Couette–Poiseuille flow of Bingham fluids between two porous parallel plates with slip conditions

Analytical solutions of Couette–Poiseuille flow of Bingham fluids between two porous parallel plates are derived. This study extends the work of Tsangaris et al. [S. Tsangaris, C. Nikas, G. Tsangaris, P. Neofytou, Couette flow of a Bingham plastic in a channel with equally porous parallel walls, J. Non-Newtonian Fluid Mech. 144 (2007) 42–48] to a general situation where the slip effect at the porous walls is considered. It is found that the form of the flow inside the channel depends not only on the Bingham number Bn, the Couette number Co (related to the moving wall) and the transverse Reynolds number Re, but also on the slip parameter Cs at the porous walls. In both the Co–Re diagram and the Co–Bn diagram, the region where plug flow appears enlarges as the slip effect increases, especially in the case where Co is negative. In the case where plug flow and double shear flow coexist, the transverse position of the plug flow and the shear rate at the boundaries exhibit two opposite behaviors when Cs increases, depending on the value of the other three dimensionless numbers. In other cases, slippage always weakens the shearing deformation of the flow.     

Viscoplastic flow around a cylinder kept between parallel plates

Numerical simulations have been undertaken for the creeping pressure-driven flow of a Bingham plastic past a cylinder kept between parallel plates. Different gap/cylinder diameter ratios have been studied ranging from 2:1 to 50:1. The Bingham constitutive equation is used with an appropriate modification proposed by Papanastasiou, which applies everywhere in the flow field in both the yielded and practically unyielded regions. The emphasis is on determining the extent and shape of yielded/unyielded regions along with the drag coefficient for a wide range of Bingham numbers. The present results extend previous simulations for creeping flow of a cylinder in an infinite medium and provide calculations of the drag coefficient around a cylinder in the case of wall effects.     

Viscoplastic flow in slightly varying channels with wall slip pertaining to a magnetorheological (MR) polishing process

In this paper, the first analytical endeavor into the fluid dynamic modeling of an MR polishing process is reported. The velocity and shear stress fields of an MR fluid running through a thin slippery channel with a slightly varying height are analytically solved using a bi-viscosity constitutive model and a Navier slip model. Estimations of the mechanical power density and the total power per unit depth applied onto the channel surfaces are also presented. Analytical solutions for the Couette–Poiseuille flow behavior of a bi-viscous fluid flowing through either parallel or non-uniform channels are obtained, and the associated necessary and sufficient conditions characterizing a total of 5 types of flow are derived.The behaviors of the fluid are examined through the use of a parametric diagram of Bingham number (Bn) and Couette number (Co), i.e., Bn–Co or 1/Bn–1/Co diagram, by changing the geometric and operating conditions. Using these diagrams, variations in the rheological characteristics of the flow are investigated in great detail, with a special focus on the movement of the pseudo-core region. Finally, the mechanical power density field obtained for the flow in a converging–diverging channel is used to explain the wear mechanism in the MR polishing process. The effects of the power density field and the total power on the material removal rate (MRR) and the within-workpiece nonuniformity (WIWNU) with respect to various geometric and operating conditions are evaluated.     

Numerical Analysis for the Bingham—Papanastasiou Fluid Flow Over a Rotating Disk

This study is conducted to investigate the Bingham—Papanastasiou fluid flow driven by a rotating infinite disk. The Bingham—Papanastasiou model is a modification of the Bingham plastic model, which is developed by introducing a continuation parameter to overcome its discontinuity. The von K´armán similarity solution is used to transform the flow equations from ordinary differential equations to a nonlinear system of partial differential equations, which is solved numerically. The effect of the Bingham flow parameters on the radial, tangential, and axial velocities, pressure, and radial and tangential skin friction coefficients is discussed.     

Peristaltic flow of a Bingham fluid in a channel

We study the peristaltic transport of a Bingham fluid in a channel with small aspect ratio whose walls behave as a periodic traveling wave. The governing equations in the unyielded phase are obtained writing the integral formulation for the momentum balance. As shown in Fusi et al. (2015), this approach allows to overcome the so-called “lubrication paradox” which may arise in the thin film approximation. We consider the case in which the inlet flux is prescribed and the one in which the flow is driven by a given pressure drop. In both cases the solution of the problem is determined solving a nonlinear integral equation for the yield surface. We perform some numerical simulations to illustrate the behavior of the yield surface, assuming that the traveling wave describing the peristaltic motion has a sinusoidal shape.     

Approximate solution of the problem of the flow of a conducting liquid in a duct with rectangular cross section

An approximate analytic solution is constructed for the problem of the fully developed stationary flow of a viscous incompressible liquid with a finite isotropic conductivity in a duct of rectangular cross section in the presence of an external magnetic field at right angles to nonconducting walls. An investigation is made of the extent to which flows in ducts with two electrodes parallel to the field resemble flows with four nonconducting walls. Theoretical and experimental investigations devoted to this problem are reviewed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 33–40, September–October, 1970.     

Stability of a Rayleigh-Bénard Poiseuille flow for yield stress fluids—Comparison between Bingham and regularized models

A linear stability analysis of a Rayleigh-Bénard Poiseuille flow is performed for yield stress fluids whether we use the Bingham or regularized models. A fundamental difference between those models is that the effective viscosity is not defined in the plug zone for the Bingham model, while it is defined in the whole domain for the regularized models. For these models, the viscosity depends highly on a parameter ? near the axis and increases drastically in an intermediate region. The convergence of the critical conditions between the simple and the Bingham models is not obtained. However, we show that the Bercovier and Papanastasiou models can tend to the exact Bingham results.     

Plane Couette flow of viscoplastic materials along a slippery vibrating wall

This study looks at the influence of slip at the wall on plane Couette flows of viscous and yield stress fluids with ultrasonic wall motion. These fluids are used in coating processes. A constant speed V at one wall creates the flow, and vibrations and slip take place at the other wall. Isothermal conditions and arbitrary (longitudinal or transverse) vibrations are considered, with negligible vibrational inertia.For the Bingham model, due to its nonlinearity, whatever the vibration direction and the wall slipperiness, significant decreases occur in the average stress as soon as moderate values of the dimensionless vibration velocity amplitude are involved. Such effects are associated with adherent or slippery walls, even with linear friction laws. They do not occur with linear viscous (Newtonian) models.Average stress reductions can reach nearly 100% for very high Oldroyd numbers, i.e. for stress values without vibration close to the yield limit. Slip velocity also decreases. The cost in terms of the power dissipated remains relatively less than in the Newtonian case, and may contribute to a change in the temperature field. Even when the flow without vibration is a pure slip one, large enough amplitude vibrations, either longitudinal or transverse, applied at the wall can reduce the average shear stress and slip velocity, giving rise to an average axial shear flow.Hence vibrations of moderate or high-velocity amplitude applied to adherent or slippery walls enhance plane Couette flow rates for viscoplastic materials. With moderate values of this amplitude, longitudinal vibrations may be 1.5–2 times more efficient than transverse vibrations with an equivalent cost. However, if for technological reasons transverse vibrations have to be preferred, they can also produce significant results. In any case, coating flows should benefit from an adequate application of ultrasound at the wall.     

Boundary element method solution of MHD flow in a rectangular duct

The magnetohydrodynamic (MHD) flow of an incompressible, viscous, electrically conducting fluid in a rectangular duct with an external magnetic field applied transverse to the flow has been investigated. The walls parallel to the applied magnetic field are conducting while the other two walls which are perpendicular to the field are insulators. The boundary element method (BEM) with constant elements has been used to cast the problem into the form of an integral equation over the boundary and to obtain a system of algebraic equations for the boundary unknown values only. The solution of this integral equation presents no problem as encountered in the solution of the singular integral equations for interior methods. Computations have been carried out for several values of the Hartmann number (1 ? M ? 10). It is found that as M increases, boundary layers are formed close to the insulated boundaries for both the velocity and the induced magnetic field and in the central part their behaviours are uniform. Selected graphs are given showing the behaviours of the velocity and the induced magnetic field.     

Lattice Boltzmann simulations of viscoplastic fluid flows through complex flow channels

We present the results of lattice Boltzmann (LB) simulations for the planar-flow of viscoplastic fluids through complex flow channels. In this study, the Bingham and Casson model fluids are covered as viscoplastic fluid. The Papanastasiou (modified Bingham) model and the modified Casson model are employed in our LB simulations. The Bingham number is an essential physical parameter when considering viscoplastic fluid flows and the modified Bingham number is proposed for modified viscoplastic models. When the value of the modified Bingham number agrees with that of the “normal” Bingham number, viscoplastic fluid flows formulated by modified viscoplastic models strictly reproduce the flow behavior of the ideal viscoplastic fluids. LB simulations are extensively performed for viscoplastic fluid flows through complex flow channels with rectangular and circular obstacles. It is shown that the LB method (LBM) allows us to successfully compute the flow behavior of viscoplastic fluids in various complicated-flow channels with rectangular and circular obstacles. For even low Re and high Bn numbers corresponding to plastic-property dominant condition, it is clearly manifested that the viscosity for both the viscoplastic fluids is largely decreased around solid obstacles. Also, it is shown that the viscosity profile is quite different between both the viscoplastic fluids due to the inherent nature of the models. The viscosity of the Bingham fluid sharply drops down close to the plastic viscosity, whereas the viscosity of the Casson fluid does not rapidly fall. From this study, it is demonstrated that the LBM can be also an effective methodology for computing viscoplastic fluid flows through complex channels including circular obstacles.     

Particle imaging velocimetry of a wet aqueous foam with an underlying liquid film

 We investigate the utility of particle imaging velocimetry (PIV) for performing kinematic measurements in wet aqueous foam with a liquid film beneath it. The flow velocities are measured near the walls of a square cross-section horizontal duct. The flow velocities are useful for validating the rheological models. We show that there is a discrepancy between the velocity profiles in the wet foam and the Bingham plastic model of flow. The velocity measurements reveal a more complex flow pattern, which may be analysed following three different regimes: a plug flow, a shear flow in a vertical plane and a three-dimensional shear flow. The transition between the plug flow and the shear flows may be explained by a shear-induced migration of bubbles. Received: 25 April 2000 / Accepted: 26 February 2001     

内通道式磁流变阻尼器研究

设计制作了一种新型的内通道式磁流变液阻尼器,该阻尼器的流场通道位于线圈内部,磁流变效应发生在两层固定的平板区域之间,并能保持磁流变液的流向与磁感应方向垂直,即保证磁流变液的大面积成链,产生大的可控阻尼力,又具备失效安全性;根据宾汉模型,建立了阻尼器的准静态力学模型;最后对研制的阻尼器进行动力学实验研究,并与理论结果进行比较,二者吻合较好。     

Motion of a circular cylinder in a viscous liquid between parallel plates

The two-dimensional motion of a cylinder in a viscous fluid between two parallel walls of a vertical channel is studied. It is found that when the cylinder moves very closely along one of the channel walls, it always rotates in the direction opposite to that of contact rolling along the nearest wall. When the cylinder is away from the walls, its rotation depends on the Reynolds number of the flow. In this study two numerical methods were used. One is for the unsteady motion of a sedimenting cylinder initially released from a position close to one of the channel walls, where the Navier-Stokes equations are solved for the fluid and Newton's equations of motion are solved for the rigid cylinder. The other method is for the steady flow in which a cylinder is fixed in a uniform flow field where the channel walls are sliding past the cylinder at the speed of the approaching flow, or equivalently a cylinder is moving with a constant velocity in a quiescent fluid. The flow field, the drag, the side force (lift), and the torque experienced by the cylinder are studied in detail. The effects of the cylinder location in the channel, the size of the channel relative to the cylinder diameter, and the Reynolds number of the flow are examined. In the limit when the cylinder is translating very closely along one of the walls, the flow in the gap between the cylinder and the wall is solved analytically using lubrication theory, and the numerical solution in the other region is used to piece together the whole flow field.This research was supported by NSF DMR91-20668 through the Laboratory for Research on the Structure of Matter at the University of Pennsylvania and from the Research Foundation of the University of Pennsylvania.     

Numerical study of a swirled turbulent flow in the separation zone of a centrifugal air separator

A mathematical model of a swirled turbulent flow in the separation zone of a pneumatic centrifugal device is presented. The model is based on the known k-? model of turbulence proposed by Wilcox. The influence of rotation of the separation-zone walls, input swirl of the gas flow, and other characteristic parameters on the mean velocity field is demonstrated. A comparison of parameters is performed, which reveals good agreement between the numerical and experimental results for a turbulent fluid flow between parallel disks.     

A numerical study of bingham turbulent flow in sudden-expansion straight circular pipe

I.IntroductionBinghamfluidisonebranchofnon-Newtonianfluid,suchascrudeparaffinoil,highsediment--ladenwaterflow,highconcentrationmudandthelikewhicharetransportedinpipelinesinmanyindustries,soit'sofgreatsignificancetostudytheflowmechanismsofBinghamfluid.Tsaietal.II]studiedthelinkagebetweenBinghamfluidandpluggedflow.Wangetal.I2]measuredtheturbulencestructureofBinghammud.Mengetal.[3]researchedthekineticenergycorrectionfactorofBinghamfluidinacircularpipe.However,thestudyofBinghamfluidsofarisn't…     

On the flow of a yield strength fluid through a contraction

This paper presents a lubrication-type analysis of the pressure gradient-driven flow in a contraction connecting two parallel plate (Poiseuille) flow regions for a Bingham fluid. The solution is complete in the streamfunction at lowest order in the slope of the contraction. I find a floating core on the downstream side of the contraction, growing to match the floating core in the downstream Poiseuille flow. This is unusual. In most contracting or distorting flows the necessary deviatoric shear requires yielding everywhere, accompanied by deviatoric normal stresses.     

Flow of a non-Newtonian fluid between heated parallel plates

The flow of a fluid of grade three between heated parallel plates is examined for two cases. In the first instance we postulate constant heat flux at the walls and via a similarity transformation calculate the Nusselt number as a function of both Γ, the parameter controlling viscous dissipation, and Λ, the non-Newtonian parameter. In the second case we restrict the temperature to change only normal to the plates; solutions in this case are obtained for two temperature-viscosity models, μ = μ(θ).     

Entropy generation during fluid flow in a channel under the effect of transverse magnetic field

Entropy generation due to fluid flow and heat transfer inside a horizontal channel made of two parallel plates under the effect of transverse magnetic field is numerically investigated. The flow is assumed to be steady, laminar, hydro-dynamically and thermally fully developed of electrically conducting fluid. Both horizontal walls are maintained at constant temperatures higher than that of the fluid. The governing equations in Cartesian coordinate are solved by an implicit finite difference technique. After the flow field and the temperature distributions are obtained, the entropy generation profiles are computed and presented graphically. The factors, which were found to affect the problem under consideration are the magnetic parameter, Eckert number, Prandtl number, and the temperature parameter (θ_∞). It was found that, entropy generation increased as all parameters involved in the present problem increased.     

On the stability of a Bingham fluid flow in an annular channelSur la stabilité de l'écoulement d'un fluide de Bingham dans une conduite annulaire

Linear stability of a fully developed Bingham fluid flow between two coaxial cylinders subject to infinitesimal axisymetric perturbations is investigated. The analysis leads to two uncoupled Orr–Sommerfeld equations with appropriate boundary conditions. The numerical solution is obtained using fourth order finite difference scheme. The computations were performed for various plug flow dimensions and radii ratios. Within the range of the parameters considered in this paper, the Poiseuille flow of Bingham fluid is found to be linearly stable. To cite this article: N. Kabouya, C. Nouar, C. R. Mecanique 331 (2003).