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1.
This paper presents the use of a parameter continuation method and a test function to solve the steady, axisymmetric incompressible
Navier–Stokes equations for spherical Couette flow in a thin gap between two concentric, differentially rotating spheres.
The study focuses principally on the prediction of multiple steady flow patterns and the construction of bifurcation diagrams.
Linear stability analysis is conducted to determine whether or not the computed steady flow solutions are stable. In the case
of a rotating inner sphere and a stationary outer sphere, a new unstable solution branch with two asymmetric vortex pairs
is identified near the point of a symmetry-breaking pitchfork bifurcation which occurs at a Reynolds number equal to 789.
This solution transforms smoothly into an unstable asymmetric 1-vortex solution as the Reynolds number increases. Another
new pair of unstable 2-vortex flow modes whose solution branches are unconnected to previously known branches is calculated
by the present two-parameter continuation method. In the case of two rotating spheres, the range of existence in the (Re
1
, Re
2
) plane of the one and two vortex states, the vortex sizes as a function of both Reynolds numbers are identified. Bifurcation
theory is used to discuss the origin of the calculated flow modes. Parameter continuation indicates that the stable states
are accompanied by certain unstable states.
Received 26 November 2001 and accepted 10 May 2002 Published online 30 October 2002
Communicated by M.Y. Hussaini 相似文献
2.
Oscillating flow near the end of a stack of parallel plates placed in a standing wave resonator is investigated using particle
image velocimetry (PIV). The Reynolds number, Re
d
, based on the plate thickness and the velocity amplitude at the entrance to the stack, is controlled by varying the acoustic
excitation (so-called drive ratio) and by using two configurations of the stacks. As the Reynolds number changes, a range
of distinct flow patterns is reported for the fluid being ejected from the stack. Symmetrical and asymmetrical vortex shedding
phenomena are shown and two distinct modes of generating “vortex streets” are identified. 相似文献
3.
Time-dependent velocity profiles V
z
(z, t) have been measured in a cylindrical Couette system for a range of Reynolds numbers corresponding to wavy vortex flow (WVF)
and modulated wavy vortex flow (MWV). The spatial distribution of the power spectrum was obtained and the behaviour of the
dynamic properties of WVF and MWV was investigated with respect to Reynolds number (Re) at four corners of cells (inside-outside and Inflow-Outflow). All modes of f
1, f
2 and B were found to be equally strong and broad at different corners for lower Re number. At large Re, however, f
2 remains broad only at the outside-Inflow corner, while B is strong at Outflow. It was also found that B disappears at the outside-Inflow corner for R
* > 18. These results suggest that the dynamic properties of WVF and MWV would have a spatial dependence within a cell structure
scale. 相似文献
4.
The interaction between the wake of a rotor blade and a downstream cylinder holds the key to the understanding and control of electronic cooling fan noise. In this paper, the aerodynamic characteristics of a circular cylinder are experimentally studied in the presence of an upstream NACA 4412 airfoil for the cylinder-diameter-based Reynolds numbers of Red=2,100–20,000, and the airfoil chord-length-based Reynolds numbers of Rec=14,700–140,000. Lift and drag fluctuations on the cylinder, and the longitudinal velocity fluctuations of the flow behind the cylinder were measured simultaneously using a load cell and two hot wires, respectively. Data analysis shows that unsteady forces on the cylinder increase significantly in the presence of the airfoil wake. The dependence of the forces on two parameters is investigated, that is, the lateral distance (T) between the airfoil and the cylinder, and the Reynolds number. The forces decline quickly as T increases. For Rec<60,000, the vortices shed from the upstream airfoil make a major contribution to the unsteady forces on the cylinder compared to the vortex shedding from the cylinder itself. For Rec>60,000, no vortices are generated from the airfoil, and the fluctuating forces on the cylinder are caused by its own vortex shedding. 相似文献
5.
We visualized the wake structure of circular disks falling vertically in quiescent water.The evolution of the wake was shown to be similar to the flow patterns behind a fixed disk.The Reynolds number,Re = Ud/ν,is in the range of 40 200.With the ascension of Reynolds numbers,a regular bifurcation occurred at the first critical Reynolds number Re c 1,leading to a transition from an axisymmetric wake structure to a plane symmetric one;A Hopf bifurcation took place at the second critical Reynolds number Re c 2,as the wake structure became unsteady.Plane symmetry of the wake structure was first lost as periodic vortex shedding appeared,but recovered at higher Reynolds number.The difference between the two critical Reynolds numbers was found to be shape-dependent,as we compared our results for thin discs with those for other falling bodies,such as spheres and cones.This observation could be understood in terms of the instability mechanism of the vortical structure. 相似文献
6.
The present paper deals with the ice-formation in a planar nozzle with various convergence angles. Experiments have been carried
out for different wall cooling parameters B in the range between 4 and 25 and for different flow rate Reynolds numbers in the range of 5,000 < Re
4h
< 50,000 for two different convergence angles of the nozzle. For all experiments with the larger convergence angle of the
nozzle (2.5°), only smooth ice-layers could be observed. However, for the nozzle with the smaller convergence angle (1.25°),
also wavy ice-layers could be detected. This interesting result is a justification for the hypothesis that the formation of
wavy ice-layers is caused by flow laminarisation (due to the rapid growth in ice-layer thickness with increasing axial position
from the inlet) and retransition to the fully turbulent state (after the acceleration falls below a certain critical value).
Thus, this paper proves for the first time, that wavy ice-layers are suppressed by superimposed strong flow acceleration. 相似文献
7.
Experimental data for a two-dimensional (2-D) turbulent boundary layer (TBL) flow and a three-dimensional (3-D) pressure-driven
TBL flow outside of a wing/body junction were obtained for an approach Reynolds number based on momentum thickness of Re
θ
=23,200. The wing shape had a 3:2 elliptical nose, NACA 0020 profiled tail, and was mounted on a flat wall. Some Reynolds
number effects are examined using fine spatial resolution (Δy
+=1.8) three-velocity-component laser-Doppler velocimeter measurements of mean velocities and Reynolds stresses at nine stations
for Re
θ
=23,200 and previously reported data for a much thinner boundary layer at Re
θ
=5,940 for the same wing shape. In the 3-D boundary layers, while the stress profiles vary considerably along the flow due
to deceleration, acceleration, and skewing, profiles of the parameter
correlate well and over available Reynolds numbers. The measured static pressure variations on the flat wall are similar
for the two Reynolds numbers, so the vorticity flux and the measured mean velocities scaled on wall variables agree closely
near the wall. The stresses vary similarly for both cases, but with higher values in the outer region of the higher Re
θ
case. The outer layer turbulence in the thicker high Reynolds number case behaves similarly to a rapid distortion of the
flow, since stream-wise vortical effects from the wall have not diffused completely through the boundary layer at all measurement
stations.
Received: 9 June 2000/Accepted: 26 January 2001 相似文献
8.
Adrian Renfer Manish K. Tiwari Thomas Brunschwiler Bruno Michel Dimos Poulikakos 《Experiments in fluids》2011,51(3):731-741
Hydrodynamics in microcavities with cylindrical micropin fin arrays simulating a single layer of a water-cooled electronic
chip stack is investigated experimentally. Both inline and staggered pin arrangements are investigated using pressure drop
and microparticle image velocimetry (μPIV) measurements. The pressure drop across the cavity shows a flow transition at pin
diameter–based Reynolds numbers (Re
d
) ~200. Instantaneous μPIV, performed using a pH-controlled high seeding density of tracer microspheres, helps visualize vortex
structure unreported till date in microscale geometries. The post-transition flow field shows vortex shedding and flow impingement
onto the pins explaining the pressure drop increase. The flow fluctuations start at the chip outlet and shift upstream with
increasing Re
d
. No fluctuations are observed for a cavity with pin height-to-diameter ratio h/d = 1 up to Re
d
~330; however, its pressure drop was higher than for a cavity with h/d = 2 due to pronounced influence of cavity walls. 相似文献
9.
Miguel R. Visbal Raymond E. Gordnier Marshall C. Galbraith 《Experiments in fluids》2009,46(5):903-922
The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis
of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and
man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar
separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging
airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected
to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil
section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated
shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately
breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged
sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle
of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation
bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re
c
= 104), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed
high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced
high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices
which convect downstream close to the airfoil. At the lowest value of Reynolds number (Re
c
= 104), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For Re
c
= 4 × 104, the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown
associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds
number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady
flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which
improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration.
For Re
c
= 4.85 × 104, it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural
response. 相似文献
10.
This paper reports results of DPIV measurements on a two-dimensional elliptic airfoil rotating about its own axis of symmetry
in a fluid at rest and in a parallel freestream. In the former case, we examined three rotating speeds (Re
c,Ω = 400, 1,000 and 2,000), and in the later case, four rotating speeds (Ro
c,Ω = 2.4, 1.2, 0.6 and 0.4), together with two freestream velocities (Re
c,u
= 200 and 1,000) and two starting configurations of the airfoil (i.e., chord parallel to (α
0 = 0°) or normal (α
0 = 90°) to the freestream). Results show that a rotating airfoil in a stationary fluid produces two distinct types of vortex
structures depending on the Reynolds number. The first type occurs at the lowest Reynolds number (Re
c,Ω = 400), where vortices shed from the two edges or tips of the airfoil dissipated quickly, resulting in the airfoil rotating
in a layer of diffused vorticity. The second type occurs at higher Reynolds numbers (i.e., Re
c,Ω = 1,000 and 2,000), where the corresponding vortices rotated together with the airfoil. Due to the vortex suction effect,
the torque characteristics are likely to be heavily damped for the first type because of the rapidly subsiding vortex shedding,
and more oscillatory for the second type due to persistent presence of tip vortices. In a parallel freestream, increasing
the tip-speed ratio (V/U) of the airfoil (i.e., decreasing the Rossby number, Ro
c,Ω) transformed the flow topology from periodic vortex shedding at Ro
c,Ω = 2.4 to the generation of a “hovering vortex” at Ro
c,Ω = 0.6 and 0.4. The presence of the hovering vortex, which has not been reported in literature before, is likely to enhance
the lift characteristics of the airfoil. Freestream Reynolds number is found to have minimal effect on the vortex formation
and shedding process, although it enhances shear layer instability and produces more small-scale flow structures that affect
the dynamics of the hovering vortex. Likewise, initial starting configuration of the airfoil, while affecting the flow transient
during the initial phase of rotation, has insignificant effect on the overall flow topology. Unfortunately, technical constraint
of our apparatus prevented us from carrying out complimentary force measurements; nevertheless, the results presented herein,
which are more extensive than those computed by Lugt and Ohring (1977), will provide useful benchmark data, from which more advanced numerical calculations can be carried out to ascertain the
corresponding force characteristics, particularly for those conditions with the presence of hovering vortex. 相似文献
11.
Zhuo Li Xue-Feng Yuan Simon J. Haward Jeffrey A. Odell Stephen Yeates 《Rheologica Acta》2011,50(3):277-290
The non-linear dynamics of a semi-dilute (c/c* = 15) polydisperse polyethylene oxide (PEO) solution in microfluidics are studied experimentally using benchmark contraction–expansion
flow geometries with three contraction–expansion ratios (4:1:4, 8:1:8 and 16:1:16) and two narrow channel lengths (L
c/D
h = 53 and 5.3, where L
c is the length of the narrow channel and D
h is its hydraulic diameter). Complex flows over a range of elasticity numbers (El), Weissenberg numbers (Wi) and Reynolds numbers (Re) are characterized using micro-particle image velocimetry (
\upmu\upmu-PIV) and pressure drop measurements. The evolution of vortex formation and dynamics has been visualized through a step-flow-rate
experiment. Various flow dynamics regimes have been quantified and are presented in a Wi–Re diagram. The experimental results reveal that the contraction ratio can result in qualitatively different vortex dynamics
of semi-dilute polymer solutions in microfluidics, whereas the length of the narrow channel merely affects the dynamics at
a quantitative level. A single elasticity number, if defined by the size of the narrow channel, is not sufficient to account
for the effects of contraction ratio on the non-linear vortex dynamics. 相似文献
12.
In this paper, a linear stability analysis is presented to trace the time evolution of an infinitesimal, two-dimensional disturbance
imposed on the base flow of an electrically conducting fluid in a channel filled with a saturated porous medium under the
influence of a transversely imposed magnetic field. An eigenvalue problem is obtained and solved numerically using the Chebyshev
collocation spectral method. The critical Reynolds number Re
c, the critical wave number α
c and the critical wave speed c
c are obtained for a wide range of the porous medium shape factor parameter S and Hartmann number H. It is found that an increase in the magnetic field intensity and a decrease in porous medium permeability have a stabilizing
effect on the fluid flow. 相似文献
13.
This paper presents results obtained by employing a modified Galerkin finite element method to analyse the steady state flow of a fluid contained between two concentric, rotating spheres. The spheres are assumed to be rigid and the cavity region between the spheres is filled with an incompressible, viscous, Newtonian fluid. The inner sphere is constrained to rotate about a vertical axis with a prescribed angular velocity, while the outer sphere is fixed. Results for the circumferential function Ω, streamfunction ψ, vorticity function ζ and inner boundary torque T1 are presented for Reynolds numbers Re ? 2000 and radius ratios 0.1 ? α ? 0.9. The method proved effective for obtaining results for a wide range of radius ratios (0.1 ? α ? 0.9) and Reynolds numbers (0 ? Re ? 2000). Previous investigators who employed the finite difference method experienced difficulties in obtaining results for cases with radius ratios α ? 0.2, except for small Reynolds numbers (Re ? 100). Results for Ω, Ψ, ζ and T1 obtained in this study for radius ratios 0.8 ≤ α ≤ 0.9 verified the development of Taylor vortices reported by other investigators. The research indicates that the method may be useful for analysing other non-linear fluid flow problems. 相似文献
14.
Scalar transport from a point source in flows over wavy walls 总被引:1,自引:0,他引:1
Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are
described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image
velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity.
The measurements are performed at three different Reynolds numbers of Re
b = 5,600, Re
b = 11,200 and Re
b = 22,400, respectively, based on the bulk velocity u
b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom
wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength
ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released
from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate
Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation
zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale
structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures
meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the
scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration.
As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between
the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the
large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to
the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared
to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the
spreading rate of the scalar plume is increased. 相似文献
15.
The change in flow characteristics downstream of a circular cylinder (inner cylinder) surrounded by an outer permeable cylinder was investigated in shallow water using particle image velocimetry technique. The diameter of the inner cylinder and the water height were kept constant during the experiments as d?=?50?mm and h w ?=?25?mm, respectively. The depth-averaged free-stream velocity was also kept constant as U?=?170?mm/s which corresponded to a Reynolds number of Red?=?8,500 based on the inner cylinder diameter. In order to examine the effect of diameter and porosity of the outer cylinder on flow characteristics of the inner cylinder, five different outer cylinder diameters (D?=?60, 70, 80, 90 and 100?mm) and four different porosities (???=?0.4, 0.5, 0.6 and 0.7) were used. It was shown that both porosity and outer cylinder diameter had a substantial effect on the flow characteristics downstream of the circular cylinder. Turbulent statistics clearly demonstrated that in comparison with the bare cylinder (natural case), turbulent kinetic energy and Reynolds stresses decreased remarkably when an outer cylinder was placed around the inner cylinder. Thereby, the interaction of shear layers of the inner cylinder has been successfully prevented by the presence of outer cylinder. It was suggested by referring to the results that the outer cylinder having 1.6????D/d????2.0 and 0.4????D/d????0.6 should be preferred to have a better flow control in the near wake since the peak magnitude of turbulent kinetic energy was considerably low in comparison with the natural case and it was nearly constant for these mentioned porosities ??, and outer cylinder to inner cylinder diameter ratios D/d. 相似文献
16.
O. D. Makinde 《国际流体数值方法杂志》2009,59(7):791-799
In this paper, the temporal development of small disturbances in a pressure‐driven fluid flow through a channel filled with a saturated porous medium is investigated. The Brinkman flow model is employed in order to obtain the basic flow velocity distribution. Under normal mode assumption, the linearized governing equations for disturbances yield a fourth‐order eigenvalue problem, which reduces to the well‐known Orr–Sommerfeld equation in some limiting cases solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials. The critical Reynolds number Rec, the critical wave number αc, and the critical wave speed cc are obtained for a wide range of the porous medium shape factor parameter S. It is found that a decrease in porous medium permeability has a stabilizing effect on the fluid flow. Copyright © 2008 John Wiley & Sons, Ltd. 相似文献
17.
Role of the shear layer instability in the near wake behavior of two side-by-side circular cylinders
Wakes, and their interaction behind two parallel cylinders lying in a plane perpendicular to the flow, have been investigated experimentally in the sub-critical Reynolds number regime. The experiments were performed in a water channel using laser Doppler velocimetry. The gap between the two cylinders was less than the cylinder diameter, a geometry referred to as strong interaction configuration. In this case the blockage is strong and a gap-jet appears between the cylinders. Two flow regimes of the near wake region have been identified: one below a critical Reynolds number Re
c ]1000;1700[, where the gap jet is stably deflected to one side and the double near-wake becomes asymmetric; the other, above Re
c, where the gap-jet deflection is unstable and a random flopping phenomenon takes place. When Re<Re
c, two different Strouhal numbers are identified, related to the Kármán vortex shedding behind each cylinder. When Re>Re
c, a third frequency appears in the near wake, related to the development of Kelvin-Helmholtz vortices in the separated shear layer of the cylinders [Prasad A, Williamson CHK (1997) J Fluid Mech 333:375]. The observed flopping behavior is attributed to the birth of these Kelvin-Helmholtz instabilities and their intermittent nature. Further downstream, beyond about five cylinder diameters, the random flopping flow phenomena disappear while a slightly asymmetric single wake persists. It is characterized by a Strouhal number St=0.13, a value that one would normally measure behind a single cylinder of twice its diameter. 相似文献
18.
This study investigates the flow past a confined circular cylinder built into a narrow rectangular duct with a Reynolds number
range of 1,500 ≤ Re
d
≤ 6,150, by employing the particle image velocimetry technique. In order to better explain the 3-D flow behaviour in the
juncture regions of the lower and upper plates and the cylinder, respectively, as well as the dynamics of the horseshoe vortex
system, both time-averaged and instantaneous flow data are presented for regions upstream and downstream of the cylinder.
The size, intensity and interaction of the vortex systems vary substantially with the Reynolds number. Although the narrow
rectangular duct with a single built-in cylinder is a geometrically symmetrical arrrangement, instantaneous flow data have
revealed that the flow structures in both the lower and upper plate–cylinder junction regions are not symmetrical with respect
to the centreline of the flow passage. The vortical flow structures obtained in side-view planes become dominant sometimes
in the lower juncture region and sometimes in the upper juncture region in unsteady mode. 相似文献
19.
20.
Spatio-temporal velocity fields of an axisymmetric sudden expansion were measured using an ultrasonic velocity profiler and analyzed to investigate the transitional scheme of the spatial structure using two-dimensional Fourier transform and proper orthogonal decomposition techniques. The variation of the zero-crossing point, the fluctuation energy directed upstream and the eigenmode spectrum all have the same transitional scheme as a function of the Reynolds number. The transitional scheme can be classified Re d<1,000 for the laminar regime, Re d=1,000–3,000 for the transitional regime and Re d>3,000 for the turbulent regime. Especially, in the transitional regime, we found large changes in the flow structure at Re d=1,500 and 2,000. The jump at Re d=2,000 is caused by the change in the flow condition upstream. The jump at Re d=1,500 clearly shows a change in the spatial structure of the flow. 相似文献