Onset Of Buoyancy-driven Instability Research Articles

Effect of vertically varying permeability on the onset of convection in a porous medium

Considering the vertically varying permeability of a porous medium, we conducted theoretical and numerical analyses on the onset of buoyancy-driven instability in an initially quiescent, fluid-saturated, horizontal porous layer. Darcy’s law was employed to explain the fluid flow through a porous medium and linear and nonlinear analyses are conducted. In the semi-infinite domain, the growth of disturbance and the onset of convection were analyzed with and without the quasi-steady state approximation. The present analysis of initial growth rate shows that the system is initially unconditionally stable regardless of a vertical heterogeneity parameter. The onset conditions of buoyancy-driven instabilities were investigated as a function of the Darcy-Rayleigh number and the heterogeneity parameter. To find the effect of a vertical heterogeneity on the flow after the onset of convection, nonlinear numerical simulations also were conducted using the result of the linear analysis as a starting point. Nonlinear numerical simulations show that the finger-like instability motion is not readily observable at a critical time and it becomes visible approximately when a mass transfer rate substantially increases.

Onset of buoyancy-driven convection in a variable viscosity liquid saturated in a porous medium

In connection with carbon dioxide (CO2) improved oil recovery (IOR), the onset of buoyancy-driven instability in an initially quiescent, fluid-saturated, horizontal porous layer is analyzed. Through the upper boundary, CO2 is gradually dissolved into heavy oil to significantly reduce its viscosity but increase its density. By considering the variation of viscosity, Darcy’s law is used to explain characteristics of fluid motion. Under the linear stability theory, the exchange of the stabilities is proved analytically. The critical conditions for the onset of buoyancy-driven convection are obtained as a function of the viscosity variation parameter of the Frank-Kamenetskii approximation. Based on the result of the linear stability analysis, the growth of disturbance is pursued by the direct nonlinear numerical simulation. The present linear and nonlinear analyses show that the viscosity variation parameter plays a critical role in the onset and the growth of the instability motion.

Onset of buoyancy-driven instability in a pure melt solidified from above

When a pure liquid is solidified from above, convection may be induced in a thermally-unstable layer. The onset of buoyancy-driven convection during time-dependent solidification is investigated by using similarly trans- formed disturbance equations. The thermal disturbance distribution of the solid phase is approximated by WKB method, and the effects of various parameters on the stability condition of melt phase are analyzed theoretically. The present constant temperature cooling model gives more unstable results than the constant solidification velocity model of Smith (1).

Onset of Buoyancy-driven Instability in Porous Medium Solidified from Above

When a porous melt layer saturated by liquid is solidified from above, convection often sets in due to buoyancy forces. In this study, the onset of buoyancy-driven convection during time-dependent solidification is investigated by using the similarly transformed disturbance equations. The thermal disturbance distribution of the solid phase is approximated by the WKB method and effects of various parameters on the stability condition of the melt phase are analyzed theoretically. For the limiting case of λ → 0 and finite kr, the critical conditions approach asymptotically \({Ra_{\rm D,c}^\ast\,{=}\,25.89}\) and \({a_{\rm c}^\ast\,{=}\,1.80}\) . This study presenting a constant-temperature cooling model predicts greater instability and gives more unstable results than those obtained from the constant solidification rate model.

Relaxation on the energy method for the transient Rayleigh–Bénard convection

The onset of buoyancy-driven instability in initially quiescent fluid layers having the various boundary conditions is analyzed by using the energy method. New energy stability equation is derived under the Boussinesq approximation and the relative stability concept. The predicted critical conditions are compared with the previous results based on the conventional energy method. The stability limits which are related to the onset time of instabilities are presented as a function of the Rayleigh number Ra and the Prandtl number Pr. The present stability results predict that the onset time of convective instability decreases with increasing Ra and Pr. For the case of high Ra, the onset time of the instability is relatively insensitive to the boundary conditions of the upper boundaries.

Relaxed energy stability analysis on the onset of buoyancy-driven instability in the horizontal porous layer

The onset of buoyancy-driven instability in an initially quiescent, isotropic fluid-saturated porous layer is analyzed theoretically. Darcy’s law is employed to examine characteristics of fluid motion under the Boussinesq approximation. The critical condition to mark the onset of convective instability is analyzed based on the relaxed energy method. The predicted critical conditions are compared with the various results based on the conventional energy method and the linear stability theory.

Onset of Buoyancy-Driven Instability in Gas Diffusion Systems

The onset of buoyancy-driven convection caused by gas absorption through the upper free boundary of an initially quiescent, horizontal liquid layer is analyzed under linear theory. It is well-known that convective motion sets in when the Rayleigh number (Ra) exceeds a certain value. In this study, the critical conditions to mark the onset of convective instability are analyzed using the dominant mode method and frozen-time model for large Ra values. The results are compared with those from the propagation theory and also the amplification theory. The dominant mode method yields the stability criteria, which agree well with those from the propagation theory. Therefore, the latter results are compared with available experimental data. It is shown that the initiated instabilities grow until detected experimentally and the upper free interface often behaves similar to a rigid one.

Onset of Buoyancy-driven Instability in Porous Media Melted from Below

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, RaH,c, are found numerically for various conditions. For small superheats, the present predictions show that RaH,c is located between 27.1 and 4π2 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 RaH,c λ = 25.89 is shown.