Convection Of Cold Water Research Articles

Linear stability analysis of Rayleigh–Bénard convection for cold water near its density maximum in a cylindrical container

In this paper, the onset of Rayleigh–Bénard convection of cold water near its density maximum in a vertical cylindrical container and the stability of the steady axisymmetric flow were studied by using linear stability analysis. The results show that the critical Rayleigh number for the onset of convection increases with increasing the density inversion parameter Tm (Tm=(Фmax-Фc)/(Фh-Фc), where Фmax is the temperature at the maximum density, and Фh and Фc are the temperature at the bottom wall and top wall, respectively), and some new flow patterns not found in the Rayleigh–Bénard convection of common fluids are presented.Within a certain range of density inversion parameters, the onset of convection is steady and axisymmetric. The steady axisymmetric basic flow is found to depend on the initial condition, and two distinctly different basic flow are obtained at identical parameters, due to the top-bottom symmetry breaking. For the upward basic flow, four different flow patterns are observed after the axisymmetry-breaking instability. In addition, a hysteresis phenomenon of the flow pattern transition is found when Tm=0.57. For the downward basic flow, six flow patterns are observed after the axisymmetry-breaking instability. In particular, it is found that there still exists stable axisymmetric flow beyond the second bifurcation in certain ranges of Rayleigh numbers. The energy analysis shows that both the primary instability and the axisymmetry-breaking instability are caused by the thermal-buoyancy mechanism.

Aspect ratio dependence of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers

The aim of this research is to understand the effect of the aspect ratio on the heat transfer ability and hydrodynamics characteristics of Rayleigh-Bénard convection of cold water near its maximum density in box-shaped containers. The Rayleigh number is fixed at 109, density inversion parameters are 0.3, 0.5 and 0.7, and the aspect ratio ranges from 1/60 to 1. Results indicate that the average Nusselt number presents a weak dependence on the aspect ratio at the large aspect ratio (A > 0.3). However, it reaches the maximum and then drops when the aspect ratio decreases from A = 0.3. Large scale circulations are observed for containers at the large aspect ratio, and the confinement of sidewalls weakens the large-scale circulation and eventually destructs it. At the large aspect ratio, the velocity fluctuation near the sidewalls is stronger than that in the center zone, because plumes primarily move along the sidewalls of the container. At a small aspect ratio, more plumes appear in the center of the container, where the fluctuation is stronger than that near sidewalls. The effect of cold plumes on the flow is reduced as the density inversion parameter increases. Therefore, the flow is mainly driven by hot plumes, and the velocity magnitude and fluctuation decrease significantly.

Large eddy simulation on Rayleigh–Bénard convection of cold water in the neighborhood of the maximum density

In order to understand the effect of the Rayleigh number, the density inversion phenomenon and the aspect ratio on the flow patterns and the heat transfer characteristics of Rayleigh–Bénard convection of cold water in the neighborhood of the maximum density, a series of large eddy simulations are conducted by using the finite volume method. The Rayleigh number ranges between 106 and 109, the density inversion parameter and the aspect ratio are varied from 0 to 0.9 and from 0.4 to 2.5, respectively. The results indicate that the reversal of the large scale circulation (LSC) occurs with the increase of the Rayleigh number. When there exists a density inversion phenomenon, the key driver for the LSC is hot plumes. When the density inversion parameter is large enough, a stagnant region is found near the top of the container as the hot plumes cannot move to the top wall. The flow pattern structures depend mainly on the aspect ratio. When the aspect ratio is small, the rolls are vertically stacked and the flow keeps on switching among different flow states. For a moderate aspect ratio, different long-lived roll states coexist at a fixed aspect ratio. For a larger aspect ratio, the flow state is everlasting. The number of rolls increases with the increase of the aspect ratio. Furthermore, the aspect ratio has only slight influence on the time averaged Nusselt number for all density inversion parameters.

Turbulent Rayleigh-Bénard convection of cold water near its maximum density in a vertical cylindrical container

In order to understand the effects of density inversion parameter and Rayleigh number on the fluid motion and heat transfer characteristics of penetrative Rayleigh-Bénard convection in a cylindrical container, a series of large eddy simulations were performed. The working fluid is cold water and Prandtl number is 11.57. Rayleigh number up to 1011 is considered and the density inversion parameter ranges from 0 to 0.7. The results indicate that the effect of cold plumes on the larger scale circulation gradually diminishes and finally disappears with the increase of density inversion parameter. Furthermore, an increase of the temperature within the bulk region and a decrease of the penetration depth are also certified with the increase of density inversion parameter. With the increase of Rayleigh number, soft and hard turbulent states are successively observed. In the soft turbulence state, the evolution of Nusselt number shows a weak fluctuation, the corresponding histogram has a Gaussian distribution, and the penetration depth increases sharply with the increase of Rayleigh number. In the hard turbulence state, the evolution of Nusselt number presents a much stronger fluctuation than that in the soft turbulence state, the corresponding histogram fits more exponential distribution, and the variation of the penetration depth with Rayleigh number is small. A single power law between the heat transfer efficiency (Nusselt number) and Rayleigh number that covers soft and hard turbulence states is developed for each density inversion parameter. It is found that the average Nusselt number decreases linearly with the increase of density inversion parameter.

Effects of enclosure geometry and thermal boundary condition on Rayleigh-Bénard convection of cold water near its maximum density

A series of three-dimensional numerical simulations on Rayleigh-Bénard convection of cold water with the density inversion phenomenon in different enclosed containers with two thermal boundary conditions on the sidewalls are performed by using the finite volume method. Rayleigh number ranges from 2 × 103 to 3 × 105. The effects of density inversion parameter, aspect ratio, geometrical shape of the enclosure and thermal boundary conditions are discussed in detail. Results indicate that the density inversion phenomenon and the aspect ratio have a significant influence on the flow pattern and heat transfer. At a large Rayleigh number, the period oscillatory R-B flow is observed in the rectangular container with conducting sidewalls. However, the unsteady R-B flow in the cylindrical container with insulating sidewalls behaves as the single period, multi-period and chaotic flow characteristics with the increase of Rayleigh number. The heat transfer ability is enhanced by increasing Rayleigh number and the aspect ratio, while it's weakened with the increase of the density inversion parameter. The average Nusselt number of Rayleigh-Bénard convection of cold water in the rectangular container is larger than that in the cylindrical container, but nearly the same for the insulating and conducting sidewalls.

Linear stability analysis of Rayleigh-Bénard convection of cold water near its density maximum in a vertically heated annular container

In order to understand the onset of Rayleigh-Benard convection of cold water near its density maximum in a vertical annular container heated from below and cooled from above, the instability of the static diffusive state was investigated by linear stability analysis. Two kinds of thermal boundary conditions, perfect insulating and conducting sidewalls, were used. The aspect ratio and radius ratio of the annular container varied from 0.5 to 4.5 and 0.1 to 0.8, respectively. Results indicate that the critical Rayleigh number and the critical wave number increase with the increase of density inversion parameter. There are some new flow modes with large azimuthal wave number near the convection onset for cold water with density maximum, which are not observed in Rayleigh-Benard convection of the Boussinesq fluids. The stratified flow phenomenon in cold water with density maximum is certified. The larger the density inversion parameter is, the more obvious the stratified flow phenomenon becomes. With the increase of the aspect ratio, the critical Rayleigh number decreases, but the critical wave number increases. However, with the increase of the radius ratio, both the critical Rayleigh number and the critical wave number increase continuously. Furthermore, the effect of thermal boundary conditions at the sidewalls on the convection stability is also validated.

Flow pattern and heat transfer in Rayleigh-Bénard convection of cold water near its density maximum in a rectangular cavity

In order to understand the characteristics of Rayleigh-Bénard convection of cold water near its density maximum in a rectangular cavity with an aspect ratio of 2, a series of direct numerical simulations are performed by using the finite volume method. The flow patterns and their evolution and heat transfer abilities are discussed in detail. Results indicate that the density maximum phenomenon affects significantly the R-B convection of cold water in a rectangular cavity. Compared with the cubical cavity, the critical Rayleigh number for the onset of convection in a rectangular cavity is small, and the effect of the aspect ratio on the critical value decreases with the increase of the density inversion parameter. Some new multiple-roll flow patterns are observed in the rectangular cavity. Furthermore, the distribution of the local Nusselt number depends on the flow pattern. Compared with the results in a cubical cavity, the overall heat transfer ability in the rectangular cavity is enhanced under the same control parameters.

Transient natural convection of cold water in a vertical channel

The two-dimensional differential transform method (DTM) is applied to analyse the transient natural convection of cold water in a vertical channel. The cold water gives rise to a density variation with temperature that may not be linearized. The vertical channel is composed of doubly infinite parallel plates, one of which has a constant prescribed temperature and the other of which is insulated. Considering the temperature-dependent viscosity and thermal conductivity of the water, approximate analytical (series) solutions for the temperature and flow velocity are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical computation is performed for the entire range of water temperature conditions around the temperature at the density extremum point, i.e.\( 4 {}^{\circ} C\) . Numerical results illustrate the effects of the temperature-dependent properties on the transient temperature and flow velocity profiles, volumetric flow rate, and skin friction. The DTM is a powerful tool for solving nonlinear transient problems as well as steady problems.

Aspect ratio dependence of Rayleigh–Bénard convection of cold water near its density maximum in vertical cylindrical containers

This paper presents a set of experimental and numerical results on the Rayleigh–Bénard convection of cold water near its density maximum in vertical cylindrical containers with different aspect ratio that is defined as the ratio of the diameter to the height of the container. The average Nusselt number on the bottom hot wall is measured and the effects of the density inversion parameter, the aspect ratio and the Rayleigh number are discussed in detail. Results indicate that there exists different local Nusselt number distributions corresponding to various flow patterns and the average Nusselt number decreases with the increase of the density inversion parameter. The negative effect of the density inversion parameter on heat transfer becomes more significant at high Rayleigh number values. The increasing aspect ratio can enhance the heat transfer of the Rayleigh–Bénard convection. However, the enhancement effect decreases gradually with the increase of the aspect ratio. Furthermore, at large aspect ratios, multiple roll flow patterns appear, the number of the rolls increasing with the aspect ratio. Based on the experimental data, an empirical correlation on heat transfer ability is obtained within an acceptable uncertainty.

Flow state multiplicity in Rayleigh–Bénard convection of cold water with density maximum in a cylinder of aspect ratio 2

A series of three-dimensional numerical simulations on Rayleigh–Bénard convection of cold water near its density maximum in a cylindrical container of aspect ratio 2 were carried out by using the finite volume approach. The critical Rayleigh numbers for the onset of convection at different density inversion parameters were determined, and the stability ranges of all flow patterns were assured by increasing or decreasing the Rayleigh number. The heat transfer rates at different flow patterns were measured by the average Nusselt number on the hot wall. The results indicated that the critical Rayleigh number for the onset of the convection increases, the number of the flow patterns decreases and the transition between the flow patterns becomes simple with the increase of the density inversion parameter. There are some new flow patterns of Rayleigh–Bénard convection of cold water, which do not appear for that of the common fluids. The flow patterns depend on not only the Rayleigh number and the density inversion parameter, but also the initial condition and the flow history. Furthermore, there is a hysteresis phenomenon during the transition of the flow pattern.

Rayleigh-Bénard convection of cold water near its density maximum in a cubical cavity

In order to understand the characteristics of Rayleigh-Bénard convection of cold water near its density maximum in a cubical cavity with different thermal boundaries on the sidewalls, a series of direct numerical simulations were carried out by using the control volume approach. Flow pattern structures and their bifurcation series were detailedly analyzed through the bifurcation diagram, and the heat transfer ability of each branch was discussed. Results showed that both the flow pattern and heat transfer characteristic of Rayleigh-Bénard convection of cold water have many notable differences as compared with those of common fluids satisfying the Boussinesq approximation; the flow behavior depends both qualitatively and quantitatively on the thermal boundary conditions on the sidewalls. Furthermore, there are multiple flow pattern coexistence and hysteresis phenomenon during the flow pattern transition.

Buoyancy- and Thermocapillary-Induced Convection of Cold Water in an Open Enclosure with Variable Fluid Properties

The aim of the present study is to investigate the buoyancy- and thermocapillary-induced convection of water near its density maximum in an enclosure with temperature-dependent properties. The viscosity and thermal conductivity of the water are varied with reference temperature. The governing equations are solved by the finite-volume method. The results are discussed for various values of reference temperature parameter, density inversion parameter, and Rayleigh and Marangoni numbers. It is observed that the temperature of maximum density leaves strong effects on flow and heat transfer due to the formation of bi-cellular structure and reduction of the average heat transfer. It is also observed that convection heat transfer is enhanced by thermocapillary force when buoyancy force is weaken.

Transition to oscillatory natural convection of water near its density maximum in a tall enclosure

Numerical simulations have been performed for three‐dimensional natural convection of water near its maximum‐density (cold water) inside rectangular enclosures with differential heating at the vertical (left and right) walls. The horizontal (top and bottom) walls and the lateral (front and rear) walls are taken as insulated. Computations are performed for the buoyancy‐driven convection of cold water with density inversion parameter θm = 0.5 in the enclosures with aspect ratio (height/width) Ay = 8 and depth ratios (depth/width) Az = 0.5, 1, and 2. The influence of the depth ratio on the onset of oscillatory convection in a cold‐water‐filled enclosure is investigated. The presence of the lateral walls tends to suppress the onset of unsteadiness in the convective flow. The main features of the oscillatory convection flow and temperature fields as well as the instability mechanism in the three‐dimensional enclosure were similar to those found in the two‐dimensional model. However, there exists a strong three‐dimensionality in the spatial distribution of the fluctuation amplitude. With the decrease of the depth ratio, the damping effect of the lateral walls becomes increasingly pronounced, leading to a reduced heat transfer rate.

Natural convection of water near its density maximum in a rectangular enclosure: Low Rayleigh number calculations

The convection of cold water in the vicinity of its density maximum in a rectangular enclosure is studied in the limit of small Rayleigh number. Results for the stream function (to lowest order) and the first corrections (for convective effects) to the temperature field and heat transfer are obtained. Results are discussed in the context of a single parameter, which fixes the orientation of the wall temperatures with respect to the extremum temperature. The effects of changing the enclosure aspect ratio are also discussed.