Onset of entrainment and degree of dispersion in dual continuous horizontal oil–water flows

The transition from stratified to dual continuous oil–water flow (where each phase retains its continuity but there is dispersion of one phase into the other) as well as the dispersed phase fractions in the layers of the dual continuous pattern, were studied experimentally. Transition to this pattern from stratified flow occurs when drops of one phase appear into the other (onset of entrainment). The studies were carried out in a 38 mm ID horizontal stainless steel test section using two different inlet geometries, a T- and a Y-junction. The patterns were visualized through a transparent acrylic section located at 7 m from the inlet using a high speed video camera. Phase distribution measurements in a pipe cross section were obtained just before the acrylic section with a local impedance probe and the results were used to calculate the volume fraction of each phase entrained into the other. The onset of entrainment was found to occur at lower superficial water velocities as the oil superficial velocities increased. However, the inlet geometry did not affect significantly the transition line. During dual continuous flow, the dispersion of one phase into the opposite was found to extend further away from the interface with increasing water superficial velocity for a certain oil superficial velocity. An increase in the superficial water velocity increased the entrained fraction of water in oil (E_w/o) but there was no trend with the oil velocity. Similarly, an increase in the superficial oil velocity increased the fraction of oil drops in water (E_o/w) but the water velocity had no clear effect. The entrainment fractions were affected by the inlet geometry, with the T-inlet resulting in higher entrainment than the Y-inlet, perhaps because of the increased mixing induced by the T-inlet. The difference between the two inlets increased as the oil and water velocities increased.     

Motion of tracer particles in supersonic flows

 Factors that may act on particle motion in high-speed flow are investigated. The classical expressions of drag coefficient C _D for a sphere are reviewed. Then, a drag expression is proposed, extending Cunningham’s method to higher velocities and Knudsen numbers. This law, valid from continuum to free molecule conditions, for Re≲200 and M≲1 (where Re and M are, respectively, the Reynolds and Mach numbers based on relative velocity), is used to compare calculated and experimental values of the drag coefficient, as well as the particle velocities across an oblique shock wave. Calculated results are found to be in agreement with experiments. Received: 3 June 1997/Accepted: 16 August 1998     

Mixing mechanisms of vortex ring formed by gravity slumping motion

 This paper is concerned with an experimental investigation of the mixing inside the vortex ring formed by the gravity slumping motion of a dense cloud in a less dense atmosphere. The dynamics of the spreading and instantaneous structures of the turbulent flow were examined by visualization, single and multi-point measurements of velocity and concentration for two heavy gases, carbondioxide (CO₂) and dichlorodifluoromethane (CCl₂F₂), in a configuration in that heavy gas, initially trapped in a reservoir, was released with the rise of a shutter into calm air of a sector-shaped dispersion channel. Visualization of the cloud as a whole showed a spreading motion in which an advancing frontal structure was followed by a stratified flow with a layer of dense fluid of higher velocities near the wall and, on top of it, a layer of dilute fluid whose concentration is controlled by the mixing mechanisms within the head. During the course of spreading, there was always a phase in which the head attained to a constant speed of advance, which occurred as 0.13 m/s for CO₂ and 0.48 m/s for CCl₂F₂. It was interesting to observe for CO₂ that the phase of constant speed took place in between two acceleration phases; the former was due to the initial slumping of the cloud at the exit of the reservoir, and the latter was attributed to the collapse of the head on the transition to the passive dispersion phase. Instantaneous two-dimensional velocity field, measured with particle image velocimeter (PIV), showed that the cloud overran the ambient air which caused the approaching dense fluid deflected away from the wall with significant vertical velocities and downstream-moving separation, and the air trapped under the head resulted in the density inversion which introduced further intricacy to the turbulent structure of the head. Instabilities at the upper free shear layer due to density and velocity discontinuity rolled into periodic array of vortices which engulfed a considerable amount of air as they were convected backwards over the head, but the incorporation of heavy and light fluids was completed with the appearance of microscales after the collapse on the stratified layer. Analyses of the cloud head at different downstream locations also revealed that its size remained unchanged when the speed of advance was constant, allowing the rate of change of the cloud volume being modeled with the rate of spreading. Contours of concentration obtained from digitized PIV pictures confirmed the kinematic features of the mixing revealed by the velocity field and that the concentration values within the large structures were higher than those at the upper part of the stratified layer. Motivated by the experimental observations, a semi-empirical analysis was presented to describe the results and based on local values of the Richardson and Reynolds numbers. Received: 4 October 1995 / Accepted: 4 July 1996     

A critical review of dispersion in packed beds

The phenomenon of dispersion (transverse and longitudinal) in packed beds is summarized and reviewed for a great deal of information from the literature. Dispersion plays an important part, for example, in contaminant transport in ground water flows, in miscible displacement of oil and gas and in reactant and product transport in packed bed reactors. There are several variables that must be considered, in the analysis of dispersion in packed beds, like the length of the packed column, viscosity and density of the fluid, ratio of column diameter to particle diameter, ratio of column length to particle diameter, particle size distribution, particle shape, effect of fluid velocity and effect of temperature (or Schmidt number). Empirical correlations are presented for the prediction of the dispersion coefficients (D _T and D _L) over the entire range of practical values of Sc and Pe_m, and works on transverse and longitudinal dispersion of non-Newtonian fluids in packed beds are also considered.     

Flow Laws in Metal Foams: Compressibility and Pore Size Effects

The aim of our experimental work was to establish a simple relation between the flow parameters and the morphological parameters of metallic foam. We used foam samples made from different metals or alloys (Cu, Ni, Ni-Cr, etc) and of various thicknesses. Pore size ranged between 500 and 5000 μm. We measured the pressure profiles in foam samples using a specific experimental set-up of 12 pressure sensors distributed 1 cm apart along the main flow axis. The experimental loop made it possible to use indifferently water or air as working fluid. For the study of the gas (air) flow, velocities ranged roughly from 0 up to 20 m/s and for the liquid (water) flow, velocities ranged between 0 and 0.1 m/s. The measurements of the pressure gradients were performed systematically. We validated the Forchheimer flow model. The influence of the compressibility effects on permeability and inertia coefficient was emphasized. We demonstrated that the pore size Dp in itself is sufficient to describe flow laws in such high porosity material: K and β are respectively proportional to Dp² and Dp⁻¹.     

Coefficient of discharge and spray cone angle of a pressure nozzle with combined axial and tangential entry of power-law fluids

Flows of incompressible, time-independent purely viscous power-law fluids through pressure nozzle with combined axial and tangential entry are analysed. Theoretical predictions of coefficient of discharge and spray cone angle are made through an approximate analytical solution of hydrodynamics of flow inside the nozzle. In the converging section of the nozzle, the boundary layer equations have been derived with modified order approximation [O(δ/R)≈1, O(δ ²/R ²)≪1] of Navier-Stokes equations for a better accuracy. Smoother attainment of the free-stream condition at the edge of the boundary layer is ensured by requiring the appropriate shear rate terms, compatible with the above order analysis, to be zero. The pertinent independent input parameters which govern the flow field are the generalized Reynolds number at inlet to the nozzle based on the tangential velocity of injection , the ratio of the axial-to-tangential velocity at the inlet to the nozzle V _R , the flow behaviour index of the fluid n, the length-to-diameter ratio of the swirl chamber L ₁/D ₁, the spin chamber angle 2α and the orifice-to-swirl-chamber-diameter ratio D ₂/D ₁. Experiments reported in the paper corroborate the qualitative trends of analytical results.     

Large eddy simulation of cross-flow through a staggered tube bundle at subcritical Reynolds number

The Large Eddy Simulation (LES) technique is used to study the vortex shedding characteristics inside a staggered tube array consisting of six rows with intermediate spacings (S_L/D×S_T/D=1.6×3.6) at the subcritical Reynolds number of 8600 (based on the gap velocity). The filtered equations are discretised using the finite volume method in an unstructured, collocated grid arrangement with second-order accurate methods in space and time. The predictions of mean velocities and Reynolds stresses are in very good agreement with detailed LDA measurements performed in 17 stations along the depth of the array. The sizes of the recirculation zones behind the cylinders in the first and third row also compare favourably with available correlations. Two distinct and independent shedding frequencies are detected behind the first two rows, but the high-frequency component vanishes in the downstream rows. The corresponding Strouhal numbers agree well with measurements available in the literature for similar tube spacings. The lift coefficient as well as instantaneous flow patterns of the whole array are also examined.     

On hot-wire diagnostics in Rayleigh–Taylor mixing layers

Two hot-wire flow diagnostics have been developed to measure a variety of turbulence statistics in the buoyancy driven, air-helium Rayleigh–Taylor mixing layer. The first diagnostic uses a multi-position, multi-overheat (MPMO) single wire technique that is based on evaluating the wire response function to variations in density, velocity and orientation, and gives time-averaged statistics inside the mixing layer. The second diagnostic utilizes the concept of temperature as a fluid marker, and employs a simultaneous three-wire/cold-wire anemometry technique (S3WCA) to measure instantaneous statistics. Both of these diagnostics have been validated in a low Atwood number (A _t  ≤ 0.04), small density difference regime, that allowed validation of the diagnostics with similar experiments done in a hot-water/cold-water water channel facility. Good agreement is found for the measured growth parameters for the mixing layer, velocity fluctuation anisotropy, velocity fluctuation p.d.f behavior, and measurements of molecular mixing. We describe in detail the MPMO and S3WCA diagnostics, and the validation measurements in the low Atwood number regime (A _t  ≤ 0.04). We also outline the advantages of each technique for measurement of turbulence statistics in fluid mixtures with large density differences.     

Secondary flow patterns and mixing in laminar pulsating flow through a curved pipe

Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r ₀/r _c  = 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced. To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe. Experiments are carried out for the Reynolds numbers range 420 ≤ Re_st ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U _max,osc/U _m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters 8.37 < (α = r ₀(ω/ν)^0.5) < 24.5, where α² is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing. The effects of each parameter (Re_st, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ _P |/|ζ _S |) and dimensionless transverse strain rates (|ε _P |/|ε _S |) during a complete oscillation period.     

On the unsteady rotational flow of a generalized Maxwell fluid through a circular cylinder

In this paper, the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized Maxwell fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. Initially, the fluid is at rest, and the motion is produced by the rotation of the cylinder about its axis with a unsteady angular velocity. The solutions that have been obtained are presented under series form in terms of the generalized G _a,b,c (, t)-functions. The similar solutions for the ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as special cases, when β → 1, respectively β → 1 and λ → 0, from general solutions. Finally, the solutions that have been obtained are compared by graphical illustrations, and the influence of the pertinent parameters on the fluid motion is also underlined by graphical illustrations.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Experimental study on interfacial area transport of a vertical downward bubbly flow

In relation to the development of the interfacial area transport equation, local flow measurements of vertical downward air–water flows in a pipe with an inner diameter of 50.8 mm were performed at three axial locations of z/D=6.50, 34.0, and 66.5 as well as ten radial locations from r/R=0 to r/R=0.9 using a multi-sensor probe. In the experiment, the superficial liquid velocity and the void fraction ranged from –0.620 m/s to –2.49 m/s and from 0.21% to 8.4%, respectively. The dependence of the interfacial area transport on the liquid velocity, void fraction, and bubble size is discussed in detail.     

Magnetic resonance imaging of velocity fields, the void fraction and gas dynamics in a cavitating liquid

In acoustic cavitation, the relationship between the bubble dynamics on the microscale and the flow properties on the macroscale is critical in determining sonochemical reaction kinetics. A new technique was developed to measure the void fraction and estimate water mobility in the vicinity of cavitating bubbles using phase-encoded magnetic resonance imaging with short characteristic measurement timescales (0.1–1 ms). The exponential behavior of the NMR signal decay indicated the fast diffusion regime, with the relationship between local mechanical dispersion D _mix and the average bubble radius R, D_mix >> \frac2R²10^-4s, D_{\rm mix}\gg \frac{2R^2}{10^{-4}\hbox{s}}, resulting in dispersion of orders of magnitude greater than diffusion in quiescent water. For two different samples (water and a surfactant solution), the independent measurements of three-dimensional void fraction and velocity fields permitted the calculation of compressibility, divergence and vorticity of the cavitating medium. The measured dynamics of the dissolved gas, compared with that of the surrounding liquid, reflected the difference in the bubble coalescence and lifetimes and correlated with the macroscopic flow parameters.     

Heat dispersion in stationary mixed convection flow about horizontal surfaces in porous media

An analysis has been performed to study the influence of velocity dependent dispersion on transverse heat transfer in mixed convection flow above a horizontal wall of prescribed temperature in a saturated porous medium. The Boussinesq approximation and boundary layer analysis were used to numerically obtain gravity affected temperature and velocity distributions within the frames of Darcy's law and a total thermal diffusivity tensor comprising both of constant coefficient heat conduction and velocity proportional mechanical heat dispersion. Dependending on Pe_∞, the molecular Peclét number basing on the effective thermal diffusivity and the velocity of the oncoming flow, density coupling has distinct influences on heat transfer rates between the wall surface and the porous medium flow region. For small Peclét numbers, when heat conduction is the prevailing mechanism, wall heat fluxes are the higher the larger the density difference between the oncoming and the near wall fluid is. The opposite is true for larger Peclét numbers, when mechanical heat dispersion is the main cause of heat spreading. For Pe_∞ tending to infinity these wall heat fluxes approach finite maximum values in the total heat diffusivity model, they grow beyond any limit if only constant coefficient heat conduction is considered. Thus, the inclusion of mechanical heat dispersion effects yields physically more realistic predictions. Received on 18 September 1996     

On the unsteady rotational flow of a fractional second grade fluid through a circular cylinder

Here the velocity field and the associated tangential stress corresponding to the rotational flow of a generalized second grade fluid within an infinite circular cylinder are determined by means of the Laplace and finite Hankel transforms. At time t=0 the fluid is at rest and the motion is produced by the rotation of the cylinder around its axis. The solutions that have been obtained are presented under series form in terms of the generalized G-functions. The similar solutions for ordinary second grade and Newtonian fluids are obtained from general solution for β→1, respectively, β→1 and α ₁→0. Finally, the influences of the pertinent parameters on the fluid motion, as well as a comparison between models, is underlined by graphical illustrations.     

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     

Flow of power-law fluids over a moving wedge surface with wall mass injection

The boundary layer problem of a power-law fluid flow with fluid injection on a wedge whose surface is moving with a constant velocity in the opposite direction to that of the uniform mainstream is analyzed. The free stream velocity, the injection velocity at the surface, moving velocity of the wedge surface, the wedge angle and the power law index of non-Newtonian fluid are assumed variables. The fourth order Runge–Kutta method modified by Gill is used to solve the non-dimensional boundary layer equations for non-Newtonian flow field. Without fluid injection, for every angle of wedge β, a limiting value for velocity ratio λ _cr (velocity of the wedge surface/velocity of the uniform flow) is found for each power-law index n. The value of λ _cr increases with the increasing wedge angle β. The value of wedge angle also restricts the physical characteristics of the fluid to be used. The effects of the different parameters on velocity profile and on skin friction are studied and the drag reduction is discussed. In case of C = 2.5 and velocity ratio λ = 0.2 for wedge angle β = 0.5 with the fluid with power law-index n = 0.5, 48.8% drag reduction is obtained.     

Motion of a sphere down an inclined plane in a viscous flow

The motion of a rigid particle near a wall in a fluid flow is an important element of particle transport by fluids. The aim of this study was to carry out an experimental and theoretical investigation of the gravity-induced motion of a rigid sphere in a viscous fluid in the presence of a transverse flow. The experimental study of this configuration is a way of understanding the specific features of the hydrodynamically constrained particle motion. It is established that the transverse motion of the fluid substantially increases the particle settling velocity, which grows with increase in the transverse flow velocity. This effect is most pronounced for small angles of inclination of the plane. The difference in the particle settling velocities in the presence and absence of the transverse flow could reach a factor of two.     

Pulsatile entrance flow in curved pipes: effect of various parameters

This paper presents the results of an experimental study on the developing pulsatile flow in curved pipes with a long, straight pipe upstream. In order to examine the dependence of flow-field development on the governing parameters, LDV measurements were conducted systematically for six cases of flow, where the Womersley number α was varied from 5.5 to 18, the mean Dean number D _m was 200 and 300, the flow rate ratio η was 0.5 and 1, and the curvature radius ratio Rc was 10 and 30. Peculiar flow phenomena, such as flow reversal for all values of α and a depression in the axial velocity profile for α = 10, were analyzed by decomposing the axial velocity into a time-mean and a varying component, as well as by obtaining the bias of their profiles. The velocity distributions abruptly change with the phase at turn angles Ω of 15–30°, corresponding to the nondimensional axial length z′ ≅ 1–2 from the bend entrance, and their development along the pipe axis is the most complicated for the flow at a moderate α of 10 and large η of 1. The entrance length in the case of pulsatile flow is shorter than that for steady flow with the same flow rate as the maximum pulsatile flow rate.     

Lp-Lq Estimate of the Stokes Operator and Navier–Stokes Flows in the Exterior of a Rotating Obstacle

We consider the motion of a viscous fluid filling the whole three-dimensional space exterior to a rotating obstacle with constant angular velocity. We develop the L _p -L _q estimates and the similar estimates in the Lorentz spaces of the Stokes semigroup with rotation effect. We next apply them to the Navier–Stokes equation to prove the global existence of a unique solution which goes to a stationary flow as t → ∞ with some definite rates when both the stationary flow and the initial disturbance are sufficiently small in L _3,∞ (weak-L ₃ space).