Unsteady three-dimensional natural convection in a fluid-saturated porous medium

Stamps, Douglas W.; Arpacı, Vedat S.; Clark, John A.

doi:10.1017/s0022112090002361

Cited by 22 publications

(8 citation statements)

References 25 publications

(30 reference statements)

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“…Schubert & Straus (1979) found that the steady cubic‐cell flow is replaced by a time‐dependent oscillatory regime at high Rayleigh numbers. Improving the numerical accuracy of the computations, Kimura et al (1989), Stamps et al (1990) and Graham & Steen (1991) located the transition of the [111] mode from the steady to the oscillatory state at R = 580.…”

Section: Introductionmentioning

confidence: 99%

Forms of hydrothermal and hydraulic flow in a homogeneous unconfined aquifer

Cserepes¹,

Lenkey²

2004

Geophysical Journal International

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SUMMARY Groundwater flow in an unconfined aquifer (a porous layer with an open top) can be driven either by hydraulic forces, i.e. the gradient of the water table, or by differences in the density of porewater due to thermal expansion and changes in salinity. In this study we assume that the salinity is constant, and we investigate the spatial forms of the hydraulic and hydrothermal flows, with emphasis on the case where both components are present. Since basic flow patterns are under consideration, the simple case of a homogeneous (but anisotropic) layer is studied by numerical solution of the governing equations. When the surface hydraulic gradient is zero, free thermal convection can occur in strictly cellular forms. Just above the critical Rayleigh number the first form of convection is 2‐D rolls; later square cells become stable. These flows exhibit asymmetrical patterns due to the different conditions prevailing at the top and bottom boundaries. In natural circumstances no strict cellularity can be expected: instead of regular squares, irregular polygonal cells develop and remain time‐dependent. When the hydraulic governing force is added to the thermal forces, i.e. the gradient of the water table is no longer zero, first we have polygonal cells. When the hydraulic gradient increases gradually, the polygons are replaced by longitudinal rolls (i.e. rolls parallel to the gradient direction). This occurs in a regime where the hydrothermal and hydraulic governing forces are equally important. Later, when the hydraulic gradient is even higher, the flow pattern changes abruptly to transverse rolls. At low anisotropies, these transverse rolls drift with the main hydraulic flow in the direction of the slope of the water table. Finally, at strong hydraulic gradients, the cells of convection are completely suppressed by the fast hydraulic flow, which is now organized in a ‘unicell’ form. Domain boundaries are established for all these circulation patterns as functions of the Rayleigh number, surface hydraulic gradient and anisotropy. Characteristics of the heat transfer are also analysed.

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Section: Introductionmentioning

confidence: 99%

Forms of hydrothermal and hydraulic flow in a homogeneous unconfined aquifer

Cserepes¹,

Lenkey²

2004

Geophysical Journal International

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“…Instead, the S3 mode was found to undergo a bifurcation to either S7 or S10 depending on the perturbation given by the time-step value chosen in the simulation when Ra * is increased from 600 to 610. Straus & Schubert 1978, 1981Horne 1979;Steen 1983;Kimura et al 1989;Stamps et al 1990;Graham & Steen 1991 Table 2. Flow structures, their range of existence and structures reached after bifurcation.…”

Section: Effect Of Rayleigh Numbermentioning

confidence: 99%

“…Both studies report that the flow pattern becomes less symmetric prior to the onset of time dependence. Stamps, Arpaci & Clark (1990) found that regularly fluctuating convection begins at Ra * between 550 and 560 from steady three-dimensional flow.…”

Section: Introductionmentioning

confidence: 99%

Flow patterns in a fluid-saturated porous cube heated from below

Sezai

2005

J. Fluid Mech.

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Natural convection in a cube of fluid-saturated porous medium heated from below and cooled from the top is studied numerically using a non-Darcy flow model. All vertical sidewalls are considered to be impermeable and adiabatic. The evolution of the various flow patterns is investigated from onset up to a Rayleigh number of 1000 where irregularly fluctuating convection prevails. New flow patterns have been found to exist in addition to those mentioned in the previous studies. In the present study, a total of ten steady flow patterns have been identified, of which five show oscillatory behaviour in some Rayleigh-number range. The results are presented in terms of average Nusselt number curves consisting of the solution branches of the convective patterns. The convective patterns are classified in terms of their symmetry properties, and the symmetries broken or gained during bifurcations from one flow structure to the other are identified.

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“…The analysis of transient natural convection in porous media has appeared frequently in the literature for two-dimensional situations, while for threedimensional problems it has been much more rare, especially for fully transient situations, mainly due to the sometimes prohibitive increase in computational effort associated with the most usual purely discrete solution approaches. Some relevant contributions to the present analysis, in dealing with two and threedimensional natural convection within porous cavities, are listed below [1][2][3][4][5][6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Integral Transforms for Heat and Fluid Flow in Two- And Three-Dimensional Porous Media

Cotta

Neto

Alves³

et al. 2001

Hyb Meth Eng

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Hybrid numerical-analytical algorithms, based on the generalized integral transform technique, are developed and reviewed to handle transient two-and three-dimensional heat and fluid flow in cavities filled with a porous material. A general formulation and solution methodology for horizontal and vertical cavities is developed. To illustrate the algorithm computational behavior, specific situations are more closely considered, under the Darcy model for natural convection in porous medium filled cavities. The problem is analyzed with and without the time derivative term in the flow equations, using a vorticity-vector potential formulation, which automatically reduces to the streamfunction-only formulation for two-dimensional situations. Results for rectangular (2D) and parallelepiped (3D) vertical cavities are presented to demonstrate the convergence behavior of the proposed eigenfunction expansion solutions and comparisons with previously reported numerical solutions are critically performed.

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Unsteady three-dimensional natural convection in a fluid-saturated porous medium

Cited by 22 publications

References 25 publications

Forms of hydrothermal and hydraulic flow in a homogeneous unconfined aquifer

Forms of hydrothermal and hydraulic flow in a homogeneous unconfined aquifer

Flow patterns in a fluid-saturated porous cube heated from below

Integral Transforms for Heat and Fluid Flow in Two- And Three-Dimensional Porous Media

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