Showing papers on "Streamlines, streaklines, and pathlines published in 2004"

Experimental Observation of Nonlinear Traveling Waves in Turbulent Pipe Flow

Abstract: Transition to turbulence in pipe flow is one of the most fundamental and longest-standing problems in fluid dynamics. Stability theory suggests that the flow remains laminar for all flow rates, but in practice pipe flow becomes turbulent even at moderate speeds. This transition drastically affects the transport efficiency of mass, momentum, and heat. On the basis of the recent discovery of unstable traveling waves in computational studies of the Navier-Stokes equations and ideas from dynamical systems theory, a model for the transition process has been suggested. We report experimental observation of these traveling waves in pipe flow, confirming the proposed transition scenario and suggesting that the dynamics associated with these unstable states may indeed capture the nature of fluid turbulence.

Elastic turbulence in curvilinear flows of polymer solutions.

Abstract: Following our first report (A Groisman and V Steinberg 2000 Nature 405 53), we present an extended account of experimental observations of elasticity-induced turbulence in three different systems: a swirling flow between two plates, a Couette–Taylor (CT) flow between two cylinders, and a flow in a curvilinear channel (Dean flow). All three set-ups had a high ratio of the width of the region available for flow to the radius of curvature of the streamlines. The experiments were carried out with dilute solutions of high-molecular-weight polyacrylamide in concentrated sugar syrups. High polymer relaxation time and solution viscosity ensured prevalence of non-linear elastic effects over inertial non-linearity, and development of purely elastic instabilities at low Reynolds number (Re) in all three flows. Above the elastic instability threshold, flows in all three systems exhibit features of developed turbulence. They include: (i) randomly fluctuating fluid motion excited in a broad range of spatial and temporal scales and (ii) significant increase in the rates of momentum and mass transfer (compared with those expected for a steady flow with a smooth velocity profile). Phenomenology, driving mechanisms and parameter dependence of the elastic turbulence are compared with those of the conventional high-Re hydrodynamic turbulence in Newtonian fluids. Some similarities as well as multiple principal differences were found. In two out of three systems (swirling flow between two plates and flow in the curvilinear channel), power spectra of velocity fluctuations decayed rather quickly, following power laws with exponents of about −3.5. It suggests that, being random in time, the flow is rather smooth in space, in the sense that the main contribution to deformation and mixing (and, possibly, elastic energy) is coming from flow at the largest scale of the system. This situation, random in time and smooth in space, is analogous to flows at small scales (below the Kolmogorov dissipation scale) in high-Re turbulence.

Three-Dimensional Separations in Axial Compressors

Abstract: Flow separations in the corner regions of blade passages are common. The separations are three dimensional and have quite different properties from the two-dimensional separations that are considered in elementary courses of fluid mechanics. In particular the consequences for the flow may be less severe than the two-dimensional separation. This paper describes the nature of three-dimensional separation and addresses the way in which topological rules, based on a linear treatment of the Navier-Stokes equations, can predict properties of the limiting streamlines, including the singularities which form. The paper shows measurements of the flow field in a linear cascade of compressor blades and compares these with the results of 3D CFD. For corners without tip clearance, the presence of three-dimensional separation appears to be universal and the challenge for the designer is to limit the loss and blockage produced. The CFD appears capable of predicting this.Copyright © 2004 by ASME

Dynamics and breakup of a contracting liquid filament

Abstract: Contraction of a filament of an incompressible Newtonian liquid in a passive ambient fluid is studied computationally to provide insights into the dynamics of satellite drops created during drop formation. This free boundary problem, which is composed of the Navier–Stokes system and the associated initial and boundary conditions that govern the evolution in time of the filament shape and the velocity and pressure fields within it, is solved by the method of lines incorporating the finite element method for spatial discretization. The finite element algorithm developed here utilizes an adaptive elliptic mesh generation technique that is capable of tracking the dynamics of the filament up to the incipience of pinch-off without the use of remeshing. The correctness of the algorithm is verified by demonstrating that its predictions accord with (a) previously published results of Basaran (1992) on the analysis of finite-amplitude oscillations of viscous drops, (b) simulations of the dynamics of contracting filaments carried out with the well-benchmarked algorithm of Wilkes et al. (1999), and (c) scaling laws governing interface rupture and transitions that can occur from one scaling law to another as pinch-off is approached. In dimensionless form, just two parameters govern the problem: the dimensionless half-length which measures the relative importance of viscous force to capillary force. Regions of the parameter space are identified where filaments (a) contract to a sphere without breaking into multiple droplets, (b) break via the so-called endpinching mechanism where daughter drops pinch-off from the ends of the main filament, and (c) break after undergoing a series of complex oscillations. Predictions made with the new algorithm are also compared to those made with a model based on the slender-jet approximation. A region of the parameter space is found where the slender-jet approximation fares poorly, and its cause is elucidated by examination of the vorticity dynamics and flow fields within contracting filaments.

Stationary shear flow around fixed and free bodies at finite Reynolds number

Abstract: (Received 26 February 2004 and in revised form 4 August 2004) Numerical solutions of stationary flow resulting from immersion of a single body in simple shear flow are reported for a range of Reynolds numbers. Flows are computed using finite-element methods. Comparisons to results of asymptotic low-Reynoldsnumber theory, experimental study, and other numerical techniques are provided. Results are presented primarily for isotropic bodies, i.e. the circular cylinder and sphere, for both of which the two conditions of a torque-free (freely-rotating) and fixed body are investigated. Conditions studied for the sphere are 0 O (1). Separation of the boundary layer is observed in the case of a fixed cylinder at Re ≈ 85, and for a fixed sphere at Re ≈ 100; similar separation phenomena are observed for a freely rotating cylinder. The surface stress and its symmetric first moment (the stresslet) are presented, with the latter providing information on the particle contribution to the mixture rheology at finite Re. Stationary flow results are also presented for elliptical cylinders and oblate spheroids, with observation of zero-torque inclinations relative to the flow direction which depend upon the aspect ratio, confirming and extending prior findings.

Elastic flow instability, curved streamlines, and mixing in microfluidic flows

Abstract: Flow instabilities are well known to occur in macroscopic flows when elastic fluids flow along curved streamlines. In this work we use flow visualization to study the mechanism underlying a purely elastic flow instability for Poiseuille flow in a micro (μ)channel having a zigzag path (curved streamlines) and quantitatively investigate its implications for fluid mixing (studied by fluorescence microscopy) in the μchannel. We find that the instability enhances mixing over the range of applied flow rates. For Newtonian streams, mixing occurs by molecular diffusion, and, as expected, mixing worsens with increasing flow rate because of decreasing residence time. However, for elastic fluid streams, we find substantial enhancement of mixing at sufficiently high throughputs, which indicates a strategy to counter the loss of diffusive mixing at high throughputs by exciting an elastic flow instability. Flow visualization is done using neutrally buoyant non-Brownian tracer particles added to the elastic fluids and also to the Newtonian fluids. In the Newtonian fluids, the tracer particles follow the streamlines. In the elastic fluids, the particles are radially displaced while flowing around bends in the zigzag μchannel, revealing the presence of secondary flow. This radial secondary flow, which promotes mixing between adjacent fluid streams, motivates us to draw an analogy between the instability observed here for the elastic fluids in the μchannel and the elastic instability that occurs in systems with curved streamlines, e.g., in the viscoelastic (non-inertial) Taylor–Couette, Dean, and Taylor–Dean instabilities.

On the effect of contraction ratio in viscoelastic flow through abrupt contractions

Abstract: A numerical study of the creeping flow of a PTT fluid through planar sudden contractions was carried out to quantify the effect of contraction ratio upon the flow characteristics (streamlines and size and intensity of recirculation vortices). The relevant governing equations were solved with a finite volume method embodying a new high-resolution scheme (Alves et al. [Int. J. Numer. Meth. Fluids 41 (2003) 47]) for the discretisation of convection terms, which is here explained and shown to yield improved accuracy and robustness. The results of the simulations, in terms of streamline patterns, give further evidence for a lip-vortex enhancement mechanism and are in remarkable agreement with flow visualization photographs from the literature. In addition, the results show that the variation of flow features in the vicinity of the re-entrant corner, such as lip vortex size and streamlines, are dominated by downstream quantities and scale with the common definition for the Deborah number in this flow, while flow characteristics in the salient corner region scale with that Deborah number divided by the contraction ratio.

Streamline-based dual-porosity simulation of reactive transport and flow in fractured reservoirs

Abstract: [1] We present a streamline-based formulation to model two processes: transport of a tracer undergoing rate-limited sorption and two-phase (water/oil or air/water) transport in fractured systems, using a dual-porosity approach. We show that these two processes can be simulated using mathematically equivalent formulations. In both cases the system conceptually has two components: a flowing fraction connected to stagnant regions with transfer between the two domains. Streamlines capture movement through the flowing fraction. Fluid transfer between flowing and stagnant regions enters as a source/sink term in the one-dimensional transport equations along a streamline. To model flow and transport in fractured systems, we develop a new formulation for the transfer function that matches experimental imbibition data. Then we illustrate the streamline approach with synthetic reservoir problems. We use a finely gridded (over one million grid blocks) three-dimensional domain with a highly heterogeneous permeability field to study both fracture flow and tracer transport. We find breakthrough curves that are consistent with anomalous transport described by an exponent that characterizes the longtime tail of the transit time distribution. For fracture flow we demonstrate that the speed of fluid advance in the fractures is controlled by the imbibition rate. The run times for the simulations scale approximately linearly with system size, making the method appropriate for the simulation of large numerical models.

Natural convection of non-Newtonian power law fluids in a shallow horizontal rectangular cavity uniformly heated from below

Abstract: Analytical and numerical study is conducted for two-dimensional steady-state buoyancy driven flow of a non-Newtonian power law fluid confined in a shallow rectangular horizontal cavity uniformly heated from below, while its short vertical rigid sides are considered adiabatic. The effect of the non-Newtonian behaviour on the onset of convection, fluid flow, temperature field, and heat transfer is examined. A closed approximate analytical solution is developed on the basis of the parallel flow assumption and the obtained results are validated numerically by solving the full governing equations.

Near-Surface Topology and Flow Structure on a Delta Wing

Abstract: The streamlines, and the corresponding patterns of velocity and vorticity, are characterized on a plane immediately adjacent to the surface of a delta wing using a laser-based technique of high-image-density particle image velocimetry. This technique provides the sequence of instantaneous states, as well as the corresponding time-averaged state, of the near-surface streamline topology and the associated critical points. These topological features are interpreted in terms of patterns of averaged and unsteady velocity, and averaged vorticity, which allow identification of regions of unsteadiness along the surface of the wing. These representations of the flow patterns on the stationary wing are also employed for the case of the wing subjected to small-amplitude perturbations in the pitching mode. Perturbations at or near the inherent frequency of the predominant unsteady event on the stationary wing yield substantial changes of the surface topology and flow structure. Furthermore, response of this topology and flow structure to transient, ramplike pitching motion is addressed to define the succession of states during the relaxation process immediately after cessation of the wing motion.

Topological segmentation in three-dimensional vector fields

Abstract: We present a new method for topological segmentation in steady three-dimensional vector fields. Depending on desired properties, the algorithm replaces the original vector field by a derived segmented data set, which is utilized to produce separating surfaces in the vector field. We define the concept of a segmented data set, develop methods that produce the segmented data by sampling the vector field with streamlines, and describe algorithms that generate the separating surfaces. This method is applied to generate local separatrices in the field, defined by a movable boundary region placed in the field. The resulting partitions can be visualized using standard techniques for a visualization of a vector field at a higher level of abstraction.

Computational Fluid Dynamics (CFD) study of the 4th generation prototype of a continuous flow Ventricular Assist Device (VAD).

Abstract: The continuous flow ventricular assist device (VAD) is a miniature centrifugal pump, fully suspended by magnetic bearings, which is being developed for implantation in humans. The CF4 model is the first actual prototype of the final design product. The overall performances of blood flow in CF4 have been simulated using computational fluid dynamics (CFD) software: CFX, which is commercially available from ANSYS Inc. The flow regions modeled in CF4 include the inlet elbow, the five-blade impeller, the clearance gap below the impeller, and the exit volute. According to different needs from patients, a wide range of flow rates and revolutions per minute (RPM) have been studied. The flow rate-pressure curves are given. The streamlines in the flow field are drawn to detect stagnation points and vortices that could lead to thrombosis. The stress is calculated in the fluid field to estimate potential hemolysis. The stress is elevated to the decreased size of the blood flow paths through the smaller pump, but is still within the safe range. The thermal study on the pump, the blood and the surrounding tissue shows the temperature rise due to magnetoelectric heat sources and thermal dissipation is insignificant. CFD simulation proved valuable to demonstrate and to improve the performance of fluid flow in the design of a small size pump.

A flow field study of an elliptic jet in cross flow using DPIV technique

Abstract: The digital particle image velocimetry (DPIV) technique has been used to investigate the flow fields of an elliptic jet in cross flow (EJICF). Two different jet orientations are considered; one with the major axis of the ellipse aligned with the cross flow (henceforth referred to as a low aspect ratio (AR) jet), and the other with the major axis normal to the cross flow (henceforth referred to as a high aspect ratio jet). Results show that the vortex-pairing phenomenon is prevalent in the low aspect ratio jet when the velocity ratio (VR)≥3, and is absent in the high aspect ratio jet regardless of the velocity ratio. The presence of vortex pairing leads to a substantial increase in the leading-edge peak vorticity compared to the lee-side vorticity, which suggests that vortex pairing may play an important role in the entrainment of ambient fluid into the jet body, at least in the near-field region. In the absence of vortex pairing, both the leading-edge and the lee-side peak vorticity increase monotonically with velocity ratio regardless of the aspect ratio. Moreover, time-averaged velocity fields for both AR=0.5 and AR=2 jets reveal the existence of an “unstable focus” (UF) downstream of the jet, at least for VR≥2. The strength and the location of this focus is a function of both the velocity ratio and aspect ratio. In addition, time-averaged vorticity fields show a consistently higher peak-averaged vorticity in the low aspect ratio jet than in the high aspect ratio jet. This behavior could be due to a higher curvature of the vortex filament facing the cross flow in the low aspect ratio jet, which through mutual interaction may lead to higher vortex stretching, and therefore higher peak-averaged vorticity.

Disappearing wakes and dispersion in numerically simulated flows through tube bundles

Abstract: Flow through a staggered array or ‘bundle’ of parallel rigid cylinders of diameter D is computed with the help of a three-dimensional direct numerical simulation (DNS) at various values of Reynolds number between 50 and 6000. Two different spacings L of the tubes, i.e. L/D= 2 and L/D= 3, have been considered. When Re≲ 500 the flow is laminar. In that case the converging flow between a pair of adjacent cylinders brings the oppositely signed vorticity at the two edges of the wake closer together behind the upstream cylinder so that the vorticity decreases quickly due to cancellation by diffusion. At Re≈ 6000, when the flow is highly turbulent, the wake vorticity disappears rather by turbulent diffusion. This ‘disappearance’ of the wakes in the closely packed flows (i.e. L/D≲ 2) causes the mean flow in a ‘cell’, which consists of the region around a single cylinder, to be effectively independent of that in other cells. Another consequence is that the mean velocity field can be very well approximated by potential flow except in a thin boundary layer along the cylinder and a short wake behind it. The results have been applied to the transport of scalars in closely packed arrays. As in other complex flows, the dispersion of the scalars is dominated by the divergence and convergence of the streamlines around the cylinder rather than by the wake turbulence. Approximate expressions are derived for this ‘topologically’ influenced dispersion in terms of the geometry of the array. The fact when most of the flow in the array can be approximated by a potential flow, allows us to introduce a fast approximate calculation method to compute the dispersion.

Instability of Inelastic Shear-Thinning Liquids in a Couette Flow Between Concentric Cylinders

Abstract: Circular Couette flow of inelastic shear-thinning materials in annuli is examined. The curved streamlines of the circular Couette flow can cause a centrifugal instability leading to toroidal vortices, well known as Taylor vortices. The presence of these vortices changes the hydrodynamic and heat transfer characteristics of the processes at which this type of flow occurs. Therefore, it is quite important to be able to predict the onset of instability. Most of the available theoretical and experimental analyses are for Newtonian and viscoelastic (dilute polymeric solutions) liquids. Te effect of the shear-thinning behavior of high concentration suspensions on the onset of the Taylor vortices is determined theoretically by solving the conservation equations, constructing the solution path as the inner cylinder speed rises and searching for the critical conditions. This procedure avoids the need for a stability analysis of the flow and the solution of an eigenproblem. The differential equations were solved by the Galerkin/finite-element method and the resulting set of nonlinear algebraic equations, by Newton's method

The effect of seafloor topography on magnetotelluric fields: an analytical formulation confirmed with numerical results

Abstract: SUMMARY Magnetotelluric fields and impedances are distorted at undulating interfaces. An analytical formulation is presented to calculate magnetotelluric effects in the presence of a sinusoidal interface. In contrast to previous analytical approaches, this formulation is not based on perturbation theory. It is applicable to observations both on land and on the seafloor. Electric and magnetic fields, as well as apparent resistivities and phases, are calculated on the interface. The topographic distortion on land mainly influences the TM mode data where the electric field is perpendicular to the geological strike. Both the TM mode and the orthogonal TE mode data are distorted on the seafloor. Systematic parameter tests indicate which modes are independent of the period and the conductivity contrast, provided that the induction depths are large relative to the amplitude of the topography. The differing physics of the seafloor and land surface is illustrated by plotting current streamlines. For the land model, contour lines diverge below a hill and converge below a valley. For the seafloor model, electric currents mainly flow in the conductive sea water. Contour lines converge above a hill and diverge above a valley. Numerical results, derived from finite-element modelling, support the analytical solutions. Streamlines of the electric current, derived from a model for the Central Andes, illustrate the connection between a graphical display of electromagnetic fields and an algebraic sensitivity analysis of the magnetotelluric impedance tensor.

Wind-driven barotropic gyre I : circulation control by eddy vorticity fluxes to an enhanced removal region

Abstract: It is well known that the barotropic, wind-driven, single-gyre ocean model reaches an inertiallydominated equilibrium with unrealistic circulation strength when the explicit viscosity is reduced to realistically low values. It is shown here that the overall circulation strength can be controlled nonlocally by retaining thin regions of enhanced viscosity parameterizing the effects of increased mixing and topographic interaction near the boundaries. The control is possible even when the inertial boundary layer width is larger than the enhanced viscosity region, as eddy e uxes of vorticity from the interior transport vorticity across the mean streamlines of the inertial boundary current to the frictional region. In relatively inviscid calculations the eddies are the major means of e ux across interior mean streamlines.

Making Use of Labyrinth Interaction Flow

Abstract: It is the aim of this publication to attract the designers attention to the end wall flow interactions of shrouded high pressure turbines. One of the key issues for designing better turbines is the understanding of the flow interactions set up by the presence of labyrinth seals. Those interaction flows are carefully examined in this publication using the control volume analysis and the radial equilibrium of forces acting on streamlines. The consequences on secondary flow development and mixing losses are discussed and quantified. Out of this insight, design recommendations are derived, which attempt to make use of the nature of the labyrinth interaction flow. The open labyrinth cavities are classified in a systematic way. The aim of this approach is to work out the characteristic differences between hub and tip cavities and those having a leakage jet or sucking main flow fluid into the labyrinth. The influence on the main flow is discussed in terms of the incidence flow angle of downstream blade rows and the associated loss production mechanisms. The design strategies presented in this paper follow two paths: (a) Optimization of the mixing losses of the leakage jets at hub and tip is estimated to result in an efficiency increase of up to 0.2%. (b) The nonaxisymmetric shaping of the labyrinth interaction flow path aims at the secondary flow control in downstream blade rows. This approach might contribute in the same magnitude of order as reduction in the mixing losses.

Solid-fluid transition in a granular shear flow.

Abstract: The rheology of a granular shear flow is studied in a quasi-2D rotating cylinder. Measurements are carried out near the midpoint along the length of the surface flowing layer where the flow is steady and nonaccelerating. Streakline photography and image analysis are used to obtain particle velocities and positions. Different particle sizes and rotational speeds are considered. We find a sharp transition in the apparent viscosity (eta) variation with rms velocity (u). Below the transition depth we find that the rms velocity decreases with depth and eta proportional to u(-1.5) for all the different cases studied. The material approaches an amorphous solidlike state deep in the layer. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The results indicate a sharp transition from a fluid to a fluid + solid state with decreasing rms velocity.

Effect of Streamline Curvature on Intensity of Streamwise Vortices in the Mixing Layer of Supersonic Jets

Abstract: The structure of supersonic nonisobaric jets with Mach numbers Ma = 1 and 2 is considered experimentally to find the effect of streamline curvature on the evolution of streamwise vortices in the mixing layer. The spatial development of steady streamwise vortices in the mixing layer of supersonic jets is considered. A method for generation of steady streamwise vortices by applying microroughness elements of controlled size onto the inner surface of the nozzle is developed. Radial profiles and azimuthal variations of total pressure are obtained; the mixing‐layer thickness and the curvature of streamlines in supersonic jets are determined. A significant effect of microroughness elements of prescribed shape located on the nozzle surface on the behavior of total pressure in the mixing layer of supersonic jets, as compared to natural disturbances, is obtained.