We report on Rayleigh-Bénard convection with strongly varying fluid properties experimentally and theoretically. Using pressurized sulfur-hexafluoride (SF6) above its critical point, we are able to make measurements at mean temperatures (Tm) and pressures (Pm) along Prandtl-number isolines in the (T,P) parameter space. This allows us to keep the mean Rayleigh- (Ram) and Prandtl number (Prm) constant while changing the temperature dependences of the fluid properties independently, e.g., probing the liquidlike or gaslike region that are left and right of the supercritical isochore. Hence, non-Oberbeck-Boussinesq (NOB) effects can be measured and analyzed cleanly. We measure the temperature at midheight (Tc) as well as the global vertical heat flux. We observe a significant heat transport enhancement of up to 112% under strong NOB conditions. Furthermore, we develop a theoretical model for the global vertical heat flux based on ideas of Grossmann and Lohse (GL) in OB systems, adjusted for nonconstant fluid properties. In this model, the NOB effects influence the boundary layer and hence Tc, but the change of the heat flux is predominantly due to a change of the fluid properties in the bulk, in particular the heat capacity cp and density ρ. Predictions from our model are consistent with our experimental results as well as with previous measurements carried out in pressurized ethane and cryogenic helium.

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Abstract: The feasibility of particle image velocimetry (PIV) in a thermally convective supercritical fluid was investigated. Hereto a Rayleigh–Bénard convection flow was studied at pressure and temperature above their critical values. The working fluid chosen was trifluoromethane because of its experimentally accessible critical point. The experiments were characterized by strong differences in the fluid density from the bottom to the top of the cell, where the maximum relative density difference was between 17 and 42%. These strong density changes required a careful selection of tracer particles and introduced optical distortions associated with strong refractive index changes. A preliminary background oriented schlieren (BOS) study confirmed that the tracer particles remained visible despite significant local blurring. BOS also allowed estimating the velocity error associated with optical distortions in the PIV measurements. Then, the instantaneous velocity and time-averaged velocity distributions were measured in the mid plane of the cubical cell. Main difficulties were due to blurring and optical distortions in the boundary layer and thermal plumes regions. An a posteriori estimation of the PIV measurement uncertainty was done with the statistical correlation method proposed by Wieneke (Measure Sci Technol 26:074002, 2015). It allowed to conclude that the velocity values were reliably measured in about 75% of the domain. Graphic abstract: [Figure not available: see fulltext.].

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Fluids above the critical point are widely used in industry. Chemical, pharmaceutical, food industry and energy production are some examples. In the energy production sector they are mainly used as cooling fluids, because they allow to increase the thermal efficiency of the power plants. However, the fundamentals of their heat transfer behavior are still unknown and current heat transfer models fail to predict it. Supercritical (SC) fluids are characterized by strongly varying fluid properties, which are responsible for their particular heat transfer behavior and make them very difficult to model, simulate and experimentally investigate. In past studies, buoyancy was identified as a key cause for the heat transfer deterioration observed in SC fluids. The aim of the research described in this thesis is to investigate the possibility of performing non-intrusive local velocity measurements with the optical technique PIV and to acquire global heat transfer measurements, with strongly changing fluid properties at SC conditions. The experiments were performed in a pure buoyancydriven flow: a Rayleigh-Bénard (RB) flow. The velocity fields of RB convection with strongly varying properties, beyond the so-called Oberbeck-Boussinesq (OB) approximation, were experimentally studied at atmospheric pressure first. An increase of the time-averaged velocity close to the bottom wall of the cell with respect to the top wall of about 13% was found. This finding confirmed experimentally a top-bottom ”broken symmetry” in the velocity field, which was observed in previous numerical and theoretical studies, but it was never experimentally demonstrated before. The heat transfer with strongly variable properties at SC conditions for constant Prandtl and Rayleigh numbers, specifically defined outside the validity range of the OB approximation, was experimentally studied. The measurements were performed at the Max Planck Institute of Dynamics and Self-Organization in Göttingen (Germany), with a European EuHIT project. It was observed that the measured Nusselt number defined for non-OB conditions was different from point to point, showing that merely the Rayleigh and Prandtl numbers are not sufficient to determine the heat transfer through the cell. It was also seen that the measured Nusselt number was 16% larger with respect to the one predicted by the Grossmann-Lohse theory (2000) for the same Rayleigh and Prandtl numbers at OB conditions. A feasibility study of particle image velocimetry (PIV) at SC conditions was done by using the background oriented schlieren technique (BOS). An estimation of the PIV experimental uncertainty at SC conditions was done with the statistical correlation method proposed by Wieneke et al., (2015). PIV was successfully performed at SC conditions. Main difficulties about its applicability were due to blurring and optical distortions in the boundary layer and thermal plumes regions. PIV measurements were performed at three different magnitudes of density difference between top and bottom of the cell. Two of the three experiments were done at similar Rayleigh and Prandtl numbers, defined for non-OB conditions: one towards the liquid phase and the other one towards the gas phase. The former showed a lower large scale circulation (LSC) velocity than the latter. All cases showed the presence of one asymmetric LSC roll, which is different from a typical RB convection flow at OB conditions. Improvements in the accuracy of PIV measurements and the acquisition of more heat transfer data at SC conditions, would help the study of the thermal and viscous boundary layer thicknesses and turbulence modifications that are responsible for different heat transfer regimes in SC fluids.@en

The High Performance Light Water Reactor (HPLWR) is one of the six innovative nuclear energy systems proposed by the Generation IV International Forum. The use of water at supercritical pressure as the coolant in the HPLWR allows a significative increase of the thermal efficiency of the power plant, a reduction in size and complexity of the system and a safety improvement with respect to the use of two phase flows. Fluids at supercritical pressure are characterized by a sharp change of properties, which may lead to an enhancement or deterioration of their heat transfer properties, whose underlying mechanisms are mainly driven by buoyancy and acceleration effects. The motivation of this research is therefore to understand the effect of the sharp change of properties in the fluid flow structure and turbulence production. This work focuses on the influence of buoyancy in particular. The effect of the strongly varying properties, which are far beyond the so-called Boussinesq approximation, was experimentally studied in a water-filled, cubical Rayleigh-Benard cell using Particle Image Velocimetry (PIV). A temperature difference of 40 K is imposed between the bottom and top plate of the cell, ensuring non-Boussinesq conditions. These experiments were conducted at Rayleigh and Prandtl numbers of 6.8 x 108 and 4.4, respectively. For the first time in literature, the instantaneous and averaged flow structures under non-Bousinesq conditions have been experimentally determined on a cross section of the whole domain. Results reveal a slight asymmetric behavior of the fluid due to the large temperature difference between the bottom arid the top plates of the cell, which is a sign of non-Boussinesq effects. The data provided in this study can be used to gain a more in depth understanding of the effect of the strongly varying proprieties of supercritical fluids on natural convection phenomena in supercritical water cooled reactors.

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