Instability Of Natural Convection Research Articles

Natural Convection Instabilities Using the Lattice Boltzmann Method: Cavity Aspect Ratio Effect

In this paper, the natural convection instability flows in a partial heating cavity filled with air and cooled by the top wall are numerically investigated using the lattice Boltzmann method; and the cavity is partially heated and contains a heat source from below that is presented as an electronic component. To track the cavity aspect ratio effect on the heat transfer over time, first, a series of numerical simulations is completed by varying the aspect ratio of the cavity from to . The results show that the change in aspect ratio has a noticeable impact on the heat transfer behavior, specifically on the temperature distribution in the cavity, and the numerical results obtained indicate two different temperature distribution regimes: a stable steady regime, and a stable oscillatory regime. In the second step, a numerical simulation is done to study the natural convection instability into the cavity for the aspect ratio configuration of . The results show that the cavity structure has an important effect on the heat transfer in the cavity. The lattice Boltzmann method choice as a numerical simulation approach is due to its considerable result in fluid flow simulation and also to its simplicity of implementation, and it has become a suitable alternative method for solving fluid dynamics and thermal problems, as well as challenged traditional methods in many sectors by its simplicity of implementation.

Instability of natural convection in a vertical fluid layer with net horizontal throughflow

The implication of a uniform horizontal throughflow on the linear stability of buoyancy-driven convection in a vertical fluid layer is studied. The vertical boundaries of the fluid layer are rigid-permeable and holding at uniform but different temperatures. The instability to small-amplitude perturbations is tested by parameterizing the basic stationary flow through the Peclet number and the Prandtl number (representative of liquid mercury, air, water and oil). A modal analysis is performed, and the stability eigenvalue problem is solved numerically using the Chebyshev collocation method. The neutral stability curves are presented, and the critical values of the wave number, wave speed as well as the Grashof number are computed for different prescribed values of the governing parameters. The effect of horizontal throughflow on the stability of fluid flow is found to be dependent on the values of Prandtl number, and their intricacies have been discussed in detail. The results for the case of no throughflow are also highlighted as a particular case from the present study.

Instability of natural convection of air in a laterally heated cube with perfectly insulated horizontal boundaries and perfectly conducting spanwise boundaries

Primary and secondary instabilities of buoyancy convection in a laterally heated cube with perfectly thermally insulated horizontal boundaries and perfectly thermally conducting spanwise boundaries are studied. It is revealed that en route to unsteadiness, the flow undergoes a steady symmetry-breaking pitchfork bifurcation. With a further increase of the Grashof number, the nonsymmetric flow bifurcates into an oscillatory state via a Hopf bifurcation.

Instability of natural convection in a laterally heated cube with perfectly conducting horizontal boundaries

Oscillatory instability of buoyancy convection in a laterally heated cube with perfectly thermally conducting horizontal boundaries is studied. The effect of the spanwise boundaries on the oscillatory instability onset is studied. The problem is treated by Krylov-subspace-iteration based Newton and Arnoldi methods. The Krylov basis vectors are calculated by a novel approach that involves the SIMPLE iteration and a projection onto a space of functions satisfying all linearized and homogeneous boundary conditions. The finite volume grid is gradually refined from 1003 to 2563 finite volumes. A self-sustaining oscillatory process responsible for the instability onset is revealed, visualized and explained.

Analysis of Membrane Fouling Reduction by Natural Convection Instability Flow in Membrane Filtration of Colloidal Solution: Application of Blocking Filtration Model

Analysis of Membrane Fouling Reduction by Natural Convection Instability Flow in Membrane Filtration of Colloidal Solution: Application of Blocking Filtration Model

Design of Dead-end Membrane Module with Increased Permeate Flux by Natural Convection Instability Flow

Design of Dead-end Membrane Module with Increased Permeate Flux by Natural Convection Instability Flow

Analysis of Membrane Fouling Reduction by Natural Convection Instability Flow in Membrane Filtration of Protein Solution Using Blocking Filtration Model

Analysis of Membrane Fouling Reduction by Natural Convection Instability Flow in Membrane Filtration of Protein Solution Using Blocking Filtration Model

Three-dimensional instabilities of natural convection between two differentially heated vertical plates: Linear and nonlinear complementary approaches.

The transition to the chaos of the air flow between two vertical plates maintained at different temperatures is studied in the Boussinesq approximation. After the first bifurcation at critical Rayleigh number Ra_{c}, the flow consists of two-dimensional (2D) corotating rolls. The stability of the 2D rolls is examined, confronting linear predictions with nonlinear integration. In all cases the 2D rolls are destabilized in the spanwise direction. Efficient linear stability analysis based on an Arnoldi method shows competition between two eigenmodes, corresponding to different spanwise wavelengths and different types of roll distortion. Nonlinear integration shows that the lower-wave-number mode is always dominant. A partial route to chaos is established through the nonlinear simulations. The flow becomes temporally chaotic for Ra=1.05Ra_{c}, but remains characterized by the spatial patterns identified by linear stability analysis. This highlights the complementary role of linear stability analysis and nonlinear simulation.

Unstable buoyant flow in a vertical porous layer with convective boundary conditions

The instability of natural convection in a vertical porous layer is analysed. The plane parallel boundaries of the vertical layer are modelled as open and subject to Robin-type temperature conditions. The latter conditions describe heat transfer to the external environment, with a finite conductance. The basic state is given by a stationary fully-developed flow with linear velocity and temperature profiles. Instability arises when the Darcy-Rayleigh number exceeds its critical value. This value depends on the Biot number associated with the temperature boundary conditions. The most unstable normal modes turn out to be transverse. By solving numerically the stability eigenvalue problem, it is shown that the critical Darcy-Rayleigh number is a decreasing function of the Biot number when the Biot number is sufficiently small. For larger Biot numbers, a minimum is attained, and then the critical Darcy-Rayleigh number becomes an increasing function of the Biot number.

Numerical analysis on initial development of longitudinal vortices over a heated horizontal plate in uniform downward flow

Fluid flow and heat transfer from an upward-facing horizontal two-dimensional heated plate in uniform downward forced flow are analyzed by means of numerical simulation. We focus our attention to a case where the plate is heated so strongly that the effect of the buoyancy force is not negligible. The Reynolds number based on the plate length is 200 and 500, and the modified Grashof number ranges from 3×106 up to 1.5×108. Assuming that the working fluid is air at room condition, the Prandtl number is kept at 0.71. Longitudinal vortices, discovered in the recent experimental study, are successfully simulated. Typical structures appear as pairs of counter-rotating vortices in the vicinity of the plate with hot fluid ejection in between. They are elongated over the whole plate and regularly allocated in spanwise direction with almost uniform height. Special attention is focused on initial formation of these structures. At the beginning, germs of the structures appear either at the center or on the edge of the plate one by one until the number of them reaches a certain value. The value is subject to the natural convection instability unless the radius of the relevant vortex becomes significantly smaller than the laminar boundary layer thickness of forced stagnation flow. Streamwise contiguity of the structure is established before the power of the relevant spanwise mode comes to a stage of exponential growth inside the boundary layer.

Three-dimensional flow instability of natural convection induced by variation in radius of inner circular cylinder inside cubic enclosure

Three-dimensional numerical simulations were conducted for the natural convection phenomena around a hot inner circular cylinder positioned in a cold cubic enclosure in the Rayleigh number range of 103⩽Ra⩽106 at the Prandtl number of Pr=0.7. The immersed boundary method (IBM) was used to capture the virtual wall boundary of the inner cylinder, based on the finite volume method (FVM). In this study, the transition of the flow regime from the steady state to the unsteady state and consequent three-dimensionality in the system induced by the increase in the flow instability were investigated. Detailed three-dimensional vortical structures of the convection cells at a relatively high Rayleigh number of Ra=106 were analyzed using the visualization technique, and the heat transfer characteristics in the system resulting from the change in the vortical structures were addressed.

Pore-scale study based on lattice Boltzmann method of density driven natural convection during CO2 injection project

Saline aquifers are chosen for geological storage of greenhouse gas CO2 because of their storage potential. In almost all cases of practical interest, CO2 is present on top of the liquid and CO2 dissolution leads to a small increase in the density of the aqueous phase. This situation results in the creation of negative buoyancy force for downward density-driven natural convection and consequently enhances CO2 sequestration. In order to study CO2 injection at pore-level, an isothermal Lattice Boltzmann Model (LBM) with two distribution functions is adopted to simulate density-driven natural convection in porous media with irregular geometry obtained by image treatment. The present analysis showed that after the onset of natural convection instability, the brine with a high CO2 concentration infringed into the underlying unaffected brine, in favor of the migration of CO2 into the pore structure. With low Rayleigh numbers, the instantaneous mass flux and total dissolved CO2 mass are very close to that derived from penetration theory (diffusion only), but the fluxes are significantly enhanced with high Ra number. The simulated results show that as the time increases, some chaotic and recirculation zones in the flow appear obviously, which promotes the renewal of interfacial liquid, and hence enhances dissolution of CO2 into brine. This study is focused on the scale of a few pores, but shows implications in enhanced oil/gas recovery with CO2 sequestration in aquifers.

Instabilities of natural convection in a periodically heated layer

AbstractNatural convection in an infinite horizontal layer subject to periodic heating along the lower wall has been investigated using a combination of numerical and asymptotic techniques. The heating maintains the same mean temperatures at both walls while producing sinusoidal temperature variations along one horizontal direction, with its spatial distribution characterized by the wavenumber $\alpha $ and the amplitude expressed in terms of a Rayleigh number $R{a}_{p} $. The primary response of the system takes the form of stationary convection consisting of rolls with the axis orthogonal to the heating wave vector and structure determined by the particular values of $R{a}_{p} $ and $\alpha $. It is shown that for sufficiently large $\alpha $ convection is limited to a thin layer adjacent to the lower wall with a uniform conduction zone emerging above it; the temperature in this zone becomes independent of the heating pattern and varies in the vertical direction only. Linear stability of the above system has been considered and conditions leading to the emergence of secondary convection have been identified. Secondary convection gives rise to either longitudinal rolls, transverse rolls or oblique rolls at the onset, depending on $\alpha $. The longitudinal rolls are parallel to the primary rolls and the transverse rolls are orthogonal to the primary rolls, and both result in striped patterns. The oblique rolls lead to the formation of convection cells with aspect ratio dictated by their inclination angle and formation of rhombic patterns. Two mechanisms of instability have been identified. In the case of $\alpha = O(1)$, parametric resonance dominates and leads to a pattern of instability that is locked in with the pattern of heating according to the relation ${\delta }_{cr} = \alpha / 2$, where ${\delta }_{cr} $ denotes the component of the critical disturbance wave vector parallel to the heating wave vector. The second mechanism, the Rayleigh–Bénard (RB) mechanism, dominates for large $\alpha $, where the instability is driven by the uniform mean vertical temperature gradient created by the primary convection, with the critical disturbance wave vector ${\delta }_{cr} \rightarrow 1. 56$ for $\alpha \rightarrow \infty $ and the fluid response becoming similar to that found in the case of a uniformly heated wall. Competition between these mechanisms gives rise to non-commensurable states in the case of longitudinal rolls and the appearance of soliton lattices, to the formation of distorted transverse rolls, and to the appearance of the wave vector component in the direction perpendicular to the forcing direction. A rapid stabilization is observed when the heating wavenumber is reduced below $\alpha \approx 2. 2$ and no instability is found when $\alpha \lt 1. 6$ in the range of $R{a}_{p} $ considered. It is shown that $\alpha $ plays the role of an effective pattern control parameter and its judicious selection provides a means for the creation of a wide range of flow responses.

Numerical Simulation and Stability Study of Natural Convection in an Inclined Rectangular Cavity

This paper examines the process of instability of natural convection in an inclined cavity based on numerical simulations. The energy gradient method is employed to analyze the physics of the flow instability in natural convection. It is found that the maximum value of the energy gradient function in the flow field correlates well with the location where flow instability occurs. Meanwhile, the effects of the flow time, the plate length, and the inclination angle on the instability have also been discussed. It is observed that the locations of instabilities migrate right as the flow time increased. With the increase of plate length, the onset time of the instability on the top wall of the cavity decreases gradually and the locations of instabilities move to the right side. Furthermore, the locations of instability move left with the increase of the inclination angle in a certain range. However, these positions move right as the accumulation of the heat flux is restrained in the lower left corner of the cavity once the inclination angle exceeds a certain range.

Non-Darcy Effects on Nonparallel Thermal Instability of Horizontal Natural Convection Flow

The non-Darcy effects on the vortex instability of natural convection e ow over a horizontal e at plate embedded in a high-porosity medium are examined. These effects include the form-drag, viscous diffusion, and convective terms in the conservation equations. The instability analysis is conducted by employing the linear theory in conjunction with a nonparallel e ow model, which takes into account both the streamwise and transverse variations of thedisturbanceamplitude functions. Theresulting system of partial differential equations forthedisturbance amplitudefunctionsisconverted to asystemofhomogeneouslinearordinary differentialequationswithhomogeneous boundary conditions by the local nonsimilarity method. This results in an eigenvalue problem that is solved by an implicit e nite difference method. The numerical results indicate that all of the three non-Darcy effects examined in the present study reduce the surface heat transfer rate as compared to the case of pure Darcy e ow. These effects also renderthee ow to become more stable to the vortex mode ofinstability. Representative neutral stability curves and critical Grashof numbers are presented. It is found that the parallel e ow model underpredicts the onset of thermal instability, that is, it provides lower critical Grashof numbers than the nonparallel e ow model.

Effect of axial magnetic field on three-dimensional instability of natural convection in a vertical Bridgman growth configuration

A study of the effect of an externally imposed magnetic field on the axisymmetry-breaking instability of an axisymmetric convective flow, associated with crystal growth from bulk of melt, is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. A parametric study of the dependence of the critical Grashof number Gr cr on the Hartmann number Ha for fixed values of the Prandtl number (Pr=0.015) and the aspect ratio of the cylinder ( A=height/radius=1, 2 and 3) is carried out. The stability diagram Gr cr(Ha) corresponding to the axisymmetric—three-dimensional transition for increasing values of the axial magnetic field is obtained. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that at relatively small values of Ha the axisymmetric flow tends to be oscillatory unstable. After the magnitude of the magnetic field (Ha) exceeds a certain value the instability switches to a steady bifurcation caused by the Rayleigh–Bénard mechanism.

Axisymmetry breaking instabilities of natural convection in a vertical bridgman growth configuration

A study of the three-dimensional axisymmetry-breaking instability of an axisymmetric convective flow associated with crystal growth from bulk of melt is presented. Convection in a vertical cylinder with a parabolic temperature profile on the sidewall is considered as a representative model. The main objective is the calculation of critical parameters corresponding to a transition from the steady axisymmetric to the three-dimensional non-axisymmetric (steady or oscillatory) flow pattern. A parametric study of the dependence of the critical Grashof number Gr cr on the Prandtl number 0⩽Pr⩽0.05 (characteristic for semiconductor melts) and the aspect ratio of the cylinder 1⩽ A⩽4 ( A=height/radius) is carried out. The stability diagram Gr cr (Pr, A) corresponding to the axisymmetric — three-dimensional transition is reported for the first time. The calculations are done using the spectral Galerkin method allowing an effective and accurate three-dimensional stability analysis. It is shown that the axisymmetric flow in relatively low cylinders tends to be oscillatory unstable, while in tall cylinders the instability sets in due to a steady bifurcation caused by the Rayleigh–Benard mechanism. The calculated neutral curves are non-monotonous and contain hysteresis loops. The strong dependence of the critical Grashof number and the azimuthal periodicity of the resulting three-dimensional flow indicate the importance of a comprehensive parametric stability analysis in different crystal growth configurations. In particular, it is shown that the first instability of the flow considered is always three-dimensional.

Instability of Natural Convection and Its Transitions to Turbulence

Instability of Natural Convection and Its Transitions to Turbulence

Effects of natural convection instability on membrane performance in dead-end and cross-flow ultrafiltration

The effects of natural convection instability on ultrafiltration performance have been tested experimentally in empty (without spacer) and spacer-filled channel cells. In dead-end operation, the permeate fluxes at the gravitationally unstable orientation of the empty cell are enhanced up to 3.5 times for dextran solution and 5.5 times for BSA solution compared with the results at the stable orientation. In cross-flow operation, flux improvement by natural convection instability occurs when the cross-flow velocity is below the critical value of around 0.1–0.2 m/s ( Re = 35–90). A general criterion for determining whether natural convection effects dominate is identified considering the mass transfer between the membrane surface and the bulk. The criterion is that when Gr Re 2 > ca . 3 (for the empty cell) or Gr Re 2 > ca . 500 (for the spacer-filled cell) natural convection instability is of importance. A mass transfer correlation for the mixed convection membrane system is presented.

Secondary instabilities of convection in a shallow cavity

Analysis of secondary instabilities of natural convection in a shallow cavity heated from a side has been carried out. For mercury with Prandtl number equal to 0.027 analysis of the primary instabilities by linear theory shows that an instability sets in as transverse cells at Grashof number equal to 9157.6. Instability resulting in oscillatory longitudinal rolls is also possible, their critical Grashof number being equal to 10608.4. The secondary instabilities of the equilibrium states of transverse cells for mercury have been determined. The results show roughly that stable transverse cells with wavelength shorter than the critical become unstable by subharmonic resonance, but the instability for longer cells sets in by a combination resonance. The instability as longitudinal oscillatory rolls reappears at larger values of Grashof number, although slightly delayed by the presence of the transverse cells.