Onset Of Buoyancy-driven Convection Research Articles

Effect of Uniform and Space-Dependent Heat Source on the Onset of Buoyancy-Driven Convection in Viscosity Fuels: A Linear Theory

The viscosity of fuel oil is significantly influenced by temperature, with higher temperatures leading to lower viscosity. To ensure optimal combustion, it's crucial to maintain the fuel's viscosity within a specific range. With regard to variable, spacedependent and uniform heat sources, the impact of variable viscosity on the stability of Buoyancy Rayleigh-Bénard convection is demonstrated. The impact of non-inertial acceleration on natural convection is also studied in the problem. The Fourier series representation of stream function, temperature distribution describes how to derive an analytical expression for the thermal Rayleigh number. Here we noticed that the heat source parameter, the viscosity parameter, and the Taylor number effect the stability of the fluid system. Also, it is demonstrated here the impact of rotational strength accompanied with the stabilized system, where as an increase in the internal Rayleigh number and thermorheological parameter is to destabilize the same. It is also observed that, it is possible to control convection by proper tuning these parameters. A comparative study of external Rayleigh number and stability analysis for the onset of instability is presented in the problem. Some of the important new results have been revealed in the context of heat sources

Onset of Buoyancy-Driven Convection in a Fluid-Saturated Porous Layer Bounded by Semi-infinite Coaxial Cylinders

Onset of Buoyancy-Driven Convection in a Fluid-Saturated Porous Layer Bounded by Semi-infinite Coaxial Cylinders

Energy Stability Analysis on the Onset of Buoyancy-Driven Convection in a Horizontal Fluid Layer Subject to Evaporative Cooling

Energy Stability Analysis on the Onset of Buoyancy-Driven Convection in a Horizontal Fluid Layer Subject to Evaporative Cooling

Effect of swelling on the onset of buoyancy-driven convection during the CO2 dissolution process in a porous medium

By considering the swelling due to the CO2 dissolution, the onset of buoyancy-driven convection in a porous medium is analyzed theoretically. Based on the Darcy equation, the flow and advection–diffusion equations are derived. The base concentration field in an interface movement system due to the volume expansion is slightly different from a fixed interface one. Based on the linear stability theory, new stability equations are obtained in the global (τ,z)-domain and in the semi-infinite (τ,ζ)-domain. Unlike the stability equations in the global (τ,z)-domain, a normal mode analysis is possible in the semi-infinite (τ,ζ)-domain. The normal mode stability equations are solved analytically for the no-swelling system, and numerically for the swelling ones. The critical conditions are obtained as a function of the Darcy–Rayleigh number and the interface movement parameter. The interface movement accelerates the onset of convection with small wavelength instability. The effect of interface movement on the stability is severe, especially in a highly soluble system such as a CO2 improved oil recovery case.

Some theoretical aspects on the onset of buoyancy-driven convection in a fluid-saturated porous medium heated impulsively from below

Some theoretical aspects of the onset of buoyancy-driven instability in an initially quiescent, isotropic fluid- saturated porous layer are considered. Darcy's law is employed to examine characteristics of fluid motion under the Boussinesq approximation. Using linear theory, we derive stability equations and transform them in the similarity domain. Based on linear stability equations in the similarity domain, we prove the principle of exchange of stabilities and show that the stability parameter is stationary. The temperature disturbance field is expressed as a series of ortho- normal functions and the vertical velocity one is obtained in simple recursive form. The validity of the quasi-steady state approximation (QSSA) is also proved by comparing the stability characteristics under the QSSA with those ob- tained from the eigenanalysis without the QSSA.

The effect of chemical reaction on the onset of gravitational instabilities in a fluid saturated within a vertical Hele-Shaw cell: Theoretical and numerical studies

In relation with the carbon dioxide sequestration into a saline aquifer, the effect of first order chemical reaction on the onset of buoyancy-driven convection in a Hele-Shaw cell is analyzed theoretically and numerically. For the steady state base concentration field, new stability equations are derived under the linear stability theory and the Brinkman equation, and solved in the global domain. However, for the transient base field, these stability equations are transformed into a similar domain. By expanding the disturbance quantities using orthonormal functions, linear stability equations for the transient base field are solved analytically. Through the present linear analysis, we identified the governing parameters for the onset of chemo-convection in a Hele-Shaw cell. The present stability criteria for the steady-state and transient cases suggested that the fast geochemical reaction suppresses the onset of buoyancy-driven instability motion, however, enhances the diffusion flux. Using the linear stability analysis result as an initial condition for the nonlinear analysis, direct numerical simulations are also conducted. The present linear stability analysis and the nonlinear numerical simulation support each other.

The Effect of Boundary Conditions on the Onset of Buoyancy-Driven Convection in a Brine-Saturated Porous Medium

The effect of a boundary condition on the onset of buoyancy-driven convection in a fluid-saturated porous medium was analyzed theoretically. Taking into account of the partially permeable zone, new linear stability equations and boundary conditions are derived in the semi-infinite domain. For the linear stability analysis, we express disturbance fields employing the spectral theory and obtain the stability conditions using eigenanalysis and initial value problem approaches. The present linear stability limits were consistently determined regardless of the solution methods. The present analyses suggest that the capillary transition zone makes the system more unstable.

Linear and nonlinear analyses on the onset of gravitational instabilities in a fluid saturated within a vertical Hele-Shaw cell

In relation with the carbon dioxide sequestration into a saline aquifer, the onset of buoyancy-driven convection in a Hele-Shaw cell is analyzed theoretically and numerically. Under the linear stability theory and the Brinkman equation, new stability equations are derived in the global domain and transformed into a similar domain. By expanding the disturbance quantities using orthonormal functions, linear stability equations are solved analytically. The present prediction suggested that the onset of convection in a Hele-Shaw cell is governed by the Hele-Shaw modified Rayleigh number and the Brinkman number (or Hele-Shaw number) rather than by the Hele-Shaw modified Rayleigh number only. Using the linear stability analysis result as an initial condition for the nonlinear analysis, direct numerical simulations are also conducted. The present linear stability analysis and the numerical DNS calculation support each other.

Onset of Buoyancy-Driven Convection in a Liquid-Saturated Cylindrical Anisotropic Porous Layer Supported by a Gas Phase

A theoretical analysis of convective instability driven by buoyancy forces under the transient concentration fields is conducted in an initially quiescent, liquid-saturated, and anisotropic cylindrical porous layer supported by a gas phase. Darcy’s law and Boussinesq approximation are used to explain the characteristics of fluid motion, and linear stability theory is employed to predict the onset of buoyancy-driven motion. Under the quasi-steady-state approximation, the stability equations are derived in a similar boundary layer coordinate and solved by the numerical shooting method. The critical \(Ra_D\) is determined as a function of the anisotropy ratio. Also, the onset time and corresponding wavelength are obtained for the various anisotropic ratios. The onset time becomes smaller with increasing \(Ra_D\) and follows the asymptotic relation derived in the infinite horizontal porous layer. Anisotropy effect makes the system more stable by suppressing the vertical velocity.

Onset of convection with fluid compressibility and interface movement

The density increase from carbon dioxide (CO2) dissolution in water or hydrocarbons creates buoyancy-driven instabilities that may lead to the onset of convection. The convection is important for both CO2 sequestration in deep saline aquifers and CO2 improved oil recovery from hydrocarbon reservoirs. We perform linear stability analyses to study the effect of fluid compressibility and interface movement on the onset of buoyancy-driven convection in porous media. Compressibility relates to a non-zero divergence of the velocity field. The interface between the CO2 phase and the aqueous or hydrocarbon phase moves with time as a result of the volume change that occurs upon CO2 dissolution. Previous stability analyses have neglected these two aspects by assuming that the aqueous or hydrocarbon phase is incompressible and that the interface remains fixed in position. The stability analyses are used to compute two key quantities: (1) the critical time and (2) the critical wavenumber. Our results indicate that compressibility has a negligible effect on the critical time and the critical wavenumber in CO2-water mixtures. We use thermodynamics to derive an expression which shows that the two opposing physical processes which contribute to the divergence are comparable in magnitude and largely cancel each other. This result explains why compressibility does not significantly affect the onset, and it also demonstrates the link between compressibility and the volume change that causes movement of the interface. Compared to when the interface is fixed in position, a moving interface in CO2-water mixtures may reduce the critical time by up to around 10%, which can be significant in low permeability formations. The decrease in the critical time due to interface movement may be much more pronounced in hydrocarbons than in water. This could have important implications for CO2 improved oil recovery.

Analysis on the onset of buoyancy-driven convection in a fluid-saturated porous medium heated uniformly from below

The onset of convective motion in an initially quiescent, horizontal isotropic porous layer is analyzed theoretically. Using linear theory, the stability equations are obtained with and without the quasi-steady state approximation (QSSA). They are solved by expanding the disturbances as a series of orthogonal functions. Initial value problem analyses also are conducted, and their results are compared with the eigenanalysis and the QSSA. For the large Darcy–Rayleigh number RaD, the critical time of the onset of convection is found to be τc=11.74RaD−1 with the critical wavenumber kc=0.29RaD1/2. Based on linear analyses, numerical simulations are conducted to consider nonlinear effects. The nonlinear analysis using the Fourier spectral method and the finite volume method reproduces the linear stability limit obtained theoretically. From the present nonlinear analysis, it is shown that manifest convection is observed experimentally from τm=51.42RaD−1.

Nonlinear numerical simulation on the onset of Soret-driven motion in a silica nanoparticles suspension

The onset of buoyancy-driven convection in an initially quiescent, horizontal silica nanoparticle suspension layer heated from above is analyzed theoretically. In this thermally-stably stratified fluid layer the Soret diffusion can induce buoyancy-driven motion for the case of the negative separation ratio. For the high Rayleigh number the convective motion sets in during the transient diffusion stage and the onset time of this motion is analyzed by employing the nonlinear numerical simulation. It is interesting that the convective motion is very weak and the diffusional process is dominant even after the onset time of convection, τc, and the nonlinear effects are manifested from the time τm (>τc). The present τm explains the existing experimental results quite well.

Onset of Buoyancy-Driven Convection in a Fluid-Saturated Porous Medium Bounded by a Long Cylinder

A theoretical analysis of convective instability driven by buoyancy forces under the transient concentration fields is conducted in an initially quiescent, liquid-saturated, cylindrical porous column. Darcy’s law and Boussinesq approximation are used to explain the characteristics of fluid motion and linear stability theory is employed to predict the onset of buoyancy-driven motion. Under the principle of exchange of stabilities, the stability equations are derived in self-similar boundary-layer coordinate. The present predictions suggest the critical $$R_D$$ , and the onset time and corresponding wavenumber for a given $$R_D$$ . The onset time becomes smaller with increasing $$R_D$$ and follows the asymptotic relation derived in the infinite horizontal porous layer.

The onset of buoyancy-driven convection in a horizontal fluid layer heated suddenly from below

The onset of buoyancy-driven convection in an initially quiescent fluid layer confined between the two infinite horizontal plates is analyzed theoretically. In the case of isothermal heating it is well known that a convective motion sets in for the Rayleigh number Ra≥1708. By using the linear stability theory, for Ra⪢1708 the onset time of instantaneous instability tc is analyzed in the self-similar coordinate. In the self-similar coordinate, the propagation theory based on the quasi-steady state approximation (QSSA) represents the eigenanalysis and the initial value approach without QSSA and therefore it seems to be a quite reasonable. It is assumed that, besides the theoretical tc, there are two more characteristic times: (1) the theoretical time tm which marks the maximum disturbance or fluctuation growth rate and (2) the experimental time scale tD which marks the detection time of motion. By employing the numerical method under the single mode of instabilities, tc and tm are analyzed. It is interesting that tc is the invariant but the predicted tm-value is dependent upon the magnitude of initial conditions forced. It is shown for the isothermally heated system of a large Prandtl number, tm(≈4tc) obtained by fitting some experimental tD-value agrees well with the available experimental tD-values for Ra>105.

Linear stability analysis on the onset of buoyancy-driven convection in liquid-saturated porous medium

The onset of convective motion in an initially quiescent, horizontal isotropic porous layer is analyzed by using linear theory. The fluid-saturated porous layer is assumed to be kept isothermal while a single solute diffuses due to an impulsive change in concentration at an upper boundary. In the semi-infinite domain, using the spectral method, the new linear stability equations are derived and solved analytically by introducing the eigenanalysis and the initial value problem approach. Also, the quasi-steady state approximation (QSSA) is considered. By comparing the stability characteristics obtained with and without QSSA, the validity of the QSSA is discussed. For the deep-pool system, the critical time to onset of convection is found to be τc = 167.547 with the critical wavenumber ac = 0.0695. The present study complements previous theoretical predictions and also will provide the starting points for further studies.

The onset of natural convection in a horizontal fluid layer heated isothermally from below

The onset of buoyancy-driven convection in an initially quiescent fluid layer confined between two horizontal plates is analyzed theoretically. In case of isothermal heating it is well known that convective motion sets in when the Rayleigh number Ra exceeds 1708. For Ra > 1708, there are three characteristic times t c , t D and t u which represent respectively, the critical time to mark the onset of intrinsic instability, the detection time of motion, and the undershoot time in a plot of the heating rate versus time. These characteristic times are analyzed by employing the numerical method under the single mode of instabilities and fitting some experimental t u -values. The new measures to represent t c and t D are suggested, based on the growth rates of fluctuations. It is interesting that t c is the invariant but the predicted t D - and t u -values are dependent upon the magnitude of initial conditions forced. It is shown that for the isothermally heated system of a large Prandtl number the relation of t u ≅ 7 t c agrees well with the available experimental t u -values for Ra > 10 5 and t D is located between t c and t u . This paper removes the confusion among the characteristic times, t c , t D and t u in the literature on stability. Also the boundary-layer instability model is discussed in order to analyze turbulent thermal convection heat transfer characteristics in the fully developed state, based on the present numerical predictions.

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).

10.2478/s11814-009-0230-7

The onset of buoyancy-driven convection in an initially motionless isothermal fluid layer is analyzed numerically. The infinite horizontal fluid layer is suddenly cooled from above to relatively low temperature. The rigid lower boundary remains at the initial temperature. In the present transient system, when the Rayleigh number Ra exceeds 1101, thermal convection sets in due to buoyancy force. To trace the temporal growth rates of the mean temperature and its fluctuations we solve the Boussinesq equation by using the finite volume method. We suggest that the system begins to be unstable when the growth rate of temperature disturbances becomes equal to that of the conduction field. Three different characteristic times are classified to interpret numerical results clearly: the onset time of intrinsic instability, the detection time of manifest convection and the undershoot time in a plot of the cooling rate versus time. The present scenario is that the thermal instability sets in at the critical time, then grows super-exponentially up to near the undershoot time, and between these two times the first visible motion is detected. Numerical results are compared with available experimental data. It is found that the above scenario looks promising and the critical time increases with decreasing the Prandtl number Pr and also the Rayleigh number Ra.

Thermal instability of a fluid layer when cooled isothermally from above

The onset of buoyancy-driven convection in an initially motionless isothermal fluid layer is analyzed numerically. The infinite horizontal fluid layer is suddenly cooled from above to relatively low temperature. The rigid lower boundary remains at the initial temperature. In the present transient system, when the Rayleigh number Ra exceeds 1101, thermal convection sets in due to buoyancy force. To trace the temporal growth rates of the mean temperature and its fluctuations we solve the Boussinesq equation by using the finite volume method. We suggest that the system begins to be unstable when the growth rate of temperature disturbances becomes equal to that of the conduction field. Three different characteristic times are classified to interpret numerical results clearly: the onset time of intrinsic instability, the detection time of manifest convection and the undershoot time in a plot of the cooling rate versus time. The present scenario is that the thermal instability sets in at the critical time, then grows super-exponentially up to near the undershoot time, and between these two times the first visible motion is detected. Numerical results are compared with available experimental data. It is found that the above scenario looks promising and the critical time increases with decreasing the Prandtl number Pr and also the Rayleigh number Ra.

The onset of buoyancy-driven convection in a ferromagnetic fluid saturated porous medium

The onset of buoyancy-driven convection in an initially quiescent ferrofluid saturated horizontal porous layer in the presence of a uniform vertical magnetic field is investigated. The Brinkman-Lapwood extended Darcy equation with fluid viscosity different from effective viscosity is used to describe the flow in the porous medium. The lower boundary of the porous layer is assumed to be rigid-paramagnetic, while the upper paramagnetic boundary is considered to be either rigid or stress-free. The thermal conditions include fixed heat flux at the lower boundary, and a general convective–radiative exchange at the upper boundary, which encompasses fixed temperature and fixed heat flux as particular cases. The resulting eigenvalue problem is solved numerically using the Galerkin technique. It is found that increase in the Biot number Bi, porous parameter σ, viscosity ratio Λ, magnetic susceptibility χ, and decrease in the magnetic number M 1 and non-linearity of magnetization M 3 is to delay the onset of ferroconvection in a porous medium. Further, increase in M 1, M 3, and decrease in χ, Λ, σ and Bi is to decrease the size of convection cells.