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1.
2.
A generalized thermal boundary condition is derived to include all thermal effects of a thin layer which is in thermal contact
with an adjacent domain. The thin layer may be a stationary or moving solid-skin or fluid-film. The included thermal effects
of the thin layer are the thermal capacity of the layer, thermal diffusion, enthalpy flow, viscous dissipation within the
layer, convective losses from the layer, and other effects. Six different kinds of thermal boundary conditions can be obtained
as special cases of the generalized boundary condition. The generalized boundary condition is given for perfect and imperfect
thermal contact between the thin layer and its adjacent domain. The importance of the generalized boundary condition is demonstrated
in an example.
Received on 23 December 1996 相似文献
3.
Saneshan Govender 《Transport in Porous Media》2007,67(3):431-439
The linear stability theory is used to investigate analytically the effect of a permeable mush–melt boundary condition on
the stability of solutal convection in a mushy layer of homogenous permeability at the near eutectic (solid) limit. The results
clearly show that, in contrast to the impermeable mush–melt interface boundary condition, the application of the permeable
mush–melt interface boundary condition destabilizes the convection in a mushy layer. 相似文献
4.
A generalized thermal boundary condition is derived for the hyperbolic heat conduction equation to include all thermal effects
of a thin layer, whether solid-skin or fluid film, moving or stationary, in perfect or imperfect thermal contact with an adjacent
domain. The thin layer thermal effects include, among others, thermal capacity of the layer, thermal diffusion, enthalpy flow,
viscous dissipation within the layer and convective losses from the layer. Six different kinds of thermal boundary conditions
can be obtained as special cases of the generalized boundary condition. The importance of the generalized boundary condition
is demonstrated comprehensively in an example. The effects of different geometrical and thermophysical properties on the validity
of the generalized thermal boundary condition are investigated.
Received on 23 May 2001 / Published online: 29 November 2001 相似文献
5.
Chou Huan-wen 《应用数学和力学(英文版)》1983,4(6):855-863
In this paper,the method of composite expansions which was proposed by W. Z. Chien (1948)[5]is extended to investigate two-parameter boundary layer problems.For the problems of symmetric deformations of the spherical shells under the action of uniformly distribution load q, its nonlinear equilibrium equations can be written as follows: where ε and δ are undetermined parameters.If δ=1 and ε is a small parameter, the above-mentioned problem is called first boundary layer problem; if ε is a small parameter, and δ is a small parameter, too, the above-mentioned problem is called second boundary layer problem.For the above-mentioned problems, however, we assume that the constants ε, δ and p satisfy the following equation: εp=1-ε In defining this condition by using the extended method of composite expansions, we find the asymptotic solution of the above-mentioned problems with the clamped boundary conditions. 相似文献
6.
. This paper is concerned with the initial‐boundary‐value problem for a nonlinear hyperbolic system of conservation laws.
We study the boundary layers that may arise in approximations of entropy discontinuous solutions. We consider both the vanishing‐viscosity
method and finite‐difference schemes (Lax‐Friedrichs‐type schemes and the Godunov scheme). We demonstrate that different regularization methods generate different boundary layers. Hence, the boundary condition can be formulated only if an approximation scheme is selected first. Assuming
solely uniform bounds on the approximate solutions and so dealing with solutions, we derive several entropy inequalities satisfied by the boundary layer in each case under consideration. A Young
measure is introduced to describe the boundary trace. When a uniform bound on the total variation is available, the boundary
Young measure reduces to a Dirac mass.
From the above analysis, we deduce several formulations for the boundary condition which apply whether the boundary is characteristic
or not. Each formulation is based on a set of admissible boundary values, following the terminology of Dubois & LeFloch[15]. The local structure of these sets and the well‐posedness of the corresponding initial‐boundary‐value problem are investigated.
The results are illustrated with convex and nonconvex conservation laws and examples from continuum mechanics.
(Accepted July 2, 1998) 相似文献
7.
The flow developing downstream of a step change from smooth to rough surface condition is studied in the light of Townsend’s
wall similarity hypothesis. Previous studies seem to support the hypothesis for channel and pipe flows, but there are considerable
controversies about its application to boundary layers and in particular to surface roughness formed by spanwise bars. It
has been suggested that this controversy arises from insufficient separation of scales between the boundary layer thickness
and the roughness length scale. An experimental investigation has therefore been undertaken where the flow evolves from a
fully developed smooth wall boundary layer at high Reynolds numbers over a step in surface roughness (Re
θ = 13,400 at the step). The flow is mapped through the development of the internal layer until the flow is fully developed
over the rough wall. The internal layer is found to grow as δ ∼ X
0.73, and after about 15 boundary layer thicknesses at the step, the internal layer has reached the outer edge of the incoming
layer. At the last rough wall measurement station, the Reynolds number has grown to Re
θ ≈ 32,600 and the ratio of boundary layer to roughness length scales is δ/k ≈ 140. The outer layer differences between the smooth and the rough wall data were found to be sufficiently small to conclude
that for this setup the Townsend’s wall similarity hypothesis appears to hold. 相似文献
8.
We study a 2 × 2 system of balance laws that describes the evolution of a granular material (avalanche) flowing downhill.
The original model was proposed by Hadeler and Kuttler (Granul Matter 2:9–18, 1999). The Cauchy problem for this system has
been studied by the authors in recent papers (Amadori and Shen in Commun Partial Differ Equ 34:1003–1040, 2009; Shen in J
Math Anal Appl 339:828–838, 2008). In this paper, we first consider an initial-boundary value problem. The boundary condition
is given by the flow of the incoming material. For this problem we prove the global existence of BV solutions for a suitable
class of data, with bounded but possibly large total variations. We then study the “slow erosion (or deposition) limit”. We
show that, if the thickness of the moving layer remains small, then the profile of the standing layer depends only on the
total mass of the avalanche flowing downhill, not on the time-law describing the rate at which the material slides down. More
precisely, in the limit as the thickness of the moving layer tends to zero, the slope of the mountain is provided by an entropy
solution to a scalar integro-differential conservation law. 相似文献
9.
The paper deals with a steady coupled dissipative layer, called Marangoni mixed convection boundary layer, which can be formed
along the interface of two immiscible fluids, in surface driven flows. The mixed convection boundary layer is generated when
besides the Marangoni effects there are also buoyancy effects due to gravity and external pressure gradient effects. We shall
use a model proposed by Golia and Viviani (L’ Aerotecnica missili e Spazio 64 (1985) 29–35, Meccanica 21 (1986) 200–204) wherein the Marangoni coupling condition has been included into the boundary conditions at the interface.
The similarity equations are first determined, and the pertinent equations are solved numerically for some values of the governing
parameters and the features of the flow and temperature fields as well as the interface velocity and heat transfer at the
interface are analysed and discussed. 相似文献
10.
H. Beirão da Veiga 《Journal of Mathematical Fluid Mechanics》2007,9(4):506-516
In reference [7] it is proved that the solution of the evolution Navier–Stokes equations in the whole of R
3 must be smooth if the direction of the vorticity is Lipschitz continuous with respect to the space variables. In reference
[5] the authors improve the above result by showing that Lipschitz continuity may be replaced by 1/2-H?lder continuity. A
central point in the proofs is to estimate the integral of the term (ω · ∇)u · ω, where u is the velocity and ω = ∇ × u is the vorticity. In reference [4] we extend the main estimates on the above integral term to solutions under the slip boundary
condition in the half-space R
+3. This allows an immediate extension to this problem of the 1/2-H?lder sufficient condition.
The aim of these notes is to show that under the non-slip boundary condition the above integral term may be estimated as well
in a similar, even simpler, way. Nevertheless, without further hypotheses, we are not able now to extend to the non slip (or
adherence) boundary condition the 1/2-H?lder sufficient condition. This is not due to the “nonlinear" term (ω · ∇)u · ω but to a boundary integral which is due to the combination of viscosity and adherence to the boundary. On the other hand,
by appealing to the properties of Green functions, we are able to consider here a regular, arbitrary open set Ω.
相似文献
11.
Marshall Slemrod 《Archive for Rational Mechanics and Analysis》1999,149(1):1-22
. We study the asymptotic behavior as time goes to infinity of solutions to the initial‐boundary‐value problem on the half
space for a one‐dimensional model system for the isentropic flow of a compressible viscous gas, the so‐called p‐system with viscosity. As boundary conditions, we prescribe the constant state at infinity and require that the velocity
be zero at the boundary . When the velocity at infinity is negative and satisfies a condition on the magnitude, we prove that if the initial data
are suitably close to those for the corresponding outgoing viscous shock profile, which is suitably far from the boundary,
then a unique solution exists globally in time and tends toward the properly shifted viscous shock profile as the time goes
to infinity. The proof is given by an elementary energy method.
(Accepted March 2, 1998) 相似文献
12.
The method of boundary layer with multiple scales and computer algebra were applied to study the asymptotic behavior of solution
of boundary value problems for a class of system of nonlinear differential equations. The asymptotic expansions of solution
were constructed. The remainders were estimated. And an example was analysed. It provides a new foreground for the application
of the method of boundary layer with multiple scales.
Contributed by Jiang Fu-ru, Original Member of Editorial Committe, AMM
Biography: Xie La-bing (1976∼); Jiang Fu-ru(1927∼) 相似文献
13.
Vortex Shedding from a Hemisphere in a Turbulent Boundary Layer 总被引:1,自引:0,他引:1
Michael Manhart 《Theoretical and Computational Fluid Dynamics》1998,12(1):1-28
Supercritical turbulent boundary layer flow over a hemisphere with a rough surface (Re= 150000) has been simulated using Large Eddy Simulation (LES) and analyzed using the Karhunen--Loève expansion (“Proper Orthogonal
Decomposition,” POD). The time-dependent inflow condition is provided from a separate LES of a boundary layer developing behind
a barrier fence and a set of vorticity generators. LES results using significantly different grid resolutions are compared
with a corresponding wind tunnel experiment to demonstrate the reliability of the simulation. The separation processes are
analyzed by inspecting second-order moments, time spectra, and instantaneous velocity distributions. Applying POD, a detailed
study of the spatiotemporal structure of the separation processes has been carried out. From this analysis it can be concluded
that the major event in the separated flow behind the obstacle is the shedding of “von Kármán”-type vortices, which can be
represented by the first three energetically dominant modes.
Received 23 January 1997 and accepted 19 February 1998 相似文献
14.
15.
This work deals with the mode III fracture problem of a cracked functionally graded piezoelectric surface layer bonded to
a cracked functionally graded piezoelectric substrate. The cracks are normal to the interface and the electro-elastic material
properties are assumed to be varied along the crack direction. Potential and flux types of boundary condition are assigned
on the edge of the surface layer. The problem under the assumptions of impermeable and permeable cracks can be formulated
to the standard singular integral equations, which are solved by using the Gauss–Chebyshev technique. The effects of the boundary
conditions, the material properties and crack interaction on the stress and electric displacement intensity factors are discussed. 相似文献
16.
In the present paper, we consider the strain analysis near the crack parallel to boundary surfaces of a linear isotropic elastic
layer of constant thickness. We pose the problem of minimizing the opening of crack faces when a normal force is applied to
the boundary of the layer. The control secondary loading is a normal stress uniformly distributed over the boundary surfaces
as to oppose the opening caused by the external applied force. We show that the most dangerous are tangential deformations,
and the normal ones are always by many times less dangerous.
__________
Published in Neliniini Kolyvannya, Vol. 8, No. 2, pp. 265–277, April–June, 2005. 相似文献
17.
Fluid flow at the interface of a porous medium and an open channel is the governing phenomenon in a number of processes of
industrial importance. Traditionally, this has been modeled by applying the Brinkman’s modification of Darcy’s law to obtain
the velocity profile in terms of an additional parameter known as the “apparent viscosity” or the “slip coefficient”. To test
this ad hoc approach, a detailed experimental investigation of the flow was conducted using Laser Doppler Anemometry (LDA) in the close
vicinity of the permeable boundary of a porous medium. The porous medium used in the experiments consisted of a network of
continuous glass strands woven together in a random fashion.
A Hele–Shaw cell was partially filled with a fibrous preform such that an open channel flow is coupled with the Darcy flow
inside the preform through the permeable interface of the preform. The open channel portion of the Hele–Shaw cell also acts
as an ideal porous medium of known in-plane permeability which is much higher than the permeability of the fibrous porous
medium. A viscous fluid is injected at a constant flow rate through the above arrangement and a saturated and steady flow
is established through the cell. Using LDA, steady state velocity profiles are accurately measured by traversing across the
cell in the direction perpendicular to the flow. A series of experiments were conducted in which fluid viscosity, flow rate,
solid volume fraction of the porous medium and depth of the Hele–Shaw cell were varied. For each and every case in which the
conditions for Hele–Shaw approximation were valid, the depth of the boundary layer zone or the screening length inside the
fibrous preform was found to be of the order of the channel depth. This is much larger as compared to the Brinkman’s prediction
of the screening length which is of the order of √K, where K is the permeability of the fibrous porous medium. Based on this finding, we modified the boundary condition in the Brinkman’s
solution and found that the velocity profile results compared well with the experimental data for the planar geometry and
the fibrous preforms for volume fractions of 7%, 14% and 21% for Hele–Shaw cell depths of 1.6 and 3.175 mm. For a cell depth
of 4.8 cm, in which the Hele–Shaw approximation was not valid, the boundary layer thickness or the screening length was found
to be less than the mold or channel depth but was still much larger than the Brinkman’s prediction.
Received: 10 May 1996 / Accepted: 26 August 1996 相似文献
18.
An experimental investigation of the three-dimensional boundary layer induced by a Rankine-like vortex with its axis normal
to a stationary disk is described. The velocity field through the boundary layer was measured for Reynolds number Re (based on the tangential velocity and radius at the disk edge) ranging from 10 000 to 25 000 at various radial distances
by means of a 4-beam, 2-component Laser Doppler Anemometer. Our results show that the nature of the boundary layer is affected
by two factors: an inflexional instability caused by the crossflow velocity profile and a stability factor caused by the favorable
pressure gradient. At lower Reynolds number, the radial pressure gradient has a very strong stabilizing effect on the boundary
layer and acts to revert it to its laminar state upstream of the effusing core. At higher Re the inflexional instability caused by the crossflow velocity dominates while the stabilizing influence of the favorable pressure
gradient recedes. As such, laminar reversion likely occurs closer to the effusion core. Thus, the point of laminar reversion
moves closer to the effusion core as the Reynolds number is increased.
Received 23 May 1996 / Accepted 29 July 1996 相似文献
19.
Guangtao Duan Takuya Matsunaga Akifumi Yamaji Seiichi Koshizuka Mikio Sakai 《国际流体数值方法杂志》2021,93(1):148-175
Corrective matrix that is derived to restore consistency of discretization schemes can significantly enhance accuracy for the inside particles in the Moving Particle Semi‐implicit method. In this situation, the error due to free surface and wall boundaries becomes dominant. Based on the recent study on Neumann boundary condition (Matsunaga et al, CMAME, 2020), the corrective matrix schemes in MPS are generalized to straightforwardly and accurately impose Neumann boundary condition. However, the new schemes can still easily trigger instability at free surface because of the biased error caused by the incomplete/biased neighbor support. Therefore, the existing stable schemes based on virtual particles and conservative gradient models are applied to free surface and nearby particles to produce a stable transitional layer at free surface. The new corrective matrix schemes are only applied to the particles under the stable transitional layer for improving the wall boundary conditions. Three numerical examples of free surface flows demonstrate that the proposed method can help to reduce the pressure/velocity fluctuations and hence enhance accuracy further. 相似文献