Investigation Of Penetrative Turbulent Rayleigh-Bénard Convection Of Fluid Near Its Maximum Density

Turbulent Rayleigh-Bénard(R-B)convection is a classic system of thermal convection,which is abstracted from natural phenomena and many applications in engineering fields.Recently,investigations on turbulent R-B convection are often performed in common fluids,where the density is assumed to be linear function of temperature.However,for the turbulent R-B convection of fluid near its maximum density,convection occurs in the unstable fluid regime and the fluid motion penetrates to the stable layer.Recently,penetrative turbulent R-B convection of fluid near its maximum density has not been investigated extensively.In the present thesis,numerical and experimental investigations on R-B convection filled with maximum density fluid in two-dimensional rectangular containers,three-dimensional cylindrical containers and box-shaped containers are performed.The effects of Rayleigh number,density inversion parameter and geometry on the flow dynamics and heat transfer are investigated.The flow and temperature fields in the whole domain are observed.The turbulent characteristics in these containers are analyzed.The mechanisms of the evolution and reversal of large-scale circulation are explained.The heat transfer correlations for different containers are obtained.The research of this topic can not only contribute to extend the research field in turbulent R-B convection,but also enrichment the study theory of penetrative convection.The main contens and conclusions are as follows:Firstly,penetrative turbulent R-B convection of fluid near its maximum density in two-dimensional rectangular containers is studied by numerical simulation.The results indicate that,(1)the existence of density maximum phenomenon suppresses the eruption of cold plumes,the suppression becomes stronger with an increase in the density inversion parameter.For small density inversion parameters,the large-scale circulation is mainly driven by hot plumes.For large density inversion parameters,hot plumes are the only driver for the large-scale circulation.(2)The reversal of large-scale circulation is observed in two-dimensional rectangular containers.The reversal is harder to occur with an increase in the density inversion parameter and the Rayleigh number.(3)The effect of aspect ratio on the flow structure is significant.For small aspect ratios,the rolls are vertically stacked,the number of rolls keeps on changing with time.For moderate aspect ratios,different flow structures coexist at a same Rayleigh number.For large aspect ratios,the flow structure is everlasting.(4)The average Nusselt number is proportional to the power of Rayleigh number,and it decreases linearly with an increase in the density inversion parameter.The average Nusselt number is insensitive to the aspect ratio.Secondly,numerical simulations on penetrative turbulent R-B convection in vertical cylindrical containers filled with fluid near its maximum density value are performed.The results indicate that,(1)the large-scale circulation is driven by the combination of hot and cold plumes for small density inversion parameters.The scale of the vortex is small,and the distribution of the vortex is close to the center.For large density inversion parameters,hot plumes drive the large-scale circulation.The scale of the vortex increases,the vortex distributes near the side walls.(2)Soft and hard turbulent states are observed with an increase in the Rayleigh number.In the soft turbulent state,the histogram of Nusselt number fits more like Gaussian distribution.When the Rayleigh number increases,the penetration depth increases sharply,the isothermal surfaces become more distorted,the scale of vortex decreases,the distribution of vortex is near the center of the container.In the hard turbulence state,the histogram of Nusselt number has an exponential distribution.Plumes appear in the hard turbulent state.With an increase in the Rayleigh number,the plumes become more visible,the scale of vortex decreases and the vortex clusters near the sidewall.(3)For extreme small aspect ratios,no plumes exist in the container,the average Nusselt number is low.As the aspect ratio increases,plumes are visible,the flow is dominated by a large-scale circulation.In this region,the heat transfer is less effected by the aspect ratio.When the aspect ratio is large enough,the large-scale circulation is diminished as the plumes move vertically,the average Nusselt number is enhanced.Thirdly,numerical studies on penetrative turbulent R-B convection of fluid near its maximum density in box-shaped containers are carried out.The results indicate that,(1)the large-scale circulation moves along the diagonal plane in a cubic container for small density inversion parameters.The vortex mainly distributes on the large-scale circulation plane.When the density inversion increases greatly,the horizontal motion of plumes weakens,and large-scale circulation is destroyed.More vortexes appear in the center of the container.(2)With an increase in the Rayleigh number,the deformation of isothermal surfaces increases until the plumes appear.Meanwhile,the scale of vortex reduces.(3)Three different heat transfer states are obtained for different aspect ratios.For large aspect ratios,boundary-layer controlled regime is presented,where the large-scale circulation dominates and the average Nusselt number is less effected by the aspect ratio.With a decrease in the aspect ratio,the heat transfer regime belongs to the plume-controlled regime,where the scale of plumes is comparable to the width of the container and a nontrivial increase in the average Nusselt number is found.A severely confined regime is observed for extreme small aspect ratios,in which the average Nusselt number decreases significantly by the strong drag force from the sidewalls.Finally,a series experiments are carried out to investigate penetrative turbulent R-B convection in a box-shaped container of aspect ratio 0.3,which is filled with cold water near its maximum density value.Results indicate that the average Nusselt numbers obtained from the correlation equation agree well with the results obtained from experiment.The reversal of LSC is harder to occur with an increase in the density inversion parameter and Rayleigh number,which is not observed for extreme large density inversion parameter and Rayleigh number.