Swirling Flow of a Viscoelastic Fluid With Free Surface: Part I — Experimental Analysis of Vortex Motion by PIV

2004 ◽  
Author(s):  
Jinjia Wei ◽  
Fengchen Li ◽  
Bo Yu ◽  
Yasuo Kawaguchi
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Particle Image Velocimetry System ◽  
Meridional Plane ◽  
Cylindrical Wall ◽  
Rotating Disc ◽  
Solution Flow ◽  
Surfactant Solutions

The swirling flows of water and CTAC (cetyltrimethyl ammonium chloride) surfactant solutions in an open cylindrical container with a rotating disc at the bottom were experimentally investigated by use of a double-pulsed PIV (particle image velocimetry) system. The mass concentrations of CTAC solutions were in the range of 50–1000 ppm, and the Reynolds number based on angular velocity, kinematic viscosity of water and radius of rotating disc was fixed at 4.3 × 104. The aspect ratio of the height of the liquid filled into the cylindrical vessel to the radius of the vessel was set to 1.0. The secondary flow patterns in the meridional plane and the tangential velocities were obtained. The flow pattern in the meridional plane for water at the present high Reynolds number differed greatly from that at low Reynolds numbers, and an inertia-driven vortex was pushed to the corner between the free surface and the cylindrical wall by a counter-rotating vortex caused by vortex breakdown. For the 1000-ppm surfactant solution flow, the inertia-driven vortex located at the corner between the bottom and the cylindrical wall whereas an elasticity-driven reverse vortex governed the majority of the flow field. The radial distributions of the time-averaged tangential velocities also differed for water and surfactant solutions. The rotation of the fluid caused a deformation of the free surface with a dip at the center. The dip was largest for the water case and decreased with increasing surfactant concentration.

Swirling Flow of a Viscoelastic Fluid With Free Surface—Part I: Experimental Analysis of Vortex Motion by PIV

2005 ◽  
Vol 128 (1) ◽  
pp. 69-76 ◽  
Author(s):  
Jinjia Wei ◽  
Fengchen Li ◽  
Bo Yu ◽  
Yasuo Kawaguchi
Keyword(s):  
Free Surface ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Vortex Motion ◽  
Surfactant Solution ◽  
Particle Image Velocimetry System ◽  
Meridional Plane ◽  
Cylindrical Wall ◽  
Rotating Disc ◽  
Solution Flow

The swirling flows of water and CTAC (cetyltrimethyl ammonium chloride) surfactant solutions (50-1000ppm) in an open cylindrical container with a rotating disc at the bottom were experimentally investigated by use of a double-pulsed PIV (particle image velocimetry) system. The flow pattern in the meridional plane for water at the present high Reynolds number of 4.3×104 differed greatly from that at low Reynolds numbers, and an inertia-driven vortex was pushed to the corner between the free surface and the cylindrical wall by a counter-rotating vortex caused by vortex breakdown. For the 1000ppm surfactant solution flow, the inertia-driven vortex located at the corner between the bottom and the cylindrical wall whereas an elasticity-driven reverse vortex governed the majority of the flow field. The rotation of the fluid caused a deformation of the free surface with a dip at the center. The dip was largest for the water case and decreased with increasing surfactant concentration. The value of the dip was related to determining the solution viscoelasticity for the onset of drag reduction.

Experimental Study of Swirling Flow of a Viscoelastic Fluid With Deformed Free Surface

2006 ◽  
Author(s):  
Feng-Chen Li ◽  
Masamichi Oishi ◽  
Yasuo Kawaguchi ◽  
Nobuyuki Oshima ◽  
Marie Oshima
Keyword(s):  
Free Surface ◽  
Water Flow ◽  
Viscoelastic Fluid ◽  
Swirling Flow ◽  
Solution Concentration ◽  
Force Balance ◽  
Meridional Plane ◽  
Solution Flow ◽  
Secondary Velocity ◽  
Cetyltrimethyl Ammonium

An experimental investigation was performed on the swirling flow of viscoelastic fluid with deformed free surface in a cylindrical container driven by the constantly rotating bottom wall. The tested fluid was an aqueous solution of CTAC (cetyltrimethyl ammonium chloride), which is a cationic surfactant. Water, 40ppm, 60ppm and 200ppm CTAC solution flows were tested at Froude numbers ranging from 2.59 to 16.3. PIV was used to measure the secondary velocity field in the meridional plane and the deformed free-surface level was extracted from the PIV images. At a similar Froude number, the depth of the dip formed at the center region of the free surface was decreased for CTAC solution flow compared with water flow. The inertia-driven vortex at the up-right corner in the meridional plane becomes more and more weakened with increase of the solution concentration or viscoelasticity. Through analyzing the overall force balance compared with water flow, the first normal stress difference or the weak viscoelasticity was estimated for the dilute CTAC solution flows.

Swirling Flow of a Viscoelastic Fluid With Free Surface: Part II — Numerical Analysis With Extended Marker-and-Cell Method

2004 ◽  
Author(s):  
Bo Yu ◽  
Jinjia Wei ◽  
Yasuo Kawaguchi
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Turbulence Model ◽  
Swirling Flow ◽  
Surfactant Solution ◽  
Secondary Flows ◽  
Surface Shape ◽  
Alternative Methods ◽  
Large Reynolds Number ◽  
Meridional Plane

In Part I [1], we presented the experimental results for swirling flows of water and cetyltrimethyl ammonium chloride (CTAC) surfactant solution in a cylindrical vessel with a rotating disk located at the bottom for a Reynolds number of around 4.3 × 104 based on the viscosity of solvent. For the large Reynolds number, violent irregular instantaneous secondary flows at the meridional plane were observed by use of a PIV system. Because of the limitations of our computer resources, we did not carry out DNS simulation for such a large Reynolds number. The LES and turbulence model are alternative methods, but a viscoelastic LES/turbulence model has not yet been developed for the surfactant solution. In this study, therefore, we limited our simulations to a laminar flow. The Marker-and-Cell (MAC) method proposed for Newtonian flow was extended to the viscoelastic flow to track the free surface, and the effects of Weissenberg number and Froude number on the flow pattern and surface shape were studied. Although the Reynolds number is much smaller than that of the experiment, the major experimental observations such as the inhibition of primary and secondary flows and the decrease of the dip of the free surface by the elasticity of the solution, were qualitatively reproduced in the numerical simulations.

Confined Swirling Flows of Aqueous Surfactant Solutions Due to a Rotating Disc in a Cylindrical Casing

2007 ◽  
Author(s):  
S. Tamano ◽  
M. Itoh ◽  
M. Yoshida ◽  
K. Yokota
Keyword(s):  
Reynolds Number ◽  
Surfactant Solution ◽  
Swirling Flows ◽  
Visualization Technique ◽  
Rotating Disc ◽  
Constant Frequency ◽  
First Normal Stress Difference ◽  
Surfactant Solutions ◽  
Aqueous Surfactant Solution ◽  
Cylindrical Casing

In this study, confined swirling flows of an aqueous surfactant solution due to a rotating disc in a cylindrical casing were investigated using a sectional flow visualization technique and a two-component laser Doppler velocimetry (LDV) system. The concentrations of aqueous surfactant solutions (C14TASal) are 0.4, 0.8, and 1.2 wt%. Rheological properties such as a shear viscosity and a first normal stress difference of the surfactant solution were measured with a rheometer. The patterns of the secondary flow were classified using the Reynolds and elastic numbers. We revealed that the projection formed near the center of the rotating disc was moving up and down at a constant frequency for C14TASal 0.8 and 1.2 wt%, which has not been reported as far as we know. The effects of the Reynolds number, elastic number, and aspect ratio on the velocity profiles were clarified. It was also found that the region of rigid body rotation existed at the higher Reynolds number tested for C14TASal 0.4 wt%.

Experiments on vortex breakdown in a confined flow generated by a rotating disc

1998 ◽  
Vol 370 ◽  
pp. 73-99 ◽  
Author(s):  
A. SPOHN ◽  
M. MORY ◽  
E. J. HOPFINGER
Keyword(s):  
Free Surface ◽  
Recirculation Zone ◽  
Vortex Breakdown ◽  
Rear Side ◽  
Asymmetric Flow ◽  
Steady State Flow ◽  
Rotating Disc ◽  
Pipe Flows ◽  
Confined Flow ◽  
Vortex Tubes

The steady-state flow generated by a rotating bottom in a closed cylindrical container and the resulting vortex breakdown bubbles have been studied experimentally. By comparing the flow inside two different container geometries, one with a rigid cover and the other with a free surface, we examined the way in which the formation and structure of the breakdown bubbles depend on the surrounding flow. Details of the flow were visualized by means of the electrolytic precipitation technique, whereas a particle tracking technique was used to characterize the whole flow field. We found that the breakdown bubbles inside the container flow are in many ways similar to those in vortex tubes. First, the bubbles are open with in- and outflow and second, their structure is, like in the case of vortex breakdown in pipe flows, highly axisymmetric on the upstream side of the bubble and asymmetric on their rear side. However, and surprisingly, we observed bubbles which are open and stationary at the same time. This shows that open breakdown bubbles are not necessarily the result of periodic oscillations of the recirculation zone. The asymmetry of the flow structure is found to be related to the existence of asymmetric flow separations on the container wall. If the angular velocity of the rotating bottom is increased the evolution of the breakdown bubbles is different in both configurations: in the rigid cover case the breakdown bubbles disappear but persist in the free surface case.

Topology of vortex breakdown bubbles in a cylinder with a rotating bottom and a free surface

2001 ◽  
Vol 428 ◽  
pp. 133-148 ◽  
Author(s):  
MORTEN BRØNS ◽  
LARS K. VOIGT ◽  
JENS N. SØRENSEN
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Hopf Bifurcation ◽  
Numerical Methods ◽  
Aspect Ratio ◽  
Vortex Breakdown ◽  
Stability Limit ◽  
Similarities And Differences ◽  
The Stability ◽  
Two Parameters

The flow patterns in the steady, viscous flow in a cylinder with a rotating bottom and a free surface are investigated by a combination of topological and numerical methods. Assuming the flow is axisymmetric, we derive a list of possible bifurcations of streamline structures on varying two parameters, the Reynolds number and the aspect ratio of the cylinder. Using this theory we systematically perform numerical simulations to obtain the bifurcation diagram. The stability limit for steady flow is found and established as a Hopf bifurcation. We compare with the experiments by Spohn, Mory & Hopfinger (1993) and find both similarities and differences.

Vortex Breakdown in a Cylindrical Enclosure With a Rotating Lid

2005 ◽  
Author(s):  
Majid Molki ◽  
Ismail Hakan Olcay
Keyword(s):  
Reynolds Number ◽  
Stokes Equations ◽  
Vortex Breakdown ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Cylindrical Wall ◽  
Navier Stokes Equations ◽  
Number Comparison ◽  
Computational Research

A computational research was conducted to explore the nature of the flow in a cylindrical enclosure with a rotating lid. The aspect ratio (AR) of the cylinder used in this research was maintained at 1.5 and 2.5, and the Reynolds number (Re) ranged from 990 to 2200. The three-dimensional Navier-Stokes equations were solved by the finite volume technique. Mesh adaptation was used to improve the quality of the mesh and computations. The results for (AR, Re) = (1.5, 1290) and (2.5, 2200) indicated the existence of one and two vortex breakdown bubbles along the axis of the cylinder, respectively. The results also showed that fluid spirals downward along the cylindrical wall and moves slowly inward towards the axis. This spiral motion was intensified at higher values of the Reynolds number. Comparison with experimental data indicated an excellent agreement. The vortex breakdown and the flow patterns predicted by this work are consistent with those reported in the existing literature.

Axisymmetric rotating flow with free surface in a cylindrical tank

2018 ◽  
Vol 861 ◽  
pp. 796-814 ◽  
Author(s):  
Wen Yang ◽  
Ivan Delbende ◽  
Yann Fraigneau ◽  
Laurent Martin Witkowski
Keyword(s):  
Reynolds Number ◽  
Free Surface ◽  
Surface Deformation ◽  
Fluid Layer ◽  
Three Dimensional ◽  
Azimuthal Velocity ◽  
Meridional Plane ◽  
Cylindrical Tank ◽  
Aspect Ratios ◽  
Steady Solutions

The flow induced by a disk rotating at the bottom of a cylindrical tank is characterised using numerical techniques – computation of steady solutions or time-averaged two-dimensional and three-dimensional direct simulations – as well as laser-Doppler velocimetry measurements. Axisymmetric steady solutions reveal the structure of the toroidal flow located at the periphery of the central solid body rotation region. When viewed in a meridional plane, this flow cell is found to be bordered by four layers, two at the solid boundaries, one at the free surface and one located at the edge of the central region, which possesses a sinuous shape. The cell intensity and geometry are determined for several fluid-layer aspect ratios; the flow is shown to depend very weakly on Froude number (associated with surface deformation) or on Reynolds number if sufficiently large. The paper then focuses on the high Reynolds number regime for which the flow has become unsteady and three-dimensional while the surface is still almost flat. Direct numerical simulations show that the averaged flow shares many similarities with the above steady axisymmetric solutions. Experimental measurements corroborate most of the numerical results and also allow for the spatio-temporal characterisation of the fluctuations, in particular the azimuthal structure and frequency spectrum. Mean azimuthal velocity profiles obtained in this transitional regime are eventually compared to existing theoretical models.

Vortex breakdown mechanics of a laminar confined swirling flow with large expansion ratio using a non-uniform finite difference approximation

2021 ◽  
pp. 095440622110071
Author(s):  
F-J Granados-Ortiz ◽  
L Rodríguez-Tembleque ◽  
J Ortega-Casanova
Keyword(s):  
Reynolds Number ◽  
Finite Difference ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Critical Value ◽  
Expansion Ratio ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Large Expansion ◽  
Swirl Parameter

Abrupt expansions are a very frequent geometry in mechanical engineering systems, i.e. in combustion chambers, valves, heat exchangers or impinging cooling devices. However, despite the large number of devices that use this geometry, the expanded flow behaviour still needs further research to understand and predict the full system performance. This paper presents the application of the non-uniform finite difference approximation method developed in Sanmiguel et al. for the numerical characterisation of a confined swirling laminar jet discharging with a large expansion ratio. This investigation can be considered an extension of previous work by Revuelta, but now a swirling flow is generated by a rotating pipe upstream the expansion. The structures found when a fully-developed rotating Hagen-Poiseuille flow discharges into a much larger pipe section are summarised in a bifurcation diagram, whose coordinates are the Reynolds number of the jet ( Rej) and the swirl parameter ( L), for which the time-dependent, axisymmetric and incompressible Navier-Stokes equations are integrated numerically. For values of the jet Reynolds number below 200, there is a critical value of the swirl parameter above which stable vortex breakdown appears. For values of the Reynolds number above 200, three different behaviours are observed, and each performance appears for a critical value of the swirl parameter. When increasing the swirl parameter from zero, the flow becomes axisymmetrically unstable, showing an oscillatory behaviour. If further increasing the swirl intensity, the oscillatory flow coexists with a vortex breakdown bubble and, finally, a steady vortex breakdown is reached. The expansion ratio ε considered in all the simulations is 1[Formula: see text]. In previous literature, the exactness of the limiting critical Rej and L values that define these behaviours has been found to be influenced by the variability in the inlet profile conditions, which affects the expanded flow. This enhances the importance in the present investigation to accurately simulate the discharge pipe inlet profiles.

Modulated rotating waves in an enclosed swirling flow

2002 ◽  
Vol 465 ◽  
pp. 33-58 ◽  
Author(s):  
H. M. BLACKBURN ◽  
J. M. LOPEZ
Keyword(s):  
Reynolds Number ◽  
Aspect Ratio ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Three Dimensional ◽  
Low Frequency ◽  
Rotating Waves ◽  
Axisymmetric Solution ◽  
Axisymmetric Mode ◽  
Very Low Frequency

The loss of axisymmetry in a swirling flow that is generated inside an enclosed cylindrical container by the steady rotation of one endwall is examined numerically. The two dimensionless parameters that govern these flows are the cylinder aspect ratio and a Reynolds number associated with the rotation of the endwall. This study deals with a fixed aspect ratio, height/radius = 2.5. At low Reynolds numbers the basic flow is steady and axisymmetric; as the Reynolds number increases the basic state develops a double recirculation zone on the axis, so-called vortex breakdown bubbles. On further increase in the Reynolds number the flow becomes unsteady through a supercritical Hopf bifurcation but remains axisymmetric. After the onset of unsteadiness, another two unsteady axisymmetric solution branches appear with further increase in Reynolds number, each with its own temporal characteristic: one is periodic and the other is quasi-periodic with a very low frequency modulation. Solutions on these additional branches are unstable to three-dimensional perturbations, leading to nonlinear modulated rotating wave states, but with the flow still dominated by the corresponding underlying axisymmetric mode. A study of the flow behaviour on and bifurcations between these solution branches is presented, both for axisymmetric and for fully three-dimensional flows. The presence of modulated rotating waves alters the structure of the bifurcation diagram and gives rise to its own dynamics, such as a truncated cascade of period doublings of very-low-frequency modulated states.

Sign in / Sign up

Export Citation Format

Share Document