow, the motion is studied as a function of surface tension and the ratio of the viscosities of the two fluids. The flow induced by the deformation of the layer is represented by an interfacial distribution of Green's functions. A Fredholm integral equation of the second kind is derived for the density of the distribution, and is solved by successive iteration. The results show that for small and moderate surface tension, the instability of the layer leads to the formation of a periodic array of viscous plumes which penetrate into the overlying fluid. The morphology of these plumes strongly depends upon the viscosity ratio and surface tension. When the viscosity of the overlying fluid is comparable with or larger than that of the layer, the plumes are composed of a well-defined leading drop on top of a narrow stem. When the viscosity of the overlying fluid is smaller than that of the layer, the plumes take the form of a compact column of rising fluid. The size of the drop leading a plume is roughly proportional to the initial thickness of the layer. When surface tension is sufficiently small, ambient fluid is entrained into the leading drop and circulates in a spiral pattern. Convection currents generated by the rising plumes are visualized with streamline patterns, and the rate of thinning of the remnant layer, as well as the speed of the rising drop or plumes, are discussed.

Creeping motion of a sphere through a Bingham plastic

1985 ◽  
Vol 158 ◽  
pp. 219-244 ◽  
Author(s):  
A. N. Beris ◽  
J. A. Tsamopoulos ◽  
R. C. Armstrong ◽  
R. A. Brown
Keyword(s):  
Boundary Layer ◽  
Drag Coefficient ◽  
Yield Stress ◽  
Variational Principles ◽  
Solid Sphere ◽  
Creeping Flow ◽  
Matched Asymptotic Expansion ◽  
Bingham Plastic ◽  
Stagnation Points ◽  
Critical Yield

A solid sphere falling through a Bingham plastic moves in a small envelope of fluid with shape that depends on the yield stress. A finite-element/Newton method is presented for solving the free-boundary problem composed of the velocity and pressure fields and the yield surfaces for creeping flow. Besides the outer surface, solid occurs as caps at the front and back of the sphere because of the stagnation points in the flow. The accuracy of solutions is ascertained by mesh refinement and by calculation of the integrals corresponding to the maximum and minimum variational principles for the problem. Large differences from the Newtonian values in the flow pattern around the sphere and in the drag coefficient are predicted, depending on the dimensionless value of the critical yield stress Yg below which the material acts as a solid. The computed flow fields differ appreciably from Stokes’ solution. The sphere will fall only when Yg is below 0.143 For yield stresses near this value, a plastic boundary layer forms next to the sphere. Boundary-layer scalings give the correct forms of the dependence of the drag coefficient and mass-transfer coefficient on yield stress for values near the critical one. The Stokes limit of zero yield stress is singular in the sense that for any small value of Yg there is a region of the flow away from the sphere where the plastic portion of the viscosity is at least as important as the Newtonian part. Calculations For the approach of the flow field to the Stokes result are in good agreement with the scalings derived from the matched asymptotic expansion valid in this limit.

Slipping of a Viscoplastic Fluid Flowing on a Circular Cylinder

2015 ◽  
Vol 137 (7) ◽  
Author(s):  
Hamdullah Ozogul ◽  
Pascal Jay ◽  
Albert Magnin
Keyword(s):  
Circular Cylinder ◽  
Drag Coefficient ◽  
Experimental Studies ◽  
Elastohydrodynamic Lubrication ◽  
Creeping Flow ◽  
Viscoplastic Fluid ◽  
Fluid Structure ◽  
Two Parameters ◽  
Rigid Zones ◽  
Bulk Behavior

The slipping effect during creeping flow of viscoplastic fluids around a circular cylinder has been investigated via numerical simulations. For the bulk behavior of the fluid, a Herschel–Bulkley law is considered. For the parietal behavior, an original and recent slip law based on an elastohydrodynamic lubrication model defined with a physical approach has been implemented. In particular, this law represents the behavior of Carbopol gels, which are commonly used during experimental studies on yield stress fluid mechanics and in industry. This law has two parameters that control the kinematic conditions at the fluid–structure interface. Variations in the plastic drag coefficient are given as a function of these parameters. It has been shown in particular the decreasing of the drag coefficient when there is slipping at the fluid–structure interface. The kinematic field has been analyzed and the evolution of rigid zones is illustrated. Results are provided for different slipping conditions ranging from the no-slip to the perfect-slip (PS) case. The sheared zone becomes smaller so the flow is more and more confined due to the slip, which induces modifications on the rigid zones. Some of the results are compared with existing asymptotic plastic drag coefficients and experimental data.

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