Numerical simulation of drop migration in channell flow under zero-gravity

The migration of deformable drops in the channel flow neglecting the gravity influence is investigated numerically by solving the incompressible Navier-Stokes equations using the finitedifference method coupled with the front-tracking technique. The objectives of this study are to examine the effectiveness of the present approach for predicting the migration of drops in a shear flow and to investigate the behavior of the drop migration in the channel flow under zero-gravity. To validate the present calculation, some typical results are compared with available computational and theoretical data, which confirms that the present approach is reliable in predicting the drop migration. With respect to the drop migration in the channel flow at finite Reynolds numbers, the drops either move to an equilibrium lateral position or undergo an oscillatory motion under different conditions. The effects of some typical parameters, e.g., the Reynolds number, the Weber number, the viscosity ratio and the density ratio of the drop fluid to the suspending medium, and the drop size, on the migration of drops are discussed and analyzed. The project supported by the National Natural Science Foundation of China (10125210) and the Hundred-Talent Programme of the Chinese Academy of Sciences     

Dynamics of dual-particles settling under gravity

As a first step towards understanding particle–particle interaction in fluid flows, the motion of two spherical particles settling in close proximity under gravity in Newtonian fluids was investigated experimentally for particle Reynolds numbers ranging from 0.01 to 2000. It was observed that particles repel each other for Re>0.1 and that the separation distance of settling particles is Reynolds number dependent. At lower Reynolds numbers, i.e. for Re<0.1, particles settling under gravity do not separate.The orientation preference of two spherical particles was found to be Reynolds number dependent. At higher Reynolds numbers, the line connecting the centres of the two particles is always horizontal, regardless of the way the two particles are launched. At lower Reynolds numbers, however, the particle centreline tends to tilt to an arbitrary angle, even of the two particles are launched in the horizontal plane. Because of the tilt, a side migration of the two particles was found to exist. A linear theory was developed to estimate the side migration velocity. It was found that the maximum side migration velocity is approximately 6% of the vertical settling velocity, in good agreement with the experimental results.Counter-rotating spinning of the two particles was observed and measured in the range of Re=0–10. Using the linear model, it is possible to estimate the influence of the tilt angle on the rate of rotation at low Reynolds numbers. Dual particles settle faster than a single particle at small Reynolds numbers but not at higher Reynolds numbers, because of particle separation. The variation of particle settling velocity with Reynolds number is presented. An equation which can be used to estimate the influence of tilt angle on particle settling velocity at low Reynolds number is also derived.     

Three-dimensional numerical simulation of sedimenting drops inside a vertical channel

Numerical simulation of sedimenting deformable drops inside a vertical channel has been performed at finite Reynolds numbers. The channel is confined by two vertical walls in x-direction and is periodic in y- and z-directions. Results are obtained using a finite difference/front-tracking method. The main dimensionless parameters are the Reynolds number, the Bond number and ratio of the length of channel to the diameter of drops. The effect of these parameters on lateral migration of drops is investigated. It is found that the wall repulsion is the main mechanism of the lateral migration of the drop, and drop migrates toward the channel axis. When the Reynolds number is relatively low, two different lateral migration regimes are observed: migration with monotonic approach and migration with damped oscillations. These regimes are affected by the dimensionless parameters. When the Bond number increases, the oscillations of drop around the centerline of channel are stronger and drop reaches the channel centerline in a larger period. Results of lateral migration of one drop are consistent with perturbation theory, and two-dimensional numerical simulations performed by Feng et al. (1994). The drag coefficient has also been calculated, and effect of various parameters has been discussed. Two drops interaction is similar to that observed by Feng et al. (1994) for two-dimensional circular cylinders. Results are consistent with experiments performed by Wu and Manasseh (1998). Simulations of four sedimenting drops show that depending on the relative size of drops, they either fall in two rows or they form a single horizontal layer and settle with a unique velocity.     

Research on particle dispersion in a plane mixing layer with coherent structures

The numerical simulation with two-way coupling was performed in a liquid -particle mixing layer and the corresponding experiment study was made. In the process of vortex rolling up and vortices pairing, the particles with different St number have a very different pattern of dispersion. The mean velocity of particle with St = 1 is higher than that of the fluid phase on the low-speed side, and lower than that of the fluid phase on the high-speed side. The RMS of particle approaches that of the fluid phase with decreasing particle St number. The RMS in the transverse direction is smaller than that in the streamwise direction. The velocity fluctuation correlation of particle is smaller than the Reynolds shear stress, the “overshoot“ phenomenon that the velocity fluctuation correlation of particle is larger than the Reynolds shear stress does not appear. The larger the St number of particle is, the wider the range of the particle dispersion will be. The computed results are in agreement with the experimental ones.     

A computational study of a capsule lateral migration in microchannel flow

A numerical method is used to model a capsule migration in a microchannel with small Reynolds number Re ≈ 0 . 01. The capsule is modeled as a liquid drop surrounded by a neo-Hookean elastic membrane. The numerical model combines immersed boundary with lattice Boltzmann method (IB-LBM). The LBM is used to simulate fixed Cartesian grid while the IBM is utilized to implement the fluid-structure interaction by a set of Lagrangian moving grids for the membrane. The effect of shear elasticity and bending stiffness are both considered. The results show the significance of elastic modulus and initial lateral position on deformation and morphological properties of a circular capsule. The wall effect becomes stronger as the capsule initial position gets closer to the channel wall. As the elastic modulus of membrane increases, the capsule undergoes less pronounced deformation and velocity in direction x is decreased, thus, the capsule motion is slower than the background flow. The best agreement between the present model and experiments for migration velocity takes place for the capsule with normal to moderate membrane elastic modulus. The results are in good agreement with experiment study of Coupier et al. and previous numerical studies. Therefore, the IB-LBM can be employed to make prediction in vitro and in vivo studies of capsule deformation.     

PIV with volume lighting in a narrow cell: An efficient method to measure large velocity fields of rapidly varying flows

In this work we test a methodology for PIV measurements when a large field of view is required in planar confined geometries. Using a depth of field larger than the channel width, we intend to measure the in-plane variations of the velocity of the fluid averaged through the width of the channel, and we examine in which operating conditions this becomes possible. Measurements of the flow through a narrow channel by PIV are challenging because of the strong velocity gradients that develop between the walls. In particular, all techniques that use small particles as tracers have to deal with the possible migration of the tracers in the direction perpendicular to the walls. Among the complex mechanisms for migration, we focus on the so called Segré-Silberberg effect which can lead to transverse migration of neutrally buoyant tracers of finite size. We report experimental PIV measurements in a Hele-Shaw cell of 1 mm gap, which have been carried out by using neutrally buoyant tracers of size around 10 μm. By considering steady flows, we have observed, in particular flow regimes, the effect of an accumulation of the tracers at a certain distance to the wall due to the so called Segré-Silberberg effect. The particle migration is expected to occur at any Reynolds numbers but the migration velocity depends on the Reynolds number. A significant migration therefore takes place each time the observation duration is large enough compared to the migration time. For a given observation duration, the tracers remain uniformly distributed at low Reynolds numbers whereas they all accumulate at the equilibrium position at large ones. When using volume lighting, the PIV algorithm provides the average velocity of the flow through the gap at low Reynolds number, while it leads to the velocity of the flow at the equilibrium position of the tracers at large Reynolds numbers. By considering unsteady flows, we have observed that the migration does not occur if the timescale of flow variation is short compared to the time required for the parabolic flow to develop across the gap. In this case, there is no transverse velocity gradient and the PIV algorithm provides the fluid velocity. Altogether, these results allow us to propose guidelines for the interpretation of PIV measurements in confined flow, which are based on the theoretical predictions of the tracer migration derived by Asmolov [1].     

Numerical investigation of a water flow in a rib-roughened channel by using Reynolds stress model

In this paper, water flow in a rib-roughened channel is investigated numerically by using Reynolds stress turbulence models (RSM) on a three-dimensional (3-D) domain. Computational results for mean streamwise velocity component and turbulent kinetic energy show good agreements with available experimental data. Five rib pitch-to-height ratios (p/h) of 1, 5, 10, 15 and 20 are analysed for six different Reynolds numbers (Re) of 3000, 7000, 12,000, 20,000, 40,000 and 65,000. Velocity vectors, streamlines and Reynolds stresses are showed for these ratios and Re numbers. Streamlines revealed that Reynolds numbers do not affect flowfield but play an important role in the Reynolds stresses.     

Moderate Reynolds number axisymmetric jet development downstream an extended conical diffuser: Influence of extension length

Low-velocity (bulk velocity of 4.4 m/s) and moderate Reynolds (7350) axisymmetrical jet development is studied by hot-film single sensor anemometry. The jet issues from a conical convergent-divergent diffuser with uniform extension (diameter 25 mm). Decreasing the length-to-diameter ratio of the extension tube from 20 down to 0.4 is shown to alter severely the mean velocity profile at the tube outlet from Blasius to top-hat whereas turbulence intensities increases from 6 up to 50%. Next, the influence of the initial velocity profile at the tube outlet on axisymmetrical jet development is assessed. The velocity development exhibits a self-similar far field characteristic for axisymmetrical jet development. Although, the jet centerline decay constant increases and the jet spreading rate decreases as length-to-diameter ratios are increased from 0.4 up to 7.2 for which the initial centerline velocity decreases. Therefore, scaling of the centerline decay constant and inverse scaling of the spreading rate with initial centerline velocity U₀ or initial velocity Reynolds number Re₀ reported for moderate Reynolds numbers and low initial turbulence levels [18,22] does not hold as the turbulence level exceeds a threshold value in the range 12–27%. In addition, the influence of initial conditions on near and far field turbulence properties is shown. A transition in near field behaviour is observed for length-to-diameters around 3.6. Flow and geometrical configurations under study are relevant to e.g. upper airway flow.     

Extended self-similar scaling law of multi-scale eddy structure in wall turbulence

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Friction factor improved correlations for laminar and turbulent gas–liquid flow in horizontal pipelines

We develop improved correlations for two-phase flow friction factor that consider the effect of the relative velocity of the phases, based on a database that includes 2560 gas–liquid flow experiments in horizontal pipes. The database includes a wide range of operational conditions and fluid properties for two-phase friction factor correlations. We classify the experiments by liquid holdup ranges to obtain composite analytical expressions for two-phase friction factor vs. the Reynolds number by fitting logistic dose curves to the experimental data with. We compute the liquid holdup values used to classify the experimental data using correlations proposed previously. The Reynolds number is based on the mixture velocity and the liquid kinematic viscosity. The Fanning friction factor for gas–liquid is defined in term of the mixture velocity and density. Additionally, we sort the experimental data by flow regime and obtain the two-phase friction factor improved correlations for dispersed bubble, slug, stratified and annular flow for different holdup ranges. We report error estimates for the predicted vs. measured friction factor together with standard deviation for each correlation. The accuracy of the correlations developed in this study is compared with that of other 21 correlations and models widely available in the specialized literature. Since different authors use different definitions for friction factors and Reynolds numbers, we present comparisons of the predicted pressure drop for each and every data point in the database. In most cases our correlations predict the pressure drop with much greater accuracy than those presented by previous authors.     

Transonic Euler computation in streamfunction co-ordinates

Numerical simulation by a finite element method is used to examine the problem of the rotating flow of a viscoelastic fluid in a cylindrical vessel agitated with a paddle impeller. The mathematical model consists of a viscoelastic constitutive equation of Oldroyd B type coupled to the hydrodynamic equations expressed in a rotating frame. This system is solved by using an unsteady approach for velocity, pressure and stress fields. For Reynolds numbers in the range 0.1–10, viscoelastic effects are taken into account up to a Deborah number De of 1.33 and viscoelasticity and inertia cross-effects are studied. Examining the velocity and stress fields as well as the power consumption, it is found that their evolutions are significantly different for low and moderate inertia. These results confirm the trends of experimental studies and show the specific contribution of elasticity without interference of the pseudoplastic character found in actual fluids.     

Transition from laminar to turbulent flow in liquid filled microtubes

The transition to turbulent flow is studied for liquids of different polarities in glass microtubes having diameters between 50 and 247 µm. The onset of transition occurs at Reynolds numbers of ~1,800–2,000, as indicated by greater-than-laminar pressure drop and micro-PIV measurements of mean velocity and rms velocity fluctuations at the centerline. Transition at anomalously low values of Reynolds number was never observed. Additionally, the results of more than 1,500 measurements of pressure drop versus flow rate confirm the macroscopic Poiseuille flow result for laminar flow resistance to within –1% systematic and ±2.5% rms random error for Reynolds numbers less than 1,800.An erratum to this article can be found at     

A unified theory of turbulent flow

Summary A general theory of turbulent flow is applied to incompressible flow in a circular pipe. The theoretical mean velocity distribution is found to be in good agreement with experiment, but there is some discrepancy in the normal stress distribution. The available pressure drop data are used to estimate the value of the apparent wall velocity as a function of Reynolds number and roughness. It is found that the results can be represented by simple expressions which in turn imply simple expressions for the pressure drop as a function of Reynolds number and roughness. However, it has not been possible to derive these results from fundamental considerations. The basis of Reynolds analogy and the application of the theory to channel flow are also discussed.     

The axisymmetric boundary layer beneath a Rankine-like vortex

 An experimental investigation of the three-dimensional boundary layer induced by a Rankine-like vortex with its axis normal to a stationary disk is described. The velocity field through the boundary layer was measured for Reynolds number Re (based on the tangential velocity and radius at the disk edge) ranging from 10 000 to 25 000 at various radial distances by means of a 4-beam, 2-component Laser Doppler Anemometer. Our results show that the nature of the boundary layer is affected by two factors: an inflexional instability caused by the crossflow velocity profile and a stability factor caused by the favorable pressure gradient. At lower Reynolds number, the radial pressure gradient has a very strong stabilizing effect on the boundary layer and acts to revert it to its laminar state upstream of the effusing core. At higher Re the inflexional instability caused by the crossflow velocity dominates while the stabilizing influence of the favorable pressure gradient recedes. As such, laminar reversion likely occurs closer to the effusion core. Thus, the point of laminar reversion moves closer to the effusion core as the Reynolds number is increased. Received 23 May 1996 / Accepted 29 July 1996     

Influence of geometry on separation efficiency in a hydrocyclone

A numerical study of the gas–liquid–solid multiphase flow in hydrocyclones is presented. Three models of turbulence, the RNG k–ε model, the Reynolds stress model and Large eddy simulation with the volume of fluid model (VOF) multiphase model for simulating air core are compared in order to predict axial and tangential velocity distributions. This presentation is mainly aimed at identifying an optimal method, used to study effective parameters, based on which, eventually, effect of inlet flow rate variations and body dimension variations such as underflow diameter, overflow diameter and cone angle on the separation performance and pressure drop are investigated. The results are then used in the simulation of particle flow described by the stochastic Lagrangian model. The results suggest that the predicted size classifications are approximately similar to those of RSM and LES methods. Predictions using the RSM model are found in agreement with experimental results with a marginal error within the range of 4 to 8%. Proceeding model validation, parametric studies have been carried out concerning the influence of velocity inlet, particle size and body dimension such as underflow and overflow diameter and cone angle. The predictions demonstrate that the flow fields in the hydrocyclones with different sizes and lengths are different, which yields different performances.     

A large eddy simulation of the near wake of a circular cylinder

Viscous flow around a circular cylinder at a subcritical Reynolds number is investigated using a large eddy simulation (LES) coupled with the Smagorinsky subgrid-scale (SGS) model. A fractional-step method with a second-order in time and a combined finite-difference/spectral approximations are used to solve the filtered three-dimensional incompressible Navier-Stokes equations. Calculations have been performed with and without the SGS model. Turbulence statistical behaviors and flow structures in the near wake of the cylinder are studied. Some calculated results, including the lift and drag coefficients, shedding frequency, peak Reynolds stresses, and time-average velocity profile, are in good agreement with the experimental and computational data, which shows that the Smagorinsky model can reasonably predict the global features of the flow and some turbulent statistical behaviors. The project supported by the National Science Fund for Distinguished Scholars (10125210), the Special Funds for Major State Basic Research Project (G1999032801) and the National Natural Science Foundation of China (19772062)     

Interaction of von Karman vortices and intersecting main streams in staggered tube bundles

 Flow visualization, heat transfer and pressure drop characteristics in flow through staggered tube bundles have been regarded as classical, with results well-documented. However, the mechanism of producing such results has been left untouched. Applications of staggered tube bundles are abundant in industry, for example as heat exchange devices like the shell-and-tube type and fuel bundles in nuclear reactor cores. An experimental study is recorded in the present paper which investigates the interaction of von Karman vortices and intersecting main streams in staggered tube bundles. Flow visualization by means of the particle tracing method, laser Doppler velocimetry (LDV) and pressure drop measurements using a piezometer are conducted. A modified Reynolds number appropriate to flow through a staggered tube arrangement is defined together with a pressure drop coefficient. Auto-correlation and power spectrum analyses of signals obtained from LDV measurements yield an optimum spectrum frequency which is correlated against the Reynolds number. It is concluded that flow characteristics in staggered tube bundles are determined by the interaction between the von Karman vortex street and X-shaped interacting main streams. Received: 4 August 1997 / Accepted: 3 October 1998     

An experimental contribution to near-wall measurements by means of a special laser Doppler anemometry technique

 A new experimental technique for the investigation of near-wall turbulence using laser Doppler anemometry is presented, which allows an accurate measurement of the flow field very close to the wall, with good resolution and a high data rate. Such a technique is tested in a fully developed turbulent flow (with Reynolds numbers between 4,300 and 67,000) by carrying out a careful statistical analysis of the streamwise and wall-normal velocity components within the near-wall region, at distances from the wall ranging from approximately y ⁺ = 1 to y ⁺ = 100. The velocity profiles, Reynolds stresses and higher-order moments of the two-dimensional boundary layer are presented. The results, which are in agreement with the most recent data in the literature, testify the validity of the proposed experimental solution. Moreover, the accuracy of the results allows the friction velocity to be calculated as the intercept at the wall of the best linear fit of the total stress profile; in this way, an unambiguous examination of the normalized statistics is possible. Received: 17 April 2001 / Accepted: 15 August 2001     

Drag and Separation Flow Past Solid Sphere with Porous Shell at Moderate Reynolds Number

Axisymmetric viscous, two-dimensional steady and incompressible fluid flow past a solid sphere with porous shell at moderate Reynolds numbers is investigated numerically. There are two dimensionless parameters that govern the flow in this study: the Reynolds number based on the free stream fluid velocity and the diameter of the solid core, and the ratio of the porous shell thickness to the square root of its permeability. The flow in the free fluid region outside the shell is governed by the Navier–Stokes equation. The flow within the porous annulus region of the shell is governed by a Darcy model. Using a commercially available computational fluid dynamics (CFD) package, drag coefficient and separation angle have been computed for flow past a solid sphere with a porous shell for Reynolds numbers of 50, 100, and 200, and for porous parameter in the range of 0.025–2.5. In all simulation cases, the ratio of b/a was fixed at 1.5; i.e., the ratio of outer shell radius to the inner core radius. A parametric equation relating the drag coefficient and separation point with the Reynolds number and porosity parameter were obtained by multiple linear regression. In the limit of very high permeability, the computed drag coefficient as well as the separation angle approaches that for a solid sphere of radius a, as expected. In the limit of very low permeability, the computed total drag coefficient approaches that for a solid sphere of radius b, as expected. The simulation results are presented in terms of viscous drag coefficient, separation angles and total drag coefficient. It was found that the total drag coefficient around the solid sphere as well as the separation angle are strongly governed by the porous shell permeability as well as the Reynolds number. The separation point shifts toward the rear stagnation point as the shell permeability is increased. Separation angle and drag coefficient for the special case of a solid sphere of radius r = a was found to be in good agreement with previous experimental results and with the standard drag curve.     

Turbulent heat transfer characteristics and pressure drop in swirling flow at upstream and downstream of an abrupt expansion

This investigation is aimed at studying the heat transfer characteristics and pressure drop for turbulent airflow in a sudden expansion pipe equipped with propeller swirl generator. The investigation is performed for the Reynolds number ranging from 10,000 to 41,000 under a uniform heat flux condition. The experiments are conducted for three locations for the propeller fan upstream the sudden expansion and three locations downstream the sudden expansion (N = 5 blades and blade angle of 45°). The influences of using a freely rotating propeller on heat transfer enhancement and pressure drop are reported. The experimental results indicate that inserting the propeller downstream of the tube provides considerable improvement of the heat transfer rate higher than inserting the propeller upstream the tube. The increase in pressure drop resulting from using the propeller upstream is found to be higher than the downstream swirler. The maximum performance enhancement for the downstream swirler is about 326% while it is about 213% for upstream one. Correlations for relative mean Nusselt number and enhancement performance are presented for different fan locations and different Reynolds numbers.