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1.
I.IntroductionItiswell4n0wnthatthecontourintergrationofcomp1exvariableftinctioncanmakealotintegrationveryconvenient.Jordan'slemmahasaveryimportantstatusintheonec0mplexvariableintegration,anditisveryusefulforavarityofintegration.Withthetheoryoffunctionsofo… 相似文献
2.
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
3.
Quadrant analysis is used to study the contributions, associated to the four quadrants of the (u,v) plane, to the production of the turbulent shear stress on rough walls. The measurements are described for a fully developed
turbulent flow between two rough plates with varying the parameterλ
z(span/height ratio of roughness elements). The application of this technique indicates that the (Q
2) events (ejections) and (Q
4) events (sweeps) cause an intense production of the Reynolds stress —ρ
as compared with the (Q
1) and (Q
3) quadrants. The (Q
2) contribution to the Reynolds stress depends on the geometry factorλ
z.
Variation of the parameterλ
zaffects the distributions of
and
forH⩽3, whereH is a particular threshold. Comparison with boundary layer flow shows that the region 0.2⩽y/h⩽0.7 is characterized by a Reynolds stress production, independent of the flow nature. The third moment of the longitudinal
velocity fluctuations is found to be sensitive to the surface roughness. 相似文献
4.
ConsidertheCauchyproblemforthewaveequationinRN×R+(N≥2):2u(x,t)t2-xiaij(x)xju=|u|p-1·u ((x,t)∈RN×(0,T)),u(x,0)=g(x) (x∈RN),ut(x,0)=h(x) (x∈RN),(1)whereu(x,t)isnontrivialsolutionwithfinitespeedofpropagationandissupportedonaforwardcone(x,t)·t≥0,|… 相似文献
5.
Inrecentyears,applicationsofquaternionmatricesarebecomingmoreandmoreimportantandextensiveinrigidmechanics,quantummechanics,controltheoryandhelicaltechnology[1~3].Withtherapiddevelopmentoftheabovedisciplines,itisgettingmoreandmorenecessaryforustofurth… 相似文献
6.
The multiaxial elongational rheometer equipped with rotary clamps is modified such that in addition to simple, equibiaxial and multiaxial elongations also tests with new modes of elongation can be performed. As an example, polyisobutylene is elongated with a ratio of the principal strain rates of
and magnitudes of the maximum strain rate
, 0.04 and 0.08 s–1. As a test result, the first elongational viscosityµ
1
(t) is obtained which follows closely the linear viscoelastic shear viscosity
. In contrast, the second elongational viscosityµ
2
(t) remains below
. By means of a further modification of the rheometer, the test modes can be varied during the deformation period. This allows one to investigate the influence of a well-defined rheological pre-history on the following rheological behaviour. As an example a variation ofm = 0.5 2 was performed. The measured normal-stress differences superpose from the single steps of deformation similar to the linear viscoelastic prediction.Dedicated to Prof. F. R. Schwarzl on the occasion of his 60th birthday 相似文献
7.
A new concept of pseudo mean wave resistance is introduced to find theoretical mean wave resistances of the precursor soliton
generation in two-layer flow over a localized topography at near-resonance in this paper. The pseudo mean wave resistance
of the precursor soliton generation of two-layer flow is determined in terms of the AfKdV equation. From the theoretical results
it is shown that the theoretical mean wave resistance is equal to the pseudo mean wave resistance times 1/m
1, wherem
1 is the coefficient of the fKdV equation. From the regional distribution of the energy of the precursor soliton generation
at the resonant points, it is shown that ratios of the theoretical mean wave resistance and regional mean energy to the total
mean energy are invariant constants, i.e.
: (−1/2):1:1, in which
and
are the mean energy of the generating regions of the precursor solitons, of the depression and of the trailing, wavetrain
at the resonant points respectively,
and <D> are the total energy of the system and the theoretical mean wave resistance at the resonant points. A prediction of the
theoretical mean wave resistance flow over the semicircular topography is carried out in terms of the theoretical results
of the present paper. The comparison shows that the theoretical mean wave resistance is in good agreement with the numerical
calculation.
The project supported by the Foundation of The State Education Commission “The Dynamics of Upper Ocean” and the Grants of
The Physical Oceanography Laboratory of Ocean University of Qingdao 相似文献
8.
Dr. V. Semjonow 《Rheologica Acta》1965,4(2):133-137
Zusammenfassung Es wird die Druckabhängigkeit des nicht -Newtonschen Fließverhältens von Polyolefinschmelzen (Hochdruck-, Niederdruck-,Phillips-Polyäthylen und Polypropylen) experimentell untersucht und gefunden, daß der durch Gl. [1] definierte Druckkoeffizient
mit zunehmender Deformationsgeschwindigkeit
kleiner wird und dabei die (im einzelnen in der Tabelle 1 angeführten) Werte
annimmt. Der Druckkoeffizient der Polyolefinschmelzen ist ebenso wie für vieleNewtonsche Flüssigkeiten bis 2000 kp cm–2 unabhängig vom Druck, er wird mit zunehmender Temperatur kleiner und nimmt mit zunehmender Verzweigung zu. Die Meßergebnisse werden mit Hilfe eines Aufweitungsvolumens interpretiert. Es wird gezeigt, daß eine Deutung des Fließverhaltens von Polyäthylen durch das freie Volumen allein nicht möglich ist.
Für die Diskussion und Förderung dieser Arbeit danke ich Herrn Professor Dr.K.-H. Hellwege und Herrn Dr.W. Knappe. 相似文献
Summary The influence of pressure of the non-Newtonian flow behaviour of polyolefin melts (Low- and High density Polyethylene,Phillips-Polyethylene and Polypropylene) was investigated. The results are: the coefficient of pressure as defined by eq. [1], decreases with increasing shear rate and reaches the values given in table 1 . The pressure coefficient of polyolefin melts does not depend on pressure up to 2000 kp cm–2. As observed with manyNewtonian fluids, decreases with increasing temperature and increases with the degree of branching. The experimental results are explained by means of a so called volume of expansion. It has been shown that it is impossible to explain the flow behaviour of polyethylene exclusively with the free volume.
Für die Diskussion und Förderung dieser Arbeit danke ich Herrn Professor Dr.K.-H. Hellwege und Herrn Dr.W. Knappe. 相似文献
9.
An analysis is presented for the unsteady laminar flow of an incompressible Newtonian fluid in an annulus between two concentric spheres rotating about a common axis of symmetry. A solution of the Navier-Stokes equations is obtained by employing an iterative technique. The solution is valid for small values of Reynolds numbers and acceleration parameters of the spheres. In applying the results of this analysis to a rotationally accelerating sphere, a virtual moment of intertia is introduced to account for the local inertia of the fluid.Nomenclature
R
i
radius of the inner sphere
-
R
o
radius of the outer sphere
-
radial coordinate
-
r
dimensionless radial coordinate,
-
meridional coordinate
-
azimuthal coordinate
-
time
-
t
dimensionless time,
- Re
i
instantaneous Reynolds number of the inner sphere,
i
R
k
2
/
- Re
o
instantaneous Reynolds number of the outer sphere,
o
R
o
2
/
-
radial velocity component
-
V
r
dimensionless radial velocity component,
-
meridional velocity component
- V
dimensionless meridional velocity component,
-
azimuthal velocity component
-
V
dimensionless azimuthal velocity component,
-
viscous torque
-
T
dimensionless viscous torque,
-
viscous torque at surface of inner sphere
-
T
i
dimensionless viscous torque at surface of inner sphere,
-
viscous torque at surface of outer sphere
-
T
o
dimensionless viscous torque at surface of outer sphere,
-
externally applied torque on inner sphere
-
T
p,i
dimensionless applied torque on inner sphere,
-
moment of inertia of inner sphere
-
Z
i
dimensionless moment of inertia of inner sphere,
-
virtual moment of inertia of inner sphere
-
Z
i,v
dimensionless virtual moment of inertia of inner sphere,
-
virtual moment of inertia of outer sphere
-
i
instantaneous angular velocity of the inner sphere
-
o
instantaneous angular velocity of the outer sphere
-
density of fluid
-
viscosity of fluid
-
kinematic viscosity of fluid,/
-
radius ratio,R
i/R
o
-
swirl function,
-
dimensionless swirl function,
-
stream function
-
dimensionless stream function,
-
i
acceleration parameter for the inner sphere,
-
o
acceleration parameter for the outer sphere,
-
shear stress
-
r
dimensionless shear stress,
相似文献
10.
In this paper we consider the equation
相似文献
11.
The in-plane deformation fields near a stationary crack tip for thin, single edge-notched (SEN) specimens, made from Plexiglas, 3003 aluminum alloy and 304 stainless steel, have been successfully obtained by using computer vision. Results from the study indicate that (a) in-plane deformations ranging from elastic to fully plastic can be obtained accurately by the method, (b) for U,
and
, the size of the HRR dominant zone is much smaller than forV and
, respectively. Since these results are in agreement with recent analytical work, suggesting that higher order terms will be needed to accurately predict trends in the data, it is clear that the region where the first term in the asymptotic solution is dominant is dependent on the component of the deformation field being studied, (c) the HRR solution can be used to quantity
only in regions where theplastic strains strongly dominate the elastic strain components (i.e., when
); forV, the HRR zone appears to extend somewhat beyond this region, (d) the displacement componentU does not have the HRR singularity anywhere within the measurement region for either 3003 aluminum or 304 SS. However, the displacement componentV agrees with the HRR slope up to the plastic-zone boundary in 3003 aluminum (
) and over most of the region where measurements were obtained (
) in 304 SS and (e) the effects of end conditions must be included in any finite-element model of typical SEN specimen geometries to accurately calculate theJ integral and the crack-tip fields.Paper was presented at the 1992 SEM Spring Conference on Experimental Mechanics held in Las Vegas, NV on June 8–11. 相似文献
12.
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
13.
Mass conservation and linear momentum balance relations for a porous body and any fluid therein, valid at any given length scale in excess of nearest-neighbour molecular separations, are established in terms of local weighted averages of molecular quantities. The mass density field for the porous body at a given scale is used to identify its boundary at this scale, and a porosity field is defined for any pair of distinct length scales. Specific care is paid to the interpretation of the stress tensor associated with each of the body and fluid at macroscopic scales, and of the force per unit volume each exerts on the other. Consequences for the usual microscopic and macroscopic viewpoints are explored.Nomenclature
material system; Section 2.1.
-
porous body (example of a material system); Sections 2.1, 3.1, 4.1
-
fluid body (example of a material system); Sections 2.1, 3.1, 4.1
-
weighting function; Sections 2.1, 2.3
-
,h
weighting function corresponding to spherical averaging regions of radius and boundary mollifying layer of thicknessh; Section 3.2
-
Euclidean space; Section 2.1
-
V
space of all displacements between pairs of points in; Section 2.1
-
mass density field corresponding to; (2.3)1
-
P
,
f
mass density fields for
,
; (4.1)
-
P
momentum density field corresponding to; (2.3)2
-
v
velocity field corresponding to; (2.4)
-
S
r
(X)
interior of sphere of radiusr with centre at pointx; (3.3)
-
boundary ofany region
-
region in which
p
> 0 with =
,h; (3.1)
-
subset of
whose points lie at least+h from boundary of
; (3.4)
-
abbreviated versions of
; Section 3.2, Remark 4
-
strict interior of
; (3.7)
-
analogues of
for fluid system
; Section 3.2
-
general version of
corresponding to any choice of weighting function; (4.6)
-
interfacial region at scale; (3.8)
-
0
scale of nearest-neighbour separations in
; Section 3.2. Remark 1
-
porosity field at scales (
1;
2); (3.9)
-
pore space at scales (
1;
2); (3.12) 相似文献
14.
The transient response of a central crack in an orthotropic strip under the in-plane shear impact loading is studied by using
the dual integral equation method proposed by Copson and Sih. The general formula for the shear stress intensity factor
near the crack tip is derived. Numerical results of
with
in various cases are obtained by solving the second kind Fredholm integral equation and by performing the inverse Laplace
transform. 相似文献
15.
Part I of this work addressed quasi-static loading of the shear compression specimen (SCS), which has been especially developed
to investigate the shear dominant response of materials at various strain rates. The stress and strain states were characterized
numerically. Approximations were presented to reduce the measured load,P, and displacement,d, into equivalent stress
and strain
. This paper addresses dynamic loading of the SCS. Several simulations were made for representative materials, whose stress-strain
behavior is assumed to be rate-independent. The results show that stress wave loading induces strong oscillations in theP-d curve. However, the
curve remains smooth in the gage section. The oscillations are about the quasistatic load values, so that with suitable filtering
of the dynamicP-d curves, the quasi-static ones are readily recovered. Consequently, the approach that was developed for quasi-static loading
of the SCS is now extended to dynamic loading situations. The average strain rate is rather constant and scales linearly with
the prescribed velocity. As the plastic modulus becomes smaller, the strain rate reaches higher values. Friction at the end
pieces of the specimen is also investigated, and shown to have a small overall influence on the determined mechanical characteristics.
This paper thereby confirms the potential of the SCS for large strain testing of materials, using a unified approach, over
a large range of strain rates in a seamless fashion. 相似文献
16.
C. F. Chan Man Fong 《Applied Scientific Research》1971,23(1):16-22
Using Stuart's energy method, the torque on the inner cylinder, for a second order fluid, in the supercritical regime is calculated. It is found that when the second normal stress difference is negative, the flow is more stable than for a Newtonian fluid and the torque is reduced. If the second normal stress difference is positive, then the flow is more stable and there is no torque reduction. Experimental data related to the present work are discussed.Nomenclature
a
amplitude of the fundamentals
-
A
ij
(1)
, A
ij
(2)
first and second Rivlin-Ericksen tensors
-
d
r
2–r
1
- D
d/dx
-
E
-
F
-
g
ij
metric tensor
-
G
torque on the inner cylinder in the supercritical regime
-
h
height of the cylinders
-
k
0
/d
2
-
k
1
/d
2
-
I
1
-
I
2
-
I
3
-
I
4
-
r
1, r
2
radii of inner and outer cylinders respectively
-
r
0
1/2(r
1+r
2)
-
R
Reynolds number
1
r
1
d/
0
-
R
c
critical Reynolds number
-
T
Taylor number r
1
1
2
d
3
2/
0
2
*)
-
T
c
critical Taylor number
-
u
1, v
1, w
1
Fundamentals of the disturbance
-
u
i
, v
i
, w
i
, (i>1)
harmonics
-
mean velocity (not laminar velocity)
-
u
–u
1/ar
1
1
-
v
v
1/Rar
1
1
-
x
(r–r
0)/d
-
,
material constants
-
0
viscosity
-
wave number d
-
density
-
1
angular velocity of inner cylinder
-
tilde denotes complex conjugate 相似文献
17.
Iterative solution of nonlinear equations with strongly accretive operators in Banach spaces 总被引:1,自引:0,他引:1
周海云 《应用数学和力学(英文版)》1999,20(3):282-289
1IntroductionandPreliminariesLetXbearealBanachspacewithnormIJ'11andadualX'.ThenormalizeddualitymappingJ:X~ZxisdefinedbyJx={x'eX*I(x,x')=11x112=11x if'},where',')denotesthegeneralizeddualitypairing.Itiswell-knownthatifX isstrictlyconvex,Jissingle-valuedandJ(tx)=tjxforallt201xeX.IfX*isuniformlyconvex,thenJisuniformlycontinuousonanyboundedsubsetSofX(of.Browde,fljandBarbuL2]).AnoperatorTwithdomainD(T)andrangeR(T)inXissaidtobeaccretiveifforeveryx,y6D(T),thereexistsajeJ(x--y)suchthat(T… 相似文献
18.
The characteristics of low-speed fluid streaks occurring under sheared air-water interfaces were examined by means of hydrogen
bubble visualization technique. A critical shear condition under which the streaky structure first appears was determined
to beu
τ≈0.19 cm/s. The mean spanwise streak spacing increases with distance from the water surface owing to merging and bursting
processes, and a linear relationship describing variation of non-dimensional spacing
versusy
+ was found essentially independent of shear stress on the interface. Values of
, however, are remarkably smaller than their counterparts in the near-wall region of turbulent boundary layers. Though low-speed
streaks occur randomly in time and space, the streak spacing exhibits a lognormal probability distribution behavior. A tentative
explanation concerning the formation of streaky structure is suggested, and the fact that
takes rather smaller values than that in wall turbulence is briefly discussed.
The project supported by the National Natural Science Foundation of China (19672070) 相似文献
19.
Existence of Weak Solutions to the Equations of Non-Stationary Motion of Non-Newtonian Fluids with Shear Rate Dependent Viscosity 总被引:1,自引:0,他引:1
Jörg Wolf 《Journal of Mathematical Fluid Mechanics》2007,9(1):104-138
In the present paper we prove the existence of weak solutions
to the equations of non-stationary motion of an incompressible fluid with shear rate dependent viscosity in a cylinder Q = Ω × (0,T), where
denotes an open set. For the power-low model with
we are able to construct a weak solution
with ∇ · u = 0. 相似文献
20.
Let E be a Banach space. We prove the instability of the trivial solution of the differential equation
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