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1.
Shunde Yin Brian F. Towler Maurice B. Dusseault Leo Rothenburg 《Transport in Porous Media》2010,84(3):773-798
Wellbore stability analysis is an important topic in petroleum geomechanics. Analytical and numerical analysis of wellbore
stability involves the study of interactions among pressure, temperature and chemical changes, and the mechanical response
of the rock, a coupled thermal–hydraulic–mechanical–chemical (THMC) process. Thermal and solute convection have usually been
overlooked in numerical models. This is appropriate for shales with extremely low permeability, but for shales with intermediate
and high permeability (e.g., shale with a disseminated microfissure network), thermal and solute convection should be considered.
The challenge of considering advection lies in the numerical oscillation encountered when implementing the traditional Galerkin
finite element approach for transient advection–diffusion problems. In this article, we present a fully coupled THMC model
to analyze the stress, pressure, temperature, and solute concentration changes around a wellbore. In order to overcome spurious
spatial temperature oscillations in the convection-dominated thermal advection–diffusion problem, we place the transient problem
into an advection– diffusion-reaction problem framework, which is then efficiently addressed by a stabilized finite element
approach, the subgrid scale/gradient subgrid scale method (SGS/GSGS). 相似文献
2.
The influence of high-frequency horizontal vibrations on convection in the Hele-Shaw cell located in a uniform gravity field
is considered experimentally and theoretically. Nonlinear regimes of vibrational convection in the supercritical region are
examined. It is shown that horizontal vibrations (directed toward the wide sides of the cell) decrease the threshold of quasi-equilibrium
stability. Regions of existence of one- and two-vortex steady flows are found, and unsteady regular and random regimes of
thermal vibrational convection are considered. New random regimes in the Hele-Shaw cell are found, which result from nonlinear
interaction of the “lower” modes responsible for the formation of regular supercritical convective regimes.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 2, pp. 40–48, March–April, 2006. 相似文献
3.
Buoyant flows often contain regions with unstable and stable thermal stratification from which counter gradient turbulent
fluxes are resulting, e.g. fluxes of heat or of any turbulence quantity. Basing on investigations in meteorology an improvement
in the standard gradient-diffusion model for turbulent diffusion of turbulent kinetic energy is discussed. The two closure
terms of the turbulent diffusion, the velocity-fluctuation triple correlation and the velocity-pressure fluctuation correlation,
are investigated based on Direct Numerical Simulation (DNS) data for an internally heated fluid layer and for Rayleigh–Bénard
convection. As a result it is decided to extend the standard gradient-diffusion model for the turbulent energy diffusion by
modeling its closure terms separately. Coupling of two models leads to an extended RANS model for the turbulent energy diffusion.
The involved closure term, the turbulent diffusion of heat flux, is studied based on its transport equation. This results
in a buoyancy-extended version of the Daly and Harlow model. The models for all closure terms and for the turbulent energy
diffusion are validated with the help of DNS data for internally heated fluid layers with Prandtl number Pr = 7 and for Rayleigh–Bénard convection with Pr = 0.71. It is found that the buoyancy-extended diffusion model which involves also a transport equation for the variance
of the vertical velocity fluctuation gives improved turbulent energy diffusion data for the combined case with local stable
and unstable stratification and that it allows for the required counter gradient energy flux. 相似文献
4.
A numerical study is performed to analyze steady laminar forced convection in a channel in which discrete heat sources covered
with porous material are placed on the bottom wall. Hydrodynamic and heat transfer results are reported. The flow in the porous
medium is modeled using the Darcy–Brinkman–Forchheimer model. A computer program based on control volume method with appropriate
averaging for diffusion coefficient is developed to solve the coupling between solid, fluid, and porous region. The effects
of parameters such as Reynolds number, Prandtl number, inertia coefficient, and thermal conductivity ratio are considered.
The results reveal that the porous cover with high thermal conductivity enhances the heat transfer from the solid blocks significantly
and decreases the maximum temperature on the heated solid blocks. The mean Nusselt number increases with increase of Reynolds
number and Prandtl number, and decrease of inertia coefficient. The pressure drop along the channel increases rapidly with
the increase of Reynolds number. 相似文献
5.
Summary The thermal instability of a Rivlin–Ericksen fluid in a porous medium is considered in the presence of a uniform vertical
magnetic field to include the effect of Hall currents. For the case of stationary convection, the magnetic field has a stabilizing
effect on the system, whereas the Hall current has a destabilizing effect on the system. The medium permeability has both
stabilizing and destabilizing effects, depending on the Hall parameter M. The kinematic viscoelasticity has no effect on stationary convection. Graphs have been plotted by giving numerical values
to the parameters, to depict the stability characteristics. The magnetic field (and corresponding Hall currents) introduces
oscillatory modes in the system, which would be nonexistent in their absence. The sufficient conditions for the nonexistence
of overstability are also obtained.
Received 20 May 1999; accepted for publication 8 March 2000 相似文献
6.
L. A. Kovaleva V. N. Kireev A. A. Musin 《Journal of Applied Mechanics and Technical Physics》2009,50(1):80-85
Results of numerical simulations of the thermal action on a high-viscosity hydrocarbon fluid with temperature-dependent viscosity
and thermal conductivity are presented. A system of equations of thermal convection in the Boussinesq approximation is used
as the constitutive equations to describe the convection of the hydrocarbon fluid. The dynamics of the temperature field and
convective structures in the fluid is studied. The spatial motion of the fluid is found to be locally nonuniform; the motion
is accompanied by vortex flows; as a result, two regions with significantly different temperatures are formed in the medium.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 1, pp. 95–100, January–February, 2009. 相似文献
7.
Daniel N. Riahi 《Transport in Porous Media》2008,72(1):121-138
We consider the problem of mixed oscillatory and steady modes of nonlinear compositional convection in horizontal mushy layers
during the solidification of binary alloys. Under a near-eutectic approximation and the limit of large far-field temperature,
we determine a number of two- and three-dimensional weakly nonlinear mixed solutions, and the stability of these solutions
with respect to arbitrary three-dimensional disturbances is then investigated. The present investigation is an extension of
the problem of mixed oscillatory and steady modes of convection, which was investigated by Riahi (J Fluid Mech 517: 71–101,
2004), where some calculated results were inaccurate due to the presence of a singular point in the equation for the linear
frequency. Here we resolve the problem and find some significant new results. In particular, over a wide range of the parameter
values, we find that the properties of the preferred and stable solution in the form of particular subcritical mixed standing
and steady hexagons appeared to be now in much better agreement with the available experimental results (Tai et al., Nature
359:406–408, 1992) than the one reported in Riahi (J Fluid Mech 517:71–101, 2004). We also determined a number of new types
of preferred supercritical solutions, which can be preferred over particular values of the parameters and at relatively higher
values of the amplitude of convection. 相似文献
8.
The finite-amplitude evolution of electroconvective structures in a weakly conducting liquid with an electroconductive charge
formation mechanism is examined. The liquid is in the electrostatic field of a horizontally placed capacitor and is heated
from below, and the electric charge time constant is much shorter than the characteristic hydrodynamic time. The interaction
between the electroconductive convection and thermogravitational convection is considered. The evolution of the supercritical
structures is investigated by direct numerical simulation using the finite-difference method. The bifurcations leading to
the formation of stationary and wave liquid flows are analyzed. Nonlinear modes of stationary convection and traveling waves
with different space-time patterns are identified and investigated.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 3, pp. 20–27, May–June, 2008. 相似文献
9.
S. M. Zen’kovskaya T. N. Rogovenko 《Journal of Applied Mechanics and Technical Physics》1999,40(3):379-385
The effect of high-frequency translational vibrations on the occurrence of filtration convection in a plane horizontal layer
of a viscous incompressible liquid saturating a porous medium is studied. Constant temperature is maintained at the boundaries
of the layer. It is established that for any vibration direction different from the vertical (transverse) direction, convection
in gravity and thermal gravitational convection under both heating from above and heating from below can arise. In the case
of reduced gravity, values of the vibration parameter that lead to transition to zero gravity are established. The results
are obtained from an analysis of the averaged equations of filtration convection, derived for an arbitrary region.
This work was presented at the joint X European and VI Russian Symposium on Physical Sciences in Microgravity (St. Petersburg,
June 15–20, 1997).
Rostov State university, Rostov-on-Don 344090. Rostov State Academy of Building, Rostov-on-Don 344022. Translated from Prikladnaya
Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 3, pp. 22–29, May–June, 1999. 相似文献
10.
A. Pantokratoras 《Heat and Mass Transfer》2000,36(4):351-360
In most studies concerning laminar natural convection along a vertical isothermal cylinder a linear relationship between
fluid density and temperature has been used and kinematic viscosity and thermal diffusivity have been considered constant
calculated at ambient temperature. However, it is known that the density–temperature relationship for water is non-linear
at low temperatures and kinematic viscosity and thermal diffusivity are functions of temperature. In this study the problem
of laminar natural convection of pure and saline water along a vertical isothermal cylinder has been investigated in the temperature
range between 20 and 0 ∘C taking into account the temperature dependence of ν, α and ρ. The results are obtained with the numerical solution of the
boundary layer equations. The variation of ν, α and ρ with temperature has a strong influence on free convection characteristics.
Received on 17 May 1999 相似文献
11.
A. V. Kistovich Yu. D. Chashechkin 《Journal of Applied Mechanics and Technical Physics》1998,39(4):528-535
The influence of the boundary conditions at the surfaces confining multicomponent stratified media on the formation of flows
in problems of multicomponent diffusion and thermoconcentration convection is investigated. Exact solutions of these problems
are given. Analysis of these solutions shows that several boundary layers (concentration and velocity layers) are formed in
the case of multicomponent diffusion, which leads to decomposition of the physical fields and splitting of the characteristic
spatial scales. In the case of thermoconcentration convection, a more complicated dynamic structure is formed, which, besides
boundary layers, includes injection fronts. The latter have a significant effect on the flow characteristics at distances
far exceeding the thickness of the boundary layers.
Institute of Mechanics Problems, Russian Academy of Sciences, Moscow 117526. Translated from Prikladnaya Mekhanika i Tekhnicheskaya
Fizika, Vol. 39, No. 4, pp. 54–63, July–August, 1998. 相似文献
12.
A. Eidelman T. Elperin N. Kleeorin A. Markovich I. Rogachevskii 《Experiments in fluids》2006,40(5):723-732
Coherent large-scale circulations of turbulent thermal convection in air have been studied experimentally in a rectangular box heated from below and cooled from above using Particle Image Velocimetry. The hysteresis phenomenon in turbulent convection was found by varying the temperature difference between the bottom and the top walls of the chamber (the Rayleigh number was changed within the range of 107–108). The hysteresis loop comprises the one-cell and two-cells flow patterns while the aspect ratio is kept constant (A=2–2.23). We found that the change of the sign of the degree of the anisotropy of turbulence was accompanied by the change of the flow pattern. The developed theory of coherent structures in turbulent convection (Phys Rev E 66:1–15, 2002, Boundary-Layer Meteorol, 2005) is in agreement with the experimental observations. The observed coherent structures are superimposed on a small-scale turbulent convection. The redistribution of the turbulent heat flux plays a crucial role in the formation of coherent large-scale circulations in turbulent convection. 相似文献
13.
M. K. Zhekamukhov L. Z. Shukhova 《Journal of Applied Mechanics and Technical Physics》1999,40(6):1042-1047
Convective instability of air in the pores between ice crystals in snow is considered. In the Boussinesq approximation, a
system of equations that describes the origin of thermal convection within the snow thickness is derived. It is shown that
for snow, as for a liquid, there is a criterial number analogous to the Rayleigh number that determines the origin of air
instability in snow. The contribution of natural convection of air to the heat- and mass-transfer processes in snow is estimated
and possible reasons for the considerable scatter of reported experimental data on the thermal conductivity and diffusivity
of snow are discussed.
Kabardino-Balkarian State University, Nal'chik 360004. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol.
40, No. 6, pp. 54–59, November–December, 1999. 相似文献
14.
B. Straughan 《Transport in Porous Media》2009,77(2):159-168
We revisit the problem of thermal convection in a bidispersive porous medium, first addressed by Nield and Kuznetsov (Int.
J. Heat Mass Transfer, 49: 3068–3074, 2006). We investigate the possibility of oscillatory convection by using a highly accurate
Chebyshev tau
numerical method. We also develop a nonlinear energy stability theory for the same problem. This yields a global stability
threshold below which instabilities cannot arise. These thresholds together with the linear instability boundaries yield a
zone where thermal instability may be found. The results and theory of Nield and Kuznetsov (Int. J. Heat Mass Transfer, 49:
3068–3074, 2006) are thus proven to be a highly important development in the modern theory of designer porous materials, cf.
Nield and Bejan (Convection in Porous Media, Springer, New York, 2006), pp. 94–97.
This work was supported in part by a Research Project Grant of the Leverhulme Trust—Grant Number F/00128/AK. 相似文献
15.
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
16.
This study investigates mixed convection heat transfer about a permeable vertical plate in the presence of magneto and thermal
radiation effects. The effects of the mixed convection parameter, the radiation–conduction parameter, the surface temperature
parameter, the magnetic parameter and the suction/injection parameter on the local skin friction and local heat transfer parameters
are presented and analyzed. 相似文献
17.
The effect of thermal/gravity modulation on the onset of convection in a Maxwell fluid saturated porous layer is investigated
by a linear stability analysis. Modified Darcy–Maxwell model is used to describe the fluid motion. The regular perturbation
method based on the small amplitude of modulation is employed to compute the critical Rayleigh number and the corresponding
wavenumber. The stability of the system characterized by a correction Rayleigh number is calculated as a function of the viscoelastic
parameter, Darcy–Prandtl number, normalized porosity, and the frequency of modulation. It is found that the low frequency
symmetric thermal modulation is destabilizing while moderate and high frequency symmetric modulation is always stabilizing.
The asymmetric modulation and lower wall temperature modulations are, in general, stabilizing while the system becomes unstable
for large values of Darcy–Prandtl number and for small frequencies. It is shown that in general the gravity modulation produces
a stabilizing effect on the onset of convection for moderate and high frequency. The small frequency gravity modulation is
found to have destabilizing effect on the stability of the system. 相似文献
18.
Sebastian Geiger Thomas Driesner Christoph A. Heinrich Stephan K. Matthäi 《Transport in Porous Media》2006,63(3):435-461
We present the benchmarking of a new finite element – finite volume (FEFV) solution technique capable of modeling transient
multiphase thermohaline convection for geological realistic p-T-X conditions. The algorithm embeds a new and accurate equation of state for the NaCl–H2O system. Benchmarks are carried out to compare the numerical results for the various component-processes of multiphase thermohaline
convection. They include simulations of (i) convection driven by temperature and/or concentration gradients in a single-phase
fluid (i.e., the Elder problem, thermal convection at different Rayleigh numbers, and a free thermohaline convection example),
(ii) multiphase flow (i.e., the Buckley–Leverett problem), and (iii) energy transport in a pure H2O fluid at liquid, vapor, supercritical, and two-phase conditions (i.e., comparison to the U.S. Geological Survey Code HYDROTHERM).
The results produced with the new FEFV technique are in good agreement with the reference solutions. We further present the
application of the FEFV technique to the simulation of thermohaline convection of a 400°C hot and 10 wt.% saline fluid rising
from 4 km depth. During the buoyant rise, the fluid boils and separates into a high-density, high-salinity liquid phase and
a low-density, low-salinity vapor phase. 相似文献
19.
A system of two stratified layers at a free surface, consisting of distilled water above a layer of salty water separated
by an interface, is studied under laboratory conditions involving uniform temperature heating from below. Shadowgraph and
particle images have been used with temperature and salt concentration measurements to investigate the interface instability
induced by convection when it is developing in the upper and lower layer. It is found that the interface is governed by local
shear flow that induces a Kelvin–Helmholtz instability. Moreover, the entrainment interface is subject to a combination of
two closely related effects: (1) double diffusion and convective motion and (2) double diffusion and Kelvin–Helmholtz instability.
Received: 22 December 1999/Accepted: 31 October 2000 相似文献
20.
Natalia Strong 《Journal of Mathematical Fluid Mechanics》2008,10(4):488-502
The present paper examines the effect of vertical harmonic vibration on the onset of convection in an infinite horizontal
layer of fluid saturating a porous medium. A constant temperature distribution is assigned on the rigid boundaries, so that
there exists a vertical temperature gradient. The mathematical model is described by equations of filtration convection in
the Darcy–Oberbeck–Boussinesq approximation. The linear stability analysis for the quasi-equilibrium solution is performed
using Floquet theory. Employment of the method of continued fractions allows derivation of the dispersion equation for the
Floquet exponent σ in an explicit form. The neutral curves of the Rayleigh number Ra versus horizontal wave number α for the
synchronous and subharmonic resonant modes are constructed for different values of frequency Ω and amplitude A of vibration. Asymptotic formulas for these curves are derived for large values of Ω using the method of averaging, and,
for small values of Ω, using the WKB method. It is shown that, at some finite frequencies of vibration, there exist regions
of parametric instability. Investigations carried out in the paper demonstrate that, depending on the governing parameters
of the problem, vertical vibration can significantly affect the stability of the system by increasing or decreasing its susceptibility
to convection.
相似文献