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1.
An analytical solution to the problem of condensation by natural convection over a thin porous substrate attached to a cooled
impermeable surface has been conducted to determine the velocity and temperature profiles within the porous layer, the dimensionless
thickness film and the local Nusselt number. In the porous region, the Darcy–Brinkman–Forchheimer (DBF) model describes the
flow and the thermal dispersion is taken into account in the energy equation. The classical boundary layer equations without
inertia and enthalpyterms are used in the condensate region. It is found that due to the thermal dispersion effect, the increasing
of heat transfer is significant. The comparison of the DBF model and the Darcy–Brinkman (DB) one is carried out. 相似文献
2.
In this study, we use the method of homogenization to develop a filtration law in porous media that includes the effects of
inertia at finite Reynolds numbers. The result is much different than the empirically observed quadratic Forchheimer equation.
First, the correction to Darcy’s law is initially cubic (not quadratic) for isotropic media. This is consistent with several
other authors (Mei and Auriault, J Fluid Mech 222:647–663, 1991; Wodié and Levy, CR Acad Sci Paris t.312:157–161, 1991; Couland
et al. J Fluid Mech 190:393–407, 1988; Rojas and Koplik, Phys Rev 58:4776–4782, 1988) who have solved the Navier–Stokes equations
analytically and numerically. Second, the resulting filtration model is an infinite series polynomial in velocity, instead
of a single corrective term to Darcy’s law. Although the model is only valid up to the local Reynolds number, at the most,
of order 1, the findings are important from a fundamental perspective because it shows that the often-used quadratic Forchheimer
equation is not a universal law for laminar flow, but rather an empirical one that is useful in a limited range of velocities.
Moreover, as stated by Mei and Auriault (J Fluid Mech 222:647–663, 1991) and Barree and Conway (SPE Annual technical conference
and exhibition, 2004), even if the quadratic model were valid at moderate Reynolds numbers in the laminar flow regime, then
the permeability extrapolated on a Forchheimer plot would not be the intrinsic Darcy permeability. A major contribution of
this study is that the coefficients of the polynomial law can be derived a priori, by solving sequential Stokes problems.
In each case, the solution to the Stokes problem is used to calculate a coefficient in the polynomial, and the velocity field
is an input of the forcing function, F, to subsequent problems. While numerical solutions must be utilized to compute each coefficient in the polynomial, these
problems are much simpler and robust than solving the full Navier–Stokes equations. 相似文献
3.
Yu. N. Gordeev A. E. Sandakov Yu. L. Chizhov 《Journal of Applied Mechanics and Technical Physics》2008,49(5):776-780
A problem of piston-induced displacement of one gas by another in cracks (porous media) in an axisymmetric case with a quadratic
drag law is studied. Self-similar solutions for determining the dynamic characteristics (velocity and pressure) of the displacing
and displaced gases are constructed in quadratures. The velocity and pressure are studied as functions of a self-similar variable
for several initial conditions and parameters.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 5, pp. 87–92, September–October, 2008. 相似文献
4.
V. M. Mirsalimov 《Journal of Applied Mechanics and Technical Physics》2007,48(5):723-733
A mathematical model is constructed for crack nucleation in an isotropic fuel cell (heat-releasing solid material) attenuated
by a biperiodic system of cooling cylindrical channels with a circular cross section. Cracks are assumed to appear with increasing
heat-release intensity in the bulk of the material. The solution of the problem on equilibrium of an isotropic perforated
fuel cell with crack nuclei reduces to the solution of a nonlinear singular integral equation with a Cauchy-type kernel. The
solution of the latter equation yields the forces in the band of crack nucleation. The condition of crack nucleation is formulated
with allowance for the criterion of ultimate extension of bonds in the material.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 5, pp. 121–133, September–October, 2007. 相似文献
5.
In Part I Moyne and Murad [Transport in Porous Media 62, (2006), 333–380] a two-scale model of coupled electro-chemo-mechanical phenomena in swelling porous media was derived by
a formal asymptotic homogenization analysis. The microscopic portrait of the model consists of a two-phase system composed
of an electrolyte solution and colloidal clay particles. The movement of the liquid at the microscale is ruled by the modified
Stokes problem; the advection, diffusion and electro-migration of monovalent ions Na+ and Cl− are governed by the Nernst–Planck equations and the local electric potential distribution is dictated by the Poisson problem.
The microscopic governing equations in the fluid domain are coupled with the elasticity problem for the clay particles through
boundary conditions on the solid–fluid interface. The up-scaling procedure led to a macroscopic model based on Onsager’s reciprocity
relations coupled with a modified form of Terzaghi’s effective stress principle including an additional swelling stress component.
A notable consequence of the two-scale framework are the new closure problems derived for the macroscopic electro-chemo-mechanical
parameters. Such local representation bridge the gap between the macroscopic Thermodynamics of Irreversible Processes and
microscopic Electro-Hydrodynamics by establishing a direct correlation between the magnitude of the effective properties and
the electrical double layer potential, whose local distribution is governed by a microscale Poisson–Boltzmann equation. The
purpose of this paper is to validate computationally the two-scale model and to introduce new concepts inherent to the problem
considering a particular form of microstructure wherein the clay fabric is composed of parallel particles of face-to-face
contact. By discretizing the local Poisson–Boltzmann equation and solving numerically the closure problems, the constitutive
behavior of the diffusion coefficients of cations and anions, chemico-osmotic and electro-osmotic conductivities in Darcy’s
law, Onsager’s parameters, swelling pressure, electro-chemical compressibility, surface tension, primary/secondary electroviscous
effects and the reflection coefficient are computed for a range particle distances and sat concentrations. 相似文献
6.
Björn Johannesson 《Transport in Porous Media》2010,85(2):565-592
A numerical scheme for the transient solution of a generalized version of the Poisson–Nernst–Planck (PNP) equations is presented.
The finite element method is used to establish the coupled non-linear matrix system of equations capable of solving the present
problem iteratively. The PNP equations represent a set of diffusion equations for charged species, i.e. dissolved ions, present
in the pore solution of a rigid porous material in which the surface charge can be assumed neglectable. These equations are
coupled to the ‘internally’ induced electrical field and to the velocity field of the fluid. The Nernst–Planck equations describing
the diffusion of the ionic species and Gauss’ law in use are, however, coupled in both directions. The governing set of equations
is derived from a simplified version of the so-called hybrid mixture theory (HMT). The simplifications used here mainly concerns
ignoring the deformation and stresses in the porous material in which the ionic diffusion occurs. The HMT is a special version
of the more ‘classical’ continuum mixture theories in the sense that it works with averaged equations at macroscale and that
it includes the volume fractions of phases in its structure. The background to the PNP equations can by the HMT approach be
described by using the postulates of mass conservation of constituents together with Gauss’ law used together with consistent
constitutive laws. The HMT theory includes the constituent forms of the quasistatic version of Maxwell’s equations making
it suitable for analyses of the kind addressed in this work. Within the framework of HTM, constitutive equations have been
derived using the postulate of entropy inequality together with the technique of identifying properties by Lagrange multipliers.
These results will be used in obtaining a closed set of equations for the present problem. 相似文献
7.
A model of flow through a porous medium with phase transitions which permits an efficient qualitative investigation is proposed
for two fluids with sharply different (high-contrast) mobilities. It is shown that the model problem of flow toward a unit
sink is singularly perturbed and can be solved using analytic asymptotic matching methods. The nature of the singularity is
associated with violation of the condition of the flow contrast in certain zones. The solution can be unstable depending on
the direction of interphase mass transfer and the zone in which the process takes place.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, pp. 124–135, March–April, 2000.
The work was carried out with support from the European Foundation INTAS (grant No. 94-4367) and the Russian Foundation for
Basic Research (project No. 95-01-01179a). 相似文献
8.
The problem of convective instability of a fluid in a system consisting of two horizontal porous strata with different permeabilities
and a permeable common boundary is considered. The problem is investigated in parametric form as a function of the stratum
thickness ratio and stratum permeabilities. As distinct from a uniform stratum, in this case the neutral curve can have one
or two minima depending on the relationship between the parameters. The case of two minima is characterized by the condition
of loss of stability of the fluid in the system as a whole and in the thinner stratum with greater permeability. These minima
correspond to significantly different wave numbers.
Makhachkala. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 165–169, January–February,
1999. 相似文献
9.
V. B. Kurzin 《Journal of Applied Mechanics and Technical Physics》2006,47(3):346-358
A model for separated incompressible flow past thin airfoils in the neighborhood of the “shockless entrance” condition is
constructed based on the averaging of the vortex shedding flow past the airfoil edges. By approximation of the vortex shedding
by two vortex curves, determination of the average hydrodynamic parameters is reduced to a twofold solution of an integral
singular equation equivalent to the equation describing steady-state nonseparated airfoil flow. In this case, the calculation
time is two orders of magnitude smaller than the time required for the solution of the corresponding evolution problem. The
results of a test calculation using the proposed method are in fair agreement with available results of calculations and experiments.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 49–63, May–June, 2006. 相似文献
10.
This paper generalizes the analysis of four magnetohydrodynamic (MHD) flow problems of an Oldroyd-B fluid discussed by Asghar
et al. [Int. J. Non-linear Mech. 40, 589–601 (2005)] into three directions: (i) to discuss the problems in a porous medium using modified Darcy’s law (ii) to
see the influence of Hall current (iii) to determine the effect of rheological parameter of Burgers’ fluid. Analytical solutions
of velocity distribution valid at large and small times are given in each problem. Comparison has been provided for Oldroyd-B
and Burgers’ fluids through graphs. The physical interpretation is also included. 相似文献
11.
Yu. D. Varlamov Yu. P. Meshcheryakov M. R. Predtechensky S. N. Ul’yankin 《Journal of Applied Mechanics and Technical Physics》2007,48(1):101-108
Microdroplet absorption by two-layer porous media is studied both theoretically and experimentally. A two-dimensional model
for liquid flow from a droplet into a porous medium is presented and veri.ed based on a simultaneous numerical solution of
the Euler equations taking into account surface tension forces and the unsteady filtration equation. The effect of the structural
parameters of the two-layer porous medium (pore size in the layers, and the thickness and porosity of the layers) on the droplet
absorption is analyzed. It is shown that the presence of the second layer can have a significant effect on the droplet absorption
rate and the liquid distribution in the medium. The pore size is found to be the main parameter that governs the effect of
the second layer.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 121–130, January–February, 2007. 相似文献
12.
An analytical study of viscous dissipation effect on the fully developed forced convection Couette flow through a parallel
plate channel partially filled with porous medium is presented. A uniform heat flux is imposed at the moving plate while the
fixed plate is insulated. In the fluid-only region the flow field is governed by Navier–Stokes equation while the Brinkman-extended
Darcy law relationship is considered in the fully saturated porous medium. The interface conditions are formulated with an
empirical constant β due to the stress jump boundary condition. Fluid properties are assumed to be constant and the longitudinal
heat conduction is neglected. A closed-form solution for the velocity and temperature distributions and also the Nusselt number
in the channel are obtained and the viscous dissipation effect on these profiles is briefly investigated. 相似文献
13.
A. O. Vatul’yan A. N. Solov’ev 《Journal of Applied Mechanics and Technical Physics》1999,40(3):539-544
A method is proposed for determination of the depolarization function of a rod of piezoelectric ceramics for a specified amplitude-frequency
characteristic of the current. The problem is reduced to a nonlinear integral equation solved by means of a combination of
Tikhonov’s linearization and regularization methods. The uniqueness of the solution is shown and a series of numerical experiments
is carried out with the aim to determine the polarization law.
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 204–210, May–June, 1999. 相似文献
14.
This article will present a set of analytical equations for the calculation of early time temperature at the edge of a porous,
finite layer experiencing linear flow of a slightly compressible fluid. The equations provide the full, transient temperature
solution for the flow of slightly compressible fluids (i.e., liquids and, sometimes, gasses) into horizontal wells. The solution
is essential for temperature transient analysis in smart wells—a monitoring approach of great potential, but in early development
stage. The early time, analytical model solution provided in the paper will be tested against a rigorous numerical simulation
model. The methods proposed here can be applied to a wide variety of well-completion types, flow conditions and system properties.
This article will first discuss the problem of transient temperature analysis, the flow conditions and the assumptions required
to sufficiently simplify the thermal model so that an analytical solution can be derived. The solution is derived for the
temperature change generated by the Joule–Thomson fluid heating under the condition of 2D heat losses to the surrounding formation. 相似文献
15.
I. S. Shivakumara S. P. Suma R. Indira Y. H. Gangadharaiah 《Transport in Porous Media》2012,92(3):727-743
Linear stability analysis has been performed to investigate the effect of internal heat generation on the criterion for the
onset of Marangoni convection in a two-layer system comprising an incompressible fluid-saturated anisotropic porous layer
over which lies a layer of the same fluid. The upper non-deformable free surface and the lower rigid surface are assumed to
be insulated to temperature perturbations. The fluid flow in the porous layer is governed by the modified Darcy equation and
the Beavers–Joseph empirical slip condition is employed at the interface between the two layers. The resulting eigenvalue
problem is solved exactly. Besides, analytical expression for the critical Marangoni number is also obtained by using regular
perturbation technique with wave number as a perturbation parameter. The effect of internal heating in the porous layer alone
exhibits more stabilizing effect on the system compared to its presence in both fluid and porous layers and the system is
least stable if the internal heating is in fluid layer alone. It is found that an increase in the value of mechanical anisotropy
parameter is to hasten the onset of Marangoni convection while an opposite trend is noticed with increasing thermal anisotropy
parameter. Besides, the possibilities of controlling (suppress or augment) Marangoni convection is discussed in detail. 相似文献
16.
Giampaolo Cicogna 《Nonlinear dynamics》2008,51(1-2):309-316
We consider the problem of performing the preliminary “symmetry classification” of a class of quasi-linear PDE’s containing
one or more arbitrary functions: we provide an easy condition involving these functions in order that nontrivial Lie point
symmetries be admitted, and a “geometrical” characterization of the relevant system of equations determining these symmetries.
Two detailed examples will elucidate the idea and the procedure: the first one concerns a nonlinear Laplace-type equation,
the second a generalization of an equation (the Grad–Schlüter–Shafranov equation) which is used in magnetohydrodynamics. 相似文献
17.
We analyze a quantum trajectory model given by a steady-state hydrodynamic system for quantum fluids with positive constant
temperature in bounded domains for arbitrary large data. The momentum equation can be written as a dispersive third-order
equation for the particle density where viscous effects are incorporated. The phenomena that admit positivity of the solutions
are studied. The cases, one space dimensional dispersive or non-dispersive, viscous or non-viscous, are thoroughly analyzed
with respect to positivity and existence or non-existence of solutions, all depending on the constitutive relation for the
pressure law. We distinguish between isothermal (linear) and isentropic (power law) pressure functions of the density. It
is proved that in the dispersive, non-viscous model, a classical positive solution only exists for “small” (positive) particle
current densities, both for the isentropic and isothermal case. Uniqueness is also shown in the isentropic
subsonic case, when the pressure law is strictly convex. However, we prove that no weak isentropic solution can exist for
“large” current densities. The dispersive, viscous problem admits a classical positive solution for all current densities,
both for the isentropic and isothermal case, with an “ultra-diffusion” condition.
The proofs are based on a reformulation of the equations as a singular elliptic second-order problem and on a variant of the
Stampacchia truncation technique. Some of the results are extended to general third-order equations in any space dimension.
Accepted July 1, 2000?Published online February 14, 2001 相似文献
18.
An analytical theory is presented for the low-frequency behavior of dilatational waves propagating through a homogeneous elastic
porous medium containing two immiscible fluids. The theory is based on the Berryman–Thigpen–Chin (BTC) model, in which capillary
pressure effects are neglected. We show that the BTC model equations in the frequency domain can be transformed, at sufficiently
low frequencies, into a dissipative wave equation (telegraph equation) and a propagating wave equation in the time domain.
These partial differential equations describe two independent modes of dilatational wave motion that are analogous to the
Biot fast and slow compressional waves in a single-fluid system. The equations can be solved analytically under a variety
of initial and boundary conditions. The stipulation of “low frequency” underlying the derivation of our equations in the time
domain is shown to require that the excitation frequency of wave motions be much smaller than a critical frequency. This frequency
is shown to be the inverse of an intrinsic time scale that depends on an effective kinematic shear viscosity of the interstitial
fluids and the intrinsic permeability of the porous medium. Numerical calculations indicate that the critical frequency in
both unconsolidated and consolidated materials containing water and a nonaqueous phase liquid ranges typically from kHz to
MHz. Thus engineering problems involving the dynamic response of an unsaturated porous medium to low excitation frequencies
(e.g., seismic wave stimulation) should be accurately modeled by our equations after suitable initial and boundary conditions
are imposed. 相似文献
19.
Dambaru Bhatta Mallikarjunaiah S. Muddamallappa Daniel N. Riahi 《Transport in Porous Media》2010,82(2):385-399
This present study considers the problem of steady magneto-convection in a horizontal mushy layer with variable permeability
and an impermeable mush–liquid interface during directional solidification of binary alloys. We model the flow by introducing
a uniform magnetic field in the mushy layer which is considered as a porous medium where Darcy’s law holds and the permeability
is a function of the local solid volume fraction. Basic-state solutions are obtained analytically using the no-flow condition.
With the help of multiple shooting techniques, we obtain numerical solutions to the linear perturbation system for non-magnetic
and magnetic cases. Numerical results are presented showing the effects of the magnetic field and the permeability of the
layer. These results demonstrate that the application of an external magnetic field has stabilizing effects on the convection
and can reduce the tendency for chimney formation in the mushy layer. In addition, variable permeability, which corresponds
to an active mushy layer, indicates more stable and realizable flow system as compared to the case of constant permeability. 相似文献
20.
M. V. Mir-Salim-zade 《Journal of Applied Mechanics and Technical Physics》2008,49(6):1030-1039
A problem of fracture mechanics on crack nucleation in a reinforced plate attenuated by a periodic system of circular holes
is considered. Crack nucleation is modeled by a pre-fracture band in the plastic flow state with a constant stress, which
is considered as a region of attenuated bonds between material particles. Determining unknown parameters characterizing the
emerging crack reduces to solving a singular integral equation. The condition of crack emergence is formulated with allowance
for the criterion of the limiting opening of the faces of the material pre-fracture band.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 6, pp. 170–180, November–December, 2008. 相似文献