The squeeze flow of a bi-viscosity fluid between two rigid spheres with wall slip

In this paper, the squeeze flow between two rigid spheres with a bi-viscosity fluid is examined. Based on lubrication theory, the squeeze force is calculated by deriving the pressure and velocity expressions. The results of the normal squeeze force are discussed, and fitting functions of the squeeze and correction coefficients are given. The squeeze force between the rigid spheres increases linearly or logarithmically with the velocity when most or part of the boundary fluid reaches the yield state, respectively. Furthermore, the slip correction coefficient decreases with the increase in the velocity. The investigation may contribute to the further study of bi-viscosity fluids between rigid spheres with wall slip.     

Numerical study of the axially symmetric motion of an incompressible viscous fluid in an annulus between two concentric rotating spheres

The research reported herein involved the study of the transient motion of a system consisting of an incompressible Newtonian fluid in an annulus between two concentric, rotating, rigid spheres. The primary purpose of the research was to study the use of a numerical method for analysing the transient motion that results from the interaction between the fluid in the annulus and the spheres which are started suddenly by the action of prescribed torques. The problems considered in this research included cases where: (a) one or both spheres rotate with prescribed constant angular velocities and (b) one sphere rotates due to the action of an applied constant or impulsive t?orque. In this research the coupled solid and fluid equations were solved numerically by employing the finite difference technique. With the approach adopted in this research, only the derivatives with respect to spatial variables were approximated with the use of the finite difference formulae. The steady state problem was also solved as a separate problem (for verification purposes), and the results were compared with those obtained from the solution of the transient problem. Newton's algorithm was employed to solve the algebraic equations which resulted from the steady state problem, and the Adams fourth-order predictor–corrector method was employed to solve the ordinary differential equations for the transient problem. Results were obtained for the streamfunction, circumferential function, angular velocity of the spheres and viscous torques acting on the spheres as a function of time for various values of the system dimensionless parameters.     

Wall Region Porosity Distributions for Packed Beds of Uniform Spheres with Modified and Unmodified Walls

A mathematical derivation of the porosity (local void fraction) distribution near the walls of packed beds of uniform spheres is presented. This investigation supports the study of methods of reducing or eliminating the so-called wall effect, or bypass flow, which accompanies the increase in porosity when spheres come in contact with a solid boundary. Limiting the amount of bypass flow is important in certain applications such as in packed bed nuclear reactors where bypass flow allows some coolant to avoid the high power density core region. Four basic porosity distributions are determined. The first investigates the case where spheres against a flat wall are packed in the tightest possible packing density. This density is then reduced by changing the sphere spacing until the minimum porosity matches that obtained experimentally. In the other cases, the effect of various ways of embedding spheres in the wall on the wall region porosity is examined. By partially embedding spheres in the wall, the porosity at the wall is reduced and the most direct cause of the bypass flow is thereby eliminated. The porosity is found by evaluating the ratio of the solid area to total area in a plane which is parallel to the wall. The local porosity is derived as a function of distance from the wall in the region within one-half a sphere diameter from the wall. The average porosity of the wall region is also calculated. This research has application to flow situations such as packed bed chemical reactors, pebble bed nuclear reactors and flow in packed beds.     

Steady rotation of a composite sphere in a concentric spherical cavity

The problem of steady rotation of a compositesphere located at the centre of a spherical container has beeninvestigated.A composite particle referred to in this paperis a spherical solid core covered with a permeable sphericalshell.The Brinkman’s model for the flow inside the composite sphere and the Stokes equation for the flow in the spherical container were used to study the motion.The torque experienced by the porous spherical particle in the presence ofcavity is obtained.The wall correction factor is calculated.In the limiting cases,the analytical solution describing thetorque for a porous sphere and for a solid sphere in an unbounded medium are obtained from the present analysis.     

Interaction between two spheres placed in tandem arrangement in steady and pulsating flow

The interaction among two spheres in tandem formation are studied for a Reynolds number of 300 using both steady and pulsating inflow conditions. The purpose is to further investigate the force characteristics as well as the shedding patterns of the two spheres as the separation distance is changed from 1.5 to 12 sphere diameters. The method used for the simulations is the volume of solid (VOS) method, an approach based on the volume of fluid (VOF) method. Comparisons with other computational methods have shown VOS to accurately resolve the flow field around solid spheres. The results show that the separation distance plays a significant role in changing the flow patterns and shedding frequencies at moderate separation distances, whereas effect on drag is observed even at a separation distance of 12 diameters.     

Stick-slip flow of high density polyethylene in a transparent slit die investigated by laser Doppler velocimetry

The oscillating flow instability of a molten linear high-density polyethylene is carefully studied using a single screw extruder equipped with a transparent slit die. Experiments are performed using laser Doppler velocimetry in order to obtain the local velocities field across the entire die width. At low flow rate, the extrusion is stable and steady state velocity profiles are obtained. During the instability, the velocity oscillates between two steady state limits, suggesting a periodic stick-slip transition mechanism. At high flow rate, the flow is mainly characterized by a pronounced wall slip. We show that wall slip occurs all along the die land. An investigation of the slip flow conditions shows that wall slip is not homogeneous in a cross section of the slit die, and that pure plug flow occurs only for very high flow rates. A numerical computation of the profile assuming wall slip boundary conditions is done to obtain the true local wall slip velocity. It confirms that slip velocities are of the same order of magnitude as those measured with a capillary rheometer.     

Resolution sensitivity of momentum‐exchange and immersed boundary methods for solid–fluid interaction in the lattice Boltzmann method

In the lattice Boltzmann method (LBM), the mechanism of fluid–solid interaction can be effectively captured by appropriately enforcing the no‐slip conditions in shear direction, and bounce‐back of the non‐equilibrium distribution portion in the normal direction at fluid–solid interfaces. Among various solid–fluid interaction schemes being proposed for LBM in recent decades, two simple fluid–solid interaction methods—the momentum exchange algorithm (MEA) and the immersed boundary scheme (IBS)—were developed based on the above concept. In this paper, MEA and IBS are implemented in a D2Q9 LBGK system and applied to measure the wall correction factors of drag force upon a stationary circular particle midway in the Poiseuille channel flow at very low Reynolds number and drag coefficients at low to moderate Reynolds numbers. MEA and IBS are also employed to compare the fluid‐induced torque over the cylinder in the Taylor–Couette flow, and the steady velocity of a particle settling under the influence of gravity inside a tube. The above experiments show that IBS seems to be more accurate and less demanding on lattice resolution. Copyright © 2010 John Wiley & Sons, Ltd.     

Molecular dynamics simulation of liquid argon flow at platinum surfaces

The micro Poiseuille flow for liquid argon flowing in a nanoscale channel formed by two solid walls was studied in the present paper. The solid wall material was selected as platinum, which has well established interaction potential. We consider the intermolecular force not only among the liquid argon molecules, but also between the liquid argon atoms and the solid wall particles, therefore three regions, i.e. the liquid argon computation domain, the top and bottom solid wall regions are included for the force interaction. The present MD (Molecular Dynamics) simulation was performed without any assumptions at the wall surface. The objective of the study is to find how the flow and the slip boundaries at the wall surface are affected by the applied gravity force, or the shear rate. The MD simulations are performed in a nondimensional unit system, with the periodic boundary conditions applied except in the channel height direction. Once the steady state is reached, the macroscopic parameters are evaluated using the statistical mechanics approach. For all the cases tested numerically in the present paper, slip boundaries occur, and such slip velocity at the stationary wall surface increases with increasing the applied gravity force, or the shear rate. The slip length, which is defined as the distance that the liquid particles shall travel beyond the wall surfaces to reach the same velocity as the wall surface, sharply decreases at small shear rate, then slightly decreases with increasing the applied shear rate. We observe that the liquid viscosity remains nearly constant at small shear rates, and the Newtonian flow occurs. However, with increasing the shear rate, the viscosity increases and the non-Newtonian flow appears.     

Numerical study of the exact solution of the Navier–Stokes equations describing free-boundary fluid flow

This paper presents a numerical study of the partially invariant solution of the Navier–Stokes equations for the plane case which describes unsteady flow in a layer bounded by a straight solid wall and a free boundary parallel to it. It is found that for different initial flow velocities, a steady state can be established with a decrease or an increase in the initial layer thickness or the layer thickness can be increased infinitely due to fluid inflow from infinity.     

Linear viscoelastic behavior of asphalt and asphalt based mastic

The rheological properties of an asphalt mastic and its matrix are investigated. For the purpose of comparison a sample of thermal aged asphalt matrix is also considered. Dynamic and creep shear measurements are reported. The reduced shear rate concept proposed by Ohl and Gleissle is used to correlate mechanical properties of the three materials at the same temperature. We found that the concept gives only qualitative trends. A similar conclusion is found concerning the applicability of the time-temperature superposition principle for each sample. Our experimental results show also that the increase in viscosity due to thermal treatment or to the inclusion of solid particles is not uniform with temperature. The differences in the increase of the Vogel temperature from the asphalt to the mastic, or to the thermally aged asphalt, relate to the different mechanisms involved. Sedimentation of steel spheres in asphalt and mastic, is studied next. The Newtonian wall correction factor for the Stokes drag law holds for the three samples. Despite the similar behavior observed in conventional shear tests, Stokes' law gives the correct trend for the two asphalts although it overestimates the experimental settling velocity by a factor of approximately two in the case of the mastic. Received: 8 June 1999/Accepted: 19 October 1999     

The settling of spheres in a viscoplastic fluid

Results on the variation in the steady settling velocity of spheres with a time interval between experiments in a 0.3 wt% aqueous Carbopol-941 dispersion are reported. Spheres made of stainless steel, brass, ceramics and soda lime glass ranging in nominal diameter from 1/4 to 3/8 in. were used. In each experiment, four identical spheres were permitted to settle in quick succession and the time interval between such sets was varied systematically. It was found that four spheres were sufficient to reach an asymptotic settling velocity which did not change with the addition of more spheres to the set. The dependence of the drag coefficient on a modified Reynolds number based on this asymptotic settling velocity was found to be consistent with that from prior work. The steady terminal settling velocity of the first sphere was found to decrease with increasing time intervals between experiments. The results are consistent with the hypothesis of network damage caused by shear with subsequent healing.     

Settling motion of interacting solid particles in the vicinity of a plane solid boundary

The sedimentation of $N?1$ small arbitrarily-shaped solid bodies near a solid plane is addressed by discarding inertial effects and using 6N boundary-integral equations. Numerical results for 2 or 3 identical spheres reveal that combined wall–particle and particle–particle interactions deeply depend on the cluster's geometry and distance to the wall and may even cancel for a sphere which then moves as it were isolated. To cite this article: A. Sellier, C. R. Mecanique 333 (2005).     

Transient response of a parallel flow shell-and-tube heat exchanger and its control

The shell and tube heat exchangers constitute the single largest component of the heat exchanger family. Though a vast number of literature is available for their steady state analyses, the number of works on transient analysis are comparatively fewer. The present paper brings out the transient response of a single pass shell and tube heat exchanger neglecting wall heat capacitance. The model is constructed with a distributed parameter approach. Unlike a number of recent analyses the numerical technique is avoided and the path of double Laplace transform has been chosen instead. This gives a scope for a unique functional representation of the response which is useful for deciding the control strategies to be adopted. This strategy has been formulated for the parallel flow model using PID controllers.     

The interaction between shock waves and solid spheres arrays in a shock tube

When a shock wave interacts with a group of solid spheres, non-linear aerodynamic behaviors come into effect. The complicated wave reflections such as the Mach reflection occur in the wave propagation process. The wave interactions with vortices behind each sphere‘s wake cause fluctuation in the pressure profiles of shock waves. This paper reports an experimental study for the aerodynamic processes involved in the interaction between shock waves and solid spheres. A schlieren photography was applied to visualize the various shock waves passing through solid spheres. Pressure measurements were performed along different downstream positions. The experiments were conducted in both rectangular and circular shock tubes. The data with respect to the effect of the sphere array, size, interval distance, incident Mach number, etc., on the shock wave attenuation were obtained.     

Flow and heat transfer due to impulsive motion of a cone in a viscous fluid

Numerical solution has been obtained for the development of the flow over a cone which is impulsively set into motion. Initially the flow is described by the solution of Rayleigh and then it tends to the ultimate steady state solution of Falkner-Skan equation. But due to the leading edge effect the semi-similar equation describing the transient flow changes its character after certain time and the solution depends also on the ultimate steady state solution of the Falkner-Skan equation. A second-order upwind difference scheme has been used for discretisation. The temperature distribution and heat transfer has also been obtained for constant wall temperature as well as for constant heat flux at the wall. With the increase ofm, Falkner-Skan parameter, the magnitude of skin friction and wall heat transfer increases. It has been found that form≥?0.275 flow separation does not occur.     

Pipe flow with solid particles fixed in space

A group of solid particles were hung by slender rods in a pipe to make a model of two-phase flow of coarse particles. Pressure gradient and velocities were measured for different types of the models. The drag on the particles (spheres) were obtained from measurements of pressure gradient with some assumptions. The results are summarized as follows. (1) Mean velocities of fluid are lower in the central part of the pipe than in the circumferential part. Turbulence is remarkably increased by particles. The spectrum distribution of turbulent velocity becomes flatter. These results are similar to the gas-solid flow of coarse particles in a vertical pipe. (2) At a large Reynolds number, the drag coefficient per one sphere in the group is larger than that of a single isolated sphere in a uniform flow. When the spheres are arranged along the same line in the longitudinal direction, the drag coefficient becomes smaller as the longitudinal distance between the spheres is shortened.     

Dynamic interaction of fixed dual spheres for several configurations and inflow conditions

The changes in force characteristics as well as the shedding patterns for various dual sphere configurations are studied. The Reynolds numbers considered are 300, 600 and two different inflow conditions are used: steady and pulsating. The sphere formations are defined by the separation distance D₀ between the spheres and the angle between the line connecting the centres of the spheres and the main flow direction, γ. The position of one of the spheres is varied in the range 0°–90° using a 15° increment. Two separation distances are studied; 1.5D and 3D. The method used for the simulations is the Volume of Solid (VOS) approach, a method based on Volume of Fluid (VOF). A major conclusion from this work is that the sphere interaction alters the wake dynamics by obstructing the vortex shedding (generating a steady wake or a wake with lower Strouhal number) and by changing the direction of the lift force so that it in most cases is directed in the plane containing the sphere centres. The results also show that changing the inflow condition gives the same relative change in drag and lift as for a single sphere. The drag is substantially reduced by placing the sphere downstream in a tandem arrangement and slightly increased in a side-by-side arrangement. However, the effect is decreased by increasing separation distance and increasing Reynolds number.     

The influence of walls on the motion of a sphere in non-Newtonian liquids

The influence of the contained wall on the drag of a sphere moving through a non-Newtonian fluid is analysed in this work separately for the low Reynolds number and the high Reynolds number regions. In the former, we make use of the two-concentric-sphere model. It is predicted that the wall effect will decrease with the increase of the shear-thinning anomaly and this is in a reasonable agreement with the available experimental data and correlations. The wall effect in the high Reynolds number region is analysed in this work using the cell model (used to study the motion of an assemblage of solid spheres) and the predictions are in satisfactory agreement with the available empirical correlation for non-Newtonian fluids. Presented at the First Conference of European Rheologists, Graz (Austria), April 14–16, 1982.     

Towards a theoretical model of heat transfer for hot-wire anemometry close to solid walls

Hot-wire anemometry readings where the sensor is close to a solid wall become erroneous due to additional heat losses to the wall. Here we examine this effect by means of experiments and numerical simulations. Measurements in both quiescent air as well as laminar and turbulent boundary layers confirmed the influences of parameters such as wall conductivity, overheat ratio and probe dimensions on the hot-wire output voltage. Compared to previous studies, the focus lies not only on the streamwise mean velocity, but also on its fluctuations. The accompanying two-dimensional steady numerical simulation allowed a qualitative discussion of the problem and furthermore mapped the temperature field around the wire for different wall materials. Based on these experimental and numerical results, a theoretical model of the heat transfer from a heated wire close to a solid wall is proposed that accounts for the contributions from both convection and conduction.