Numerical solutions of one-dimensional self-similar problems of gas motion in a porous medium for a quadratic drag law

1983 ◽  
Vol 45 (4) ◽  
pp. 1155-1159
Author(s):  
V. M. Kolobashkin ◽  
N. A. Kudryashov ◽  
V. V. Murzenko
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
One Dimensional ◽  
Quadratic Drag ◽  
Self Similar ◽  
Drag Law

A similarity problem of a porous material drying

2008 ◽  
Vol 6 ◽  
pp. 75-81
Author(s):  
D.Ye. Igoshin
Keyword(s):  
Mass Transfer ◽  
Porous Medium ◽  
Gas Mixture ◽  
Dimensional Problem ◽  
Vapor Mixture ◽  
Initial State ◽  
One Dimensional ◽  
Similarity Problem ◽  
Self Similar ◽  
Similar Solutions

The plano-one-dimensional problem of heat and mass transfer is considered when a porous semi-infinite material layer dries. At the boundary, which is permeable for the gas-vapor mixture, the temperature and composition of the gas are kept constant. Self-similar solutions are set describing the propagation of the temperature field and the moisture content field arising when heat is supplied. The intensity of dry flows is studied, depending on the initial state of the wet-porous medium, as well as the temperature and concentration composition of the vapor-gas mixture at the boundary of the porous medium.

Two-dimensional viscous gravity currents flowing over a deep porous medium

2001 ◽  
Vol 440 ◽  
pp. 359-380 ◽  
Author(s):  
JAMES M. ACTON ◽  
HERBERT E. HUPPERT ◽  
M. GRAE WORSTER
Keyword(s):  
Porous Medium ◽  
Numerical Solutions ◽  
Gravity Current ◽  
Constant Volume ◽  
Two Dimensional ◽  
Theoretical Predictions ◽  
Self Similar ◽  
Coefficient Of Viscosity ◽  
Good Agreement

The spreading of a two-dimensional, viscous gravity current propagating over and draining into a deep porous substrate is considered both theoretically and experimentally. We first determine analytically the rate of drainage of a one-dimensional layer of fluid into a porous bed and find that the theoretical predictions for the downward rate of migration of the fluid front are in excellent agreement with our laboratory experiments. The experiments suggest a rapid and simple technique for the determination of the permeability of a porous medium. We then combine the relationships for the drainage of liquid from the current through the underlying medium with a formalism for its forward motion driven by the pressure gradient arising from the slope of its free surface. For the situation in which the volume of fluid V fed to the current increases at a rate proportional to t3, where t is the time since its initiation, the shape of the current takes a self-similar form for all time and its length is proportional to t2. When the volume increases less rapidly, in particular for a constant volume, the front of the gravity current comes to rest in finite time as the effects of fluid drainage into the underlying porous medium become dominant. In this case, the runout length is independent of the coefficient of viscosity of the current, which sets the time scale of the motion. We present numerical solutions of the governing partial differential equations for the constant-volume case and find good agreement with our experimental data obtained from the flow of glycerine over a deep layer of spherical beads in air.

scholarly journals The use of flows with uniform velocity gradient in modelling free expansion of a polytropic gas

1987 ◽  
Vol 5 (4) ◽  
pp. 643-658 ◽  
Author(s):  
G. J. Pert
Keyword(s):  
Velocity Gradient ◽  
Numerical Solutions ◽  
Linear Velocity ◽  
Symmetric Form ◽  
Free Expansion ◽  
Matching Conditions ◽  
One Dimensional ◽  
Polytropic Gas ◽  
Uniform Velocity ◽  
Self Similar

The free expansion of a heated mass of uniform gas (e.g. a laser produced plasma) can be modelled by self-similar motion with a linear velocity gradient. Using a series of numerical solutions we have shown that a reasonable representation is obtained by the use of a matching parameter relating the scale lengths in the prototype and its model, and that the representation improves as the ratio of the heating and disassembly times increases. In this paper we re-examine these two inferred results, and re-derive them on an analytic basis. The extension of the theory to multi-structured bodies shows that such systems of symmetric form allow self-similar motion, as does the particular case of an asymmetric one-dimensional foil. The case of isothermal foils is examined in detail to illustrate the derivation of the matching conditions.

Gas Injection into Porous Reservoir Partly Saturated by Water

2015 ◽  
Vol 756 ◽  
pp. 336-341 ◽  
Author(s):  
М.K. Khasanov
Keyword(s):  
Porous Medium ◽  
Gas Injection ◽  
Hydrate Formation ◽  
Critical Conditions ◽  
Frontal Surface ◽  
One Dimensional ◽  
Gas Hydrate Formation ◽  
Porous Reservoir ◽  
Self Similar ◽  
Similar Solutions

Specific features of formation of gas hydrates due to injection of a gas into a porous medium initially filled by a gas and water are considered. Self-similar solutions to the planar one-dimensional problem are constructed, which give the distribution of main bed characteristics. The influence of the initial parameters of the porous medium and the intensity of the gas injection on the dynamics of the processes of hydrate formation is studied. The existence of solutions is demonstrated, which predict gas hydrate formation both on the frontal surface and in the volume zone. The critical conditions that separate the different modes of hydrate formation are found.

Conservative solute transport with periodic velocity and sinusoidal source concentration in semi-infinite porous media: An analytical solution

2014 ◽  
Vol 6 (1) ◽  
pp. 1024-1031
Author(s):  
R R Yadav ◽  
Gulrana Gulrana ◽  
Dilip Kumar Jaiswal
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Laplace Transformation ◽  
Seepage Velocity ◽  
Transformation Technique ◽  
Numerical Examples ◽  
One Dimensional ◽  
Porous Domain ◽  
Conservative Solute Transport ◽  
Source Concentration

The present paper has been focused mainly towards understanding of the various parameters affecting the transport of conservative solutes in horizontally semi-infinite porous media. A model is presented for simulating one-dimensional transport of solute considering the porous medium to be homogeneous, isotropic and adsorbing nature under the influence of periodic seepage velocity. Initially the porous domain is not solute free. The solute is initially introduced from a sinusoidal point source. The transport equation is solved analytically by using Laplace Transformation Technique. Alternate as an illustration; solutions for the present problem are illustrated by numerical examples and graphs.

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