Experiments on elongational flow of dilute polymer solutions: Part II: velocity field for the flow through small apertures

Following Part I which reported on the jet reaction and the excess pressure drop, this paper describes the results of flow velocities measured upstream of small apertures for dilute polymer solutions. The results suggest the existence of the two flow regimes reorted by Boger and Cable: the vortex growth regime and the divergent flow regime. The former corresponds to the regime of zero jet reaction and the latter to the regime of positive jet reaction. The axial velocity development for PEO solutions along the center line upstream of the aperture is found to yield an extremely high velocity rise at the onset of the vortex region and to give a nearly constant elongational rate within the vortex region. The constant elongational rate takes values such that the product with the relaxation time is about 0.5. Separan solutions do not provide so high a velocity rise at the onset of the vortex region but show an exponential rate of elongation in the vortex region.It is shown, by using the upper convected Maxwell model, that the steep velocity rise at the onset of the vortex region is given in the simplified flow model and the constant elongational rate within the vortex region holds the elongational stress nearly constant.     

Anomalous flow properties of spherical micelle surfactant solutions passing through small-sized slits

The flow properties of complex fluids, such as aqueous solutions of polymers and surfactants, have been investigated in many studies, which revealed interesting and anomalous tendencies for several types of complex fluids in abrupt contraction and expansion flows, such as flows passing through small-sized orifices and slits. In the study, the jet thrust and excess pressure drop (net differential pressure) for experimentally observing their flow properties of water and aqueous solutions of several types of surfactants with spherical micelles in slit flows were measured. Different properties were observed for various surfactant solutions depending on the charge of the solute. The resultant jet thrust and excess pressure drop of cationic and non-ionic surfactant solutions were lower than the experimental values of water. For anionic surfactant solutions, the experimental results were similar to those of water. The types can be arranged as cationic > non-ionic > anionic in order of diminishing the jet thrust and excess pressure drop. Moreover, the effect of strong strain, boundary slip, contraction ratio, size effect, concentration, and interface phenomena was discussed.     

Simultaneous measurements of velocity and deformation in flows through compliant diaphragms

Flow through a circular orifice in a deformable diaphragm mounted in a pipe was studied experimentally as a simple yet suitable case for validating numerical fluid/structure interaction (FSI) codes including structures with significant deformation and strain. The flow was characterized using pressure taps, particle image velocimetry (PIV), and hot-film anemometry while deformation of the compliant diaphragm was determined directly from PIV images. The diaphragm material properties were measured independently by a uniaxial tensile testing machine. The diaphragm material modulus, orifice diameter, and pipe Reynolds number were varied over ranges appropriate for simulations of flows through heart valves. Pipe Reynolds numbers ranged from 600 (laminar upstream condition) to 8800 (turbulent upstream condition). The pressure drop across the diaphragm resulted in a concave deformation for all cases studied. For the range of Reynolds number tested, the Euler number decreased with increasing Reynolds number as a result of orifice expansion. The flow immediately downstream of compliant diaphragms was jet-like with strong inward radial velocity components and vena contracta. Laminar low Reynolds number flow (Re=600) through both rigid and compliant diaphragms yielded early and regular roll up of coherent vortex rings at a fixed frequency in contrast to turbulent higher Reynolds number flow (Re=3900), which yielded a broad range of vortex passage frequencies. Expansion of the compliant orifice for Re=3900 resulted in an initially broader slower jet with delayed shear layer development compared with the equivalent rigid case.     

Rheological interpretation of pressure anomalies of aqueous dilute polymer solutions (ADPS) in orifice flow

The response of a considerable number of solutions of several polymers (PEO, HPAM, PAM) with concentrations of less than 100 ppm in orifice flow has been investigated. It is shown that the excess pressure (difference between the ADPS and the solvent total pressure drop) behaves linearly as a function of a superficial strain rate (ratio between a velocity and a length scale). In rheological terms this behaviour is interpreted as the result of a constant elongational viscosity whose values are two to three orders of magnitude larger than the shear viscosity. A formal approach to this phenomenological interpretation is suggested.     

Experimental investigation on flow modes of electrospinning

Electrospinning experiments are performed byusing a set of experimental apparatus,a stroboscopic systemis adopted for capturing instantaneous images of the conejet configuration.The cone and the jet of aqueous solutionsof polyethylene oxide(PEO) are formed from an orifice of acapillary tube under the electric field.The viscoelastic constitutive relationship of the PEO solution is measured anddiscussed.The phenomena owing to the jet instability aredescribed,five flow modes and corresponding structures areobtained with variations of the fluid flow rate Q,the electricpotential U and the distance h from the orifice of the capillary tube to the collector.The flow modes of the cone-jetconfiguration involves the steady bending mode,the rotating bending mode,the swinging rotating mode,the blurringbending mode and the branching mode.Regimes in the Q-Uplane of the flow modes are also obtained.These results mayprovide the fundamentals to predict the operating conditionsexpected in practical applications.     

The flow behavior of fiber suspensions in Newtonian fluids and polymer solutions.

This is the second part of a study examining the mechanical properties and capillary flow of fiber suspensions in Newtonian fluids and in polymer solutions. In part I results for the viscous and elastic properties of the fiber suspensions were presented and it was shown that the fiber suspensions exhibited normal stresses in Newtonian as well as in viscoelastic suspending media. It was thus expected that circulating secondary flows would occur near the entrance to a capillary. Four types of fillers (glass, carbon, nylon and vinylon fibers) suspended in glycerin, HEC solutions and Separan solutions were investigated. The entrance flow patterns were visualized and the pressure fluctuations measured. The visualization enabled the eddies occurring in the fiber suspensions in Newtonian fluids to be analysed and classified into two tpyes. The results from the flow visualization were correlated with the pressure fluctuations. Empirical equations for the tube length correction factor due to the elasticity were obtained.     

DNS of viscoelastic turbulent channel flow with rectangular orifice at low Reynolds number

Direct numerical simulations of turbulent viscoelastic-fluid flow in a channel with a rectangular orifice were performed to investigate the influence of viscoelasticity on turbulence statistics and turbulent structures downstream of the orifice. The geometry considered is periodic rectangular orifices with 1:2 expansion. The constitutive equation follows the Giesekus model, valid for polymer (or surfactant) solutions, which are generally capable of reducing the turbulent frictional drag in a smooth channel. The friction Reynolds number and the Weissenberg number were set to 100 and 20-30, respectively. A drag reduction of about 20% was achieved in the viscoelastic flows. The onset Reynolds number for the transition from a symmetric to an asymmetric state was found to be shifted to higher values than that for the Newtonian flow. In the viscoelastic flow, the turbulent kinetic energy was decreased and fewer turbulent eddies were observed, as the Kelvin-Helmholtz vortices were quickly damped. Away from the orifice, quasi-streamwise vortices in the viscoelastic flow were sustained for a longer period, accompanied by energy exchange from elastic energy of the viscoelastic fluid to kinetic energy.     

Measurements in the near flow field of an isosceles triangular turbulent free jet

The near field mean flow and turbulence characteristics of a turbulent jet of air issuing from a sharp-edged isosceles triangular orifice into still air surroundings have been examined experimentally using hot-wire anemometry and a pitot-static tube. For comparison, some measurements were made in an equilateral triangular free jet and in a round free air jet, both of which also issued from sharp-edged orifices. The Reynolds number, based on the orifice equivalent diameter, was 1.84×10⁵ in each jet. The three components of the mean velocity vector, the Reynolds normal and primary shear stresses, the one-dimensional energy spectra of the streamwise fluctuating velocity signals and the mean static pressure were measured. The mean streamwise vorticity, the half-velocity widths, the turbulence kinetic energy and the local shear in the mean streamwise velocity were obtained from the measured data. It was found that near field mixing in the equilateral triangular jet is faster than in the isosceles triangular and round jets. The mean streamwise vorticity field was found to be dominated by counter-rotating pairs of vortices, which influenced mixing and entrainment in the isosceles triangular jet. The one-dimensional energy spectra results indicated the presence of coherent structures in the near field of all three jets and that the equilateral triangular jet was more energetic than the isosceles triangular and round jets.     

Visualization and structure of confined, milliscale, unsteady impinging slot jets and associated vortices

Flow characteristics of confined, laminar milliscale slot jets are investigated from visualizations, as they impinge upon a flat target plate, with a fully developed velocity profile at the nozzle exit. The effects of Reynolds number Re and normalized nozzle-to-plate distance H/B are considered for a nozzle width B of 1.0 mm. Transition from a stable symmetric jet to an unsteady oscillating jet is observed as the Reynolds number increases (with H/B constant), where the Reynolds number associated with this transition decreases as the normalized nozzle-to-plate distance H/B increases. Instantaneous visualizations show unsteady lateral distortions of jet columns at experimental conditions corresponding to the presence of continuous sinusoidal oscillations, intermittent oscillating motion of the jet column, and jet flow fluctuation/flapping motion. Also apparent in flow visualization sequences are smoke signatures associated with instantaneous vortex structures, which form as secondary flows develop in fluid which, initially, is just adjacent to and within the jet column. Associated jet and vortex structural changes are described as different modes of unsteadiness are present, including characterization of jet column unsteadiness using jet column oscillation frequency, and lateral and streamwise extents of jet distortion.     

Flow Separation and Turbulence in Jet Pumps for Thermoacoustic Applications

The effect of flow separation and turbulence on the performance of a jet pump in oscillatory flows is investigated. A jet pump is a static device whose shape induces asymmetric hydrodynamic end effects when placed in an oscillatory flow. This will result in a time-averaged pressure drop which can be used to suppress acoustic streaming in closed-loop thermoacoustic devices. An experimental setup is used to measure the time-averaged pressure drop as well as the acoustic power dissipation across two different jet pump geometries in a pure oscillatory flow. The results are compared against published numerical results where flow separation was found to have a negative effect on the jet pump performance in a laminar flow. Using hot-wire anemometry the onset of flow separation is determined experimentally and the applicability of a critical Reynolds number for oscillatory pipe flows is confirmed for jet pump applications. It is found that turbulence can lead to a reduction of flow separation and hence, to an improvement in jet pump performance compared to laminar oscillatory flows.     

Non-linear dynamics of semi-dilute polydisperse polymer solutions in microfluidics: A study of a benchmark flow problem

The complex flow behaviour of semi-dilute (15 < c/c^* < 22.5) polydisperse polyethylene oxide (PEO) aqueous solutions flowing through a planar microfluidic geometry with an 8:1:8 contraction-expansion is systematically studied. The molecular weight and distribution of the PEO samples are analysed by Gel Permeation Chromatography (GPC). Full rheometric characterizations using various techniques including piezoelectric axial vibrator (PAV) measurements at frequencies as high as 6700 Hz are carried out for one semi-dilute PEO solution. Complex flows over a wide range of elasticity numbers (20 ? El ? 120), Weissenberg numbers (7 ? Wi ? 121) and Reynolds numbers (0.08 ? Re ? 4.5) are characterized using micro-particle image velocimetry (μ-PIV) and pressure drop measurements. The evolution of vortex formation and dynamics has been visualized through a step-flow-rate experiment. The effect of El on vortex stability has been studied. Various flow dynamics regimes have been quantified and are presented in a Wi-Re diagram. The experimental results reveal that the elastic behaviour of polymer solutions is very sensitive to high molecular weight polymer in the polydisperse polymer samples, and the contraction ratio and the aspect ratio of flow geometry are the important design parameters in controlling the non-linear dynamics of semi-dilute polymer solutions in microfluidics.     

Drag reduction for liquid flow through micro-apertures

Pressure drops in the flow through micro-orifices and capillaries were measured for silicone oils, aqueous solutions of polyethylene glycol (PEG), and surfactant aqueous solutions. The diameter of micro-orifices ranged from 5 μm to 400 μm. The corresponding length/diameter ratio was from 4 to 0.05 and capillary diameters were 105 μm and 450 μm. The following results were obtained: silicone oils of 10^?6 m²/s and 10^?5 m²/s in kinematic viscosity generated a reduction of pressure drop (RPD), that is, drag reduction, similar to the RPD of water and a glycerol/water mixture reported in the previous paper by the present authors. When RPD occurred, the pressure drop (PD) of silicone oils of 10^?6 m²/s and 10^?5 m²/s had nearly the same magnitude. Namely, the difference in viscosity did not influence RPD. A 10³ ppm aqueous solution of PEG20000 provided almost the same PD as that of PEG8000 for the 400 μm to 15 μm orifices, but a greater PD than that of PEG8000 for the 10 μm to 5 μm orifices. A non-ionic surfactant and a cationic surfactant were highly effective in RPD compared with anionic surfactants: the non-ionic and cationic surfactant solutions had PD one order of magnitude lower than that of water under some flow conditions in the concentration range from 1 ppm to 10⁴ ppm, but the anionic surfactant solutions did not generate RPD except in the case of the smallest orifice of 5 μm in diameter. The PD of the non-ionic surfactant solution showed a steep rise at a Reynolds number (Re_t) for 400 μm to 15 μm orifices. The Re_t provides the relationship Re_t = K/D, where D is the orifice diameter, and K is a constant of 2 × 10^?2 m for the 100–20 μm orifices irrespective of liquid concentration. Capillary flow experiment revealed that the PEG, non-ionic and cationic surfactant solutions generated RPD also in a laminar flow through the capillary of 105 μm in diameter, but not in the flow through the capillary of 450 μm in diameter. In order to clarify the cause of RPD, an additional experiment was carried out by changing the orifice material from metal to acrylic resin. The result gave a different appearance of RPD, suggesting that RPD is related to an interfacial phenomenon between the liquid and wall. The large RPDs found in the present experiment are very interesting from both academic and practical viewpoints.     

Friction reduction and degradation in turbulent flow of dilute polymer solutions

An experimental study of friction reduction and polymer degradation in turbulent pipe flow is described for dilute water solutions of guar gum, CMC, Separan NP-10 and Polyox WSR-301. The tests are made in a turbulent-flow rheometer with a 2 mm I.D. pipe over a Reynolds number range from 8,000 to 25,000. The maximum attainable friction reduction for guar gum, Separan NP-10 and Polyox WSR-301 is found to be almost equal, but large differences in effectiveness occur. The most effective polymers (Polyox WSR-301 and Separan NP-10) are also the most liable to degradation. Mixing of polymers does not ameliorate the maximum friction reducing ability of the most effective component.     

Numerical simulation of turbulent free surface flow with two‐equation k–ε eddy‐viscosity models

This paper presents a finite difference technique for solving incompressible turbulent free surface fluid flow problems. The closure of the time‐averaged Navier–Stokes equations is achieved by using the two‐equation eddy‐viscosity model: the high‐Reynolds k–ε (standard) model, with a time scale proposed by Durbin; and a low‐Reynolds number form of the standard k–ε model, similar to that proposed by Yang and Shih. In order to achieve an accurate discretization of the non‐linear terms, a second/third‐order upwinding technique is adopted. The computational method is validated by applying it to the flat plate boundary layer problem and to impinging jet flows. The method is then applied to a turbulent planar jet flow beneath and parallel to a free surface. Computations show that the high‐Reynolds k–ε model yields favourable predictions both of the zero‐pressure‐gradient turbulent boundary layer on a flat plate and jet impingement flows. However, the results using the low‐Reynolds number form of the k–ε model are somewhat unsatisfactory. Copyright © 2004 John Wiley & Sons, Ltd.     

Flow of a shear-thinning liquid in a cylindrical container with a rotating end wall

The flow patterns produced by rotating one end wall of a circular cylinder completely filled with a strongly shear-thinning viscoelastic liquid have been investigated using the laser-induced fluorescence flow visualization technique. An intense toroidal vortex is produced in the vicinity of the rotating end wall with outward spiraling flow over the end wall itself. This vortex drives a second countercirculating vortex of low intensity in the region of the stationary end wall. Under some circumstances an axial jet of fluid is observed moving away from the rotating end wall. This jet showed evidence of instability, whereas all flows were otherwise completely steady. The double-vortex structure is different from those recently observed in either a Newtonian or slightly shear-thinning liquid or in the low Reynolds number flow of an elastic liquid. There are, however, similarities with older work for a viscoelastic liquid at relatively high Reynolds numbers. The observations highlight the suitability of the cylinder/rotating end wall configuration as a sensitive test case for computational work.     

Experimental study of the pressure drop after fractal-shaped orifices in turbulent pipe flows

Fractal-shaped orifices are thought to have a significant effect on the flow mixing properties downstream a pipe owing to their edge self-similarity shape. Here, we investigate the pressure drop after such fractal orifices and measure the pressure recovery at different stations downstream the orifice. A direct comparison is made with the pressure drop measured after regular circular orifices with the same flow area. Our results show that the fractal-shaped orifices have a significant effect on the pressure drop. Furthermore, the pressure drop measured across the fractal-shaped orifices is found to be lower than that from regular circular orifices of the same flow areas. This result could be important in designing piping systems from the point of view of losses. It looks promising to use the fractal-shaped orifices as flowmeters as they can sense the pressure drop across them accurately with lower losses than the regular circular-shaped ones.     

Flow regime transitions due to cavitation in the flow through an orifice

This paper presents both experimental and theoretical aspects of the flow regime transitions caused by cavitation when water is passing through an orifice. Cavitation inception marks the transition from single-phase to two-phase bubbly flow; choked cavitation marks the transition from two-phase bubbly flow to two-phase annular jet flow.

It has been found that the inception of cavitation does not necessarily require that the minimum static pressure at the vena contracta downstream of the orifice, be equal to the vapour pressure liquid. In fact, it is well above the vapour pressure at the point of inception. The cavitation number [σ = (P₃ − P_v)/(0.5 pV²); here P₃ is the downstream pressure, P_v is the vapour pressure of the liquid, ρ is the density of the liquid and V is the average liquid velocity at the orifice] at inception is independent of the liquid velocity but strongly dependent on the size of the geometry. Choked cavitation occurs when this minimum pressure approaches the vapour pressure. The cavitation number at the choked condition is a function of the ratio of the orifice diameter (d) to the pipe diameter (D) only. When super cavitation occurs, the dimensionless jet length [L/(D - d); where L is the dimensional length of the jet] can be correlated by using the cavitation number. The vaporization rate of the surface of the liquid jet in super cavitation has been evaluated based on the experiments.

Experiments have also been conducted in which air was deliberately introduced at the vena contracta to simulate the flow regime transition at choked cavitation. Correlations have been obtained to calculate the critical air flow rate required to cause the flow regime transition. By drawing an analogy with choked cavitation, where the air flow rate required to cause the transition is zero, the vapour and released gas flow rate can be predicted.     

Sessile drop deformations under an impinging jet

The problem of steady axisymmetric deformations of a liquid sessile drop on a flat solid surface under an impinging gas jet is of interest for understanding the fundamental behavior of free surface flows as well as for establishing the theoretical basis in process design for the Aerosol \({{\rm Jet}^{\circledR}}\) direct-write technology. It is studied here numerically using a Galerkin finite-element method, by computing solutions of Navier–Stokes equations. For effective material deposition in Aerosol \({{\rm Jet}^{\circledR}}\) printing, the desired value of Reynolds number for the laminar gas jet is found to be greater than ~500. The sessile drop can be severely deformed by an impinging gas jet when the capillary number is approaching a critical value beyond which no steady axisymmetric free surface deformation can exist. Solution branches in a parameter space show turning points at the critical values of capillary number, which typically indicate the onset of free surface shape instability. By tracking solution branches around turning points with an arc-length continuation algorithm, critical values of capillary number can be accurately determined. Near turning points, all the free surface profiles in various parameter settings take a common shape with a dimple at the center and bulge near the contact line. An empirical formula for the critical capillary number for sessile drops with \({45^{\circ}}\) contact angle is derived for typical ranges of jet Reynolds number and relative drop sizes especially pertinent to Aerosol \({{\rm Jet}^{\circledR}}\) printing.     

Experimental investigation of helical structures in swirling flows

In this investigation the flow in a generic swirl tube with a tangential double-inlet swirl generator and variable exit orifices was experimentally investigated. Using magnetic resonance velocimetry (MRV) three-dimensional, three-component velocity fields were measured for two different Reynolds numbers: 10,000 and 15,000, and for three different exit orifices. The swirl generator had a fixed geometry producing an initial swirl number of 1.6 for all cases. One major observation is the occurrence of a three-layered flow structure. An annular main flow was surrounded by a recirculation zone, as reported in previous literature. However, this recirculation zone – also of an annular shape – exhibited a third layer inside: a thin, high speed jet in the center of the tube with the same flow direction as the main flow. Therefore, the conventional classification of swirling flows into ring and recirculation zone, has to be extended by a core zone. This three-layered flow structure develops independently of the exit configuration. Helical structures were observed in the near-wall region for all cases investigated. Applying an eccentric exit orifice results in the occurrence of strong stationary helical structures not only in the near-wall region but also in the center of the tube. The results, deviating significantly from previous results in the literature, underline the need for more detailed research on the topic of cyclone type flows.     

Evaluating cavitation regimes in an internal orifice at different temperatures using frequency analysis and visualization

Experiments on a water cavitating orifice were conducted to investigate the influence of pressure and temperature on flow regime transition due to cavitation. The thermal effects could be important in cases with cryogenic cavitation or hot fluid injection. The investigations were based on CCD observations and a pressure fluctuations frequency analysis.The high-speed photographic recordings were used to analyze the cavitation evolution and individuate the frequency content of the two-phase flow by processing the pixel-intensity time-series data.The cavitating structures showed different behaviors and characteristics with variations in operating conditions, as the pressure inside the orifice and the flow temperature .The flow regime map for the cavitating flow was obtained using experimental observations to analyze the occurrence of the different two-phase flow regime transitions at various operating conditions.As the pressure at the orifice inlet increased, at the same downstream pressure, cavitation inception occurred. The decrease of the cavitation number brought a significant increase in cavitation zone extension. As the pressure drop inside the orifice increased, the cavitation was characterized by an evident increase in cavitation zone length to the outlet of the orifice. With a further cavitation number decrease, the transition to jet cavitation was evident.The temperature influenced both the cavitation intensity and the cavitation number at which different two-phase flow regime transitions occurred, which tended to increase with temperature.The vapor fraction was estimated using an image processing algorithm.The frequency content given by the pressure fluctuations was analyzed and compared with the frequency spectra obtained from the visual observations. The behavior of the different cavitating flows could be correlated to the frequency spectrum of the pressure fluctuations measured upstream and downstream of the orifice. The cavitation number reduction and consequent increase in cavitating area width were related to a corresponding significant increase in the amplitude of typical frequency components. The transition to jet cavitation was characterized by a significant increase in the first peak in the frequency spectrum; weaker spectral peaks were also present at high cavitation numbers.