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1.
Numerical simulations are used to study laminar vortex ring formation under the influence of background flow. The numerical
setup includes a round-headed axisymmetric body with an opening at the posterior end from which a column of fluid is pushed
out by a piston. The piston motion is explicitly included into the simulations by using a deforming mesh. A well-developed
wake flow behind the body together with a finite-thickness boundary layer outside the opening is taken as the initial flow
condition. As the jet is initiated, different vortex evolution behavior is observed depending on the combination of background
flow velocity to mean piston velocity () ratio and piston stroke to opening diameter () ratio. For low background flow () with a short jet (), a leading vortex ring pinches off from the generating jet, with an increased formation number. For intermediate background
flow () with a short jet (), a leading vortex ring also pinches off but with a reduced formation number. For intermediate background flow () with a long jet (), no vortex ring pinch-off is observed. For high background flow () with both a short () and a long () jet, the leading vortex structure is highly deformed with no single central axis of fluid rotation (when viewed in cross-section)
as would be expected for a roll-up vortex ring. For , the vortex structure becomes isolated as the trailing jet is destroyed by the opposite-signed vorticity of the background
flow. For , the vortex structure never pinches off from the trailing jet. The underlying mechanism is the interaction between the vorticity
layer of the jet and the opposite-signed vorticity layer from the initial wake. This interaction depends on both and . A comparison is also made between the thrust generated by long, continuous jets and jet events constructed from a periodic
series of short pulses having the same total mass flux. Force calculations suggest that long, continuous jets maximize thrust
generation for a given amount of energy expended in creating the jet flow. The implications of the numerical results are discussed
as they pertain to adult squid propulsion, which have been observed to generate long jets without a prominent leading vortex
ring.
PACS 02.60.Cb, 47.32.cf, 47.32.cb, 47.20.Ft, 47.63.M- 相似文献
2.
The unsteady dynamics of the Stokes flows, where
, is shown to verify the vector potential–vorticity (
) correlation
, where the field
is the pressure-gradient vector potential defined by
. This correlation is analyzed for the Stokes eigenmodes,
, subjected to no-slip boundary conditions on any two-dimensional (2D) closed contour or three-dimensional (3D) surface. It is established that an asymptotic linear relationship appears, verified in the core part of the domain, between the vector potential and vorticity,
, where
is a constant offset field, possibly zero. 相似文献
3.
Experiments were conducted to investigate the vortex formation process in gravity-driven starting jets at three Reynolds numbers
( 3,528 and 4,716, where D is the nozzle diameter, the average discharging velocity and ν the kinematic viscosity). Planar laser induced fluorescence (PLIF) was used to visualize
the flow while particle image velocimetry (PIV) was used to quantify the 2D velocity and vorticity fields. Vortex leapfrogging
was found to appear at Re = 2,358, while pinch-off for the leading vortex was observed in the other two cases. Conditions for the vortex pinch-off
appeared to be different from those found in the piston-driven starting jets. Although the leading vortex attained the maximum
circulation and energy level very quickly after the jet was initiated, its detachment from the main stem may not be achieved
necessarily. Attempt had been made to elaborate the different flow characteristics for respective cases from the related distribution
of circulation and energy level via the measured velocity field by PIV. 相似文献
4.
The gas entrainment in a hollow cone spray submitted to variable density is studied experimentally in order to better understand
the effect on mixture formation. Particle image velocimetry on fluorescent tracers, associated with a specific processing
of the instantaneous velocity fields have been applied to obtain measurement in the close vicinity of the spray edge. In the
“quasi-steady” region of the spray, important effect of the ambient density on the mass flow rate of entrained gas
have been pointed out. The axial evolution of is in good agreement with an integral model that takes the momentum exchange between phases into account. 相似文献
5.
Momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel 总被引:2,自引:0,他引:2
Unsteady momentum and heat transfer from an asymmetrically confined circular cylinder in a plane channel is numerically investigated using FLUENT for the ranges of Reynolds numbers as 10≤Re≤500, of the blockage ratio as 0.1≤β≤0.4, and of the gap ratio as 0.125≤γ≤1 for a constant value of the Prandtl number of 0.744. The transition of the flow from steady to unsteady (characterized by critical Re) is determined as a function of γ and β. The effect of γ on the mean drag
and lift
coefficients, Strouhal number (St), and Nusselt number (Nu
w
) is studied. Critical Re was found to increase with decreasing γ for all values of β.
and St were found to increase with decreasing values of γ for fixed β and Re. The effect of decrease in γ on
was found to be negligible for all blockage ratios investigated. 相似文献
6.
Particle image velocimetry (PIV) was employed to measure the two components of the turbulent velocity field in the initial
stage of an open-channel flow in a streamwise-wall-normal plane, and the free-surface level was discriminated from the PIV
image. The details of this technique was described and demonstrated by showing the instantaneous velocity field together with
the free-surface shape, statistics of velocity field, and the wave-turbulence interaction terms. Preliminary experimental
results showed that the turbulence intensity of the streamwise velocity fluctuations (u′) decreased, whereas that of the wall-normal velocity (v′) increased near the bottom wall with downstream distance in the initial stage of an open-channel flow; (g is the fluctuation of free-surface level) had a negative value, had a positive value near the free surface, and the surface-wave-affected depth deepened with downstream distance. 相似文献
7.
H. M. Duwairi 《Transport in Porous Media》2009,79(2):285-300
A rigid frame, cylindrical capillary theory of sound propagation in porous media that includes the nonlinear effects of the
Forchheimer type is laid out by using variational solutions. It is shown that the five main parameters governing the propagation
of sound waves in a fluid contained in rigid cylindrical tubes filled with a saturated porous media are: the shear wave number,
, the reduced frequency parameter, , the porosity, ε, Darcy number, , and Forchheimer number, . The manner in which the flow influences the attenuation and the phase velocities of the forward and backward propagating
non-isentropic acoustic waves is deduced. It is found that the inclusion of the solid matrix increases wave’s attenuations
and phase velocities for both forward and backward sound waves, while increasing the porosity and the reduced frequency number
decreased attenuation and increased phase velocities. The effect of the steady flow is found to decrease the attenuation and
phase velocities for forward sound waves, and enhance them for the backward sound waves.
This work is done during a sabbatical leave year granted form the University of Jordan to Dr. Hamzeh Duwairi for the academic
year 2007/2008 at the German Jordanian University. 相似文献
8.
A Jordan Curve Spanned by a Complete Minimal Surface 总被引:1,自引:0,他引:1
Francisco Martín Nikolai Nadirashvili 《Archive for Rational Mechanics and Analysis》2007,184(2):285-301
In this paper we construct complete (conformal) minimal immersions
which admit continuous extensions to the closed disk,
. Moreover,
is a homeomorphism and
is a (non-rectifiable) Jordan curve with Hausdorff dimension 1.
It turns out that the set of Jordan curves
constructed by the above procedure is dense in the space of Jordan curves of
with the Hausdorff metric. 相似文献
9.
The work presented is a wind tunnel study of the near wake region behind a hemisphere immersed in three different turbulent boundary layers. In particular, the effect of different boundary layer profiles on the generation and distribution of near wake vorticity and on the mean recirculation region is examined. Visualization of the flow around a hemisphere has been undertaken, using models in a water channel, in order to obtain qualitative information concerning the wake structure.List of symbols
C
p
pressure coefficient,
-
D
diameter of hemisphere
-
n
vortex shedding frequency
-
p
pressure on model surface
-
p
0
static pressure
-
Re
Reynolds number,
-
St
Strouhal number,
-
U, V, W
local mean velocity components
-
mean freestream velocity inX direction
-
U
*
shear velocity,
-
u, v, w
velocity fluctuations inX, Y andZ directions
-
X
Cartesian coordinate in longitudinal direction
-
Y
Cartesian coordinate in lateral direction
-
Z
Cartesian coordinate in direction perpendicular to the wall
- it*
boundary layer displacement thickness,
-
diameter of model surface roughness
-
elevation angleI
-
O
boundary layer momentum thickness,
-
w
wall shearing stress
-
dynamic viscosity of fluid
-
density of fluid
-
streamfunction
- x
longitudinal component of vorticity,
- y
lateral component of vorticity,
-
z
vertical component of vorticity,
This paper was presented at the Ninth symposium on turbulence, University of Missouri-Rolla, October 1–3, 1984 相似文献
10.
We study the limit of the hyperbolic–parabolic approximation
The function is defined in such a way as to guarantee that the initial boundary value problem is well posed even if is not invertible. The data and are constant. When is invertible, the previous problem takes the simpler form
Again, the data and are constant. The conservative case is included in the previous formulations. Convergence of the , smallness of the total variation and other technical hypotheses are assumed, and a complete characterization of the limit
is provided. The most interesting points are the following: First, the boundary characteristic case is considered, that is,
one eigenvalue of can be 0. Second, as pointed out before, we take into account the possibility that is not invertible. To deal with this case, we take as hypotheses conditions that were introduced by Kawashima and Shizuta
relying on physically meaningful examples. We also introduce a new condition of block linear degeneracy. We prove that, if
this condition is not satisfied, then pathological behaviors may occur. 相似文献
11.
We study the global attractor of the non-autonomous 2D Navier–Stokes (N.–S.) system with singularly oscillating external force of the form . If the functions g
0(x, t) and g
1 (z, t) are translation bounded in the corresponding spaces, then it is known that the global attractor is bounded in the space H, however, its norm may be unbounded as since the magnitude of the external force is growing. Assuming that the function g
1 (z, t) has a divergence representation of the form where the functions (see Section 3), we prove that the global attractors of the N.–S. equations are uniformly bounded with respect to for all . We also consider the “limiting” 2D N.–S. system with external force g
0(x, t). We have found an estimate for the deviation of a solution of the original N.–S. system from a solution u
0(x, t) of the “limiting” N.–S. system with the same initial data. If the function g
1 (z, t) admits the divergence representation, the functions g
0(x, t) and g
1 (z, t) are translation compact in the corresponding spaces, and , then we prove that the global attractors converges to the global attractor of the “limiting” system as in the norm of H. In the last section, we present an estimate for the Hausdorff deviation of from of the form: in the case, when the global attractor is exponential (the Grashof number of the “limiting” 2D N.–S. system is small).
相似文献
12.
Michael Winkler 《Journal of Dynamics and Differential Equations》2008,20(1):87-113
The paper deals with positive solutions of the initial-boundary value problem for with zero Dirichlet data in a smoothly bounded domain . Here is positive on (0,∞) with f(0) = 0, and λ1 is exactly the first Dirichlet eigenvalue of −Δ in Ω. In this setting, (*) may possess oscillating solutions in presence
of a sufficiently strong degeneracy. More precisely, writing , it is shown that if then there exist global classical solutions of (*) satisfying and . Under the additional structural assumption , s > 0, this result can be sharpened: If then (*) has a global solution with its ω-limit set being the ordered arc that consists of all nonnegative multiples of the
principal Laplacian eigenfunction. On the other hand, under the above additional assumption the opposite condition ensures that all solutions of (*) will stabilize to a single equilibrium.
相似文献
13.
Let be the set of m × m matrices A(λ) depending analytically on a parameter λ in a closed interval . Consider one-parameter families of quasi-periodic linear differential equations: , where is analytic and sufficiently small. We prove that there is an open and dense set in , such that for each the equation can be reduced to an equation with constant coefficients by a quasi-periodic linear transformation for almost
all in Lebesgue measure sense provided that g is sufficiently small. The result gives an affirmative answer to a conjecture of Eliasson (In: Proceeding of Symposia in
Pure Mathematics).
Dedicated to Professor Zhifen Zhang on the occasion of her 80th birthday 相似文献
14.
The response of a turbulent boundary layer to a short roughness strip is investigated using laser Doppler velocimetry (LDV) and laser induced fluorescence (LIF). Skin friction coefficients are inferred from accurate near-wall measurements. There is an undershoot in
, where
is the undisturbed smooth wall skin friction coefficient, immediately after the strip. Downstream of the strip,
overshoots before relaxing back to unity in an oscillatory manner. The roughness strip has a major effect on the turbulent stresses
; these quantities increase, relative to the undisturbed smooth wall, in the region between the two internal layers originating at the upstream and downstream edges of the strip. The increase in the ratio
suggests a decrease in near-wall anisotropy. From the flow visualizations, it is inferred that streamwise vortical structures are weakened immediately downstream of the strip. Consistently, streamwise length scales are also reduced; direct support for this is provided by measured two-point velocity correlations. 相似文献
15.
Valery M. Levin Juan M. Alvarez-Tostado 《Archive of Applied Mechanics (Ingenieur Archiv)》2006,76(3-4):199-214
An arbitrary anisotropic micro-inhomogeneous (composite) poroelastic medium is considered, containing a random set of ellipsoidal inhomogeneities with different poroelastic characteristics. The properties of these constituents are described by the linear porothermoelastic theory of Biot. One of the self-consistent schemes named effective field method is used to develop explicit expressions for the effective porothermoelastic constants (tensor of the frame elastic compliances , tensor of the generalized Skempton’s coefficients , tensor of thermal expansion coefficients , Biot’s constants , and the heat capacity at constant stress for the static porothermoelastic theory. It is shown that for two components composite porous material these expressions are interconnected and can be expressed only via the components of tensor . Some special cases are considered for the isotropic main material (matrix). 相似文献
16.
A system is described which allows the recreation of the three-dimensional motion and deformation of a single hydrogen bubble time-line in time and space. By digitally interfacing dualview video sequences of a bubble time-line with a computer-aided display system, the Lagrangian motion of the bubble-line can be displayed in any viewing perspective desired. The u and v velocity history of the bubble-line can be rapidly established and displayed for any spanwise location on the recreated pattern. The application of the system to the study of turbulent boundary layer structure in the near-wall region is demonstrated.List of Symbols
Reynolds number based on momentum thickness u
/v
- t+
nondimensional time
-
u
shear velocity
-
u
local streamwise velocity, x-direction
-
u
+
nondimensional streamwise velocity
-
v
local normal velocity, -direction
-
x
+
nondimensional coordinate in streamwise direction
- +
nondimensional coordinate normal to wall
-
+
wire
wire nondimensional location of hydrogen bubble-wire normal to wall
-
z
+
nondimensional spanwise coordinate
-
momentum thickness
-
v
kinematic viscosity
-
W
wall shear stress 相似文献
17.
Carlos Rocha 《Journal of Dynamics and Differential Equations》2007,19(3):571-591
We consider the set of 2π-periodic solutions of the ordinary differential equation u′′ + g(u) = 0 for a nonlinearity , satisfying a dissipative condition of the form for , and under the generic assumption that the potential G, given by , is a Morse function. Under these assumptions, we characterize the period maps realizable by planar Hamiltonian systems of
the form . Considering the Morse type of G, the set of periodic orbits in the phase space is decomposed into disks and annular regions. Then, the realizable period maps are described in terms of sets of sequences
of positive integers corresponding to the lap numbers of the 2π-periodic solutions. This leads to a characterization of the
classes of Morse–Smale attractors that are realizable by dissipative semilinear parabolic equations of the form defined on the circle, .
相似文献
18.
We show two examples of systems
in
with
such that |Zt| is strictly decreasing in time for any n but
as
. 相似文献
19.
An experimental study is made of turbulent axisymmetric cavity flow. The flow configuration consists of a sudden expansion and contraction pipe joint. In using the LDV system, in an effort to minimize refraction of laser beams at the curved interface, a refraction correction formula for the Reynolds shear stress is devised. Three values of the cavity length (L = 300, 600 and 900 mm) are chosen, and the cavity height (H) is fixed at 55 mm. Both open and closed cavities are considered. Special attention is given to the critical case L = 600 mm, where the cavity length L is nearly equal to the reattachment length of the flow. The Reynolds number, based on the inlet diameter (D = 110 mm) is 73,000. Measurement data are presented for the static wall pressure, mean velocity profiles, vorticity thickness distributions, and turbulence quantities.List of symbols
C
f
velocity correction factor
-
C
p
static wall pressure coefficient
-
D
diameter of inlet pipe = 110 mm
-
H
step height or difference in radii of two pipes = 55 mm
-
L
cavity length = 300, 600 and 900 mm
-
n
a
, n
w
, n
f
refraction indices of the medium between the transmitting lens and window, the window itself, and the working fluid
-
signal validation rate in LDV, Hz
-
P
wall static pressure, Pa
-
P
ref
wall static pressure at x = -70 mm, Pa
-
r
radial distance from centreline, m
-
r
a
radial position of the virtual intersection, m
-
r
d
radial location of the dividing streamline, m
-
r
f
radial position of the real beam intersection, m
-
Re
Reynolds number based on the inlet diameter
-
R
i
inner radius of the cylindrical cavity=110 mm
-
t
thickness of the window, m
-
T
1
integral time scale, s
-
U
streamwise mean velocity, m/s
-
U
c
centreline mean velocity, m/s
-
U
ref
maximum upstream velocity at x= -70 mm, m/s
-
r.m.s. intensity of streamwise, radial and circumferential velocity fluctuations respectively, m/s
-
Reynolds shear stress, m2/s2
-
x
distance in the streamwise direction, m
-
x
a
streamwise position of virtual intersection, m
-
x
f
streamwise position of real beam intersection, m
-
x
r
mean reattachment length, m
-
x
nondimensional streamwise distance
-
y
distance normal to the wall=R–r, m
Greek symbols
vorticity thickness
-
stream function of dividing streamline
相似文献
20.
We study crystal dynamics in the harmonic approximation. The atomic masses are weakly disordered, in the sense that their deviation from uniformity is of the order
. The dispersion relation is assumed to be a Morse function and to suppress crossed recollisions. We then prove that in the limit
, the disorder-averaged Wigner function on the kinetic scale, time and space of order
, is governed by a linear Boltzmann equation. 相似文献