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1.
Heat transfer in laminar and turbulent flows in the thermal entrance region of concentric annuli: Axial heat conduction effects in the fluid 总被引:2,自引:0,他引:2
The present analytical study investigates the influence of axial heat conduction within the flow on the heat transfer in
the thermal entrance region of a concentric annular duct with laminar and turbulent internal flow. The solution is based on
a decomposition of the elliptic energy equation into a pair of first order partial differential equations. By using a new
defined vector norm it is possible to obtain a selfadjoint eigenvalue problem for the extended Graetz problem even though
the original convective diffusion operator is non-selfadjoint. The obtained exact analytical solutions for the Graetz problem
with axial heat conduction are as simple to compute as the related solutions of the parabolic problem.
Received on 28 October 1996 相似文献
2.
Steady convective mass transfer to or from fluid interfaces in pores of angular cross-section is theoretically investigated.
This situation is relevant to a variety of mass transport process in porous media, including the fate of residual non-aqueous
phase liquid ganglia and gas bubbles. The model incorporates the essential physics of capillarity and solute mass transfer
by convection and diffusion in corner fluid filaments. The geometry of the corner filaments, characterized by the fluid–fluid
contact angle, the corner half-angle and the interface meniscus curvature, is accounted for. Boundary conditions of zero surface
shear (‘perfect-slip’) and infinite surface shear (‘no-slip’) at the fluid–fluid interface are considered. The governing equations
for laminar flow within the corner filament and convective diffusion to or from the fluid–fluid interface are solved using
finite-element methods. Flow computations are verified by comparing the dimensionless resistance factor and hydraulic conductance
of corner filaments against recent numerical solutions by Patzek and Kristensen (J. Colloid Interface Sci 236, 305–317 2001). Novel results are obtained for the average effluent concentration as a function of flow geometry and pore-scale
Peclet number. These results are correlated to a characteristic corner length and local pore-scale Peclet number using empirical
equations appropriate for implementation in pore network models. Finally, a previously published “2D-slit” approximation to
the problem at hand is checked and found to be in considerable error. 相似文献
3.
The problem of mass transfer of aerosols with axial, as well as radial, diffusion in laminar flow in a narrow rectangular
channel is studied. Two cases are investigated. The first case is where all particles enter the channel inlet and none form
within the channel; and the second, where no particles enter the channel, and “formation in flight” occurs within the channel.
For each case, analyses are made for both slug and Poiseuille flows.
The first twenty modes of the eigenvalues, the eigenfunctions, and the coefficients of series expansion are obtained for several
diffusion Péclet numbers, Pe. The first twelve of them are presented for Pe=1, 5, 10, 100, and ∞. Asymptotic expressions for
the eigenvalues and the eigenfunctions are also given.
The effects of axial diffusion on the local particle concentration, the bulk concentration, the Sherwood number, and the fraction
of aerosols arriving at any cross-section of the channel are studied for various diffusion Péclet numbers. It was found that,
for diffusion with or without formation in flight, the effect of axial diffusion may be neglected at an axial distance from
the channel inlet greater than one and a half times that of the channel height for 1<Pe<100. 相似文献
4.
This investigation explores the mass/heat transfer from a wall-mounted block in a rectangular fully developed channel flow.
The naphthalene sublimation scheme was used to measure the level of local mass transfer from the block’s surfaces. The heat
transfer coefficient can be obtained by analogy between heat and mass transfer. The effects of the Reynolds number on the
local mass transfer from the block’s surfaces have been widely discussed. Results showed that, owing to the flow complexity
induced by vortices around the block, the block’s surfaces appeared four different spatial Sherwood number distributions,
termed “Wave type”, “U type”, “Slant type”, and “Pit type”. A change in the Reynolds number significantly altered the spatial Sherwood number distributions on the block’s surfaces.
Besides, four correlations between the Reynolds number and the surface-averaged Sherwood number were presented for the front,
top, side, and rear surfaces of the block at a given block’s height, for the purpose of practical applications. 相似文献
5.
The interior transmission problem (ITP), which plays a fundamental role in inverse scattering theories involving penetrable
defects, is investigated within the framework of mechanical waves scattered by piecewise-homogeneous, elastic or viscoelastic
obstacles in a likewise heterogeneous background solid. For generality, the obstacle is allowed to be multiply connected,
having both penetrable components (inclusions) and impenetrable parts (cavities). A variational formulation is employed to
establish sufficient conditions for the existence and uniqueness of a solution to the ITP, provided that the excitation frequency does not belong
to (at most) countable spectrum of transmission eigenvalues. The featured sufficient conditions, expressed in terms of the
mass density and elasticity parameters of the problem, represent an advancement over earlier works on the subject in that
(i) they pose a precise, previously unavailable provision for the well-posedness of the ITP in situations when both the obstacle
and the background solid are heterogeneous, and (ii) they are dimensionally consistent, i.e., invariant under the choice of
physical units. For the case of a viscoelastic scatterer in an elastic solid it is further shown, consistent with earlier
studies in acoustics, electromagnetism, and elasticity that the uniqueness of a solution to the ITP is maintained irrespective
of the vibration frequency. When applied to the situation where both the scatterer and the background medium are viscoelastic, i.e., dissipative, on the other hand, the same type of analysis
shows that the analogous claim of uniqueness does not hold. Physically, such anomalous behavior of the “viscoelastic-viscoelastic”
case (that has eluded previous studies) has its origins in a lesser known fact that the homogeneous ITP is not mechanically
insulated from its surroundings—a feature that is particularly cloaked in situations when either the background medium or
the scatterer are dissipative. A set of numerical results, computed for ITP configurations that meet the sufficient conditions
for the existence of a solution, is included to illustrate the problem. Consistent with the preceding analysis, the results
indicate that the set of transmission values is indeed empty in the “elastic-viscoelastic” case, and countable for “elastic-elastic”
and “viscoelastic-viscoelastic” configurations. 相似文献
6.
In this paper a rigorous dual-porosity model is formulated, which accurately represents the coupling between large-scale fractures
and the micropores within dual porosity media. The overall structure of the porous medium is conceptualized as being blocks
of diffusion dominated micropores separated by natural fractures (e.g. cleats for coal) through which Darcy’s flow occurs.
In the developed model, diffusion in the matrix blocks is fully coupled to the pressure distribution within the fracture system.
Specific assumptions on the pressure behaviour at the matrix boundary, such as step-time function employed in some earlier
studies, are not invoked. The model involves introducing an analytical solution for diffusion within a matrix block, and the
resultant combined flow equation is a nonlinear integro-(partial) differential equation. Analyses to the equation in this
text, in addition to the theoretical development of the proposed model, include: (1) discussion on the “fading memory” of
the model; (2); one-dimensional perturbation solution subject to a specific condition; and (3) asymptotic analyses of the
“long-time” and “short-time” responses of the flow. Two previous models, the Warren-Root and the modified Vermeulen models,
are compared with the proposed model. The advantages of the new model are demonstrated, particularly for early time prediction
where the approximations of these other models can lead to significant error. 相似文献
7.
The dye visualization experiments show that a dual leading-edge vortex (LEV) structure exists on the suction side of a simplified
butterfly model of Papilio ulysses at α = 8°−12°. Furthermore, the results of particle image velocimetry (PIV) measurement indicate that the axial velocity of the
primary (outer) vortex core reaches the lower extreme value while a transition from a “wake-like” to a “jet-like” axial velocity
profile occurs. The work reveals for the first time the existence of dual LEV structure on the butterfly-like forward-sweep
wing configuration. 相似文献
8.
V. K. Kedrinskii 《Journal of Applied Mechanics and Technical Physics》2011,52(3):363-370
Specific features of the dynamics of the wave field structure and growth of a “collective” bubble behind the decompression
wave front in the “Lagrangian” section of the formed cavitation zone are numerically analyzed. Two cases are considered: with
no diffusion of the dissolved gas from the melt to cavitation nuclei and with the diffusion flux providing an increase in
the gas mass in the bubbles. In the first case, it is shown that an almost smooth decompression wave front approximately 100
m wide is formed, with minor perturbations that appear when the front of saturation of the cavitation zone with nuclei is
passed. In the case of the diffusion process, the melt state behind the saturation front is principally different: jumps in
mass velocity and viscosity are observed in the vicinity of the free surface, and the pressure in the “collective” cavitation
bubble remains unchanged for a sufficiently long time interval, despite the bubble growth and intense diffusion of the gas
from the melt. It is assumed that the diffusion process (and, therefore, viscosity) actually become factors determining the
dynamics of growth of cavitation bubbles beginning from this time interval. A pressure jump is demonstrated to form near the
free surface. 相似文献
9.
Francisco J. Valdés-Parada Jose Alvarez-Ramirez Benoît Goyeau J. Alberto Ochoa-Tapia 《Transport in Porous Media》2009,78(3):459-476
In this paper, mass transfer at the fluid–porous medium boundaries is studied. The problem considers both diffusive and convective
transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that
is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction
and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved
as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., ), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a
microporous medium. 相似文献
10.
According to constructal theory, the “generation of flow configuration” is a universal phenomenon in physics. This phenomenon is covered by the constructal law: “For a finite-size flow system to persist in time (to live)
it must evolve such that it provides greater and greater access to the currents that flow through it.” This paper shows how
the constructal law can be used to (1) predict and explain features of “design” in nature, and (2) design effective strategies
and configurations for engineering. Many natural flow designs rely on two flow mechanisms: channels with relatively low resistivity,
interwoven with diffusion across the interstices. The “design” is the balance between the two mechanisms. The flow from line
to line (or plane to plane) through a sufficiently fine porous medium encounters less resistance than the flow through parallel
channels when it is configured as trees that alternate with upside down trees: from this follows the prediction that natural
porous media (e.g., hill slope) should be multiscale (bidisperse) and non-uniformly distributed. A porous medium contaminated
with ionic species is decontaminated the fastest when the ionic flow is configured as two flow mechanisms in balance: “channeling”
driven by potential differences between optimally positioned electrodes, and diffusion driven by concentration differences
across the interstices between the channels. 相似文献
11.
M. Sugawara E. Tamura Y. Satoh Y. Komatsu M. Tago H. Beer 《Heat and Mass Transfer》2007,43(10):1009-1018
Visual observations reveal a complicated flow in the liquid melt and a melting front configuration resulting from horizontal
ice plate melting from above into a 20 wt% calcium chloride aqueous solution. The initial temperature of the ice plate and
the mixture are both −5°C. Small scale “mountain and valley” structures (∼1 mm) appear on the flat melting front just after
melting begins, which have been called “sharkskin”. Innumerable upward and downward flows appear near the sharkskin and are controlled by its “mountain and valley” structure. These typical flows will considerably promote the melting of the
ice plate to be 30% larger as compared to the numerically predicted results assuming a flat melting front (i.e., without the
sharkskin), and also by three times larger compared with the results for melting from below. 相似文献
12.
There are problems in linear elasticity theory whose corresponding deformations, usually associated with singular stress fields,
are open to question because they are not one-to-one and predict self-intersection. Recently, a theory has been advanced to
handle such situations, which consists in minimizing the quadratic energy functional of linear elasticity subject to the constraint
of local injectivity. In particular, the Jacobian of the deformation gradient is required to be not less than an arbitrarily
small positive quantity, and, thus, the local orientation is preserved. Here, this theory is applied to the classical Lekhnitskii
problem of an elastic aelotropic circular disk which is loaded on its boundary by a uniform radial pressure. Without the injectivity
constraint, this classical linear problem has a unique solution. This example, with the injectivity constraint, already has
been considered in previous works, but radial symmetry was assumed in order to reduce the problem from 2D to 1D. Here, making
use of an interior penalty formulation, a numerical scheme is implemented that solves a full 2D problem. Remarkably, it is
shown that there are values of the material moduli for which the minimal potential energy solution is no longer symmetric,
producing a strong azimuthal shear and nominally a 180° rotation of an internal central core of the disk. Although the elastic
strain energy is quadratic and convex, the strongly nonlinear character of the constraint allows for bifurcation instabilities.
We gratefully acknowledge the partial support of the Minnesota Supercomputing Institute and the Italian “Ministero per l’Università e la Ricerca Scientifica” under the program PRIN 2005 “Affidabilità di elementi
in vetro strutturale: indagini teoriche e sperimentali sulla risposta termo-meccanica del materiale e di strutture trasparenti
di tipo innovativo”. R.F. gratefully acknowledges the Department of Civil and Environmental Engineering at the Politecnico di Bari, Italy, for their kind hospitality and support during his visit of 2006. We appreciate the helpful comments and suggestions
of Paolo Podio-Guidugli on an earlier draft of this work. 相似文献
13.
The mechanical model was established for the anti-plane fracture problem of a functionally graded coating–substrate system
with a coating crack inclined to the weak/micro-discontinuous interface. The Cauchy singular integral equation for the crack
was derived using Fourier integral transform, and the Lobatto–Chebyshev collocation method put up by Erdogan and Gupta was
used to get its numerical solution. Finally, the effects of the weak/micro-discontinuity of the interface on SIFs were analyzed,
the “affected regions” corresponding to the two crack tips have been obtained and their engineering significance was discussed.
It was indicated that, for the crack tip in the corresponding “affected region”, to reduce the weak-discontinuity of the interface
and to make the interface micro-discontinuous are the two effective ways to reduce the SIF, and the latter way always has
more remarkable SIF-reduction effect. For the crack tip outside the “affected region”, its SIF is mainly influenced by material
stiffness, and to prevent such a tip from growing toward the interface “softer coating and stiffer substrate” is a more advantageous
combination than “stiffer coating and softer substrate”. 相似文献
14.
Manufacturing tolerant topology optimization 总被引:6,自引:0,他引:6
Ole Sigmund 《Acta Mechanica Sinica》2009,25(2):227-239
In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization approach, under- and over-etching is modelled by image processing-based "erode" and "dilate" operators and the optimization problem is formulated as a worst case design problem. Applications of the method to the design of macro structures for minimum compliance and micro compliant mechanisms show that the method provides manufacturing tolerant designs with little decrease in performance. As a positive side effect the robust design formulation also eliminates the longstanding problem of one-node connected hinges in compliant mechanism design using topology optimization. 相似文献
15.
The paper presents a generic solution methodology for a quasi-static homogeneous monoclinic piezoelectric beam under axially
distributed electric and mechanical surface loads and body forces expressed as polynomials of degree K≥ 0 of the axis variable. (In the absence of any electrical loading, this problem is known as the Almansi–Michell problem). The stress and the electrical displacement components are presented as a set of polynomials of degree ≤K+2 of the axis variable (“solution hypothesis”) containing 4K unknown tip loading constants and 3K stress functions of two variables. The cases K=0,1 stand for uniform or linear distributed loads in the axis direction. The analysis is initiated by the Kth level and continues down to lower levels. The main result of this work generalizes the “elastic” solution given recently
by O. Rand and the first author (2005). Examples of solutions for axially uniform distributed loads (K=0), and equilibrium in which the stress and the electrical displacement do not depend on the axis variable, are presented.
The applications to constant body loads and a hydrostatic pressure are considered.
相似文献
16.
Numerical investigation on the flowfield of "swallowtail" cavity for supersonic mixing enhancement 总被引:1,自引:0,他引:1
A "swallowtail" cavity for the supersonic combustor was proposed to serve as an efficient flame holder for scramjets by enhancing the mass exchange between the cavity and the main flow. A numerical study on the "swallow- tail" cavity was conducted by solving the three-dimensional Reynolds-averaged Navier-Stokes equations implemented with a k-e turbulence model in a multi-block mesh. Turbu- lence model and numerical algorithms were validated first, and then test cases were calculated to investigate into the mechanism of cavity flows. Numerical results demonstrated that the certain mass in the supersonic main flow was sucked into the cavity and moved spirally toward the combustor walls. After that, the flow went out of the cavity at its lateral end, and finally was efficiently mixed with the main flow. The comparison between the "swallowtail" cavity and the conventional one showed that the mass exchanged between the cavity and the main flow was enhanced by the lateral flow that was induced due to the pressure gradient inside the cavity and was driven by the three-dimensional vortex ring generated from the "swallowtail" cavity structure. 相似文献
17.
Treatment of interface problems with Godunov-type schemes 总被引:5,自引:0,他引:5
A correction is proposed of Godunov-type schemes, yielding a perfect capture of contact discontinuities in hydrodynamic flows.
The correction method is based upon the following simple idea: If an Euler scheme is employed starting from a non-degraded
solution at a certain instant of time, the presence of a discontinuity will entail, at the next instant, the degradation of
the solution at the two points adjacent to the discontinuity only. On the other hand, an exact solution of the Riemann problem
yields the state variables at the nodes affected by numerical diffusion can be corrected. The method is applied to problems
involving a gas-liquid interface. The liquid is supposed to be compressible, obeying an equation of state of the “Stiffened
Gas” type, for which a solution to Riemann's problem is readily obtained. 相似文献
18.
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
19.
J. M. P. Q. Delgado 《Heat and Mass Transfer》2008,44(12):1427-1434
The concentration distribution in the wake of a soluble sphere immersed in a granular bed of inert particles, through which
fluid flows with “uniform velocity”, has been obtained numerically, for solute transport by both advection and diffusion/dispersion.
Fluid flow in the granular bed around the sphere was assumed to follow Darcy’s law and, at each point, dispersion of solute
was considered in both the cross-stream and streamwise directions. The elliptic PDE equation, resulting from a differential
material balance on the solute, was solved numerically over a wide range of values of the relevant parameters (Peclet number
and Schmidt number). The solution gives the concentration contour plots and, for each concentration level, the width and downstream
length of the corresponding contour surface were determined. General expressions are presented to predict contaminant “plume”
size downstream of the polluting source. 相似文献
20.
This article deals with the onset of thermosolutal natural convection in horizontal superposed fluid and porous layers. A
linear stability analysis is performed using the one-domain approach. As in the thermal convection case, the results show
a bimodal nature of the marginal stability curves where each mode corresponds to a different convective instability. At small
wave numbers, the convective flow occurs in the whole cavity (“porous mode”) while perturbations of large wave numbers lead
to a convective flow mainly confined in the fluid layer (“fluid mode”). Furthermore, it is shown that the onset of thermosolutal
natural convection is characterized by a multi-cellular flow in the fluid region for negative thermal Rayleigh numbers. For
positive thermal Rayleigh numbers, the convective flow takes place both in the fluid and porous regions. The influence of
the depth ratio and thermal diffusivity ratio is also investigated for a wide range of the thermal Rayleigh numbers. 相似文献