Showing papers on "Streamlines, streaklines, and pathlines published in 2005"

Numerical solutions of 2‐D steady incompressible driven cavity flow at high Reynolds numbers

Abstract: SUMMARY Numerical calculations of the 2-D steady incompressible driven cavity flow are presented. The NavierStokes equations in streamfunction and vorticity formulation are solved numerically using a fine uniform grid mesh of 601 × 601. The steady driven cavity solutions are computed for Re ≤ 21,000 with a maximum absolute residuals of the governing equations that were less than 10 −10 . A new quaternary vortex at the bottom left corner and a new tertiary vortex at the top left corner of the cavity are observed in the flow field as the Reynolds number increases. Detailed results are presented and comparisons are made with benchmark solutions found in the literature.

Phase-resolved characterization of vortex shedding in the near wake of a square-section cylinder at incidence

Abstract: The vortex formation and shedding process in the near wake region of a 2D square-section cylinder at incidence has been investigated by means of particle image velocimetry (PIV). Proper orthogonal decomposition (POD) is used to characterize the coherent large-scale flow unsteadiness that is associated with the wake vortex shedding process. A particular application of the POD analysis is to extract the vortex-shedding phase of individual velocity fields, which were acquired at asynchronous low rate with respect to the vortex shedding cycle. The phase of an individual flow field is determined from its projection on the first pair of POD modes, allowing phase averaging of the measurement data to be performed. In addition, a low-order representation of the flow, constructed from the mean and the first pair of POD modes, is found to be practically equivalent to the phase-averaged results. It is shown that this low-order representation corresponds to the basic Fourier component of the flow field ensemble with respect to the reconstructed phase. The phase-averaged flow representations reveal the dominant flow features of the vortex-shedding process and the effect of the angle of incidence upon it.

Parametric and internal study of the vortex tube using a CFD model

Abstract: A computational fluid dynamics (CFD) model is used to investigate the energy separation mechanism and flow phenomena within a counter-flow vortex tube. A two-dimensional axi-symmetric CFD model has been developed that exhibits the general behavior expected from a vortex tube. The model results are compared to experimental data obtained from a laboratory vortex tube operated with room temperature compressed air. The CFD model is subsequently used to investigate the internal thermal-fluid processes that are responsible for the vortex tube's temperature separation behavior. The model shows that the vortex tube flow field can be divided into three regions that correspond to: flow that will eventually leave through the hot exit (hot flow region), flow that will eventually leave through the cold exit (cold flow region), and flow that is entrained within the device (re-circulating region). The underlying physical processes are studied by calculating the heat and work transfers through control surfaces defined by the streamlines that separate these regions. It was found that the energy separation exhibited by the vortex tube can be primarily explained by a work transfer caused by a torque produced by viscous shear acting on a rotating control surface that separates the cold flow region and the hot flow region. This work transfer is from the cold region to the hot region whereas the net heat transfer flows in the opposite direction and therefore tends to reduce the temperature separation effect. A parametric study of the effect of varying the diameter and length of the vortex tube is also presented.

Modeling strain hardening and texture evolution in friction stir welding of stainless steel

Abstract: Steady-state friction stir welding of stainless steel has been modeled using an Eulerian formulation that considers coupled viscoplastic flow and heat transfer in the vicinity of the tool pin. Strain hardening is incorporated with a scalar state variable that evolves with deformation as material moves along streamlines of the flow field. The model equations are solved using the finite element method to determine the velocity field and temperature distribution, with a modified Petrov–Galerkin employed to stabilize the temperature distribution. The evolution equation for the state variable for strength is integrated along streamlines using an adaptive procedures to determine step size based on the element size. The intense shearing and associated heating lead to complex behavior near the tool pin. The effect of this complex response is demonstrated with the crystallographic texture, which displays a nonmonotonic strengthening and weakening history along streamlines that pass close to the tool pin.

Batchelor versus Stewartson flow structures in a rotor-stator cavity with throughflow

Abstract: The present work considers the turbulent flow inside a high-speed rotor-stator cavity with or without superimposed throughflow. New extensive measurements made at IRPHE by a two-component laser Doppler anemometer technique and by pressure transducers are compared to numerical predictions based on one-point statistical modeling using a low-Reynolds-number second-order full stress transport closure (Reynolds stress model). The advanced second-order model provides good predictions for the mean flow as well as for the turbulent field and so is the adequate level of closure to describe such complex flows. A better insight into the dynamics of such flows is also gained from this study. Indeed the transition between a Batchelor type of flow with two boundary layers separated by a central rotating core and a Stewartson type of flow with only one boundary layer on the rotating disk is characterized in the (r*,Ro) plane, where r* is the dimensionless radial location and Ro a modified Rossby number. The 5∕7 power-la...

Farthest point seeding for efficient placement of streamlines

Abstract: We propose a novel algorithm for placement of streamlines from two-dimensional steady vector or direction fields. Our method consists of placing one streamline at a time by numerical integration starting at the furthest away from all previously placed streamlines. Such a farthest point seeding strategy leads to high quality placements by favoring long streamlines, while retaining uniformity with the increasing density. Our greedy approach generates placements of comparable quality with respect to the optimization approach from Turk and Banks, while being 200 times faster. Simplicity, robustness as well as efficiency is achieved through the use of a Delaunay triangulation to model the streamlines, address proximity queries and determine the biggest voids by exploiting the empty circle property. Our method handles variable density and extends to multiresolution.

Strategy for seeding 3D streamlines

Abstract: This paper presents a strategy for seeding streamlines in 3D flow fields. Its main goal is to capture the essential flow patterns and to provide sufficient coverage in the field while reducing clutter. First, critical points of the flow field are extracted to identify regions with important flow patterns that need to be presented. Different seeding templates are then used around the vicinity of the different critical points. Because there is significant variability in the flow pattern even for the same type of critical point, our template can change shape depending on how far the critical point is from transitioning into another type of critical point. To accomplish this, we introduce the /spl alpha/-/spl beta/ map of 3D critical points. Next, we use Poisson seeding to populate the empty regions. Finally, we filter the streamlines based on their geometric and spatial properties. Altogether, this multi-step strategy reduces clutter and yet captures the important 3D flow features.

The driven cavity flow over the whole range of the Knudsen number

Abstract: The flow of a rarefied gas in a rectangular enclosure due to the motion of the upper wall is solved over the whole range of the Knudsen number. The formulation is based on the two–dimensional linearized Bhatnagar-Gross-Krook (BGK) kinetic equation with Maxwell diffuse-specular boundary conditions. The integro-differential equations are solved numerically implementing the discrete velocity method. The discontinuity at the boundaries between stationary and moving walls is treated accordingly. A detailed investigation of the rarefaction effects on the flow pattern and quantities is presented over the whole range of the Knudsen number and various aspect (height/width) ratios. Numerical results of flow characteristics, including the streamlines, the velocity profiles, the pressure and temperature contours, and the drag force of the moving wall, are presented for different aspect ratios and various degrees of gas rarefaction from the free molecular through the transition up to the continuum limit. On several occasions, depending upon the flow parameters, in addition to the main vortex, corner eddies are created. As the depth of the cavity is increased, these eddies grow and merge into additional vortices under the top one. The mesoscale kinetic-type approach proves to be efficient and suitable for problems that incorporate multiscale physics, such as the present nonequilibrium flow.

Simulation of gas flow in microchannels with a sudden expansion or contraction

Abstract: Two-dimensional simulations based on the isothermal lattice-Boltzmann method have been undertaken on microchannels with a sudden expansion or contraction. The study provides insight into the analysis of flows in complicated microdevices. The flow is pressure driven, and computations are performed for several Knudsen numbers, and area and pressure ratios, allowing the effects of compressibility and rarefaction to be assessed. The pressure drop for both the converging and diverging channels shows a discontinuity in slope at the junction, and is accompanied by a jump in velocity. The pressure drop in each section can be predicted well by the theory for straight channels. The mass flow ratio between converging and diverging channels is close to unity, and the streamlines are attached in both cases. It is deduced that compressibility and rarefaction have opposite effects on the flow. These results suggest that complex channels of the type considered here can be understood in terms of their primary units, and they experience only small secondary losses.

Comparative study of the continuous phase flow in a cyclone separator using different turbulence models

Abstract: Numerical calculations were carried out at the apex cone and various axial positions of a gas cyclone separator for industrial applications. Two different NS-solvers (a commercial one (CFX 4.4 ANSYS GmbH, Munich, Germany, CFX Solver Documentation, 1998), and a research code (Post-doctoral Thesis, Technical University of Chemnitz, Germany, September, 2002)) based on a pressure correction algorithm of the SIMPLE method have been applied to predict the flow behaviour. The flow was assumed as unsteady, incompressible and isothermal. A κ-e turbulence model has been applied first using the commercial code to investigate the gas flow. Due to the nature of cyclone flows, which exhibit highly curved streamlines and anisotropic turbulence, advanced turbulence models such as Reynolds stress model (RSM) and large eddy simulation (LES) have been used as well. The RSM simulation was performed using the commercial package activating the Launder et al.'s approach, while for the LES calculations the research code has been applied utilizing the Smagorinsky model. It was found that the κ-e model cannot predict flow phenomena inside the cyclone properly due to the strong curvature of the streamlines. The RSM results are comparable with LES results in the area of the apex cone plane. However, the application of the LES reveals qualitative agreement with the experimental data, but requires higher computer capacity and longer running times than RSM. This paper is organized into five sections. The first section consists of an introduction and a summary of previous work. Section 2 deals with turbulence modelling including the governing equations and the three turbulence models used. In Section 3, computational parameters are discussed such as computational grids, boundary conditions and the solution algorithm with respect to the use of MISTRAL/PartFlow-3D. In Section 4, prediction profiles of the gas flow at axial and apex cone positions are presented and discussed. Section 5 summarizes and concludes the paper.

Unsteady flow evolution in swirl injector with radial entry. I. Stationary conditions

Abstract: The vortical flow dynamics in a gas-turbine swirl injector were investigated by means of large eddy simulations. The flow enters the injector through three sets of radial-entry, counter-rotating swirl vanes. The formulation treats the Favre-filtered conservation equations in three dimensions along with a subgrid-scale model, and is solved numerically using a density-based, finite-volume approach with explicit time marching. Several methods, including proper orthogonal decomposition, spectral analysis, and flow visualization, are implemented to explore the flow dynamics in the complex three-dimensional flowfields. Various underlying mechanisms dictating the flow evolution, such as vortex breakdown, the Kelvin–Helmholtz instability, and helical instability, as well as their interactions, are studied for different swirl numbers. The flowfield exhibits well-organized motion in a low swirl-number case, in which the vortex shedding arising from shear instabilities downstream of the guide vanes drives acoustic o...

Rheology of surface granular flows

Abstract: The rheology of surface granular flows is investigated by means of measurements of velocity and number density profiles in a quasi-two-dimensional rotating cylinder, half-filled with mono-disperse steel balls. The measurements are made at the center of the cylinder, where the flow is fully-developed, using streakline photography and image analysis . The stress profile is computed from the number density profile using a force balance taking into account wall friction. The profiles for the mean velocity superimpose when distance is scaled by the particle diameter and the velocity by a characteristic shear rate and the particle diameter. The mean velocity is found to decay exponentially with depth in the bed with a decay length of $\lambda=1.1d$. The r.m.s. velocity is nearly constant near the free surface and below a transition point it decays linearly with depth. The shear rate, obtained by numerical differentiation of the velocity profile, shows a maximum which occurs at the same depth as the transition in the r.m.s. velocity profile. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The variation of the apparent viscosity ($\eta$) with r.m.s. velocity ($u$) shows a relatively sharp transition at the shear rate maximum, and in the region below this point the apparent viscosity varies as $\eta\sim u^{-1.5}$. The experimental data is compared to predictions of three models for granular flow.

Computational Validation for Flow around a Marine Propeller Using Unstructured Mesh Based Navier-Stokes Solver

Abstract: Results of computational fluid dynamics validation for flow around a marine propeller are presented. Computations were performed for various advance ratios following experimental conditions. The objectives of the study are to propose and verify a hybrid mesh generation strategy and to validate computational results against experimental data with advanced computational fluid dynamics tools. Computational results for both global and local flow quantities are discussed and compared with experimental data. The predicted thrust and torque are in good agreement with the measured values. The limiting streamlines on and the pathlines off the propeller blade as well as the pressure distribution on the blade surface reproduce the physics of highly skewed marine propeller flow with tip vortex very well. The circumferentially averaged velocity components compare well with the measured values, while the velocity magnitude and turbulence kinetic energy in the highly concentrated tip vortex region are under-predicted. The overall results suggest that the present approach is practicable for actual propeller design procedures.

On the linear stability of plane Couette flow for an Oldroyd-B fluid and its numerical approximation

Abstract: It is well known that plane Couette flow for an Oldroyd-B fluid is linearly stable, yet, most numerical methods predict spurious instabilities at sufficiently high Weissenberg number. In this paper we examine the reasons which cause this qualitative discrepancy. We identify a family of distribution-valued eigenfunctions, which have been overlooked by previous analyses. These singular eigenfunctions span a family of nonmodal stress perturbations which are divergence-free, and therefore do not couple back into the velocity field. Although these perturbations decay eventually, they exhibit transient amplification during which their “passive" transport by shearing streamlines generates large crossstream gradients. This filamentation process produces numerical under-resolution, accompanied with a growth of truncation errors. We believe that the unphysical behavior has to be addressed by fine-scale modelling, such as artificial stress diffusivity, or other non-local couplings. © 2005 Elsevier B.V. All rights reserved.

Microscopic steady streaming eddies created around short cylinders in a channel: Flow visualization and Stokes layer scaling

Abstract: Microscale steady streaming eddies created using low-intensity fluid oscillations offer appealing options for controlling fluids in microfluidic systems. We describe the three-dimensional (3D) steady streaming flow formed in a small channel containing single fixed cylinders when the channel fluid is oscillated at low intensity. Experiments include three cylinder sizes (length 1.5mm; radii a=125, 250, and 500μm) within identical channels (height 2h=1.5mm; width 4mm) over a range of oscillation frequencies (40⩽ω⩽1000Hz). The size of key flow features is measured from steady particle pathline images recorded within three flow symmetry planes. The resulting 3D streaming exhibits two distinct recirculating flows that are governed by the Stokes layer thickness δAC and geometric length scales. Four symmetric recirculating eddies are created adjacent to the cylinder far from channel walls, and their size is governed by δAC∕a as described by steady streaming theory for a 2D geometry. The cylinder/wall boundary lay...

Centrifugal Flow in a Rotor-Stator Cavity

Abstract: The present work considers the turbulent flow inside an annular rotor-stator cavity with and without centrifugal throughflow. Extensive measurements performed using a two-component laser-Doppler anemometer technique, and pressure transducers are compared to numerical predictions based on one-point statistical modeling using a low-Reynolds-number second-order full-stress transport closure. A study of the flow control parameters is performed, and, for the first time, a better insight into the transition from Batchelor to Stewartson types of flow is gained from this study. The advanced second-order model is confirmed to be the adequate level of closure to describe such complex flows.

Natural convection flow of water near its density maximum in a rectangular enclosure having isothermal walls with heat generation

Abstract: We consider unsteady laminar natural convection flow of water subject to density inversion in a rectangular cavity formed by isothermal vertical walls with internal heat generation. The top and bottom horizontal walls are considered to be adiabatic, whereas the temperature of the left vertical wall is assumed to be greater than that of the right vertical wall. The equations are non-dimensionalized and are solved numerically by an upwind finite difference method together with a successive over-relaxation (SOR) technique. The effects of both heat generation and variations in the aspect ratio on the streamlines, isotherms and the rate of heat transfer from the walls of the enclosure are presented. Investigations are performed for water taking Prandtl number to be Pr=11.58 and the Rayleigh number to be Ra=105.

Visualizations of Boger fluid flows in a 4:1 square/square contraction

Abstract: Visualizations of the 3-D flow in a 4:1 square–square sudden contraction for two viscoelastic Boger fluids and two Newtonian fluids were carried out at low Reynolds numbers. In these creeping flow conditions, the vortex length remained unchanged for Newtonian fluids, whereas a nonmonotonic variation with flow rate was observed for the Boger fluids. Initially, the corner vortex slightly increased with flow rate to a local peak at a Deborah number of De2 ≈ 6, before decreasing significantly to a minimum at De2 ≈ 15 (De2 is based on downstream characteristics). Finally, for Deborah numbers > 20 there was intense vortex enhancement until a periodic flow was established at higher flow rates (De2 ≈ 45–52). The strong elastic vortex enhancement was preceded by the appearance of diverging streamlines on the approach flow and, for the Boger fluid with higher polymer concentration, vortex enhancement took place through a lip vortex mechanism. AIChE J, 2005

Calculation of the separation streamlines of barchans and transverse dunes

Abstract: We use FLUENT to calculate the wind profile over barchans and transverse dunes. The form of the streamlines of flow separation at the lee side of the dunes is determined for a symmetric barchan dune in three dimensions, and for the height profile of a measured transverse dune field in the Lencois Maranhenses.

The method of fundamental solutions for Stokes flow in a rectangular cavity with cylinders

Abstract: Numerical solutions based on the method of fundamental solutions are discussed for Stokes flow inside a rectangular cavity in the presence of circular cylinders. The Stokeslets are used as the fundamental solutions to obtain the solution for the flow field by a linear combination of fundamental solutions. Flow results on the cellular structure of flow field resulting from the dynamics of cylinders and the horizontal walls of the cavity are reported for (i) one rotating cylinder in a rectangular cavity with two parallel horizontal sides moving in the same directions as well as in the opposite directions, (ii) two rotating cylinders kept apart in a rectangular cavity with two parallel horizontal sides moving in the same directions as well as in the opposite directions. The effect of aspect ratio of the rectangular cavity, direction of movement of the two parallel horizontal sides of the cavity and the diameter of the rotating cylinder on the flow structure are studied. The flow results obtained for the single cylinder case are in accordance with the results available in the literature. From the computational point of view, the present numerical procedure based on the method of fundamental solutions is efficient and simple to implement as compared to the mesh-dependent schemes, which needs complex mesh generation procedure for the multiply connected geometrical domains considered in this article.

Flow and forced-convection characteristics of turbulent flow through parallel plates with periodic transverse ribs

Abstract: Two general turbulence models, the standard k–ϵ model and the Reynolds stress model (RSM), were used to predict the forced convection of a fully developed turbulent flow through an assembly of two horizontally oriented parallel plates in the Reynolds number range 22,000 < Re D < 94,000. The upper smooth plate was thermally insulated, whereas the bottom plate, attached with rectangular-cross-sectional ribs perpendicular to the mean air flow, was provided with a uniform heat flux. The ribs were uniformly spaced with the pitch-to-height ratio of p/e = 4, a height-to-hydraulic-diameter ratio of e/D = 0.25, and a width-to-height ratio of w/e = 2. The numerical approaches were based on the finite-volume technique. A second-order upwind scheme was applied in the calculation and a very fine mesh density was arranged in the regions near the wall boundaries. The SIMPLE algorithm was adopted to handle the pressure–velocity coupling in the calculation. Local Nusselt number distribution along the heated bott...

Steady axisymmetric flow in an open cylindrical container with a partially rotating bottom wall

Abstract: The steady motion of a viscous fluid in a cylindrical container with a partially rotating bottom wall and a free surface is investigated by means of axisymmetric Navier–Stokes simulations. The flow above the spinning disk at the center of the bottom wall is dominated by an Ekman boundary layer that drives the fluid radially outward. In contrast, an inward flow ensues along the outer, stationary part of the bottom wall, where the radially increasing pressure distribution set up by the rotating fluid motion near the free surface is not balanced by a corresponding centrifugal force. As a result, flow separation occurs at an intermediate radial location close to the outer edge of the rotating disk. Thus a flow configuration results that is dominated by a meridional vortex above the spinning disk, and a counterrotating vortex above the stationary part of the bottom wall. Simulations are conducted for various aspect ratios and Reynolds numbers, in order to evaluate the resulting changes in the vortex breakdown configurations. As the ratio of container radius to disk radius increases above a value of about 2.3, the influence of the lateral container wall on the features of the central flow in the neighborhood of the spinning disk becomes insignificant. By means of a simplified model problem, it is demonstrated that this rapid loss of influence is due to the exponential decay of the azimuthal surface velocity beyond the edge of the disk. This exponential decay is confirmed by the numerical data, and it reflects the fact that as the lateral wall moves outward, the stationary part of the end wall becomes the main sink for the azimuthal momentum of the fluid.