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1.
Limitation and improvement of PIV 总被引:7,自引:0,他引:7
In this second part of the paper, the Particle Image Distortion (PID) technique is described. It is proposed to overcome the limitations of conventional PIV due to the local deformations u/x, u/y, v/x and v/y in two-dimensional flows. Both simulation and experiment demonstrate that high accuracy and high spatial resolution are possible with this technique. The large time required to compute the cross-correlations, however, limits its wide applications at present. 相似文献
2.
S. Kase 《Rheologica Acta》1982,21(2):210-211
The general integral of the very simple equation
21/n/() was found to describe the cross sectional area of filaments of isothermal power law fluids while in transient stretching where is time and is the initial location of fluid molecules at time = 0 given as the distance from a reference point fixed in space. Any such stretching transient given as a solution of the above equation is physically realizable subject to the restrictions > 0 and/ < 0. 相似文献
3.
For thin bodies placed in a hypersonic flow at a small angle of attack the similarity law is known. From this law it follows that for various numbers M, angles of attack , and relative thicknesses the similarity conditions will be observed if in the flows under consideration the parameters M and / are the same. This similarity law is obtained with the assumption M 1, 1. But even for M=3 and 1/3 the results of solving the complete system of gasdynamic equations for affino-similar bodies is in a good agreement with the similarity law [1], In [2] it is shown that this similarity law is generalized for the case of a flow around a thin pointed body at large angles of attack. According to the similarity law, at large angles of attack the flows near bodies with an identical distribution of cross-sectional shapes will be similar if the parameters K1= cotan and K2=m sin for all cases have one and the same value. As the angle of attack decreases, the requirements of constancy of K1 and K2 become analogous to the conditions M=const, /=const.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 78–83, May–June, 1976.The authors thank V. V. Lunev for the useful discussions and valuable observations. 相似文献
4.
The deformation of particle image patterns due to velocity gradients causes errors of velocity measurements and false velocity detections in PIV (Particle Image Velocimetry). A novel technique to overcome those limitations inherent in the conventional PIV by correcting the particle image pattern according to the local velocity gradients in two dimensional flows, i.e. u/x, u/y, v/x and v/y, is proposed and successfully applied to a water flow downstream of a backward facing step. 相似文献
5.
岑燕明 《应用数学和力学(英文版)》1991,12(5):445-453
Based on a general assumption for plastic potential and yield surface, some properties of the nonassociated plasticity are studied, and the existence and uniqueness of the distribution of incremental stress and displacement for work-hardening materials are proved by using nonsymmetric Lax-Milgram lemma, when the work-hardening parameter A>F/Q/–F/, Q/. 相似文献
6.
In this paper, we show that the maximum principle holds for quasilinear elliptic equations with quadratic growth under general structure conditions.Two typical particular cases of our results are the following. On one hand, we prove that the equation (1) {ie77-01} where {ie77-02} and {ie77-03} satisfies the maximum principle for solutions in H
1()L(), i.e., that two solutions u
1, u
2H1() L() of (1) such that u
1u2 on , satisfy u
1u2 in . This implies in particular the uniqueness of the solution of (1) in H
0
1
()L().On the other hand, we prove that the equation (2) {ie77-04} where fH–1() and g(u)>0, g(0)=0, satisfies the maximum principle for solutions uH1() such that g(u)¦Du|{2L1(). Again this implies the uniqueness of the solution of (2) in the class uH
0
1
() with g(u)¦Du|{2L1().In both cases, the method of proof consists in making a certain change of function u=(v) in equation (1) or (2), and in proving that the transformed equation, which is of the form (3) {ie77-05}satisfies a certain structure condition, which using ((v1
-v
2)+)n for some n>0 as a test function, allows us to prove the maximum principle. 相似文献
7.
In technical reactors like catalytic honeycombreactors with a reaction at the wall and with an unknown field of concentrationc
A
(r,z) the diffusive flux
A,D.w
is replaced by the transferflux
A,. The transferflux
A, i.e. the Sherwood-number only depends on processes, which effect the diffusive flux, i.e. the gradient of concentration c
A
/r¦
w
. For vaporisation with a constant concentrationc
A,w
at the wall or for a heterogeneous reaction with a variable concentrationc
A,w
the fluidstream would be such a process. In any case Sherwood-numberSh depends only on Bodenstein-numberBo and is — even for a heterogeneous reaction — no function of Damköhler-number. Only in case of a homogeneous reaction in the fluid phase there is a influence on the gradient of concentration and it followsSh (Bo, Da
I).According toSh
neu (Bo, Da
II) the gradient of concentration c
A
/r in
A,D
is replaced in
A,
by the mean concentration
and not, as usual, by the difference of concentration
. Both concentrations depends on the Damköhler-numberDa
II. The difference of concentrations shows either no or only little dependence ofDa
II (this illustrates the quality of representation of
A,D,w
by
A,
). If is defined by
, than neu depends onDa
II
Sh
neu =Sh
neu (Bo, Da
II). According to this definition of neu no new facts will arise. The common theoretical or experimental values of orSh are applicable to every process with heterogeneous reactions. In analogous cases the following explanations are also valid for heat-transfer at the wall, if a heterogeneous reaction takes place.Zusammenfassung In technischen Reaktoren, wie z. B. einem katalytischen Wabenrohrreaktor, in denen sich das Konzentrationsfeldc
A
(r, z) nicht genau ermitteln läßt, ersetzt die Übergangsstromdichte
A,
vereinfachend die Diffusionsstromdichte
A,D,w
an die Wand. Die Übergangsstromdichte
A,
bzw. dieSh-Zahl ist nur von den Vorgängen abhängig, die die Diffusionsstromdichte an die Wand,
A,D,w
, d. h. den Konzentrationsgradienten c
A
/r¦
w
beeinflussen. Bei Verdampfung mit konstanter Wandkonzentrationc
A,w
oder bei einer heterogenen Reaktion an der Wand mit veränderlichemc
A,w
ist ein solcher Vorgang z. B. die Strömung, d. h. in beiden Fällen istSh =Sh (Bo) und hängt auch bei einer heterogenen Reaktion nicht von der Damköhler-II-Zahl ab. Nur wenn in der strömenden Phase (zusätzlich) eine homogene Reaktion vorliegt [12], hat diese einen Einfluß auf den Gradienten und es giltSh =Sh (Bo, Da
I).Die AbhängigkeitSh
neu (Bo, Da
II) entsteht definitorisch dadurch, daß der in
A,D
auftretende Gradient c
A
/r in
A,
z. B. durch eine mittlere Konzentration
( neu), statt wie üblich durch eine Konzentrationsdifferenz
, erfaßt wird. Beide Konzentrationen sind von der DamköhlerzahlDa
II abhängig, ihre Differenz aber nicht bzw. wenig (worin sich die Güte der Abbildbarkeit von
A,D,w
durch
A,
verdeutlicht). Läßt man also in der Definitionsgleichung für die Stoffübergangszahl die veränderliche Wandkonzentrationc
A,w
weg, dann entsteht eine entsprechende starke Abhängigkeit der Größe neu (bzw.Sh
neu) von derDa-II-Zahl:Sh
neu=Sh
neu (Bo, Da
II). Neue Sachverhalte werden mit solchen Definitionen von neu nicht begründet. Die üblichen theoretisch oder experimentell ermittelten - oderSh-Werte können beim Auftreten von Stoffwandlungsvorgängen an der Wand für reaktionstechnische Berechnungen verwendet werden. Die folgenden Ausführungen gelten bei gegebener Analogie auch für den Wärmeübergang mit physikalischen oder chemischen Wandvorgängen, wie Verdampfung oder chemischer Wandreaktion. 相似文献
8.
Laminar mixed convection over a horizontal plate with uniform wall temperature or uniform wall heat flux is analyzed by introducing proper buoyancy parameters and transformation variables for fluids of any Prandtl number between 0.001 and 10,000. Both cases of buoyancy assisting and opposing flow conditions are investigated. For the buoyancy-assisting case, the obtained numerical results are very accurate over the entire range of mixed convection intensity from pure forced convection limit to pure free convection limit. For the buoyancy-opposing case, solutions are obtained from the forced convection limit to the point of breakdown.
Nomenclature C f local friction coefficient - f reduced stream function - g gravitational acceleration - Gr local Grashof number for UWT,g (T w –T )x 3/ 2 - Gr* local Grashof number for UHF,g q w x 4/k 2 - m =10 for UWT; and =6 for UHF - n =5 for UWT; and =3 for UHF - Nu local Nusselt number - p pressure - Pr Prandtl number,/ - q w wall heat flux - Ra local Rayleigh number for UWT,Gr Pr - Ra* local Rayleigh number for UHF,Gr*Pr - Re local Reynolds number,u x/ - T fluid temperature - T w wall temperature - T free-stream temperature - u velocity component inx-direction - u free-stream velocity - v velocity component iny-direction - x coordinate parallel to the plate - y coordinate normal to the plate Greek symbols thermal diffusivity - thermal expansion coefficient - =0 for UWT; and =1 for UHF - buoyancy parameter, =( Ra)1/5/( Re)1/2 for UWT; and =( Ra*)1/6/( Re)1/2 for UHF - pseudo-similarity variable, (y/x) - dimensionless temperature, =(T–T )/(T w –T ) for UWT; and =(T–T )/(q w x/k) for UHF - =[( Re)1/2+( Ra)1/5] for UWT; and =[( Re)1/2+( Ra*)1/6] for UHF - dynamic viscosity - kinematic viscosity - /(1+) - dimensionless pressure - density - Pr/(1+Pr) - w wall shear stress,(u/y) y=0 - stream function - Pr/(1+Pr)1/3 相似文献
Mischkonvektion an einer horizontalen Platte für Fluide mit beliebiger Prandtl-Zahl
Zusammenfassung Es wurde laminare Mischkonvektion an einer horizontalen Platte mit einheitlicher Wandtemperatur oder einheitlicher Wandwärmestromdichte bei Einführung zweckmäßiger Auftriebsparameter und Transformationsvariablen für Fluide mit beliebiger Prandtl-Zahl zwischen 0,001 und 10 000 untersucht. Es wurden die Fälle der Strömung entgegen und in Richtung der Auftriebskraft untersucht. Für den Fall der Strömung in Richtung der Auftriebskraft wurden sehr genaue numerische Ergebnisse für den gesamten Bereich der gemischten Konvektion von rein erzwungener Konvektion bis zu rein freier Konvektion erhalten. Für den Fall der Strömung entgegen der Auftriebsrichtung wurden Lösungen für erzwungene Konvektion bis zum Umkehrpunkt erhalten.
Nomenclature C f local friction coefficient - f reduced stream function - g gravitational acceleration - Gr local Grashof number for UWT,g (T w –T )x 3/ 2 - Gr* local Grashof number for UHF,g q w x 4/k 2 - m =10 for UWT; and =6 for UHF - n =5 for UWT; and =3 for UHF - Nu local Nusselt number - p pressure - Pr Prandtl number,/ - q w wall heat flux - Ra local Rayleigh number for UWT,Gr Pr - Ra* local Rayleigh number for UHF,Gr*Pr - Re local Reynolds number,u x/ - T fluid temperature - T w wall temperature - T free-stream temperature - u velocity component inx-direction - u free-stream velocity - v velocity component iny-direction - x coordinate parallel to the plate - y coordinate normal to the plate Greek symbols thermal diffusivity - thermal expansion coefficient - =0 for UWT; and =1 for UHF - buoyancy parameter, =( Ra)1/5/( Re)1/2 for UWT; and =( Ra*)1/6/( Re)1/2 for UHF - pseudo-similarity variable, (y/x) - dimensionless temperature, =(T–T )/(T w –T ) for UWT; and =(T–T )/(q w x/k) for UHF - =[( Re)1/2+( Ra)1/5] for UWT; and =[( Re)1/2+( Ra*)1/6] for UHF - dynamic viscosity - kinematic viscosity - /(1+) - dimensionless pressure - density - Pr/(1+Pr) - w wall shear stress,(u/y) y=0 - stream function - Pr/(1+Pr)1/3 相似文献
9.
Summary The subject of this article is the thermodynamics of perfect elastic-plastic materials undergoing unidimensional, but not necessarily isothermal, deformations. The first and second laws of thermodynamics are employed in a form in which only the following quantities appear: the temperature , the elastic strain
e, the plastic strain
p, the elastic modulus (gq), the yield strain (gq), the heat capacity
(e,
p,), the latent elastic heat
e(e,
p, ), and the latent plastic heat
p(e,
p, ). Relations among the response functions , ,
,
e, and
p are derived, and it is shown that a set of these relations gives a necessary and sufficient condition for compliance with the laws of thermodynamics. Some observations are made about the existence and uniqueness of energy and entropy as functions of state.Dedicated to Clifford Truesdell on the occasion of his 60th birthdayThis research was supported by the U.S. National Science Foundation. 相似文献
10.
C. Y. Wang 《Applied Scientific Research》1982,39(3):181-189
An undulating electric wire generates internal heat by Joule heating. The surface temperature is maintained constant by forced convection. The heat conduction in the wire is solved by using intrinsic coordinates and a perturbation about the (small) ratio of the wire radius to the minimum radius of curvature of the centerline. For the non-uniformly heated wire undulations cause an increase in total heat transfer in comparison with a straight wire of same length and volume.Nomenclature
a
radius of wire
-
A
surface area
-
f
function of
-
G
function of ,
-
I
current
-
I
n
, J
n
Bessel functions of order n
-
k
a
-
K
thermal conductivity
-
L
differential operator
-
N
unit normal
-
q
0
Joule heating per volume
-
r
radial coordinate
-
R
position vector of axis
-
R
0
resistance at T
0
-
s
arc length along axis
-
t
s/a
-
T
temperature
-
u
local heat transfer
-
U
total heat transfer
-
V
volume
-
x
position vector
-
X, Y
Cartesian coordinates
-
z
n
J
n
or I
n
-
a/(K/q
0
)1/2
-
temperature coefficient of electric resistivity
-
a|| max
-
r/a
-
angle
-
curvature
-
2a/period of undulation
-
normalized temperature 相似文献
11.
The problem of thermal entry heat transfer for Hartmann flow in parallel-plate channels with uniform but unequal wall temperatures considering viscous dissipation, Joule heating and axial conduction effects is approached by the eigenfunction expansion method. The series expansion coefficients for the nonorthogonal eigenfunctions are obtained by using a method for nonorthogonal series described by Kantorovich and Krylov [21]. Numerical results are obtained for the case with entrance condition parameter o=1 and open circuit condition K=1. The parametric values of Ha=0, 2, 6, 10 and Br=0, –1 are considered for Hartmann and Brinkman numbers, respectively.
Nomenclature a one-half of channel height - ¯B,B0 magnetic field Induction vector and magnitude of applied magnetic field - Br Brinkman number, f Um 2/(kc) - Cn,Dn coefficients in the series expansion of e, see eq. 16 - cp specific heat at constant pressure - ,E0 electric field intensity vector and component - En,On even and odd eigenfunctions - Ha Hartmann number, (/f)1/2 Bo a - h1,h2 local heat transfer coefficients at lower and upper plates - ¯J,Jy electric current density vector and component - K external loading parameter, Eo/(Bo Um) - k thermal conductivity - Nu1, Nu2 local Nusselt numbers, h1,a/k and h2a/k, respectively - P fluid pressure - Pe Peclet number, PrRe - Pr Prandtl number, Cp f/k - q1,q2 rates of heat transfer per unit area,–k(T/Z)Z=–a'–k(T/Z) Z=a respectively - Re Reynolds number, Uma/uf - T,T0,T1,T2 fluid temperature, uniform entrance temperature, uniform but different lower and upper plate temperatures, respectively - Tb,Tm bulk temperature and (T1+T2)/2 - U,Um,u axial, mean and dimensionless velocities, respectively - ¯V velocity vector - X,Z axial and transverse coordinates - x,z dimensionless coordinates - n,n even and odd eigenvalues - ,0,b dimensionless fluid, entrance and bulk temperatures, respectively - c,e,f characteristic temperature difference (T2-Tm), and dimensionless fluid temperatures, defined by eq. (10) - e,f magnetic permeability and viscosity of fluid - fluid density - electric conductivity - viscous dissipation function - (1-)/2 相似文献
Zusammenfassung Das Problem der Wärmeübertragung im thermischen Einlauf einer Hartmannströmung im ebenen Spalt mit einheitlichen, aber ungleichen Wandtemperaturen wurde unter Berücksichtigung viskoser Dissipation, Joulescher Heizung und axialer Wärmeleitung mit Hilfe einer Entwicklung nach Eigenfunktionen behandelt. Die Koeffizienten der Entwicklung für nichtorthogonale Eigenfunctionen wurde nach einer Methode für nichtorthogonale Reihen nach Kantorovicz und Krylow [21] berechnet. Numerische Ergebnisse werden für den Eintrittsparameter o=1 und die Bedingung für den offenen Stromkreis K=1 erhalten. Die Parameterwerte Ha=0, 2, 6, 10 und Br=0, –1 werden für die jeweiligen Werte der Hartmann- und der Brinckman-Zahl betrachtet.
Nomenclature a one-half of channel height - ¯B,B0 magnetic field Induction vector and magnitude of applied magnetic field - Br Brinkman number, f Um 2/(kc) - Cn,Dn coefficients in the series expansion of e, see eq. 16 - cp specific heat at constant pressure - ,E0 electric field intensity vector and component - En,On even and odd eigenfunctions - Ha Hartmann number, (/f)1/2 Bo a - h1,h2 local heat transfer coefficients at lower and upper plates - ¯J,Jy electric current density vector and component - K external loading parameter, Eo/(Bo Um) - k thermal conductivity - Nu1, Nu2 local Nusselt numbers, h1,a/k and h2a/k, respectively - P fluid pressure - Pe Peclet number, PrRe - Pr Prandtl number, Cp f/k - q1,q2 rates of heat transfer per unit area,–k(T/Z)Z=–a'–k(T/Z) Z=a respectively - Re Reynolds number, Uma/uf - T,T0,T1,T2 fluid temperature, uniform entrance temperature, uniform but different lower and upper plate temperatures, respectively - Tb,Tm bulk temperature and (T1+T2)/2 - U,Um,u axial, mean and dimensionless velocities, respectively - ¯V velocity vector - X,Z axial and transverse coordinates - x,z dimensionless coordinates - n,n even and odd eigenvalues - ,0,b dimensionless fluid, entrance and bulk temperatures, respectively - c,e,f characteristic temperature difference (T2-Tm), and dimensionless fluid temperatures, defined by eq. (10) - e,f magnetic permeability and viscosity of fluid - fluid density - electric conductivity - viscous dissipation function - (1-)/2 相似文献
12.
Diffusion in anisotropic porous media 总被引:2,自引:0,他引:2
An experimental system was constructed in order to measure the two distinct components of the effective diffusivity tensor in transversely isotropic, unconsolidated porous media. Measurements were made for porous media consisting of glass spheres, mica particles, and disks made from mylar sheets. Both the particle geometry and the void fraction of the porous media were determined experimentally, and theoretical calculations for the two components of the effective diffusivity tensor were carried out. The comparison between theory and experiment clearly indicates that the void fraction and particle geometry are insufficient to characterize the process of diffusion in anisotropic porous media.
Roman Letters
A
interfacial area between - and -phases for the macroscopic system, m2
-
A
e
area of entrances and exits of the -phase for the macroscopic system, m2
-
A
interfacial area contained within the averaging volume, m2
-
a
characteristic length of a particle, m
-
b
average thickness of a particle, m
-
c
A
concentration of species A, moles/m3
-
c
o
reference concentration of species A, moles/m3
- c
A
intrinsic phase average concentration of species A, moles/m3
-
c
a
c
A–c
A, spatial deviation concentration of species A, moles/m3
-
C
c
A/c
0, dimensionless concentration of species A
-
binary molecular diffusion coefficient, m2/s
-
D
eff
effective diffusivity tensor, m2/s
-
D
xx
component of the effective diffusivity tensor associated with diffusion parallel to the bedding plane, m2/s
-
D
yy
component of the effective diffusivity tensor associated with diffusion perpendicular to the bedding plane, m2/s
-
D
eff
effective diffusivity for isotropic systems, m2/s
-
f
vector field that maps c
A on to c
a
, m
-
h
depth of the mixing chamber, m 相似文献
13.
Prof. S. Suzuki 《Archive of Applied Mechanics (Ingenieur Archiv)》1988,58(2):97-102
Summary Stress analysis has been carried out for a finite cylinder subjected to arbitrarily distributed axisymmetrical surface loads. Direct stress x in the axial direction is assumed to be of the form
x =
0+r
1 +r
2 where
0 to
2 are functions of x. Using the equations of equilibrium and compatibility the other direct stresses and the shearing stress are expressed by
1 and 2. Fundamental equations governing
1 and
2 are introduced using the variational principle of complementary energy. From the results of the present analysis it is evident that the boundary conditions can be satisfied completely even for the case where the external forces are specified in complicated form, and that more accurate solutions can easily be obtained by introducing additional terms in
x.
Spannungsanalyse für den Zylinder unter axialsymmetrischer Last in beliebiger Verteilung
Übersicht Für einen endlichen Zylinder unter axialsymmetrischer Oberflächenlast in beliebiger Verteilung werden die Spannungen ermittelt. Die Normalspannung in Axialrichtung wird in der Form x = 0+r 1 +r 2 angesetzt mit 0, 1, 2 als Funktionen von x. Mit Hilfe der Gleichgewichtsund Verträglichkeitsbedingungen werden die anderen Normalspannungen und die Schubspannung durch 1 und 2 ausgedrückt. Über das Variationsprinzip für die Komplementärenergie werden die grundlegenden Gleichungen für 1 und 2 eingeführt. Die Ergebnisse zeigen, daß die Randbedingungen selbst für komplizierte Belastungsarten vollständig erfüllbar sind und mit zusätzlichen Termen in x mühelos noch genauere Lösungen bestimmt werden können.相似文献
14.
Determination of permeability tensors for two-phase flow in homogeneous porous media: Theory 总被引:1,自引:0,他引:1
In this paper we continue previous studies of the closure problem for two-phase flow in homogeneous porous media, and we show how the closure problem can be transformed to a pair of Stokes-like boundary-value problems in terms of pressures that have units of length and velocities that have units of length squared. These are essentially geometrical boundary value problems that are used to calculate the four permeability tensors that appear in the volume averaged Stokes' equations. To determine the geometry associated with the closure problem, one needs to solve the physical problem; however, the closure problem can be solved using the same algorithm used to solve the physical problem, thus the entire procedure can be accomplished with a single numerical code.Nomenclature a
a vector that maps V onto
, m-1.
-
A
a tensor that maps V onto
.
-
A
area of the - interface contained within the macroscopic region, m2.
-
A
area of the -phase entrances and exits contained within the macroscopic region, m2.
-
A
area of the - interface contained within the averaging volume, m2.
-
A
area of the -phase entrances and exits contained within the averaging volume, m2.
-
Bo
Bond number (= (=(–)g2/).
-
Ca
capillary number (= v/).
- g
gravitational acceleration, m/s2.
-
H
mean curvature, m-1.
- I
unit tensor.
-
permeability tensor for the -phase, m2.
-
viscous drag tensor that maps V onto V.
-
*
dominant permeability tensor that maps
onto v
, m2.
-
*
coupling permeability tensor that maps
onto v
, m2.
-
characteristic length scale for the -phase, m.
-
l
characteristic length scale representing both and , m.
-
L
characteristic length scale for volume averaged quantities, m.
-
n
unit normal vector directed from the -phase toward the -phase.
-
n
unit normal vector representing both n
and n
.
-
n
unit normal vector representing both n
and n
.
-
P
pressure in the -phase, N/m2.
- p
superficial average pressure in the -phase, N/m2.
- p
intrinsic average pressure in the -phase, N/m2.
-
p
–p
, spatial deviation pressure for the -phase, N/m2.
-
r
0
radius of the averaging volume, m.
-
r
position vector, m.
-
t
time, s.
-
v
fluid velocity in the -phase, m/s.
- v
superficial average velocity in the -phase, m/s.
- v
intrinsic average velocity in the -phase, m/s.
-
v
–v
, spatial deviation velocity in the -phase, m/s.
-
V
volume of the -phase contained within the averaging volmue, m3.
-
averaging volume, m3.
Greek Symbols
V
/, volume fraction of the -phase.
-
viscosity of the -phase, Ns/m2.
-
density of the -phase, kg/m3.
-
surface tension, N/m.
-
(v
+v
T
), viscous stress tensor for the -phase, N/m2. 相似文献
15.
The results of the hydraulic studies of gas-liquid media, wave processes in two-phase media and critical phenomena are described. Some methodological foundations to describe these media and methods to obtain the basic similarity criteria for the hydraulics and gas-dynamics of bubble suspensions are discussed. A detailed consideration is given for the phase transition processes on interfaces and the interface stability. A relation has been revealed between the wave and critical phenomena in two-phase systems.Nomenclature
a
thermal diffusivity
- Ar
Archimedes number
-
B
gas constant
-
C
heat capacity
-
C
p
heat capacity at constant pressure
-
C
v
heat capacity at constant volume
-
c
0
acoustic velocity in the mixture
-
c
l
acoustic velocity in the liquid
-
C
f
flow resistance coefficient
-
G
mass rate of flow
-
g
gravitational acceleration
-
L
latent heat of evaporation
-
l
initial perturbation width
- M
Mach number
- Nu
Nusselt number
-
P
pressure
- Pr
Prandtl number
-
R
bubble radius
- (3P
0/R
0
2
f
)–1
bubble resonance frequency square
-
T
temperature
-
U
medium motion velocity
-
W
heavy phase velocity
-
W
light phase velocity
- We
Weber number
-
heat release coefficient
-
dispersion coefficient
-
void fraction
-
adiabatic index
-
film thickness
-
dimensionless film thickness
-
kinematic viscosity coefficient
-
dynamical viscosity coefficient
-
dissipation coefficient in the mixture
-
dispersion parameter
-
f
liquid phase density
-
light phase density
-
heat conductivity
-
surface tension
-
frequency,
0
2
=3P
0/
f
R
0
2 相似文献
16.
A. C. M. Beljaars 《Applied Scientific Research》1976,32(5):509-518
The time dependent differential equation for the local wire temperature of a constant temperature anemometer is solved by a perturbation method in case of a harmonically changing heat transfer coefficient. The time dependent power supply to the wire follows from the condition of constant mean temperature imposed by the anemometer circuit. The influence of thin supporting wires, or copper-plated wire ends, is evaluated also. Numerical results are given for a number of cases that are of practical interest.Nomenclature
c
specific heat
-
D
diameter of the wire
-
D
u
diameter of the copper-plated ends of the wire
-
f
D
-
g
I
2
r
0
-
I
electric current
-
L
length of the wire
-
P
1/4D
2
c
-
q
1/4D
2
-
r
resistance of the wire per unit length at temperature T'
-
r
0
resistance of the wire per unit length at temperature T
-
T
T' – T
-
T'
local temperature of the wire
-
T
ambient temperature
-
T
w
constant mean temperature imposed by the anemometer circuit
-
T
u
local difference between the temperature of the supporting wire and the ambient temperature
-
t
time
-
x
axial coordinate with the origin in the middle of the wire
-
heat transfer coefficient
-
temperature coefficient of the resistance
-
small parameter
-
time constant = cD
2/4D
-
u
time constant of the copper-plated ends cD
u
2
/4D
u
-
thermal conductivity of wire material
-
u
thermal conductivity of the copper-plated wire ends
-
density
-
circular frequency 相似文献
17.
On the basis of a spectral representation of the rapid part
ij,2 of the correlation tensor p(u
i
/x
j
) using Cramer's theorem the inequality
ij,2(U
j
/x
i
)0 is obtained. As distinct from the realizability conditions, it can serve as a direct and very rigorous test of the adequacy of model expressions for
ij,2. In particular, it is shown that the best known of such expressions do not satisfy this test.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.2, pp. 42–46, March–April, 1992. 相似文献
18.
Per Åke Lindberg 《Applied Scientific Research》1994,53(1-2):139-162
Calculations of the three-dimensional boundary layer in an S shaped duct are performed with various – models. Three different near-wall models are used for the – model, of which one is using a new set of near-wall damping functions deduced from direct numerical simulations of turbulent channel flow available in the literature. The results show that it is possible to obtain damping functions giving better agreement, especially for and , with direct simulation data and experiments than with damping functions deduced from trial and error. 相似文献
19.
M. E. Erguven 《Meccanica》1991,26(2-3):117-123
The problem considered in this paper describes the torsion of a homogeneous isotropic elastic layer (0zd
1) of finite thickness d
1, perfectly bonded to another elastic layer (-d
2z0) of finite thickness d
2. The problem is reduced to the solution of a Fredholm integral equation of the second kind. The solutions are given for some particular cases.
Sommario In questo lavoro si considera il problema della torsione di uno strato elastico omogeneo ed isotropo (0zd 1) di spessore finito d 1, perfettamente incollato ad un altro strato elastico (-d 2z0) di spessore finito d 2. II problema é ricondotto alla soluzione di una equazione integrale di Freedholm del secondo ordine. Le soluzioni sono ottenute per alcuni casi particolari.相似文献
20.
This paper presents details of an experimental investigation into the nature of turbulence generated in the wake of a single grid node. The latter has been considered as two members placed perpendicular to each other in the geometry of a cross, with square and circular sections representing bars and rods respectively. The effect of member spacing has been examined in an attempt to identify the complex flow phenomena associated with such a configuration, and in this respect a critical gap width has been found.List of symbols
C
p
pressure coefficient, (p — p
0)/1/2 U
0
2
-
C
pb
pressure coefficient measured on the base centre-line
-
C
ps
pressure coefficient measured at stagnation point
-
D
diameter/section depth of model
-
L
distance between central axis of two cylinders or bars
-
n
vortex shedding frequency
-
p
local pressure on model's surface
-
p
0
static pressure
-
R ()
autocorrelation coefficient
-
R
e
Reynolds number, DU
0/v
-
St
Strouhal number, n D/U
0
-
U
0
mean freestream velocity in X-direction
-
ovu
local mean velocity in X-direction
-
u
velocity fluctuation in X-direction
-
ovv
local mean velocity in Y-direction
-
ovw
local mean velocity in Z-direction
-
X
cartesian co-ordinate in longitudinal direction
-
Y
cartesian co-ordinate perpendicular to wind tunnel floor
-
Z
cartesian co-ordinate in lateral direction
-
dynamic viscosity of fluid
-
v
kinematic viscosity of fluid, /
-
n
spectral energy, 4 0
R () cos 2 n d
-
density of fluid
-
x
longitudinal component of vorticity, /y – /z
This paper was presented at the 10th Symposium on Turbulence, University of Missouri-Rolla, Sept. 22–24, 1986 相似文献