Structure and dynamics of finite-amplitude pressure perturbations in a porous medium saturated with gassy fluid

1992 ◽  
Vol 27 (1) ◽  
pp. 60-63
Author(s):  
V. E. Dontsov
Keyword(s):  
Porous Medium ◽  
Finite Amplitude ◽  
Structure And Dynamics ◽  
Pressure Perturbations

scholarly journals Unsteady Finite Amplitude Convection of Water–Copper Nanoliquid in High-Porosity Enclosures

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
P. G. Siddheshwar ◽  
K. M. Lakshmi
Keyword(s):  
Porous Medium ◽  
Heat Transport ◽  
Heat Storage ◽  
Finite Amplitude ◽  
High Porosity ◽  
Two Phase ◽  
Onset Of Convection ◽  
Maximum Heat ◽  
Rayleigh Benard Convection ◽  
Rayleigh Benard

Unicellular Rayleigh–Bénard convection of water–copper nanoliquid confined in a high-porosity enclosure is studied analytically. The modified-Buongiorno–Brinkman two-phase model is used for nanoliquid description to include the effects of Brownian motion, thermophoresis, porous medium friction, and thermophysical properties. Free–free and rigid–rigid boundaries are considered for investigation of onset of convection and heat transport. Boundary effects on onset of convection are shown to be classical in nature. Stability boundaries in the R1*–R2 plane are drawn to specify the regions in which various instabilities appear. Specifically, subcritical instabilities' region of appearance is highlighted. Square, shallow, and tall porous enclosures are considered for study, and it is found that the maximum heat transport occurs in the case of a tall enclosure and minimum in the case of a shallow enclosure. The analysis also reveals that the addition of a dilute concentration of nanoparticles in a liquid-saturated porous enclosure advances onset and thereby enhances the heat transport irrespective of the type of boundaries. The presence of porous medium serves the purpose of heat storage in the system because of its low thermal conductivity.

The Influence of Coupled Molecular Diffusion on Double-Diffusive Convection in a Porous Medium

1986 ◽  
Vol 108 (4) ◽  
pp. 872-876 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty
Keyword(s):  
Porous Medium ◽  
Molecular Diffusion ◽  
Normal Mode Analysis ◽  
Finite Amplitude ◽  
Mode Analysis ◽  
Double Diffusive Convection ◽  
Amplitude Analysis ◽  
Cross Diffusion ◽  
Diffusive Convection ◽  
Double Diffusive

The effect of coupled molecular diffusion on double-diffusive convection in a horizontal porous medium is studied using linear and nonlinear stability analyses. In the case of linear theory, normal mode analysis is employed incorporating two cross diffusion terms. It is found that salt fingers can form by taking cross-diffusion terms of appropriate sign and magnitude even when both concentrations are stably stratified. The conditions for the diffusive instability are compared with those for the formation of fingers. It is shown that these two types of instability will never occur together. The finite amplitude analysis is used to derive the condition for the maintenance of fingers. The stability boundaries are drawn for three different combinations of stratification and the effect of permeability is depicted.

Finite amplitude analysis of non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium

2018 ◽  
Vol 857 ◽  
pp. 469-507 ◽  
Author(s):  
Abhishek K. Sharma ◽  
Manish K. Khandelwal ◽  
P. Bera
Keyword(s):  
Porous Medium ◽  
Energy Spectrum ◽  
Kinetic Energy ◽  
Critical Point ◽  
Bifurcation Point ◽  
Vertical Channel ◽  
Finite Amplitude ◽  
Parallel Flow ◽  
Kinetic Energy Spectrum ◽  
Nonlinear Kinetic

This paper addresses the finite amplitude instability of stably stratified non-isothermal parallel flow in a vertical channel filled with a highly permeable porous medium. A cubic Landau equation is derived to study the limiting value of growth of instabilities under nonlinear effects. The non-Darcy model is considered to describe the flow instabilities in a porous medium. The nonlinear results are presented for air as well as water. The analysis is carried out in the vicinity of as well as away from the critical point (bifurcation point). It is found that when the medium is saturated by water then supercritical bifurcation is the only type of bifurcation at and beyond the bifurcation point. However, for air, depending on the strength of the flow and permeability of the medium, both supercritical and subcritical bifurcations are observed. The influence of nonlinear interaction of different harmonics on the heat transfer rate, friction coefficient, nonlinear kinetic energy spectrum and disturbance flow is also studied in both supercritical as well as subcritical regimes. The variation of neutral stability curves of parallel mixed convection flow of air with wavenumber reveals that a bifurcation that is supercritical for some wavenumber may be subcritical orvice versaat other nearby wavenumbers. The analysis of the nonlinear kinetic energy spectrum of the fundamental disturbance also supports the existence of supercritical/subcritical bifurcation at and away from the critical point. The effect of different harmonics on the pattern of secondary flow, based on linear stability theory, is also studied and a significant influence is found, especially in the subcritical regime.

The effects of temperature-dependent viscosity and the instabilities in convection rolls of a layer of fluid-saturated porous medium

1989 ◽  
Vol 206 ◽  
pp. 497-515 ◽  
Author(s):  
A. C. Or
Keyword(s):  
Porous Medium ◽  
Variable Viscosity ◽  
Saturated Porous Medium ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Mean Flow ◽  
Temperature Dependent ◽  
Temperature Dependent Viscosity ◽  
Fluid Saturated Porous Medium ◽  
Dependent Viscosity

Convection of two-dimensional rolls in an infinite horizontal layer of fluid-saturated porous medium heated from below is studied numerically. Several important finite-amplitude states are isolated, and their bifurcation properties are shown. Effects of the temperature-dependent viscosity are included. The stability of these states is investigated with respect to the class of disturbances that have a ½π phase shift relative to the basic state. In particular, the oscillatory mechanism and the mean-flow generating mechanism through the variable viscosity are discussed.

Propagation of finite-amplitude pressure perturbations in a bubbling vapor-Liquid medium

1982 ◽  
Vol 23 (3) ◽  
pp. 387-392 ◽  
Author(s):  
V. E. Nakoryakov ◽  
B. G. Pokusaev ◽  
N. A. Pribaturin ◽  
I. R. Shreiber
Keyword(s):  
Liquid Medium ◽  
Finite Amplitude ◽  
Pressure Perturbations ◽  
Vapor Liquid

The three-dimensional stability of finite-amplitude convection in a layered porous medium heated from below

1990 ◽  
Vol 211 ◽  
pp. 437-461 ◽  
Author(s):  
D. A. S. Rees ◽  
D. S. Riley
Keyword(s):  
Porous Medium ◽  
Parameter Space ◽  
Dimensional Stability ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Neutral Curve ◽  
Horizontal Extent ◽  
Square Cells ◽  
The Stability

Landau–Ginzburg equations are derived and used to study the three-dimensional stability of convection in a layered porous medium of infinite horizontal extent. Criteria for the stability of convection with banded or square planform are determined and results are presented for two-layer and symmetric three-layer systems. In general the neutral curve is uni-modal and parameter space is divided into regions where either rolls or square cells are stable. For certain ranges of parameters, however, the neutral curve is bimodal and there exists a locus of parameters where two modes with different wavenumbers have simultaneous onset.

Finite Amplitude Convection in a Rotating Porous Medium

1987 ◽  
Vol 42 (1) ◽  
pp. 13-20
Author(s):  
B. S. Dandapat
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Interstitial Fluid ◽  
Saturated Porous Medium ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Linear Stability Theory ◽  
Onset Of Convection

The onset of convection in a horizontal layer of a saturated porous medium heated from below and rotating about a vertical axis with uniform angular velocity is investigated. It is shown that when S ∈ σ >1, overstability cannot occur, where ε is the porosity, σ the Prandtl number and S is related to the heat capacities of the solid and the interstitial fluid. It is also shown that for small values of the rotation parameter T1, finite amplitude motion with subcritical values of Rayleigh number R (i.e. R < Re, where Re is the critical Rayleigh number according to linear stability theory) is possible. For large values of T1, overstability is the preferred mode.

Growth and decay of acoustic acceleration waves in Darcy-type porous media

2005 ◽  
Vol 461 (2061) ◽  
pp. 2749-2766 ◽  
Author(s):  
P.M Jordan
Keyword(s):  
Porous Medium ◽  
Porous Media ◽  
Acoustic Waves ◽  
Blow Up ◽  
Equation Of Motion ◽  
Travelling Wave ◽  
Finite Amplitude ◽  
Numerical Work ◽  
Hyperbolic Form ◽  
Acceleration Waves

The propagation of acoustic waves in a fluid that saturates a Darcy-type porous medium is considered under finite-amplitude theory. The equation of motion is derived, an acceleration wave analysis is carried out, and a travelling wave solution (TWS) is obtained. In addition, analytical findings are supported with numerical work generated by a simple, but effective, finite-difference scheme and results obtained are compared with those of the nonporous and linear cases. Most notably, this analysis reveals the following: (i) that the equation of motion is a new, hyperbolic form of Kuznetsov's equation; (ii) that finite-time blow-up of the wave amplitude is possible even if dissipation is present; (iii) the presence of a porous medium increases, with respect to the nonporous case, the rate at which amplitude growth/decay occurs; (iv) in the case of porous media propagation, not all compressive acceleration waves suffer blow up; and (v) that there exists a connection between acceleration waves and TWSs.

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