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1.
The axisymmetric vortex sheet model developed by Nitsche & Krasny (1994) has been extended to study the formation of vortex
rings (pairs) at the edge of circular (2D) tube and opening. Computations based on this model are in good agreement with the
experiments (Didden (1979) for circular tube and Auerbach (1987) for 2D tube and opening). Using this new model, evidences
are provided to show that the main failure of the similarity theory (the false prediction of axial trajectory of vortex ring)
is due to its ignorance of the self-induced ring velocity (mutual induction for vortex pair). We further reason why the similarity
theory succeeds in its prediction of radial movement of vortex ring. The effects of various parameters such as turning angle
α and piston speed U
p
(t) on the formation of vortex ring are investigated. Numerical result shows that turning angle α has no effect on circulation
shed τ. We also discuss Glezer (1988)'s summary on the influence of U
p
upon the shedding circulation, and finally give the variation of core distribution of vortex ring with α and U
p
(t).
The project is supported by National Natural Science Foundation of China and Doctoral Program of Institution of Higher Education 相似文献
2.
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
3.
The aerodynamic shape of a closed-box girder plays an important role in the wind-induced stabilization of long-span suspension bridges. The purpose of this study is to investigate the effects of the combination of five aspect ratios and a downward vertical central stabilizer (DVCS) on nonlinear flutter and aerostatic behaviors of a super long-span suspension bridge with closed-box girders. Through conducting a series of wind-tunnel tests and nonlinear finite element analysis, the results show that the nonlinear self-excited forces and the critical wind speed (Ucr) gradually increase as the increase of the aspect ratio (i.e. the width to depth ratios). Furthermore, the application of 20% deck depth DVCS could significantly increase the nonlinear self-excited forces and Ucr for small aspect ratios of 7.9 and 7.1. Particularly, the installation of the DVCS could change the flutter divergence patterns of the bridge from soft flutter to hard flutter, especially for a relatively small aspect ratio. In addition, the aerostatic force coefficients and torsional divergence critical wind speeds of the larger aspect ratio with DVCS are significantly larger than that without DVCS. A relatively small aspect ratio of the bridge has better aerostatic performance than that with a larger aspect ratio. 相似文献
4.
The boundary layer problem of a power-law fluid flow with fluid injection on a wedge whose surface is moving with a constant
velocity in the opposite direction to that of the uniform mainstream is analyzed. The free stream velocity, the injection
velocity at the surface, moving velocity of the wedge surface, the wedge angle and the power law index of non-Newtonian fluid
are assumed variables. The fourth order Runge–Kutta method modified by Gill is used to solve the non-dimensional boundary
layer equations for non-Newtonian flow field. Without fluid injection, for every angle of wedge β, a limiting value for velocity ratio λ
cr
(velocity of the wedge surface/velocity of the uniform flow) is found for each power-law index n. The value of λ
cr
increases with the increasing wedge angle β. The value of wedge angle also restricts the physical characteristics of the fluid to be used. The effects of the different
parameters on velocity profile and on skin friction are studied and the drag reduction is discussed. In case of C = 2.5 and velocity ratio λ = 0.2 for wedge angle β = 0.5 with the fluid with power law-index n = 0.5, 48.8% drag reduction is obtained. 相似文献
5.
In this paper, the dynamical behaviors of a perturbed hyperchaotic system is studied. The fast subsystem is examined using
local stability and bifurcations, including simple bifurcation, Hopf bifurcation, and fold bifurcation of limit cycle. The
results of these analysis are applied to the perturbed hyperchaotic system, where two types of periodic bursting, i.e., symmetric
subHopf/fold-cycle bursting and subHopf/fold-cycle bursting, can be observed. In particular, the symmetric subHopf/fold-cycle
bursting is new and has not been reported in previous work. With variation of the parameter, subHopf/fold-cycle bursting with
symmetric structure may bifurcate into two coexisted subHopf/fold-cycle bursting symmetric to each other. Moreover, 3-torus
and quasi-periodic bursting (2-torus) are presented. The relation among 3-torus, quasi-periodic bursting, and symmetric subHopf/fold-cycle
bursting is discussed, which suggests that 3-torus may develop to quasi-periodic bursting, while quasi-periodic bursting may
further evolve to symmetric subHopf/fold-cycle bursting. 相似文献
6.
The ‘plug’ flow emerging from a long rotating tube into a large stationary reservoir was used in the experimental investigation
of swirling jets with Reynolds numbers, Re = 600, 1,000 and 2,000, and swirl numbers, S = Ω R/ U, in the range 0–1.1, to cover flow regimes from the non-rotating jet to vortex breakdown. Here Ω is the nozzle rotation rate,
R is the radius of the nozzle exit, and U is the mean mass axial velocity. The jet was more turbulent and eddies shed faster at larger Re. However the flow criticality and shear layer morphology remained unchanged with Re. After the introduction of sufficient rotation, co-rotating and counter-winding helical waves replaced vortex rings to become
the dominant vortex structure. The winding direction of the vortex lines suggests that Kelvin–Helmholtz and generalized centrifugal
instability dominated the shear layer. A quantitative visualization study has been carried out for cases where the reservoir
was rotating independently with S
a
= Ω
a
R/ U = ±0.35, ±0.51 and ±0.70 at Re = 1,000 and 2000, where Ω
a
is the rotation rate of the reservoir. The criterion for breakdown was found to be mainly dependent on the absolute swirl
number of the jet, S. This critical swirl number was slightly different in stationary and counter-swirl surroundings but obviously smaller when
the reservoir co-rotated, i.e. S
c
= 0.88, 0.85 and 0.70, respectively. These results suggest that the flow criticality depends mainly on the velocity distributions
of the vortex core, while instabilities resulting from the swirl difference between the jet and its ambient seem to have only
a secondary effect. 相似文献
7.
The qualitative and quantitative behaviour of double row vortical structures in the near field region of a plane wall jet are studied experimentally by flow visualization and hot-wire measurements. Ensemble averaging is employed to investigate the interaction of vortices with the wall. In the flow visualization study, a double row vortical structure, which includes a primary vortex formed in the outer layer region and a secondary vortex induced in the inner layer region, and the vortex lift-off phenomenon are clearly observed during the development of the wall jet. The phase averaged results of the velocity measurements show that the instability leading to induction of the secondary vortex is stimulated by the primary vortex. In the early stage of wall jet transition, the inflection point of the inner layer velocity profile moves transversely from the wall surface to the inner layer region due to passage of the well-organized primary vortex in the outer layer region. The inner layer instability is thus induced and the instability wave rolls up to form the secondary vortex. Furthermore, the secondary vortex will convect downstream faster than the primary vortex, and this difference in convective speed will lead to the subsequent phenomenon of vortex lift-off from the wall surface.List of symbols A1, A2, . . .
primary vortex
-
B1, B2, . . .
secondary vortex
-
fe
forcing frequency
-
f
fundamental frequency
-
H
nozzle exit height
-
Re
Reynolds number, U
j
H/
-
T
period of the referred signal (=13.5 ms)
-
t, t
time scale
-
U
streamwise mean velocity
-
U
c
convection speed
-
U
j
jet exit velocity
-
U
m
local maximum velocity
-
ut'
streamwise turbulence intensity
-
uv
turbulent shear stress
-
V
transverse mean velocity
-
v
transverse turbulence intensity
-
X
streamwise coordinate
-
Y
transverse coordinate
-
X
Ai
streamwise location of vortex Ai
-
X
Bi
streamwise location of vortex Bi
-
X
ave
averaged streamwise location of the vortex
-
Y
m
wall jet inner layer width, the distance from wall to where U= U
m
-
Y
1/2
wall jet half-width, the distance from wall to where U=1/2 U
m
in outer layer region
- t
time interval (=0.267 s)
-
phase averaged value 相似文献
8.
In this paper we consider a five-parameter family of planar vector fields where μ = ( μ
1, μ
2, μ
3, μ
4, μ
5), which is a small parameter vector, and c(0) ≠ 0. The family X
μ
represents the generic unfolding of a class of nilpotent cusp of codimension five. We discuss the local bifurcations of X
μ, which exhibits numerous kinds of bifurcation phenomena including Bogdanov-Takens bifurcations of codimension four in Li
and Rousseau (J. Differ. Eq. 79, 132–167, 1989) and Dumortier and Fiddelaers (In: Global analysis of dynamical systems, 2001), and Bogdanov-Takens bifurcations
of codimension three in Dumortier et al. (Ergodic Theory Dynam. Syst. 7, 375–413, 1987) and Dumortier et al. (Bifurcations of planar vector fields. Nilpotent singularities and Abelian integrals,
1991). After making some rescalings, we obtain the truncated systems of X
μ
. For a truncated system, all possible bifurcation sets and related phase portraits are obtained. When the truncated system
is a Hamiltonian system, the bifurcation diagram and the related phase portraits are given too. Hopf bifurcations are studied
for another truncated system. And it shows that the system has the Hopf bifurcations of codimension at most three, and at
most three limit cycles occur in the small neighborhood of the Hopf singularity.
Dedicated to Professor Zhifen Zhang in the occasion of her 80th birthday 相似文献
9.
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
10.
Wakes behind disk-shaped axisymmetric bodies of varying solidity are studied using flow visualization and two-dimensional Fourier decomposition of velocity measurements. Evidence of a reverse flow region behind some of the bodies is observed to coincide with the presence of large-scale structures in the near and far wake. Fourier analysis shows that these large-scale structures are predominately helical ( m= ±1) and occur at a characteristic frequency which corresponds to their wavelength as observed from flow visualization. Our measured value for this characteristic frequency agrees with vortex shedding frequencies observed for these types of wakes. 相似文献
11.
Three-dimensional vorticity in the wake of an inclined stationary circular cylinder was measured simultaneously using a multi-hot
wire vorticity probe over a streamwise range of x/ d = 10–40. The study aimed to examine the dependence of the wake characteristics on cylinder inclination angle α (=0°–45°).
The validity of the independence principle (IP) for vortex shedding was also examined. It was found that the spanwise mean
velocity which represents the three-dimensionality of the wake flow, increases monotonically with α. The root-mean-square (rms) values
of the streamwise ( u) and spanwise ( w) velocities and the three vorticity components decrease significantly with the increase of α, whereas the transverse velocity
( v) does not follow the same trend. The vortex shedding frequency decreases with the increase of α. The Strouhal number ( St
N), obtained by using the velocity component normal to the cylinder axis, remains approximately a constant within the experimental
uncertainty (±8%) when α is smaller than about 40°. The autocorrelation coefficients ρ
u
and ρ
v
of the u and v velocity signals show apparent periodicity for all inclination angles. With increasing α, ρ
u
and ρ
v
decrease and approach zero quickly. In contrast, the autocorrelation coefficient ρ
w
of w increases with α in the near wake, implying an enhanced three-dimensionality of the wake. 相似文献
12.
The experimental simulation of solitary vortex rings in a stratified fluid performed using high-frequency echo-sounding and optical visualization methods shows that on the range from turbulent to laminar regimes the vortex is a volume inhomogeneity with a sound scattering cross-section m
vU
5, where U is the translational velocity. The absolute value of m
v is determined by the microscale component of the vortex microstructure, which is commensurable with the sounding sonic wave length. 相似文献
13.
An experimental study of a turbulent backward-facing step (BFS) was undertaken to investigate the vortex structures behind the step. Attention was given to the secondary vortex because of its poor representation in literature and its potential for evaluating computational turbulence models. A 2D, cross-correlation particle image velocimeter (PIV) was developed, which allowed measurement of the highly turbulent, reversing step flow. Global, high resolution data was obtained for the cross-sectional plane of the BFS and for several other planes parallel to it. Measurement planes across the step revealed the 3D nature of the secondary vortex and an unexpected flow structure was identified. The secondary vortex was found to traverse across the flow, from the cross-sectional plane towards the step edge–sidewall corner.List of symbols AR aspect ratio - d particle displacement (m) - d error in particle displacement (m) - D expansion channel height (mm) - D0 inlet channel height (mm) - ER expansion ratio - H step height (mm) - N number of samples - ReH Reynolds number based on step height - Sp( x, y) centre coordinates of primary vortex (mm) - Ss( x, y) centre coordinates of secondary vortex (mm) - t laser pulse separation time (s) - t error in pulse separation time (s) - U horizontal velocity (m/s) -
̄ mean horizontal velocity (m/s) -
horizontal velocity variance (m 2/s 2) -
inlet centreline mean velocity (m/s) -
inlet centreline velocity variance (m 2/s 2) - V vertical velocity (m/s) - VM velocity magnitude (m/s) - VM error in velocity magnitude (m/s) - W step width (mm) - x length dimension (mm) - y height dimension (mm) - z width dimension (mm) - Xr shear layer reattachment point (mm) - Xr reattachment point for infinite step width (mm) - Xs secondary vortex separation point (mm) - Ys secondary vortex reattachment point (mm) - U velocity error (m/s) -
mean velocity error estimate (m/s) -
velocity variance error estimate (m 2/s 2) - bot bottom inlet boundary layer thickness (mm) - top top inlet boundary layer thickness (mm) - 99 0.99
boundary layer thickness (mm) 相似文献
14.
Vortex rings were generated by driving pistons within circular cylinders of inner diameter D = 72.8 mm at a constant velocity U
0 over a distance L = D. The Reynolds number, U
0
L/(2ν), was 2500. The flow downstream of circular and inclined exits was examined using volumetric 3-component velocimetry
(V3V). The circular exit yields a standard primary vortex ring that propagates downstream at a constant velocity and a lingering
trailing ring of opposite sign associated with the stopping of the piston. By contrast, the inclined nozzle yields a much
more complicated structure. The data suggest that a tilted primary vortex ring interacts with two trailing rings; one associated
with the stopping of the piston, and the other associated with the asymmetry of the cylinder exit. The two trailing ring structures,
which initially have circulation of opposite sign, intertwine and are distorted and drawn through the center of the primary
ring. This behavior was observed for two inclination angles. Increased inclination was associated with stronger interactions
between the primary and trailing vortices as well as earlier breakdown. 相似文献
15.
Mixing by secondary flow is studied by particle image velocimetry (PIV) in a developing laminar pulsating flow through a circular curved pipe. The pipe curvature ratio is η = r
0/ r
c
= 0.09, and the curvature angle is 90°. Different secondary flow patterns are formed during an oscillation period due to
competition among the centrifugal, inertial, and viscous forces. These different secondary-flow structures lead to different
transverse-mixing schemes in the flow. Here, transverse mixing enhancement is investigated by imposing different pulsating
conditions (Dean number, velocity ratio, and frequency parameter); favorable pulsating conditions for mixing are introduced.
To obviate light-refraction effects during PIV measurements, a T-shaped structure is installed downstream of the curved pipe.
Experiments are carried out for the Reynolds numbers range 420 ≤ Re st ≤ 1,000 (Dean numbers 126.6 ≤ Dn ≤ 301.5) corresponding to non-oscillating flow, velocity component ratios 1 ≤ (β = U
max,osc/ U
m,st) ≤ 4 (the ratio of velocity amplitude of oscillations to the mean velocity without oscillations), and frequency parameters
8.37 < (α = r
0(ω/ν) 0.5) < 24.5, where α 2 is the ratio of viscous diffusion time over the pipe radius to the characteristic oscillation time. The variations in cross-sectional
average values of absolute axial vorticity (|ζ|) and transverse strain rate (|ε|) are analyzed in order to quantify mixing.
The effects of each parameter (Re st, β, and α) on transverse mixing are discussed by comparing the dimensionless vorticities (|ζ
P
|/|ζ
S
|) and dimensionless transverse strain rates (|ε
P
|/|ε
S
|) during a complete oscillation period. 相似文献
16.
This paper investigates the feasibility of using holographic interferometry in wind tunnel flows for measuring velocity fields
rather than density or temperature fields. First results were obtained in a vortex street behind a cylinder at Re=190( U
∞=0.7 m/s). The light scattered from an illuminated fluid plane was holographically recorded twice with the same reference
beam. Using a time interval of 10 μs, local fluid displacements smaller than a few microns were recorded. The holographic
plate was placed in front and as close as possible to the fluid plane. The interferograms obtained from the hologram reconstruction
give information about one velocity component, at 45° with the illuminated plane. The alignment of the cylinder axis with
this 45° direction provided definite confirmation about the vortex street having a non-negligible axial velocity. The constant
velocity fluid region has proven to be very useful for quantifying the velocity information contained in the interferogram.
Received: 8 November 1999/Accepted: 14 March 2000 相似文献
17.
The convection velocity of vortices in the wake of a circular cylinder has been obtained by two different approaches. The first, implemented in a wind tunnel using an array of X-wires, consists in determining the velocity at the location of maximum spanwise vorticity. Four variants of the second method, which estimates the transit time of vortices tagged by heat or dye, were used in wind and water tunnels over a relatively large Reynolds number range. Results from the two methods are in good agreement with each other. Along the most probable vortex trajectory, there is only a small streamwise increase in the convection velocity for laminar conditions and a more substantial variation when the wake is turbulent. The convection velocity is generally greater than the local mean velocity and does not depend significantly on the Reynolds number.Nomenclature
d
diameter of circular cylinder
-
f
frequency in spectrum analysis
-
f
v
average vortex frequency
-
r
v
vortex radius
-
Re
Reynolds number U
o
d/v
-
t
time
-
Th
, Th
, Th
r
thresholds for
zp, , and r
v respectively
-
U
o
free stream velocity
-
U
1
maximum value of ( U
o – U)
-
U
c
convection velocity of the vortex, as obtained either by Eq. (1) or Eq. (2)
-
U
co
convection velocity used in Eq. (3) U
cd, U
cu average convection velocities of downstream and up-stream regions respectively of the vortex
-
U
cv
the value of U
c at y = 0.5
-
u, v
the velocity fluctuations in x and y directions respectively
-
U, V
mean velocity components in x and y directions respectively
-
U,V
U = U + u, V = V + v
-
x, y, z
co-ordinate axes, defined in Fig. 1
Greek Symbols
circulation
-
mean velocity half-width
-
x
spacing between two cold wires or grid spacing
-
1,
2
temperature signals from upstream and downstream cold wires respectively
-
v
kinematic viscosity
-
c
transit time for a vortex to travel a distance x
-
phase in the cross-spectrum of
1 and
2
-
z
instantaneous spanwise vorticity
-
zc
cut-off vorticity used in determining the vortex size
-
zp
peak value of
z
- a
denotes conditional average, defined in Eq. (12)
- a
prime denoting rms value 相似文献
18.
The near-field flow structure of a tip vortex behind a sweptback and tapered NACA 0015 wing was investigated and compared
with a rectangular wing at the same lift force and Re=1.81×10 5. The tangential velocity decreased with the downstream distance while increased with the airfoil incidence. The core radius
was about 3% of the root chord c
r, regardless of the downstream distance and α for α<8°. The core axial velocity was always wake-like. The core Γ c and total Γ o circulation of the tip vortex remained nearly constant up to x/ c
r=3.5 and had a Γ c/Γ o ratio of 0.63. The total circulation of the tip vortex accounted for only about 40% of the bound root circulation Γ b. For a rectangular wing, the axial flow exhibited islands of wake- and jet-like velocity distributions with Γ c/Γ o=0.75 and Γ o/Γ b=0.70. For the sweptback and tapered wing tested, the inner region of the tip vortex flow exhibited a self-similar behavior
for x/ c
r≥1.0. The lift force computed from the spanwise circulation distributions agreed well with the force-balance data. A large
difference in the lift-induced drag was, however, observed between the wake integral method and the inviscid lifting-line
theory. 相似文献
19.
The evolution of wake structures and variation of the forces on a flat plate in harmonic oscillatory and in-line combined
flows are obtained numerically by improved discrete vortex method. For the oscillatory oncoming flow cases, wyen Kc number varies from 2 to 40, the vortex pattern changes from a “harmonic wave” shaped (in a range of small Kc number) to a slight inclined “harmonic wave” shaped (in a range of moderate Kc numbers), then to inclined vortex clusters with an angle of 50° to the oncoming flow direction (at Kc=20), at last, as Kc number becomes large, the vortex pattern is like a normal Karman vortex street. The well predicted drag and inertia force
coefficients are obtained, which are more close to the results of Keulegan & Carpenter's experiment as compared with previous
vortex simulation by other authors. The existence of minimum point of inertia force coefficient C
m
near Kc=20 is also well predicted and this phenomenon can be interpreted according to the vortex structure. For steady-oscillatory
in-line combined flow cases, the vortex modes behave like a vortex street, exhibit a “longitudinal wave” structure, and a
vortex cluster shape corresponding to the ratios of U
m
to U
0 which are of O (10 −1) O(1) and O(10), respectively. The effect on the prediction of forces on the flat plate from the disturbance component in a combined
flow has been demonstrated qualitatively. In addition to this, the lock in phenomenon of vortex shedding has been checked.
The project supported by National Natural Science Foundation of China & LNM, Institute of Mechanics, CAS 相似文献
20.
An asymptotic theory is presented for the determination of velocity and linear stability of a steady symmetric bubble in a Hele-Shaw cell for small surface tension. In the first part, the bubble velocity U relative to the fluid velocity at infinity is determined for small surface tension T by determining a transcendentally small correction to the asymptotic series solution. It is found that for any relative bubble velocity U in the interval ( U
c
, 2), solutions exist at a countably infinite set of values of T (which has zero as its limit point) corresponding to the different branches of bubble solutions. The value of U
c
decreases monotonically from 2 to 1 as the bubble area increases from 0 to . However, for a bubble of an arbitrarily given size, as T 0, a solution exists on any given branch with the relative bubble velocity U satisfying the relation 2– U= cT
2/3, where c depends on the branch but is independent of the bubble area. The analytical evidence further suggests that there are no solutions for U>2. These results are in agreement with earlier analytical results for a finger.In Part II an analytic theory is presented for the determination of the linear stability of the bubble in the limit of zero surface tension. Only the solution branch corresponding to the largest possible U for given surface tension is found to be stable, while all the others are unstable, in accordance with earlier numerical results.This research has been supported by National Science Foundation Grant DMS-8713246. Partial support was also provided by the NASA Langley Research Center (NAS1-18605) while the author was in residence at the Institute of Computer Applications in Science and Engineering. 相似文献
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