共查询到20条相似文献,搜索用时 31 毫秒
1.
G. Juncu 《Heat and Mass Transfer》1998,34(2-3):203-208
The reverse of the transfer direction in the unsteady conjugate heat transfer between a spherical particle and a surrounding
fluid flow has been analysed. The aspect this work is focused on is the influence of the continuous phase convection on the
occurrence and development of this phenomenon. The energy equations are solved by the ADI finite difference method. The range
of the Pe numbers investigated is between 0 and 10. The ratios of the thermal conductivity and volume heat capacity between
the particle and its ambient flow belong to the interval 0.01–100. It was found that, in creeping flow, the thermal wake occurs
at Pe=0.690·10−3. Increasing the Pe number up to 1 the dimension of thermal wake increases. For Pe>1, the increase in Pe decreases thermal
wake.
Received on 13 January 1998 相似文献
2.
《International Journal of Multiphase Flow》2005,31(10-11):1155-1180
Visualization experiments of the unsteady immiscible displacement of a fluid by another are performed on glass-etched pore networks of well-controlled morphology by varying the fluid system and flow conditions. The measured transient responses of the fluid saturation and pressure drop across the porous medium are introduced into numerical solvers of the macroscopic two-phase flow equations to estimate the non-wetting phase, krnw, and wetting phase, krw, relative permeability curves and capillary pressure, Pc, curve. The correlation of krnw, krw, and Pc with the displacement growth pattern is investigated. Except for the capillary number, wettability, and viscosity ratio, the immiscible displacement growth pattern in a porous medium may be governed by the shear-thinning rheology of the injected or displaced fluid, and the porous sample length as compared to the thickness of the frontal region. The imbibition krnw increases as the flow pattern changes from compact displacement to viscous fingering or from viscous to capillary fingering. The imbibition krw increases as the flow pattern changes from compact displacement or capillary fingering to viscous fingering. As the shear-thinning behaviour of the NWP strengthens and/or the contact angle decreases, then the flow pattern is gradually dominated by irregular interfacial configurations, and the imbibition krnw increases. The imbibition Pc is a decreasing function of the capillary number or increasing function of the injected phase viscosity in agreement with the linear thermodynamic theory. 相似文献
3.
Sherifull-Din Jamalud-Din D. Andrew S. Rees B. V. K. Reddy Arunn Narasimhan 《Heat and Mass Transfer》2010,46(3):333-343
Steady state natural convection of a fluid with Pr ≈ 1 within a square enclosure containing uniformly distributed, conducting square solid blocks is investigated. The side
walls are subjected to differential heating, while the top and bottom ones are kept adiabatic. The natural convection flow
is predicted employing the nondimensional volumetric flow rate (Qmax* Q_{\max }^{*} ) by using a network model and also using numerical simulations. For identical solid and fluid thermal conductivities (i.e.
k
s
= k
f
), a parametric study of the effect of number of blocks (N
2), gap size (δ) and enclosure Rayleigh number (Ra) on Qmax* Q_{\max }^{*} is performed using the two approaches. Network model predictions are observed to agree well with that from the simulations
until Raδ3 ~ 12. Considering the enclosure with blocks as a porous medium, for a fixed enclosure Ra number, increasing the number of blocks for a fixed volumetric porosity leads to a decrease in enclosure permeability, which
in turn reduces the flow rate. When the number of blocks is fixed, and for a given Ra number, the flow rate increases as the porosity increases by widening the gap between the blocks. 相似文献
4.
Robert McKibbin 《Transport in Porous Media》1986,1(3):271-292
The theory describing the onset of convection in a homogeneous porous layer bounded above and below by isothermal surfaces
is extended to consider an upper boundary which is partly permeable. The general boundary condition p + λ ∂p/∂n = constant is applied at the top surface and the flow is investigated for various λ in the range 0 ⩽ λ < ∞. Estimates of the magnitude and horizontal distribution of the vertical mass and heat fluxes at the surface, the horizontally-averaged
heat flux (Nusselt number) and the fraction of the fluid which recirculates within the layer are found for slightly supercritical
conditions. Comparisons are made with the two limiting cases λ → ∞, where the surface is completely impermeable, and λ = 0, where the surface is at constant pressure. Also studied are the effects of anisotropy in permeability, ξ = K
H
/K
V
, and anisotropy is thermal conductivity, η = k
H
/k
V
, both parameters being ratios of horizontal to vertical quantities. Quantitative results are given for a wide variety of
the parameters λ, ξ and η. In the limit ξ/η → 0 there is no recirculation, all fluid being converted out of the top surface, while in the limit ξ/η → ∞ there is full recirculation. 相似文献
5.
In this paper, a linear stability analysis is presented to trace the time evolution of an infinitesimal, two-dimensional disturbance
imposed on the base flow of an electrically conducting fluid in a channel filled with a saturated porous medium under the
influence of a transversely imposed magnetic field. An eigenvalue problem is obtained and solved numerically using the Chebyshev
collocation spectral method. The critical Reynolds number Re
c, the critical wave number α
c and the critical wave speed c
c are obtained for a wide range of the porous medium shape factor parameter S and Hartmann number H. It is found that an increase in the magnetic field intensity and a decrease in porous medium permeability have a stabilizing
effect on the fluid flow. 相似文献
6.
This work experimentally studies the flow characteristics and forced convective heat transfer in a sintered porous channel
that filled with sintered copper beads of three average diameters (
0.830, and 1.163 mm). The pressure drop and the local temperature measurements can be applied to figure out the distributions
of the friction coefficient and the heat transfer coefficient. Three sintered porous channels differ in the arrangement of
obstacle blocks. Model A has no obstacle. Models B and C have five obstacle blocks facing down and up, respectively, in a
sintered porous channel. The range of experimental parameters, porosity, heat flux, and effect of forced convection are 0.370
≤ ɛ ≤ 0.385, q=0.228, 0.872, 1.862 W/cm2, and 200 ≤ Re
d ≤ 800. The permeability and inertia coefficient of each of the three sintered porous channels are analyzed. The results for
Model A agree with those obtained by previous investigations in C
f distribution. The heat transfer of Model C exceeds that of Model A by approximately 20%. Finally, a series of empirical correlation
equations were obtained for practical applications and engineering problems. 相似文献
7.
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
8.
Dissolution and Seepage Coupling Effect on Transport and Mechanical Properties of Glauberite Salt Rock 总被引:1,自引:0,他引:1
Weiguo Liang Yangsheng Zhao Suguo Xu Maurice B. Dusseault 《Transport in Porous Media》2008,74(2):185-199
Potential high rates of aqueous dissolution are characteristic of salt rocks, and solute and mass flux through a soluble porous
medium are functions of solute concentration gradients and pressure gradients. Due to different dissolution properties for
different mineral components in glauberite salt rock, an interaction between mineral dissolution and solvent seepage arises,
driven by the hydraulic pressure gradient in the rock. The originally almost impermeable glauberite rock becomes an increasingly
permeable porous medium with dissolution, changing the transport and mechanical properties because of the progressive removal
of solid sodium sulfate (Na2SO4), one of the constitutive components of glauberite salt rock. Glauberite is often found in bedded salt rock deposits, and
the mineral glauberite has economic value and has been mined for many years in China. More economic and safe technologies,
such as controlled solution mining, are inherently attractive. Thus, investigations into relevant physical and mechanical
properties of glauberite in the context of solution mining have value, and to clarify glauberite behaviour, a series of experiments
were performed. It is observed through experiments that the permeability of the rock mass during dissolution of glauberite
is a function of the dissolution duration and the hydraulic pressure gradient applied to the system. For example, in laboratory
tests, after 49, 53 and 70 h of dissolution, the relationships between permeability (k—cm2) and pressure gradient (Δp—MPa across the specimen of length 100 mm) of the glauberite specimens were observed to be k = 0.24 for a Δp of 0.10, k = 0.30 for a Δp of 0.12, and k = 0.41 for a Δp of 0.18, with the empirical functional relationship becoming gradually steeper with pressure. Also, the triaxial compression
(mechanical) characteristics of glauberite salt rock change substantially after a period of dissolution: the compressive strength
under a confining stress of σ3 = 2.0 MPa changes initially from 46 to 11 MPa after 70 h of dissolution and seepage. Along with strength degradation, the
Young’s modulus (stiffness) changed from 4.6 to 0.5 GPa. Evidently, coupled dissolution and seepage rate greatly impact both
transport and mechanical properties of the rock as fabric evolves in a time-dependent manner. 相似文献
9.
The onset of buoyancy-driven convection in an initially quiescent ferrofluid saturated horizontal porous layer in the presence
of a uniform vertical magnetic field is investigated. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different
from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed
to be rigid-paramagnetic, while the upper paramagnetic boundary is considered to be either rigid or stress-free. The thermal
conditions include fixed heat flux at the lower boundary, and a general convective–radiative exchange at the upper boundary,
which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved numerically
using the Galerkin technique. It is found that increase in the Biot number Bi, porous parameter σ, viscosity ratio Λ, magnetic susceptibility χ, and decrease in the magnetic number M
1 and non-linearity of magnetization M
3 is to delay the onset of ferroconvection in a porous medium. Further, increase in M
1, M
3, and decrease in χ, Λ, σ and Bi is to decrease the size of convection cells. 相似文献
10.
Effects of Temperature-Dependent Viscosity on Forced Convection Inside a Porous Medium 总被引:1,自引:0,他引:1
Considering the exponential viscosity–temperature relation, effect of temperature-dependent viscosity on forced convection
of a liquid through a porous medium, bounded by isoflux parallel plates, is investigated numerically based on the general
model of momentum transfer. Local effects of viscosity variation on the distribution of velocity and temperature are analyzed.
Moreover, global aspects of the problem are investigated where corrections are proposed for total pressure drop and the fully
developed Nusselt number, in the form of out/in viscosity ratio. Results are obtained over a wide range of permeabilities
from clear (of solid material) fluid to very low permeability, where for constant properties one expects a nearly slug flow. 相似文献
11.
A finite-difference scheme has been developed to solve the equations governing the laminar forced convection heat transfer
around and inside a spherical fluid droplet moving steadily in another immiscible fluid for both steady and transient thermal
conditions. For large values of the external flow Reynolds number (Re), results not available in the literature have been
obtained for circulating droplets at intermediate and high interior-to-exterior viscosity ratios (μ*). Detailed results over a wide range of viscosity ratio (μ*) and for 200≤Re≤1000 are presented for the temperature profiles outside and inside the sphere, Nusselt number, the time required
to attain a uniform surface temperature and the time required to reach the steady-state temperature. Results show that convective
heating is dependent on the external flow Reynolds number (Re) and the interior-to-exterior viscosity ratio (μ*) where increasing Re or decreasing μ* result in increasing heat transfer rate convected to the liquid sphere.
Received on 1 March 1999 相似文献
12.
Steady laminar forced convection gaseous slip-flow through parallel-plates micro-channel filled with porous medium under Local
Thermal Non-Equilibrium (LTNE) condition is studied numerically. We consider incompressible Newtonian gas flow, which is hydrodynamically
fully developed while thermally is developing. The Darcy–Brinkman–Forchheimer model embedded in the Navier–Stokes equations
is used to model the flow within the porous domain. The present study reports the effect of several operating parameters on
velocity slip and temperature jump at the wall. Mainly, the current study demonstrates the effects of: Knudsen number (Kn),
Darcy number (Da), Forchheimer number (Γ), Peclet number (Pe), Biot number (Bi), and effective thermal conductivity ratio
(K
R) on velocity slip and temperature jump at the wall. Results are given in terms of skin friction (C
f
Re
*) and Nusselt number (Nu). It is found that the skin friction: (1) increases as Darcy number increases; (2) decreases as Forchheimer
number or Knudsen number increases. Heat transfer is found to (1) decreases as the Knudsen number, Forchheimer number, or
K
R increases; (2) increases as the Peclet number, Darcy number, or Biot number increases. 相似文献
13.
Prof. N. Seki Ass. Prof. S. Fukusako Grad. Stud. Y. Ariake 《Heat and Mass Transfer》1980,13(1-2):61-71
Experiments have been performed to investigate the heat transfer of a horizontal porous bed saturated by liquid heated from below. Attention was especially focussed on the heat-transfer characteristics at the high Rayleigh number where the observed data deviate to a great extent from the linear dependence of the Nusselt number on the Rayleigh number predicted by the previous investigators. The porous bed was made up of packed spherical glass beads with diameter ranging from 3.02 mm to 16.4 mm, while the depth of the bed was varied from 16.4 mm to 103.0 mm. Distilled water, ethylalcohol, fluorocarbon R-11 and transformer oil as testing liquids were used. The results revealed that the effects of particle diameter, depth of bed, and the Prandtl number on the heat-transfer characteristics at the high Rayleigh number are unexpectively large. It was also elucidated that the heat-transfer data which do not exhibit linear dependence of Nu on Ra with Prm ranging from 1.1 to 7.3 can well be correlated by the following equations: Nu= 0.10Prm
0.132(d/H)–0.655Ra0.5 200 < Ra < 1400 Nu=0.88 Pr0.132(d/H)–0.655Ra0.2 1400 < Ra < 40000
Nomenclature Cpf specific heat of liquid - d diameter of spherical particles - g gravitational acceleration - H depth of porous bed - k permeability of porous bed - Nu Nusselt number for porous bed, defined in Eq.(4) - Prm modified Prandtl number for porous bed, as defined in Eq. (3) - q rate of heat transfer per unit cross-sectional area of porous bed - Ra Rayleigh number for porous bed, as defined in Eq.(1) - Tc temperature of cold wall - Th temperature of hot wall - T temperature of environment Greek symbols coefficient of volumetric expansion of liquid - temperature difference between hot wall and cold wall - porosity of porous bed - m modified thermal diffusivity for porous bed - f thermal conductivity of liquid - m modified thermal conductivity for porous bed - f kinematic viscosity of liquid - f density of liquid 相似文献
Experimentelle Untersuchung des Wärmeübergangs bei freier Konvektion in einem flüssigkeits-gesättigten porösen Bett bei hohen Rayleigh-Zahlen
Zusammenfassung Die Versuche betrachten den Wärmeübergang in einem waagerechten porösen Bett, das mit Flüssigkeit gesättigt war und von unten beheizt wurde. Insbesondere wurde der Bereich hoher Rayleigh-Zahlen untersucht, wo die beobachteten Daten stark von der linearen Abhängigkeit der Nusselt-Zahl von der Rayleigh-Zahl abwichen, wie sie in der älteren Literatur behauptet wurde. Das poröse Bett bestand aus Glasperlen mit Durchmessern von 3,02 mm bis 16,4 mm bei einer Tiefe von 16,4 mm bis 103,0 mm. Destilliertes Wasser, Äthylalkohol, Fluorkohlenstoff R-11 und Transformatorenöl wurden verwendet. Die Versuche zeigen, daß die Einflüsse des Teilchendurchmessers, der Tiefe des Betts und der Prandtl-Zahl unerwartet hoch sind. Die Wärmeübergangsdaten, die keine lineare Abhängigkeit zwischen Nu und Ra im Bereich von Prm =1,1 bis 7,3 aufwiesen, ließen sich durch folgende Beziehungen wiedergeben: Nu=0,10 Prm 0,132(d/H)–0,655Ra0.5 200 < Ra < 1400 Nu=0,88 Prm 0,132(d/H)0,655Ra0.2 1400 < Ra < 40000.
Nomenclature Cpf specific heat of liquid - d diameter of spherical particles - g gravitational acceleration - H depth of porous bed - k permeability of porous bed - Nu Nusselt number for porous bed, defined in Eq.(4) - Prm modified Prandtl number for porous bed, as defined in Eq. (3) - q rate of heat transfer per unit cross-sectional area of porous bed - Ra Rayleigh number for porous bed, as defined in Eq.(1) - Tc temperature of cold wall - Th temperature of hot wall - T temperature of environment Greek symbols coefficient of volumetric expansion of liquid - temperature difference between hot wall and cold wall - porosity of porous bed - m modified thermal diffusivity for porous bed - f thermal conductivity of liquid - m modified thermal conductivity for porous bed - f kinematic viscosity of liquid - f density of liquid 相似文献
14.
Two-dimensional steady-state thermal concentration convection in a rectangular porous cavity is simulated numerically. The temperature and concentration gradients are horizontal and the buoyancy forces act either in the same or in opposite directions. The flow through the porous medium is described by the Darcy-Brinkman or Forchheimer equations. The SIMPLER numerical algorithm based on the finite volume approach is used for solving the problem in the velocity-pressure variables.Numerous series of calculations were carried out over the range Ra
t
=3·106 and 3·107, 10-6 < Da < 1, 1 < N < 20, Le=10 and 100, where Ra, Da, Le, and N are the Rayleigh, Darcy, and Lewis numbers and the buoyancy ratio, respectively. It is shown that the main effect of the presence of the porous medium is to reduce the heat and mass transfer and attenuate the flow field with decrease in permeability. For a certain combination of the Ra, Le, and N numbers the flow has a multicellular structure. The mean Nusselt and Sherwood numbers are presented as functions of the governing parameters. 相似文献
15.
I-Chung Liu 《Transport in Porous Media》2006,64(3):375-392
The present paper deals with the flow and heat transfer of a viscous fluid saturated in a porous medium past a permeable and
non-isothermal stretching sheet with internal heat generation or absorption and radiation. Closed-form solutions to steady,
two dimensional momentum equations with neglecting quadratic inertia terms and heat transfer equation are found using a similarity
transformation. Asymptotic expressions of the temperature functions are also presented valid for both very large and very
small modified Prandtl numbers. Attention is focused on the effects of porous parameter K, suction parameter R, radiation parameter Nr, viscosity ratio Λ, internal heat parameter α and Prandtl number P to the characteristics of flow and heat transfer. 相似文献
16.
The effect of magnetic field dependent viscosity on thermosolutal convection in a ferromagnetic fluid saturating a porous medium is considered for a fluid layer heated and soluted from below in the presence of uniform magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For case of stationary convection, medium permeability has a destabilizing effect, whereas a stable solute gradient and magnetic field dependent viscosity have a stabilizing effect on the system. In the absence of magnetic field dependent viscosity, the destabilizing effect of non-buoyancy magnetization is depicted but in the presence of magnetic field dependent viscosity non-buoyancy magnetization may have a destabilizing or stabilizing effect on the onset of instability. The critical wave number and the critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetization parameter M1 and the results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were non-existent in its absence. A sufficient condition for the non-existence of overstability is also obtained. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study. 相似文献
17.
Non-Newtonian fluid flow through porous media is of considerable interest in several fields, ranging from environmental sciences
to chemical and petroleum engineering. In this article, we consider an infinite porous domain of uniform permeability k and porosity f{\phi} , saturated by a weakly compressible non-Newtonian fluid, and analyze the dynamics of the pressure variation generated within
the domain by an instantaneous mass injection in its origin. The pressure is taken initially to be constant in the porous
domain. The fluid is described by a rheological power-law model of given consistency index H and flow behavior index n; n, < 1 describes shear-thinning behavior, n > 1 shear-thickening behavior; for n = 1, the Newtonian case is recovered. The law of motion for the fluid is a modified Darcy’s law based on the effective viscosity μ
ef
, in turn a function of f, H, n{\phi, H, n} . Coupling the flow law with the mass balance equation yields the nonlinear partial differential equation governing the pressure
field; an analytical solution is then derived as a function of a self-similar variable η = rt
β
(the exponent β being a suitable function of n), combining spatial coordinate r and time t. We revisit and expand the work in previous papers by providing a dimensionless general formulation and solution to the problem
depending on a geometrical parameter d, valid for plane (d = 1), cylindrical (d = 2), and semi-spherical (d = 3) geometry. When a shear-thinning fluid is considered, the analytical solution exhibits traveling wave characteristics,
in variance with Newtonian fluids; the front velocity is proportional to t
(n-2)/2 in plane geometry, t
(2n-3)/(3−n) in cylindrical geometry, and t
(3n-4)/[2(2−n)] in semi-spherical geometry. To reflect the uncertainty inherent in the value of the problem parameters, we consider selected
properties of fluid and matrix as independent random variables with an associated probability distribution. The influence
of the uncertain parameters on the front position and the pressure field is investigated via a global sensitivity analysis
evaluating the associated Sobol’ indices. The analysis reveals that compressibility coefficient and flow behavior index are
the most influential variables affecting the front position; when the excess pressure is considered, compressibility and permeability
coefficients contribute most to the total response variance. For both output variables the influence of the uncertainty in
the porosity is decidedly lower. 相似文献
18.
Laminar, single-phase, finite-volume solutions to the Navier–Stokes equations of fluid flow through a fracture within permeable
media have been obtained. The fracture geometry was acquired from computed tomography scans of a fracture in Berea sandstone,
capturing the small-scale roughness of these natural fluid conduits. First, the roughness of the two-dimensional fracture
profiles was analyzed and shown to be similar to Brownian fractal structures. The permeability and tortuosity of each fracture
profile was determined from simulations of fluid flow through these geometries with impermeable fracture walls. A surrounding
permeable medium, assumed to obey Darcy’s Law with permeabilities from 0.2 to 2,000 millidarcies, was then included in the
analysis. A series of simulations for flows in fractured permeable rocks was performed, and the results were used to develop
a relationship between the flow rate and pressure loss for fractures in porous rocks. The resulting friction-factor, which
accounts for the fracture geometric properties, is similar to the cubic law; it has the potential to be of use in discrete
fracture reservoir-scale simulations of fluid flow through highly fractured geologic formations with appreciable matrix permeability.
The observed fluid flow from the surrounding permeable medium to the fracture was significant when the resistance within the
fracture and the medium were of the same order. An increase in the volumetric flow rate within the fracture profile increased
by more than 5% was observed for flows within high permeability-fractured porous media. 相似文献
19.
Relative permeability functions for immiscible displacements in porous media show a wide range of profiles. Although, this
behavior is well known, its impact on the stability of the displacement process is unexplored. Our analysis clearly demonstrates
for the first time that the viscous instability characteristics of two-phase flows are governed not only by their end point
values, but are strongly dependent on the actual profile of relative permeability functions. Linear stability analysis predicts
the capacity of the flow to develop large scale fingers which can result in substantial bypassing of the resident fluid. It
is observed that relative permeability functions attributed to drainage processes yield a more unstable displacement as compared
to functions related to imbibition processes. Moreover, instability is observed to increase for those relative permeability
functions which result from increased wettability of the wetting fluid. High accuracy numerical simulations show agreement
with these predictions and demonstrate how large amplitude viscous fingers result in significant bypassing for certain relative
permeability functions. In the nonlinear regime, the finger amplitude grows at a rate ∝ t1/2 initially, drops to t1/4 at a later time and finally grows ∝ t. The basic mechanisms of finger interaction, however, are not substantially influenced by relative permeability functions. 相似文献
20.
A linear stability analysis determining the critical Rayleigh number R
c for onset of convection in a bounded vertical cylinder containing a fluid-saturated porous medium is performed for insulated sidewalls, isothermal top surface, and bottom surface heated by forced convection. This Newtonian heating of the bottom surface involves a Biot number Bi that allows consideration of the continuum of boundary conditions ranging from constant heat flux, with global minimum R
min=27.096 found as Bi→0, to isothermal, with global minimum R
min=4π2 found as Bi→ ∞. In both cases and for most cylinder aspect ratios, incipient convection sets in as an asymmetric mode, though islands of aspect ratio exist where the onset mode is symmetric. Sample three-dimensional renderings of disturbance temperature distributions showing preferred modes at onset of convection for fixed Bi are provided and an analytical fit to R
min as a function of Bi is given. 相似文献