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1.
Mahesha Narayana P. Sibanda S. S. Motsa P. A. Lakshmi-Narayana 《Heat and Mass Transfer》2012,48(5):863-874
The stability analysis of the quiescent state in a Maxwell fluid-saturated densely packed porous medium subject to vertical
concentration and temperature gradients is presented. A single phase model with local thermal equilibrium between the porous
matrix and the Maxwell fluid is assumed. The critical Darcy–Rayleigh numbers and the corresponding wave numbers for the onset
of stationary and oscillatory convection are determined. A Lorenz like system is obtained for weakly nonlinear stability analysis. 相似文献
2.
V. B. Bekezhanova 《Journal of Applied Mechanics and Technical Physics》2007,48(2):200-207
The convection of a heat-conducting viscous liquid is considered. It is assumed that the liquid density depends quadratically
on the temperature and pressure. The instability of the equilibrium state of a free-boundary horizontal layer with respect
to small perturbations is studied using a linearization method. It is found that the state of mechanical equilibrium is unstable.
Neutral curves are constructed and the critical Rayleigh numbers are found. The results are compared with the well-known solution
of the same problem for the limiting case where the density is a quadratic function of temperature and does not depend on
pressure.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 66–74, March–April, 2007. 相似文献
3.
In the present study laminar transition to oscillatory convection of fluids having different Prandtl numbers in a laterally
heated vertical cylindrical enclosure for different aspect ratios (melt height to crucible radius) of 2–4 is investigated
numerically for 0.01 ≤ Pr ≤ 10. Numerical solution to two-dimensional axisymmetric transient Navier Stokes equations and energy equation were solved
by finite volume method using SIMPLE algorithm. Numerical results illustrate that there exists a critical Rayleigh number
for each Prandtl number beyond which sustained laminar oscillatory flow sets in. The oscillatory regime was characterised
by the oscillation of the average kinetic energy and average thermal energy of the melt. For a given aspect ratio, critical
Rayleigh number increases with Pr upto 1 and then flattens. It was observed that for low Prandtl number fluids, Pr < 1.0, critical Rayleigh number is found to increase with increase in aspect ratio while for high Prandtl number fluids,
Pr ≥ 1.0, it is found to decrease with increase in aspect ratio. The influence of aspect ratio on the transient behaviour of
the melt volume below and above the critical Rayleigh number was studied. 相似文献
4.
The stability of a fluid-saturated horizontal rotating porous layer subjected to time-periodic temperature modulation is investigated
when the condition for the principle of exchange of stabilities is valid. The linear stability analysis is used to study the
effect of infinitesimal disturbances. A regular perturbation method based on small amplitude of applied temperature field
is used to compute the critical values of Darcy–Rayleigh number and wavenumber. The shift in critical Darcy–Rayleigh number
is calculated as a function of frequency of modulation, Taylor number, and Darcy–Prandtl number. It is established that the
convection can be advanced by the low frequency in-phase and lower-wall temperature modulation, where as delayed by the out-of-phase
modulation. The effect of Taylor number and Darcy–Prandtl number on the stability of the system is also discussed. We found
that by proper tuning of modulation frequency, Taylor number, and Darcy–Prandtl number it is possible to advance or delay
the onset of convection. 相似文献
5.
We investigate in this paper two numerical methods for solving low Mach number compressible flows and their application to
single-phase natural convection flow problems. The first method is based on an asymptotic model of the Navier–Stokes equations
valid for small Mach numbers, whereas the second is based on the full compressible Navier–Stokes equations with particular
care given to the discretization at low Mach numbers. These models are more general than the Boussinesq incompressible flow
model, in the sense that they are valid even for cases in which the fluid is subjected to large temperature differences, that
is when the compressibility of the fluid manifests itself through low Mach number effects. Numerical solutions are computed
for a series of test problems with fixed Rayleigh number and increasing temperature differences, as well as for varying Rayleigh
number for a given temperature difference. Numerical difficulties associated with low Mach number effects are discussed, as
well as the accuracy of the approximations.
Received on 17 January 2000 相似文献
6.
Antonio Barletta Eugenia Rossi di Schio Leiv Storesletten 《Transport in Porous Media》2010,81(3):461-477
The vertical throughflow with viscous dissipation in a horizontal porous layer is studied. The horizontal plane boundaries
are assumed to be isothermal with unequal temperatures and bottom heating. A basic stationary solution of the governing equations
with a uniform vertical velocity field (throughflow) is determined. The temperature field in the basic solution depends only
on the vertical coordinate. Departures from the linear heat conduction profile are displayed by the temperature distribution
due to the forced convection effect and to the viscous dissipation effect. A linear stability analysis of the basic solution
is carried out in order to determine the conditions for the onset of convective rolls. The critical values of the wave number
and of the Darcy–Rayleigh number are determined numerically by the fourth-order Runge–Kutta method. It is shown that, although
generally weak, the effect of viscous dissipation yields an increase of the critical value of the Darcy–Rayleigh number for
downward throughflow and a decrease in the case of upward throughflow. Finally, the limiting case of a vanishing boundary
temperature difference is discussed. 相似文献
7.
A. N. Ermolenko 《Journal of Applied Mechanics and Technical Physics》2007,48(2):166-175
The stability of the state of rest of a heated infinite horizontal layer of a viscous heat-conducting fluid (the Rayleigh-Benard
problem) is considered. The equation of state for the fluid takes into account the nonmonotonic temperature and pressure dependence
of water density. Instability of the mechanical equilibrium with respect to small monotonic perturbations is studied. The
effect of the problem parameters on the Rayleigh numbers and their corresponding critical motions is investigated numerically
using linear theory. Numerical investigation of the spectral problem is based on the Godunov-Abramov orthogonalization method.
The calculation results are compared with the well-known results for the limiting case where the density is considered a quadratic
function of temperature and does not depend on pressure.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 27–38, March–April, 2007. 相似文献
8.
The wave instability of convective boundary layers in a horizontal cylindrical layer of ethanol under the action of vertical
hamonic high-frequency vibration is studied. A strong destabilizing effect of the vibration on the stability of the convective
boundary layers is detected. In the plane of the gravity and vibration Rayleigh numbers (Ra and R
V
), the excitation limit of the wave instability is determined. The periods of the temperature oscillations caused by the waves
in the boundary layers near the inner and outer cavity boundaries are studied as functions of the Rayleigh numbers.
Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 32–40, May–June, 1998. 相似文献
9.
The problem of the convective instability of a plane fluid layer bounded by rigid walls with heating in a narrow layer running
parallel to the walls inside the volume in question is solved. Instability criteria depending on the location of the heated
layer and the Rayleigh numbers of the upper and lower layers are found. The results are compared with those for a plane layer
with uniform energy release inside the volume.
Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 8–15, January–February,
1997.
The work was carried out with partial support from the Russian Foundation for Fundamental Research (project No. 95-01-00354a). 相似文献
10.
V. K. Andreev V. B. Bekezhanova 《Journal of Applied Mechanics and Technical Physics》2007,48(4):479-485
The convective stability of a system of two immiscible liquids with close densities is studied. The densities of the liquids
depend nonlinearly on temperature and pressure. It is shown that the state of mechanical equilibrium is unstable. Neutral
curves are plotted, and the critical values of the Rayleigh number are found. The calculations are performed for physical
parameters characteristic of various northern, central, and southern zones of lake Baikal.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 4, pp. 15–22, July–August, 2007. 相似文献
11.
The problem of the onset of convective roll instabilities in a horizontal porous layer with isothermal boundaries at unequal
temperatures, well known as the Horton–Rogers–Lapwood problem, is revisited including the effect of pressure work and viscous
dissipation in the local energy balance. A linear stability analysis of rolls disturbances is performed. The analysis shows
that, while the contribution of viscous dissipation is ineffective, the contribution of the pressure work may be important.
The condition of marginal stability is investigated by adopting two solution procedures: method of weighted residuals and
explicit Runge–Kutta method. The pressure work term in the energy balance yields an increase of the value of the Darcy–Rayleigh
number at marginal stability. In other words, the effect of pressure work is a stabilizing one. Furthermore, while the critical
value of the Darcy– Rayleigh number may be considerably affected by the pressure work contribution, the critical value of
the wave number is affected only in rather extreme cases, i.e. for very high values of the Gebhart number. A nonlinear stability
analysis is also performed pointing out that the joint effects of viscous dissipation and pressure work result in a reduction
of the excess Nusselt number due to convection, when the Darcy–Rayleigh number is replaced by the superadiabatic Darcy–Rayleigh
number. 相似文献
12.
L. Arkeryd R. Esposito R. Marra A. Nouri 《Archive for Rational Mechanics and Analysis》2010,198(1):125-187
We consider the Boltzmann equation for a gas in a horizontal slab, subject to a gravitational force. The boundary conditions
are of diffusive type, specifying the wall temperatures, so that the top temperature is lower than the bottom one (Benard
setup). We consider a 2-dimensional convective stationary solution, which for small Knudsen numbers is close to the convective
stationary solution of the Oberbeck–Boussinesq equations, near and above the bifurcation point, and prove its stability under
2-d small perturbations, for Rayleigh numbers above and close to the bifurcation point and for small Knudsen numbers. 相似文献
13.
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
14.
When a nonhomogeneous solid is melting from below, convection may be induced in a thermally–unstable melt layer. In this study,
the onset of buoyancy-driven convection during time-dependent melting is investigated by using similarly transformed disturbance
equations. The critical Darcy–Rayleigh numbers based on the melt-layer thickness, Ra
H,c, are found numerically for various conditions. For small superheats, the present predictions show that Ra
H,c is located between 27.1 and 4π
2 and it approaches the well-known results of the original Horton–Rogers–Lapwood problem. However, for high superheats, it
is dependent on the phase change rate λ and the relation of Ra
H,c λ = 25.89 is shown. 相似文献
15.
A theoretical analysis of buoyancy-driven instability under transient basic fields is conducted in an initially quiescent,
fluid-saturated, horizontal porous layer. Darcy’s law is used to explain characteristics of fluid motion and the anisotropy
of permeability is considered. Under the Boussinesq approximation and the principle of exchange of stabilities, the stability
equations are derived by using the linear stability theory and the energy method. The linear stability equations are analyzed
numerically by using the frozen-time model and the linear amplification theory and the global stability limits are obtained
numerically from the energy method. For the various anisotropic ratios, the critical times are predicted as a function of
the Darcy–Rayleigh number and the critical Darcy–Rayleigh number is also obtained. The present predictions are compared each
another and with existing theoretical ones. 相似文献
16.
Akhilesh Gupta V. Eswaran Prabhat Munshi N. K. Maheshwari P. K. Vijayan 《Heat and Mass Transfer》2009,45(3):275-285
Strong heat source at the isolation condenser wall of an Advanced Heavy Water Reactor, results in natural convection in gravity
driven water pool, which leads to a thermally stratified pool. Governing equations simulating fluid flow and heat distribution
are solved numerically by a general purpose Computational Fluid Dynamics solver developed at Indian Institute of Technology,
Kanpur. Incompressible finite volume method with non-staggered grid arrangement is used in this exercise. This algorithm is
fully implicit and semi-coupled. Turbulent natural convection in a boundary layer for high Rayleigh numbers is analyzed by
the Lam–Bremhorst k − ε turbulence model. Analysis of unsteady laminar natural convection in a side-heated water cavity is also done for different
values of Rayleigh number. Results show a warm fluid layer floating on the top of gradually colder layer (along the vertical
direction) that indicates the presence of thermal stratification phenomenon. This fact necessitates additional safety features
in such a system so that the detrimental effect such as stratification is minimized. 相似文献
17.
The shell model of developed convective turbulence of an incompressible fluid is considered. Regimes developing at high Rayleigh
numbers are investigated numerically for three- and two-dimensional motion. It is shown that in the three-dimensional turbulent
convection model the inertial Obukhov-Bolgiano interval is developed on large scales, but this interval is unstable and gives
way to the Kolmogorov regime in which the temperature behaves as a passive admixture. In the two-dimensional turbulent convection
model a finite scale interval on which the buoyancy forces determine the nature of the fluctuations but the spectral laws
established differ from those that follow from dimensional considerations for the Obukhov-Bolgiano interval is detected.
Perm’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 37–46, November–December,
1998.
The work was carried out with financial support from the Russian Foundation for Basic Research (project No. 94-01-00951a). 相似文献
18.
Based on a modified Darcy–Brinkman–Maxwell model, a linear stability analysis of a Maxwell fluid in a horizontal porous layer
heated from below by a constant flux is carried out. The non-oscillatory instability and oscillatory instability with different
hydrodynamic boundaries such as rigid and free surfaces at the bottom are studied. Compared with the rigid surface cases,
onset of fluid motion due to non-oscillatory instability and oscillatory instability is found to occur both more easily for
the system with a free bottom surface. The critical Rayleigh number for onset of fluid motion due to non-oscillatory instability
is lower with a constant flux heating bottom than with an isothermal heating bottom, but the result due to oscillatory instability
is in contrast. The effects of the Darcy number, the relaxation time, and the Prandtl number on the critical Rayleigh number
are also discussed. 相似文献
19.
Natural convection in a partially filled porous square cavity is numerically investigated using SIMPLEC method. The Brinkman-Forchheimer
extended model was used to govern the flow in the porous medium region. At the porous-fluid interface, the flow boundary condition
imposed is a shear stress jump, which includes both the viscous and inertial effects, together with a continuity of normal
stress. The thermal boundary condition is continuity of temperature and heat flux. The results are presented with flow configurations
and isotherms, local and average Nusselt number along the cold wall for different Darcy numbers from 10−1 to 10−6, porosity values from 0.2 to 0.8, Rayleigh numbers from 103 to 107, and the ratio of porous layer thickness to cavity height from 0 to 0.50. The flow pattern inside the cavity is affected
with these parameters and hence the local and global heat transfer. A modified Darcy–Rayleigh number is proposed for the heat
convection intensity in porous/fluid filled domains. When its value is less than unit, global heat transfer keeps unchanged.
The interfacial stress jump coefficients β
1 and β
2 were varied from −1 to +1, and their effects on the local and average Nusselt numbers, velocity and temperature profiles
in the mid-width of the cavity are investigated. 相似文献
20.
A. Douiebe M. Hannaoui G. Lebon A. Benaboud A. Khmou 《Flow, Turbulence and Combustion》2001,67(3):185-204
The coupled buoyancy and thermocapillary instability, the Bénard–Marangoniproblem, in an electrically conducting fluid layer
whose upper surface is deformed and subject to a temperature gradient is studied. Both influences of an a.c. electric field
and rotation are investigated. Special attention is directed at the occurrence of convection both in the form of stationary
motion and oscillatory convection. The linear stability problem is solved for different values of the relevant dimensionless
numbers, namely the a.c. electric Rayleigh number, the Taylor, Rayleigh, Biot, Crispation and Prandtl numbers. For steady
convection, it is found that by increasing the angular velocity, one reinforces the stability of the fluid layer whatever
the values of the surface deformation and the applied a.c. electric field. We have also determined the regions of oscillatory
instability and discussed the competition between both stationary and oscillatory convections.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献