Showing papers on "Streamlines, streaklines, and pathlines published in 2001"

Detection and visualization of closed streamlines in planar flows

Abstract: The analysis and visualization of flows is a central problem in visualization. Topology-based methods have gained increasing interest in recent years. This article describes a method for the detection of closed streamlines in flows. It is based on a special treatment of cases where a streamline reenters a cell to prevent infinite cycling during streamline calculation. The algorithm checks for possible exits of a loop of crossed edges and detects structurally stable closed streamlines. These global features are not detected by conventional topology and feature detection algorithms.

Steady Herschel–Bulkley fluid flow in three-dimensional expansions

Abstract: In this paper we study steady flow of Herschel–Bulkley fluids in a canonical three-dimensional expansion. The fluid behavior was modeled using a regularized continuous constitutive relation, and the flow was obtained numerically using a mixed-Galerkin finite element formulation with a Newton–Raphson iteration procedure coupled to an iterative solver. Results for the topology of the yielded and unyielded regions, and recirculation zones as a function of the Reynolds and Bingham numbers and the power-law exponent, are presented and discussed for a 2:1 and a 4:1 expansion ratio. The results reveal the strong interplay between the Bingham and Reynolds numbers and their influence on the formation and break up of stagnant zones in the corner of the expansion and on the size and location of core regions.

A Numerical Study of Flow and Heat Transfer in a Smooth and Ribbed U-Duct With and Without Rotation

Abstract: Computations were performed to study the three-dimensional flow and heat transfer in a U-shaped duct of square cross section under rotating and non-rotating conditions. The parameters investigated were two rotation numbers (0, 0.24) and smooth versus ribbed walls at a Reynolds number of 25,000, a density ratio of 0. 13, and an inlet Mach number of 0.05. Results are presented for streamlines, velocity vector fields, and contours of Mach number, pressure, temperature, and Nusselt numbers

Enhancement of the traveling front speeds in reaction-diffusion equations with advection

Abstract: We establish rigorous lower bounds on the speed of traveling fronts and on the bulk burning rate in reaction-diffusion equation with passive advection. The non-linearity is assumed to be of either KPP or ignition type. We consider two main classes of flows. Percolating flows, which are characterized by the presence of long tubes of streamlines mixing hot and cold material, lead to strong speed-up of burning which is linear in the amplitude of the flow, U. On the other hand the cellular flows, which have closed streamlines, are shown to produce weaker increase in reaction. For such flows we get a lower bound which grows as U1/5 for a large amplitude of the flow.

Accelerated diffusion in the centre of a vortex

Abstract: The spiral wind-up and diffusive decay of a passive scalar in circular streamlines is considered. An accelerated diffusion mechanism operates to destroy scalar fluctuations on a time scale of order P1/3 times the turn-over time, where P is a Peclet number. The mechanism relies on differential rotation, that is, a non-zero gradient of angular velocity. However if the flow is smooth, the gradient of angular velocity necessarily vanishes at the centre of the streamlines, and the time scale becomes greater. The behaviour at the centre is analysed and it is found that scalar there is only destroyed on a time scale of order P1/2. Related results are obtained for magnetic field and for weak vorticity, a scalar coupled to the stream function of the flow. Some exact solutions are presented.

The three-dimensional structure of confined swirling flows with vortex breakdown

Abstract: In a recent experimental study, Spohn, Mory and Hopfinger (1998) investigated in detail the flow in a closed cylindrical container with a rotating bottom for Reynolds numbers in the steady and unsteady regimes. Their visualization photographs revealed that the stationary vortex breakdown bubbles, which form along the container axis within a range of governing parameters, are open, with inflow and outflow, and asymmetric at their downstream end. For Reynolds numbers within the unsteady regime, visualizations of the limiting streamlines on the cylindrical wall showed that the Stewartson layer separates asymmetrically along stationary spiral convergence lines that form below the top cover. We study numerically the container flow, by solving the unsteady, three-dimensional Navier-Stokes equations, in order to clarify the origin and elucidate the underlying physics of these complex, three-dimensional flow features. The stationary vortex breakdown bubbles we simulate exhibit all the asymmetries observed in the laboratory. By analysing the Lagrangian characteristics of the calculated flow fields, we explain the origin of these asymmetries, clarify the experimentally documented filling and emptying mechanisms, and show that the flow in the interior of stationary vortex breakdown bubbles exhibits chaotic particle paths. We also show that the spiral separation lines observed by Spohn et al. (1998) inside the Stewartson layer at high Reynolds numbers are due to the growth of pairs of counter-rotating, spiral vortices and the interaction of these vortices with the stationary-cover boundary layer.

Stratified Flow along a Corrugated Slope: Separation Drag and Wave Drag

Abstract: Lee wave generation and horizontal flow separation in stratified flow along a slope, with corrugations or a ridge running directly downslope, are explored using analytical and numerical methods. Both of these processes are important to the drag on alongslope currents. The analytical solution for steady wave generation by stratified flow along a corrugated slope is extended to the evanescent flow regimes. There are two evanescent regimes, having intrinsic frequencies either above the buoyancy frequency N (fast flow), or below N sin(a) (slow flow), for nonrotating fluid and slope angle, a. Streamlines of the low speed evanescent solution tend to follow isobaths, while those of wave solutions tend to flow up over ridges and down in canyons. An analytical expression is developed for the wave drag felt by an isolated ridge on a slope. For a Gaussian ridge of alongslope length L, the drag becomes small when U/LN > 1 (the fast flow regime), or when U/(LN sin a) < 1/2 (the slow flow regime). Numerical ex...

Creeping flow through a pipe of varying radius

Abstract: Creeping flow of a Newtonian fluid through tubes of varying radius is studied. Using an asymptotic series solution for low Reynolds number flow, velocity profiles and streamlines are obtained for constricted tubes, for various values of constriction wavelength and amplitude. A closed-form expression is derived to estimate the pressure drop through this type of tube. The results obtained with this new expression are compared to data from previous experimental and numerical studies for sinusoidally constricted tubes. Good agreement is found in the creeping flow regime for the pressure drop versus flow rate relationship. Our method offers an improvement over the integrated form of the Hagen–Poiseuille equation (i.e., lubrication approximation), which does not account for the wavelength of the constrictions.

Edge flow measurements with Gundestrup probes

Abstract: The ion current collected by a probe in a magnetized plasma is sensitive to the angle between its surface and the flow streamlines. This intuitive concept is the basis of the Gundestrup probe, a polar array of planar collectors mounted around an insulating housing. Probe theory for measuring flows has been developed on two fronts: Recent kinetic and fluid models, reviewed here, give similar predictions for the collected current within the range of applicability of the model assumptions. A comparison with measurements by a rotating Mach probe in the CASTOR tokamak (Czech Academy of Sciences Torus) [J. Stockel, J. Badalec, I. Ďuran et al., Plasma Phys. Controlled Fusion, 41, 577 (1999)] highlights the role of magnetization in ion collection at grazing angles of incidence between the probe surface and the magnetic field lines.

A Numerical Investigation on the Volute/Diffuser Interaction Due to the Axial Distortion at the Impeller Exit

Abstract: A numerical simulation is performed on a single-stage centrifugal compressor using the commercially available CFD software, CFX-TASCflow. The steady flow is obtained by circumferentially averaging the exit fluxes of the impeller. Three runs are made at the design condition and off-design conditions. The predicted performance is in agreement with experimental data. The flow details inside the stationary components are investigated, resulting in a flow model describing the volute/diffuser interaction at design and off-design conditions

Stratified flow over topography: models versus observations

Abstract: Essential mechanisms identified in the authors‘ observations of flow establishment over topography are restated, with emphasis on those which are at variance with numerical simulations. Specifically, small–scale instabilities were observed to lead to upwards transport of fluid from the primary flow so as to form a nearly stationary intermediate layer, and boundary–layer separation significantly delays establishment of the downslope flow. Simulations that force the streamlines to follow the topography generate a large–amplitude breaking wave, which we did not observe. Our observations show that small–scale instability and separation act in concert to determine the time–dependent evolution of the stratified flow response.

Three‐dimensional numerical simulation of Marangoni instabilities in liquid bridges: influence of geometrical aspect ratio

Abstract: Oscillatory Marangoni convection in silicone oil–liquid bridges with different geometrical aspect ratios is investigated by three-dimensional and time-dependent numerical simulations, based on control volume methods in staggered cylindrical non-uniform grids. The three-dimensional oscillatory flow regimes are studied and compared with previous experimental and theoretical results. The results show that the critical wavenumber (m), related to the azimuthal spatio-temporal flow structure, is a monotonically decreasing function of the geometrical aspect ratio of the liquid bridge (defined as the ratio of length to diameter). For this function, a general correlation formula is found, which is in agreement with the previous experimental findings. The critical Marangoni number and the oscillation frequency are decreasing functions of the aspect ratio; however, the critical Marangoni number, based on the axial length of the bridge, does not change much with the aspect ratio. For each aspect ratio investigated, the onset of the instability from the axisymmetric steady state to the three-dimensional oscillatory one is characterized by the appearance of a standing wave regime that exhibits, after a certain time, a second transition to a travelling wave regime. The standing wave regime is more stable for lower aspect ratios since it lasts for a long time. This behaviour is explained on the basis of the propagation velocity of the disturbances in the liquid phase. For this velocity, a general correlation law is found as a function of the aspect ratio and of the Marangoni number. Copyright © 2001 John Wiley & Sons, Ltd.

Vibrational effects on convection in a square cavity at zero gravity

Abstract: In this numerical study, we investigate natural convection in a two-dimensional square-section enclosure vibrating sinusoidally parallel to the applied temperature gradient in a zero-gravity field. The full Navier-Stokes equations are simplified with the Boussinesq approximation and solved by a finite difference method. Whereas the Prandtl number Pr is fixed to 7.1 (except for some test cases with Pr = 7.0, 6.8), the vibrational Rayleigh number Ra based on acceleration amplitude is varied from 1.0 x 10 4 to 1.0 x 10 5 , and dimensionless angular frequency ω is varied from 1.0 x 10° to 1.0 x 10 3 . In the tested range, time evolutions exhibit synchronous, 1/2-subharmonic and non-periodic responses, and flow patterns are characterized mainly by one- or two-cell structures. Flow-regime diagrams show considerable differences from results in a non-zero-mean-gravity field even at large acceleration amplitudes, and suggest that some parts of non-periodic-response regimes may be related to transitions between flow patterns. The amplitude of fluctuations in spatially averaged kinetic energy density K (equal to the difference between maximum and minimum kinetic energies over a cycle) tends to be large when fluid is stationary everywhere over some interval of time during each period, and has a peak when fluid begins to move continuously throughout one period. Such peaks are caused by impulsively started convection, and are not connected to resonant oscillations in a constant-gravity field.

Multiresolution flow visualization

Abstract: Flow visualization has been an active research field for several years and various techniques have been proposed to visualize vector fields, streamlines and textures being the most effective and popular ones. While streamlines are suitable to get rough information on the behavior of the flow, textures depict the flow properties at the pixel level. Depending on the situation the suitable representation could be streamlines or texture. This paper presents a method to compute a sequence of streamline-based images of a vector field with different densities, ranging from sparse to texturelike representations. It is based on an effective streamline placement algorithm and a production scheme that recalls those used in the multiresolution theory. Indeed a streamline defined at level J of the hierarchy is defined for all levels J’>J. A viewer allows us to interactively select the desired density while zooming in and out in a vector field. The density of streamlines in the image can also be automatically computed as a function of a derived quantity, such as velocity or vorticity.

Numerical solution of fiber suspension flow through a parallel plate channel by coupling flow field with fiber orientation distribution

Abstract: The coupled flow kinematics and fiber orientation distribution were computed to study the development of fiber suspension flows through a parallel plate channel. The effect of fiber-concentration distribution on the flow field was also examined. The suspension used in the computations consisted of high aspect-ratio rigid fibers in a Newtonian fluid. A parabolic velocity profile for a Newtonian flow and an isotropic fiber orientation were taken at the inlet of the channel. Planar orientations of a large number of fibers were evaluated from computation of the Jeffery equation along the streamlines (statistical scheme, the number of fibers N =180) instead of direct solutions of the Fokker–Plank equation or the evolution equation of the fourth-order orientation tensor with a closure approximation. For the uniform concentration of fibers, the anisotropic characteristics of fiber orientations and stress field remarkably appear in the region near the inlet. As a result, the flow kinematics for fiber suspensions can change more significantly from the Newtonian counterpart in the region near the inlet as the volume fraction and/or aspect-ratio of fibers increase. When the volume fraction of fibers decreases in the width direction as the channel wall is approached, the velocity profile becomes more plug-like and the anisotropic characteristics more remarkably appear than those for the uniform concentration case.

Time-Resolved FT-IR Spectroscopy of Chemical Reactions in Solution by Fast Diffusion-Based Mixing in a Micromachined Flow Cell

Abstract: A new concept for the study of chemical reactions in solution by time-resolved Fourier transform infrared spectroscopy (TR/FT-IR) is presented. The key element of this concept is a micromachined mixing unit for fast and highly reproducible diffusion-based mixing that is incorporated in a flow cell for transmission measurements and operated in the stopped-flow mode. The mixing unit achieves multilamination of two liquid streamlines inside the flow cell. When the flow in both feeding channels is maintained, there is almost no mixing of the liquids, because of the short residence time inside the mixer, hence allowing for the recording of a reference spectrum of the reactants prior to reaction. When the flow is stopped by rapid switching of a dedicated injection valve, highly reproducible diffusion-controlled mixing takes place inside the flow cell so that spectral changes induced by the reaction under investigation can be directly followed. The total volume required for one experiment is ∼5μL, and mixing times achieved so far are in the millisecond range. Factors governing time resolution in this new concept are the time required to stop the flow, the spacing of the individual streamlines, the diffusion coefficients of the reactants involved, and the signal strength of the spectral changes induced by the reaction under study. In this paper, the possibilities and limitations of the new concept are studied with the use of three model reactions, which are an acid-base neutralization reaction, the addition of sulfite to formaldehyde, and the basic hydrolysis of methyl monochloroacetate. In addition, the complete mixing process in the system was studied by computational fluid dynamics (CFD) simulations, which provided valuable insights into details of the mixing process itself as well as confirming the experimental results obtained.

Non-isothermal modification of purely elastic flow instabilities in torsional flows of polymeric fluids

Abstract: Previous experimental measurements and linear stability analyses of curvilinear shearing flows of viscoelastic fluids have shown that the combination of streamwise curvature and elastic normal stresses can lead to flow destabilization. Torsional shear flows of highly elastic fluids with closed streamlines can also accumulate heat from viscous dissipation resulting in nonuniformity in the temperature profile within the flow and nonlinearity in the viscometric properties of the fluid. Recently, it has been shown by Al-Mubaiyedh et al. [Phys. Fluids 11, 3217 (1999)] that the inclusion of energetics in the linear stability analysis of viscoelastic Taylor–Couette flow can change the dominant mode of the purely elastic instability from a nonaxisymmetric and time-dependent secondary flow to an axisymmetric stationary Taylor-type toroidal vortex that more closely agrees with the stability characteristics observed experimentally. In this work, we present a detailed experimental study of the effect of viscous heati...

Method of determining fluid flow

Abstract: A method of determining fluid flow in a volume containing two or more fluid components, comprising determining a pressure field for the volume. One or more streamlines are determined from the pressure field, and the fluid composition is solved for the fluid composition along the or each streamline. The pressure may also be solved along the or each streamline. The step of solving along the or each streamline may be performed using a finite difference technique.

A Simple Family of Models for Eccentric Keplerian Fluid Disks

Abstract: To be in a long-lived configuration, the density in a fluid disk should be constant along streamlines to prevent compressional (PdV) work from being done cyclically around every orbit. In a pure Kepler potential, flow along aligned elliptical streamlines of constant eccentricity will satisfy this condition. For most density profiles, differential precession driven by the pressure gradient will destroy the alignment; however, in the razor-thin approximation there is a family of simple equilibria in which the precession frequency is the same at all radii. These disks may therefore be long-lived at significant eccentricities. The density can be made axisymmetric as r → 0 while maintaining the precession rate by relaxing the requirement of constancy along streamlines in an arbitrarily small transition region near the center. In the limit of small eccentricity, the models can be seen as acoustically perturbed axisymmetric disks, and the precession rate is shown to agree with linear theory. The perturbation is a traveling wave similar to an ocean wave, with the fluid rising and falling epicyclically in the gravitational field of the central mass. The expected emission-line profiles from the eccentric disks are shown to be strongly asymmetric in general and, in extreme cases, prone to misinterpretation as single narrow lines with significant velocity offsets.

Melting of a Solid Sphere Under Forced and Mixed Convection: Flow Characteristics

Abstract: An experimental investigation on flow around a melting ice sphere in horizontally flowing water is conducted. The flow field is measured quantitatively using the particle image velocimetry (PIV) technique. The distributions of velocity, streamline, and z-component of rotation vector around the ice sphere are obtained for different upstream velocities and temperatures. General flow characteristics around the melting ice sphere and effects of velocity and temperature are analyzed. The visualization of melting of a dyed ice sphere is also conducted to investigate the motion of the melt, its mixing with mainstream, and the separation of the boundary layer. Comparisons with the flow around a non-melting ball are made to investigate the effect of melting on the flow boundary layer