Showing papers on "Hele-Shaw flow published in 2008"

Experimental and numerical studies of the flow over a circular cylinder at Reynolds number 3900

Abstract: This work contributes to the study of flow over a circular cylinder at Reynolds number Re=3900. Although this classical flow is widely documented in the literature, especially for this precise Reynolds number that leads to a subcritical flow regime, there is no consensus about the turbulence statistics immediately just behind the obstacle. Here, the flow is investigated both numerically with large eddy simulation and experimentally with hot-wire anemometry and particle image velocimetry. The numerical simulation is performed using high-order schemes and a specific immersed boundary method. The present study focuses on turbulence statistics and power spectra in the near wake up to ten diameters. Statistical estimation is shown to need large integration times increasing the computational cost and leading to an uncertainty of about 10% for most flow characteristics considered in this study. The present numerical and experimental results are found to be in good agreement with previous large eddy simulation da...

Fluid flow and optical flow

Abstract: The connection between fluid flow and optical flow is explored in typical flow visualizations to provide a rational foundation for application of the optical flow method to image-based fluid velocity measurements. The projected-motion equations are derived, and the physics-based optical flow equation is given. In general, the optical flow is proportional to the path-averaged velocity of fluid or particles weighted with a relevant field quantity. The variational formulation and the corresponding Euler–Lagrange equation are given for optical flow computation. An error analysis for optical flow computation is provided, which is quantitatively examined by simulations on synthetic grid images. Direct comparisons between the optical flow method and the correlation-based method are made in simulations on synthetic particle images and experiments in a strongly excited turbulent jet.

Stability of a jet in confined pressure-driven biphasic flows at low Reynolds number in various geometries.

Abstract: We adress the question of the stability of a confined coflowing jet at low Reynolds number in various geometries. Our study is motivated by recent experiments in microfluidic devices. When immiscible fluids flow in microchannels, either monodisperse droplets or parallel flows are obtained depending upon the flow rate of the aqueous phase and the oil phase. In these experiments, the confining and the shape of the geometry play a fundamental role. In a previous paper [Guillot et al., Phys. Rev. Lett 99, 104502 (2007)], we analyzed the stability of the jet in the framework of the lubrication approximation at low Reynolds number in a cylindrical geometry, and we related the transition between the droplets regime and the jet regime to the absolute-convective transition of the Rayleigh plateau instability. In this work, the effect of the channel geometry and the jet position within the microfluidic device are discussed. New flow patterns are pointed out. Bidimensional jets are encountered in square and rectangular geometry. Contrary to jets occuring in circular geometry, these two-dimensional jets are absolutely stable. Focusing on situations where the inner fluid is more viscous than the outer one, we evidence a range of parameters where droplets are produced through a blocking and pinching mechanism. In this particular case, the flow is unstable, the growing perturbations are convected upstream. This induces the clogging of the channel by the internal phase and its pinching by the external one. In a future presentation we will give a comparison between this model and experimental data.

Turbulent structures in planar gravity currents and their influence on the flow dynamics

Abstract: [1] Direct numerical simulations (DNS) of planar gravity current in the Boussinesq limit have been conducted with the objective of identifying, visualizing, and describing turbulent structures and their influence on the flow dynamics. The simulations are performed for Reynolds numbers of Re = 8950 and Re = 15,000 with 31- and 131-million grid point resolutions, respectively. This range of Reynolds numbers ensures fully developed turbulent gravity currents, which have never been simulated before using DNS. The flow develops zones with different turbulence characteristics, which eventually interact with each other. The near-wall bottom flow resembles boundary layer flow with several hairpin-like vortices oriented in the direction of the flow and preferential patterns of low- and high-speed streaks. The separation between low-speed streaks at the front scales with the lobe size, which is about 200 wall units for Re = 15,000. Upstream of the front, the separation between low-speed streaks scales with the well-accepted value of 100 wall units for turbulent boundary layers. These patterns have associated regions of low and high bottom shear stresses with implications for sediment erosion and bed load transport. Most of the erosive power of the flow is found in the gravity current front. The interface between heavy and light fluids rolls up by baroclinic generation of Kelvin-Helmholtz vortices, which undergo sudden breakup and decay to small-scale turbulence. The effect of turbulence and three-dimensionality on the flow dynamics is addressed by comparing two- and three-dimensional simulations. Three-dimensional simulations present active mechanisms that undermine the strong flow coherence, comparing well with experimental observations.

Homotopy perturbation method for heat transfer flow of a third grade fluid between parallel plates

Abstract: The present paper studies the heat transfer flow of a third grade fluid between two heated parallel plates for the constant viscosity model. Three flow problems, namely plane Couette flow, plane Poiseuille flow and plane Couette–Poiseuille flow have been considered. In each case the non-linear momentum equation and the energy equation have been solved using the homotopy perturbation method. Explicit analytical expressions for the velocity field and the temperature distribution have been derived.

Competing geometric and inertial effects on local flow structure in thick gravity-driven fluid films

Abstract: The formation and presence of eddies within thick gravity-driven free-surface film flow over a corrugated substrate are considered, with the governing equations solved semianalytically using a complex variable method for Stokes flow and numerically via a full finite element formulation for the more general problem when inertia is significant. The effect of varying geometry (involving changes in the film thickness or the amplitude and wavelength of the substrate) and inertia is explored separately. For Stokes-like flow and varying geometry, excellent agreement is found between prediction and existing flow visualizations and measured eddy center locations associated with the switch from attached to locally detached flow. It is argued that an appropriate measure of the influence of inertia at the substrate is in terms of a local Reynolds number based on the characteristic corrugation length scale. Since, for small local Reynolds numbers, the local flow structure there becomes effectively decoupled from the i...

Asymmetry and transition to turbulence in a smooth axisymmetric constriction

Abstract: The flow through a smooth axisymmetric constriction (a stenosis in medical applications) of 75% restriction in area is measured using stereoscopic and time-resolved particle image velocimetry (PIV) in the Reynolds number range Re ~ 100–1100. At low Reynolds numbers, steady flow results reveal an asymmetry of the flow downstream of the constriction. The jet emanating from the throat of the nozzle is deflected towards the wall causing the formation of a one-sided recirculation region. The asymmetry results from a Coanda-type wall attachment already observed in symmetric planar sudden expansion flows. When the Reynolds number is increased above the critical value of 400, the separation surface cannot remain attached and an unsteady flow regime begins. Low-frequency axial oscillations of the reattachment point are observed along with a slow swirling motion of the jet. The phenomenon is linked to a periodic discharge of the unstable recirculation region inducing alternating laminar and turbulent flow phases. The resulting flow is highly non-stationary and intermittent. Discrete wavelet transforms are used to discriminate between the large-scale motions of the mean flow and the vortical and turbulent fluctuations. Continuous wavelet transforms reveal the spectral structure of flow disturbances. Temporal measurements of the three velocity components in cross-sections are used with the Taylor hypothesis to qualitatively reconstruct the three-dimensional velocity vector fields, which are validated by comparing with two-dimensional PIV measurements in meridional planes. Visualizations of isosurfaces of the swirling strength criterion allow the identification of the topology of the vortices and highlight the formation and evolution of hairpin-like vortex structures in the flow. Finally, with further increase of the Reynolds number, the flow exhibits less intermittency and becomes stationary for Re ~ 900. Linear stochastic estimation identifies the predominance of vortex rings downstream of the stenosis before breakdown to turbulence.

Simulation of Flow Past a Sphere using the Fluent Code

Abstract: : We use the commercial computational fluid dynamics code Fluent to simulate the flow around a sphere in several different flow regimes; steady-state laminar flow at a Reynolds number (Re) of 100, time-dependent laminar flow at Re = 300, and turbulent flow at Re = 10,000 and Re = 1,000,000. These simulations provide a test of the ability of the code to accurately reproduce typical flow structures observed in generic bluff body flows, such as those experienced by submarines and Unmanned Underwater Vehicles (UUVs). The simulations are compared both with experimental results and computations from other computer codes and it is found that Fluent is able to accurately simulate the fluid behaviour in each of the above flow regimes.

Interfacial instabilities in a microfluidic Hele-Shaw cell

Abstract: This paper describes surfactant-sensitive, dynamic instabilities that occur to aqueous droplets translating in a continuous flow of hexadecane in a microfluidic Hele-Shaw cell (HSC). A very low interfacial tension (on the order of 0.01 mN m−1) between water and hexadecane allowed for deformation of the droplets along the fields of flow and tip-streaming from moving droplets. In the system of water and hexadecane that we investigated, the use of surfactants in both fluids was necessary to achieve interfacial tension sufficiently low for the instabilities to occur. The droplets entering the HSC stretched orthogonally to the main direction of flow into elongated shapes, with aspect ratios greater than ten to one (width to length). These droplets exhibited two types of instabilities. The first included elongation of droplets, and Rayleigh–Plateau instabilities in the stretched droplets. Arrays of these stretched droplets formed three characteristic patterns that depended on the rates of flow of water and hexadecane. The second was driven by the shear stress exerted on the interface between the two fluids by the top and bottom boundaries of the HSC; this instability is named a “shear-driven instability” (SDI). Our observations supported that the SDI—an effect similar to tip-streaming—resulted from a redistribution of surfactants at the interface between the two fluids.

Recent developments in scaling of wall-bounded flows

Abstract: Proper scaling of a fluid flow permits convenient, dimensionless representation of experimental data, prediction of one flow based on a similar one, and extrapolation of low-Reynolds-number, laboratory-scale experiments to field conditions. This is a particularly powerful technique for turbulent flows where analytical solutions derived from first principles are not possible. We review in the present paper the topical development in scaling the canonical turbulent boundary layer and pipe and channel flows. Additional to utilizing some of the most comprehensive and high-quality databases available to date, the article focuses on contemporary advances in analytical and asymptotic approaches to determine the mean-velocity profile as well as to scale higher-order statistics. The current debate concerning the mean-velocity profile of turbulent wall-bounded flows has ruled out neither a logarithmic nor power law behavior. Furthermore, a Reynolds number dependence of the mean-velocity profile has not been excluded either. Clearly, a more complex functional form is needed to describe the profile. The present results can be utilized to extrapolate the available low-Reynolds-number physical and numerical data to the more practically important high-Reynolds-number field conditions. Knowledge of the proper scaling of the canonical cases can also be useful to non-canonical wall-bounded flows as well as to calibrate turbulence models and flow sensors in the vicinity of walls.

Turbulent flow between counter-rotating concentric cylinders : a direct numerical simulation study

Abstract: We report three-dimensional direct numerical simulations of the turbulent flow between counter-rotating concentric cylinders with a radius ratio 0.5. The inner- and outer-cylinder Reynolds numbers have the same magnitude, which ranges from 500 to 4000 in the simulations. We show that with the increase of Reynolds number, the prevailing structures in the flow are azimuthal vortices with scales much smaller than the cylinder gap. At high Reynolds numbers, while the instantaneous small-scale vortices permeate the entire domain, the large-scale Taylor vortex motions manifested by the time-averaged field do not penetrate a layer of fluid near the outer cylinder. Comparisons between the standard Taylor–Couette system (rotating inner cylinder, fixed outer cylinder) and the counter-rotating system demonstrate the profound effects of the Coriolis force on the mean flow and other statistical quantities. The dynamical and statistical features of the flow have been investigated in detail.

Steady inlet flow in stenotic geometries: convective and absolute instabilities

Abstract: Steady inlet flow through a circular tube with an axisymmetric blockage of varying size is studied both numerically and experimentally. The geometry consists of a long, straight tube and a blockage, semicircular in cross-section, serving as a simplified model of an arterial stenosis. The stenosis is characterized by a single parameter, the aim being to highlight fundamental behaviours of constricted flows, in terms of the total blockage. The Reynolds number is varied between 50 and 2500 and the stenosis degree by area between 0.20 and 0.95. Numerically, a spectral-element code is used to obtain the axisymmetric base flow fields, while experimentally, results are obtained for a similar set of geometries, using water as the working fluid. At low Reynolds numbers, the flow is steady and characterized by a jet flow emanating from the contraction, surrounded by an axisymmetric recirculation zone. The effect of a variation in blockage size on the onset and mode of instability is investigated. Linear stability analysis is performed on the simulated axisymmetric base flows, in addition to an analysis of the instability, seemingly convective in nature, observed in the experimental flows. This transition at higher Reynolds numbers to a time-dependent state, characterized by unsteadiness downstream of the blockage, is studied in conjunction with an investigation of the response of steady lower Reynolds number flows to periodic forcing.

The dynamics of turbulent, transitional and laminar clay-laden flow over a fixed current ripple.

Abstract: Most aqueous sedimentary environments contain varying concentrations of fine-grained, often clay-rich, sediment that is transported in suspension and may modify the properties of the flow and underlying mobile bed. This paper presents results from a series of laboratory experiments examining the mean and turbulent properties of clay-laden (kaolinite) flows, of various volumetric sediment concentrations between 0·046% and 12·7%, moving over a fixed, idealized current ripple. As the kaolinite concentration was raised, with flow velocity and depth constant, four flow types were observed to occur: (i) turbulent flow, in which flow separation is dominant in the leeside of the ripple; (ii) turbulence-enhanced transitional flow, in which turbulence in the leeside separation zone region is enhanced; (iii) turbulence-attenuated transitional flow, in which turbulence along the separation zone shear layer and in the free flow above it becomes damped, eventually leading to a reduction in the size of the separation zone wake region; and (iv) laminar plug flow, in which turbulence is damped and flow is almost stagnant in the lee of the ripple. Such modulation of turbulence by increasing clay concentrations suggests that many paradigms of flow and bedform dynamics, which have been based on extensive past work in clear water flows, require revision. The present results highlight a need to fully characterize the boundary conditions for turbulence modulation as a function of clay type and applied flow conditions, and the effects of such flows on fully mobile cohesionless beds.

Viscoplastic fluid displacements in horizontal narrow eccentric annuli: stratification and travelling wave solutions

Abstract: We consider laminar displacement flows in narrow eccentric annuli, oriented horizontally, between two fluids of Herschel–Bulkley type, (i.e. including Newtonian, power-law and Bingham models). This situation is modelled via a Hele-Shaw approach. Whereas slumping and stratification would be expected in the absence of any imposed flow rate, for a displacement flow we show that there are often steady-state travelling wave solutions in this displacement. These may exist even at large eccentricities and for large density differences between the fluids. When heavy fluids displace light fluids, annular eccentricity opposes buoyancy and steady states are more prevalent than when light fluids displace heavy fluids. For large ratios of buoyancy forces to viscous forces we derive a lubrication-style displacement model. This simplification allows us to find necessary and sufficient conditions under which a displacement can be steady, which can be expressed conveniently in terms of a consistency ratio. It is interesting that buoyancy does not appear in the critical conditions for a horizontal well. Instead a competition between fluid rheologies and eccentricity is the determining factor. Buoyancy acts only to determine the axial length of the steady-state profile.

Separated-Shear-Layer Development on an Airfoil at Low Reynolds Numbers

Abstract: Flow transition in the separated shear layer on the upper surface of a NACA 0025 airfoil at low Reynolds numbers was investigated. The study involved wind-tunnel experiments and linear stability analysis. Detailed measurements were conducted for Reynolds numbers of 100,000 and 150,000 at 0-, 5- and 10-degree angles of attack. For all cases examined, laminar boundary-layer separation takes place on the upper surface of the airfoil. The separated shear layer fails to reattach to the airfoil surface for the lower Reynolds number, but reattachment occurs for the higher Reynolds number. Despite this difference in flow development, experimental results show that a similar transition mechanism is attendant for both Reynolds number flow regimes. Flow transition occurs due to the amplification of natural disturbances in the separated shear layer within a band of frequencies centered at some fundamental frequency. The initial growth of disturbances centered at the fundamental frequency is followed by the growth of a subharmonic component, eventually leading to flow transition. The growing disturbances also cause shear-layer roll-up and the formation of roll-up vortices. The results show that inviscid stability theory can be employed to adequately estimate such salient characteristics as the frequency of the most amplified disturbances and their propagation speed. This implies that the roll-up vortices can be attributed to inviscid instability. However, the results suggest that viscous and nonparallel effects need to be accounted for to effectively model the convective growth of the disturbances in the separated shear layer.

Condensation in Microchannels

Abstract: Condensation in microchannels has applications in a wide variety of advanced microthermal devices. Presented here is a review of both experimental and theoretical analyses of condensation in these microchannels, with special attention given to the effects of channel diameter and surface conditions on the flow regimes of condensing flows occurring in these channels. This review suggests that surface tension, rather than body or buoyancy forces, is the dominant force that governs the condensation and two-phase flow in these microchannels. Recent experimental results indicate that with decreases in the channel diameter, the dominant condensing flow pattern is intermittent injection/slug/bubble flow, as opposed to stratified or annular flow, which is typically found in two-phase flows in larger one-g channel flows. As a result, existing annular flow condensation models cannot be used to accurately represent or predict the actual physical mechanisms that occur in these condensing flows in microchannels. This t...

Effect of Pressure on Fluid Damping in MEMS Torsional Resonators with Flow Ranging from Continuum to Molecular Regime

Abstract: High quality factor of dynamic structures at micro and nano scale is exploited in various applications of micro electro-mechanical systems (MEMS) and nano electro-mechanical system. The quality factor of such devices can be very high in vacuum. However, when vacuum is not desirable or not possible, the tiny structures must vibrate in air or some other gas at pressure levels that may vary from atmospheric to low vacuum. The interaction of the surrounding fluid with the vibrating structure leads to dissipation, thus bringing down the quality factor. Depending on the ambient fluid pressure or the gap between the vibrating and the fixed structure, the fluid motion can range from continuum flow to molecular flow giving a wide range of dissipation. The relevant fluid flow characteristics are determined by the Knudsen number which is the ratio of the mean free path of the gas molecule to the characteristic flow length of the device. This number is very small for continuum flow and reasonably big for molecular flow. In this paper, we study the effect of fluid pressure on the quality factor by carrying out experiments on a MEMS device that consists of a double gimbaled torsional resonator. Such devices are commonly used in optical cross-connects and switches. We only vary fluid pressure to make the Knudsen number go through the entire range of continuum flow, slip flow, transition flow, and molecular flow. We experimentally determine the quality factor of the torsional resonator at different air pressures ranging from 760 Torr to 0.001 Torr. The variation of this pressure over six orders of magnitude ensures required rarefaction to range over all flow conditions. Finally, we get the variation of quality factor with pressure. The result indicates that the quality factor, Q, follows a power law, Q ∝P –r , with different values of the exponent r in different flow regimes. In the second part of the paper, we propose the use of effective viscosity for considering velocity slip conditions in solving Navier–Stokes equation numerically. This concept is validated with analytical results for a simple case and then compared with the experimental results presented in this paper. The study shows that the effective viscosity concept can be used effectively even for the molecular regime if the air-gap to length ratio is sufficiently small (h 0/L<0.01). As this ratio increases, the range of validity decreases.

Flow Patterns in a Four-Branch Junction with Supercritical Flow

Abstract: This paper describes the flow structures that occur in a 90° junction of four open channels with supercritical flow in two orthogonal inlet channels. An experimental facility was constructed to permit the measurement of flow rates, water depths, and the positions of hydraulic jumps in the channels. The various flow patterns which appear depend on the characteristics of the incoming flows and can be classified into three main types, depending on the location and shape of the hydraulic jumps that develop. These jumps can either be normal to the flow and located in the upstream channels, or can be oblique and confined within the junction. The explanation for the existence of various flow patterns is derived from previous studies of the rapid deflection of supercritical flow. A detailed description of each flow regime is provided, with information on the surface elevations, the behavior of the hydraulic jumps, the deflections of the incoming flows, and the formation and characteristics of recirculation zones.

Stability of flows past a pair of circular cylinders in a side-by-side arrangement

Abstract: The stability and transition of flow past a pair of circular cylinders in a side-by-side arrangement are investigated by numerical simulations and linear stability analyses. Various flow patterns around the cylinders have been reported to appear due to an instability of the steady symmetric flow that is realized at small Reynolds numbers, among which deflected oscillatory flow is particularly noticeable. The physical origin of the flow is explored by bifurcation analyses of the numerical data. We found that the deflected oscillatory flow arises from the steady symmetric flow through sequential instabilities due to stationary and oscillatory unstable modes. Steady asymmetric flow with respect to the streamwise centreline between the two cylinders was also found to be induced by the instability due to a stationary mode in a very narrow range of the gap width between the two cylinders. We classify the instability modes of the steady symmetric flow into four groups in the parameter space of the gap width, and evaluate the critical Reynolds number for each mode of instability.

Effect of arbitrary magnetic Reynolds number on MHD flows in convergent‐divergent channels

Abstract: – The objective of the present study is to investigate the effect of arbitrary magnetic Reynolds number on steady flow of an incompressible conducting viscous liquid in convergent‐divergent channels under the influence of an externally applied homogeneous magnetic field., – The solution of the non‐linear 2D Navier‐Stokes equations modeling the flow field is obtained using a perturbation technique coupled with a special type of Hermite‐Pade approximation method implemented numerically on MAPLE and a bifurcation study is performed., – The results show that increasing values of magnetic Reynolds number causes a general decrease in the fluid velocity around the central region of the channel. The flow reversal control is also observed by increasing magnetic field intensity. The bifurcation study reveals the solution branches and turning points., – The reported results are very useful in the field of engineering flow control and industrial metal casting for the control of molten metal flows., – Effect of arbitrary magnetic Reynolds on the overall flow structure in converging‐diverging channels are presented and studied using a newly developed numerical approach.