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1.
Low-order moments of the increments δu andδv where u and v are the axial and radial velocity fluctuations respectively, have been obtained using single and X-hot wires mainly on the
axis of a fully developed pipe flow for different values of the Taylor microscale Reynolds numberR
λ. The mean energy dissipation rate〉ε〈 was inferred from the uspectrum after the latter was corrected for the spatial resolution of the hot-wire probes. The corrected Kolmogorov-normalized
second-order structure functions show a continuous evolution withR
λ. In particular, the scaling exponentζ
v
, corresponding to the v structure function, continues to increase with R
λ in contrast to the nearly unchanged value of ζ
u
. The Kolmogorov constant for δu shows a smaller rate of increase with R
λ than that forδv. The level of agreement with local isotropy is examined in the context of the competing influences ofR
λ and the mean shear. There is close but not perfect agreement between the present results on the pipe axis and those on the
centreline of a fully developed channel flow.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
2.
Large scale dynamic behavior of buoyant diffusion flames were studied experimentally. It was found that buoyant diffusion
flames originating from circular nozzles exhibit two different modes of flame instabilities. The first mode results in a sinuous
meandering of the diffusion flame, characteristic of flames originating from small diameter nozzles. This instability originates
at some distance downstream of the nozzle exit in the contraction region of the buoyant flame envelope and develops into a
sinuous motion of the flame. The second mode is the varicose mode which develops very close to the nozzle exit as axisymmetric
perturbations of a contracting flame surface. In this mode, flame oscillations result in the formation of toroidal vortical
structures that convect through the flame and cause periodic burn out at the flame top resulting in the observed flame height
fluctuations. The average flame heights are found to be typically shorter for these flames. The oscillation frequencies and
their scaling for the two modes are also different with the sinuous mode having higher frequencies than the varicose mode.
It was also observed that the instability can switch from one mode to the other and the probability of observing the varicose
mode appears to increase with increasing Richardson number. Additionally, the feasibility of altering the behavior of buoyant
diffusion flames was explored through variation of the oxidizer medium density. It was found that the flame oscillations can
be completely suppressed for flames burning in helium rich helium–oxygen mixtures. At lower helium concentrations, the oscillation
frequency can be significantly reduced. In order to enhance the buoyancy effect, CO2–O2 mixtures were also studied. However, the density increase and its effects on flame oscillation frequency were found to be
small compared to those flames burning in air. These experiments point towards the feasibility of altering buoyant flame behavior
under earth gravity and studying the large scale dynamical aspects of buoyant flames without the need of variable gravity
environment.
Received: 2 March 1999/Accepted: 6 August 1999 相似文献
3.
The mixed convection flow over a continuous moving vertical slender cylinder under the combined buoyancy effect of thermal
and mass diffusion has been studied. Both uniform wall temperature (concentration) and uniform heat (mass) flux cases are
included in the analysis. The problem is formulated in such a manner that when the ratio λ(= u
w/(u
w + u
∞), where u
w and u
∞ are the wall and free stream velocities, is zero, the problem reduces to the flow over a stationary cylinder, and when λ = 1
it reduces to the flow over a moving cylinder in an ambient fluid. The partial differential equations governing the flow have
been solved numerically using an implicit finite-difference scheme. We have also obtained the solution using a perturbation
technique with Shanks transformation. This transformation has been used to increase the range of the validity of the solution.
For some particular cases closed form solutions are obtained. The surface skin friction, heat transfer and mass transfer increase
with the buoyancy forces. The buoyancy forces cause considerable overshoot in the velocity profiles. The Prandtl number and
the Schmidt number strongly affect the surface heat transfer and the mass transfer, respectively. The surface skin friction
decreases as the relative velocity between the surface and free stream decreases.
Received on 17 May 1999 相似文献
4.
陈光祖 《应用数学和力学(英文版)》1987,8(12):1191-1199
Expressing the total potential energy of the system of a cracked body П by Williams’ infinite series solution of stress and displacement components containing coefficients An(n = 1,2,...), we obtain a set of simultaneous linear equations of unknown coefficients An by using the principle of minimum potential energy. When the set of equations is solved, the stress intensity factor K1 can be easily determined. It is equal to √2πaA1 Take a sample plate as an example. A single-edgc-cracked plate under tension, with the ratio of crack length to the width of the plate being 0.5 and the ratio of half plate height to the width of the plate being 2.0 and 2. 5, has been calculated. Only 20 - 30 coefficients are taken, and the errors in stress intensity factors are within 5%. 相似文献
5.
Craig Cowan Pierpaolo Esposito Nassif Ghoussoub Amir Moradifam 《Archive for Rational Mechanics and Analysis》2010,198(3):763-787
We study the regularity of the extremal solution of the semilinear biharmonic equation ${{\Delta^2} u=\frac{\lambda}{(1-u)^2}}We study the regularity of the extremal solution of the semilinear biharmonic equation
D2 u=\fracl(1-u)2{{\Delta^2} u=\frac{\lambda}{(1-u)^2}}, which models a simple micro-electromechanical system (MEMS) device on a ball
B ì \mathbbRN{B\subset{\mathbb{R}}^N}, under Dirichlet boundary conditions u=?n u=0{u=\partial_\nu u=0} on ?B{\partial B}. We complete here the results of Lin and Yang [14] regarding the identification of a “pull-in voltage” λ* > 0 such that a stable classical solution u
λ with 0 < u
λ < 1 exists for l ? (0,l*){\lambda\in (0,\lambda^*)}, while there is none of any kind when λ > λ*. Our main result asserts that the extremal solution ul*{u_{\lambda^*}} is regular (supB ul* < 1 ){({\rm sup}_B u_{\lambda^*} <1 )} provided
N \leqq 8{N \leqq 8} while ul*{u_{\lambda^*}} is singular (supB ul* = 1){({\rm sup}_B u_{\lambda^*} =1)} for
N \geqq 9{N \geqq 9}, in which case
1-C0|x|4/3 \leqq ul* (x) \leqq 1-|x|4/3{1-C_0|x|^{4/3} \leqq u_{\lambda^*} (x) \leqq 1-|x|^{4/3}} on the unit ball, where
C0:=(\fracl*[`(l)])\frac13{C_0:=\left(\frac{\lambda^*}{\overline{\lambda}}\right)^\frac{1}{3}} and
[`(l)]: = \frac89(N-\frac23)(N- \frac83){\bar{\lambda}:= \frac{8}{9}\left(N-\frac{2}{3}\right)\left(N- \frac{8}{3}\right)}. 相似文献
6.
We consider reaction diffusion equations of the prototype form u
t
= u
xx
+ λ u + |u|
p-1
u on the interval 0 < x < π, with p > 1 and λ > m
2. We study the global blow-up dynamics in the m-dimensional fast unstable manifold of the trivial equilibrium u ≡ 0. In particular, sign-changing solutions are included. Specifically, we find initial conditions such that the blow-up
profile u(t, x) at blow-up time t = T possesses m + 1 intervals of strict monotonicity with prescribed extremal values u
1, . . . ,u
m
. Since u
k
= ± ∞ at blow-up time t = T, for some k, this exhausts the dimensional possibilities of trajectories in the m-dimensional fast unstable manifold. Alternatively, we can prescribe the locations x = x
1, . . . ,x
m
of the extrema, at blow-up time, up to a one-dimensional constraint. The proofs are based on an elementary Brouwer degree
argument for maps which encode the shapes of solution profiles via their extremal values and extremal locations, respectively.
Even in the linear case, such an “interpolation of shape” was not known to us. Our blow-up result generalizes earlier work
by Chen and Matano (1989), J. Diff. Eq. 78, 160–190, and Merle (1992), Commun. Pure Appl. Math. 45(3), 263–300 on multi-point blow-up for positive solutions, which were not constrained to possess global extensions for all
negative times. Our results are based on continuity of the blow-up time, as proved by Merle (1992), Commun. Pure Appl. Math. 45(3), 263–300, and Quittner (2003), Houston J. Math. 29(3), 757–799, and on a refined variant of Merle’s continuity of the blow-up profile, as addressed in the companion paper Matano
and Fiedler (2007) (in preparation).
Dedicated to Palo Brunovsky on the occasion of his birthday. 相似文献
7.
Giovanni Alberti Guy Bouchitté Pierre Seppecher 《Archive for Rational Mechanics and Analysis》1998,144(1):1-46
We make the connection between the geometric model for capillarity with line tension and the Cahn‐Hilliard model of two‐phase
fluids. To this aim we consider the energies where u is a scalar density function and W and V are double‐well potentials. We show that the behaviour of F
ε
in the limit ε→0 and λ→∞ depends on the limit of ε log λ. If this limit is finite and strictly positive, then the singular limit of the energies F
ε
leads to a coupled problem of bulk and surface phase transitions, and under certain assumptions agrees with the relaxation
of the capillary energy with line tension. These results were announced in [ABS1] and [ABS2].
(Accepted November 5, 1997) 相似文献
8.
Nicolae Tarfulea 《应用数学和力学(英文版)》2000,21(3):283-290
IntroductionInthispaper,weconsidertheellipticsystem(1λ) -Δu=f(λ,x,u)-v (inΩ),-Δv=δu-γv(inΩ),u=v=0(onΩ),whereΩisasmoothboundeddomaininRN(N≥2)andλisarealparameter.Thesolutions(u,v)ofthissystemrepresentsteadystatesolutionsofreactiondiffusionsystemsderivedfromseveralap… 相似文献
9.
The transport equations for the second-order velocity structure functions 〈(δu)2〉 and 〈(δq)2〉 are used as a scale-by-scale budget to quantify the effect of initial conditions at low Reynolds numbers, typical of grid
turbulence. The validity of these equations is first investigated via hot-wire measurements of velocity and transverse vorticity
fluctuations. The transport equation for 〈(δq)2〉 is shown to be balanced at all scales, while anisotropy of the large scales leads to a significant imbalance in the equation
for 〈(δu)2〉. The effect of using similarity to evaluate the transport equation is rigorously tested. This approach has the desirable
benefit of requiring less extensive measurements to calculate the inhomogeneous term of the transport equation. The similarity
form of the 〈(δq)2〉 equation produces nearly identical results as those obtained without the similarity assumption. In the case of the 〈(δu)2〉 equation, the similarity method forces a balance at large separation, although the imbalance due to large scale anisotropy
remains. The initial conditions of the turbulence at constant R
M
≃ 10,400 (28≤ R
λ≤ 55) are changed by using three grids of different geometries. Initial conditions affect the shape and magnitude of the second-
and third-order structure functions, as well as the anisotropy of the large scales. The effect of initial conditions on the
scale-by-scale budget is restricted to the inhomogeneous term of the transport equations, while the dissipation term remains
unaffected despite the low R
λ. Scales as small as λ are affected by the changes in initial conditions. 相似文献
10.
When a nonhomogeneous solid is melting from below, convection may be induced in a thermally–unstable melt layer. In this study,
the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance
equations. The critical Darcy–Rayleigh numbers based on the melt-layer thickness, Ra
H,c, are found numerically for various conditions. For small superheats, the present predictions show that Ra
H,c is located between 27.1 and 4π
2 and it approaches the well-known results of the original Horton–Rogers–Lapwood problem. However, for high superheats, it
is dependent on the phase change rate λ and the relation of Ra
H,c λ = 25.89 is shown. 相似文献
11.
Alain Haraux 《Journal of Dynamics and Differential Equations》2007,19(4):915-933
Résumé A l’aide d’inégalités différentielles, on établit une estimation proche de l’optimalité pour la norme dans de l’unique solution bornée de u′′ + cu′ + Au = f(t) lorsque A = A
* ≥ λ I est un opérateur borné ou non sur un espace de Hilbert réel H, V = D(A
1/2) et λ, c sont des constantes positives, tandis que .
By using differential inequalities, a close-to-optimal bound of the unique bounded solution of u′′ + cu′ + Au = f(t) is obtained whenever A = A
* ≥ λ I is a bounded or unbounded linear operator on a real Hilbert space H, V = D(A
1/2) and λ, c are positive constants, while .
相似文献
12.
Juan Dávila Manuel del Pino Monica Musso Juncheng Wei 《Archive for Rational Mechanics and Analysis》2006,182(2):181-221
We consider the boundary value problem
where Ω is a smooth and bounded domain in ℝ2 and λ > 0. We prove that for any integer k ≧ 1 there exist at least two solutions u
λ
with the property that the boundary flux satisfies up to subsequences λ → 0,
where the ξ
j
are points of ∂Ω ordered clockwise in j. 相似文献
13.
We have investigated the rheological changes in two particulate-filled dental composite resin cements during the curing process
using a Micro-Fourier Rheometer (MFR). In the MFR, the sample was sandwiched between two parallel plates, and pseudorandom
small amplitude squeezing was applied by oscillating the upper plate over a range of frequencies. Fourier transforms of the
displacement signal and the resulting time dependent force signal enabled the rapid determination of the dynamic properties
G′ and G′′ over the frequency range 2π–200π rad/s . This technique permitted us to follow changes in the rheological properties of
the resin cements through the setting period. A typical result was that G′ increased from 2×103 Pa to 2×105 Pa after about 120 s, and that G′′ changed from 4×103 Pa to 4×104 Pa over the same period at frequency 40π rad/s. We also found that the dental composite resin cements show linear viscoelastic
behaviour over a range of strain amplitudes before curing, but the response becomes distinctly non-linear at the later stages
of curing for strain amplitudes γ>0.067%. 相似文献
14.
15.
In the theory of solid-solid phase transitions the deformation of an elastic body is determined via a functional containing a nonconvex energy density and a singular perturbation. We study
Frame indifference, within a linearized setting, requires that W depends only on the symmetric part of ∇u. The potential W is nonnegative and vanishes on two wells, i.e., for d = 2, on two lines in the space of matrices.
We determine, for d = 2, the Gamma limit I0 = Γ− lim ɛ→0 Iɛ. The limit I0[u] is finite only for deformations u that fulfill W(∇u)=0 almost everywhere and have sharp interfaces where ∇u has jumps. For these u, I0[u] equals the line integral over the interfaces of a surface energy density. 相似文献
16.
.Dipl.-Ing. C. Krebs .Dipl.-Ing. P. Tunte .Prof. Dr.-Ing. E. -U. Schlünder 《Heat and Mass Transfer》1982,16(4):243-250
Zusammenfassung Bei der Verdunstung eines Zweistoffgemisches in ein inertes Trägergas in einer Rieselfilmsäule hängt der Trenneffekt nicht allein von der relativen Flüchtigkeit, sondern auch vom Verhältnis der Diffusionsgeschwindigkeiten beider Stoffe im Trägergas ab. Bei der Verdunstung von Isopropanol-Wasser-Gemischen in trockene Luft zeigte sich, daß das Verhältnis der gasseitigen Stoffübergangskoeffizienten bei großen Gasgeschwindigkeiten etwa gleich der Wurzel aus dem Verhältnis der Diffusionskoeffizienten war. Da der Alkolhol im Trägergas langsamer diffundiert als das Wasser, konnten flüssige Mischungen durch absatzweise Verdunstung mit Alkohol angereichert werden, obwohl der Alkohol leichterflüchtig war.Bei kleinen Gasgeschwindigkeiten lieferte der Gleichstrom immer höhere Stoffübergangskoeffizienten als der Gegenstrom. Beim Gleichstrom wurde der Einfluß des Diffusionskoeffizienten auf den Stoffübergangskoeffizienten mit abnehmender Geschwindigkeit größer, beim Gegenstrom wurde er schwächer.
The influence of diffusion on selectivity of desorption in a wetted wall column
The desorption of a binary mixture into a stripping gas flowing through a wetted-wall column is not only governed by the vapour-liquid-equilibrium. Gas-phase diffusivities of the evaporating components have also to be taken into account. Batch wise stripping experiments of Propanol(2)-water-mixtures using dry air as the stripping gas showed, that at high gas rates the mass transfer coefficients were proportional to the square root of the diffusivities. Therefore it was possible to enrich the residual mixture with Propanol(2) because of its lower diffusivity, although Propanol(2) is more volatile.At low gas rates the mass-transfer coefficients were higher for cocurrent flow than for countercurrent flow. Besides at low gas rates the diffusivities had more influence on mass-transfer for cocurrent flow than for countercurrent flow.
Abbreviations
Formelzeichen A [m2] Oberfläche des Rieselfilms2 rph·L - F [m2] freie Strömungsquerschnittfläche für das Gas in der Rieselfilmsäule: r ph 2 - K g [–] kinetischer Trennfaktor - k l [–] Kennzahl für den flüssigseitigen Widerstand - L [m] Länge der Rieselfilmsäule - n [mol/m3] molare Dichte - n l [mol] Behältermolmenge - N l,0 [mol] Behältermolmenge zu Beginn des Versuchs - n i [mol/m2 s] Molenstromdichte der Komponentei - N i [mol/s] Molenstrom der Komponentei - N g [mol/s] Molenstrom des Trägergases - p [Pa] Druck - p i 0 [Pa] Dampfdruck der reinen Komponente - r [m] Radius - r i [m] Innenradius des Rieselrohres - r 1 [–] molarer bezogener Verdunstungsstrom, definiert in Gl. (3) - r 1 [–] molarer bezogener Verdunstungsstrom, definiert in Gl. (9) - S 1 [–] Selektivität der Desorption - s l [m] Filmdicke - u [m/s] Geschwindigkeit - t [s] Zeit - V [m3/s] Volumenstrom - x [–] Molenbruch in der Flüssigkeit - y [–] Molenbruch in der Gasphase - z [m] Längenkoordinate Griechische Buchstaben T [–] thermodynamischer Trennfaktor - [m/s] Stoffübergangskoeffizient - [–] Aktivitätskoeffizient - [m2/s] Diffusionszahl - [°C] Temperatur - v [m2/s] kinematische Viskosität - [–] Absättigung Indices a Austritt - e Eintritt - g gasseitig - i Komponente - l flüssigseitig - Ph Phasengrenze, Gleichgewicht - RFS Rieselfilmsäule - 1 Isopropanol - 2 Wasser dimensionslose Kennzahlen St g = g/¯u g - Gz g =4/ V g/ g·L - Sh g = g·2r ph - Re g =¯u g·2r ph/vg - Sc g =v g/ g - NTU g =·A{itdng/N g - Re l =V l/2r i·v l 相似文献17.
Simulations of monodisperse and polydisperse (μ
2(A) = 0.13±0.002) 2D foam samples undergoing simple shear are performed using the 2D viscous froth (VF) model. These simulations
clearly demonstrate shear localisation. The dependence of localisation length on the product λV (shearing velocity V times the wall drag coefficient λ) is examined and is shown to agree qualitatively with published experimental data. A wide range of localisation lengths is
found at low λV, an effect which is attributed to the existence of distinct yield and limit stresses. The general continuum model is extended
to incorporate such an effect and its parameters are subsequently related to those of the VF model. A Herschel–Bulkley exponent
of a = 0.3 is shown to accurately describe the observed behaviour. The localisation length is found to be independent of λV for monodisperse foam samples. 相似文献
18.
If a pair of material line elements, passing through a typical particle P in a body, subtend an angle Θ before deformation, and Θ+γ after deformation, the pair of material elements is said to be
sheared by the amount γ. Here all pairs of material elements at P are considered for arbitrary deformations. Two main problems are addressed and solved. The first is the determination of
all pairs of material line elements at P which are unsheared. The second is the determination of that pair of material line elements at P which suffers the maximum shear.
All unsheared pairs of material elements in a given plane π(S) with normal S passing through P are considered. Provided π(S) is not a plane of central circular section of the C-ellipsoid at P (where C is the right Cauchy-Green strain tensor), it is seen that corresponding to any material element in π(S) there is, in general, one companion material element in π(S) such that the element and its companion are unsheared.
There are, however, two elements in π(S) which have no companions. We call their corresponding directions \textit{limiting directions.} Equally inclined to the direction
of least stretch in the plane π(S), the limiting directions play a central role. It is seen that, in a given plane π(S), the pair of material line elements which suffer the maximum shear lie along the limiting directions in π(S). If Θ
L
is the acute angle subtended by the limitig directions in π(S) before deformation, then this angle is sheared into its supplement π−Θ
L
so that the maximum shear γ*;(S) is γ*=π− 2 Θ
L
. If S is given and C is known, then Θ
L
may be determined immediately. Its calculation does not involve knowing the eigenvectors or eigenvalues of C.
When all possible planes through P are considered, it is seen that the global maximum shear γ*
G
occurs for material elements lying along the limiting directions in the plane spanned by the eigenvectors of C corresponding to the greatest principal stretch λ3 and the least λ1. The limiting directions in this principal plane of C subtend the angle and . Generally the maximum shear does not occur for a pair of material elements which are originally orthogonal.
For a given material element along the unit vector N, there is, in general, in each plane π(S passing through N at P, a companion vector M such that material elements along N and M are unsheared. A formula, originally due to Joly (1905), is presented for M in terms of N and S.
Given an unsheared pair π(S), the limiting directions in π(S) are seen to be easily determined, either analytically or geometrically.
Planar shear, the change in the angle between the normals of a pair of material planar elements at X, is also considered. The theory of planar shear runs parallel to the theory of shear of material line elements. Corresponding
results are presented.
Finally, another concept of shear used in the geology literature, and apparently due to Jaeger, is considered. The connection
is shown between Cauchy shear, the change in the angle of a pair of material elements, and the Jaeger shear, the change in
the angle between the normal N to a planar element and a material element along the normal N. Although Jaeger's shear is described in terms of one direction N, it is seen to implicitly include a second material line element orthogonal to N.
Accepted: May 25, 1999 相似文献
19.
The Xu & Yan scale-adaptive simulation (XYSAS) model is employed to simulate the flows past wavy cylinders at Reynolds number 8 × 10 3.This approach yields results in good agreement with experimental measurements.The mean flow field and near wake vortex structure are replicated and compared with that of a corresponding circular cylinder.The effects of wavelength ratios λ/D m from 3 to 7,together with the amplitude ratios a /D m of 0.091 and 0.25,are fully investigated.Owing to the wavy configuration,a maximum reduction of Strouhal number and root-meansquare (r.m.s) fluctuating lift coefficients are up to 50% and 92%,respectively,which means the vortex induced vibration (VIV) could be effectively alleviated at certain larger values of λ/D m and a /D m.Also,the drag coefficients can be reduced by 30%.It is found that the flow field presents contrary patterns with the increase of λ/D m.The free shear layer becomes much more stable and rolls up into mature vortex only further downstream when λ/D m falls in the range of 5-7.The amplitude ratio a /D m greatly changes the separation line,and subsequently influences the wake structures. 相似文献
20.
The existence and linear stability problem for the Stokes periodic wavetrain on fluids of finite depth is formulated in terms
of the spatial and temporal Hamiltonian structure of the water-wave problem. A proof, within the Hamiltonian framework, of
instability of the Stokes periodic wavetrain is presented. A Hamiltonian center-manifold analysis reduces the linear stability
problem to an ordinary differential eigenvalue problem on ℝ4. A projection of the reduced stability problem onto the tangent space of the 2-manifold of periodic Stokes waves is used
to prove the existence of a dispersion relation Λ(λ,σ, I
1, I
2)=0 where λ ε ℂ is the stability exponent for the Stokes wave with amplitude I
1 and mass flux I
2 and σ is the “sideband’ or spatial exponent. A rigorous analysis of the dispersion relation proves the result, first discovered
in the 1960's, that the Stokes gravity wavetrain of sufficiently small amplitude is unstable for F ε (0,F0) where F
0 ≈ 0.8 and F is the Froude number. 相似文献