Fundamental research

Natural convection is a complex type of turbulent flow occurring on many length scales across the Universe. At large scales (high Rayleigh numbers), for example, it controls the weather through atmospheric and oceanic flows, terrestrial magnetic field, continental drift, and solar or Jupiter flares. Although the equations describing turbulent flow are known, our ability of prediction, especially for very intense convection, is very limited or even absent. The ideal laterally-infinite Rayleigh-Bénard convection (RBC) serves as a model for fundamental studies of these flows. The unsettled issue in study of RBC is the existence of the ultimate scaling regime theoretically predicted by Kraichnan in 1962. The transition to the ultimate regime is commonly believed to lie in the range of Rayleigh numbers 1013 < Ra < 1014. The efficiency of the convective heat transfer, described by the Nusselt number via the Nu(Ra,Pr) dependence, should then reach the scaling law Nu ~ Ra0.5.

Several years ago, the discrepancy between various experiments motivated us to build a cryostat with a helium cryogenic experimental cell with the height L = 0.3m and diameter D = 0.3 m (aspect ratio G = D/L = 1) with particular effort to minimize the influence of the cell structure and materials on the observed convection (Grant Agency of the Academy of Sciences of the Czech Republic, Grant No. KJB200650902, “Elucidation of fundamental questions in turbulent convection”). Using our new large cryogenic cylindrical cell (ASEP 350813), arguably the best of its kind in regard to various corrections connected with finite thermal conductivity of sidewalls and plates (ASEP 391089), we have studied RBC at Ra numbers of up to 1015. We have obtained valuable experimental results and knowledge about the convective heat transfer efficiency by RBC and, additionally, about the large-scale circulation (LSC) by detection of temperature fluctuations inside the cell.

As regards the heat transfer efficiency study characterised by Nusselt number Nu, our aim was to elucidate the disagreement in the published results on Nu(Ra) scaling between various experiments at Rayleigh numbers Ra of up to 1015. In our work (ASEP 368244) we have shown full agreement among all G ≃ 1 cryogenic experiments (Brno, Grenoble and Trieste) by applying suitable sidewall corrections, for Ra of up to about 1011, while at higher Ra all these sets of data differ considerably (Czech Science Foundation, Grant No. P203-12-P897, “Cryogenic Rayleigh-Bénard convection at Rayleigh numbers above 1011”). Our experimental data for Ra > 1012 does not meet the Boussinesq approximation due to temperature dependent fluid properties; as we have demonstrated by our data, at Ra of 1012 up to 1015, the non-Oberbeck-Boussinesq (NOB) effects lead to significant changes in Nu(Ra) scaling (ASEP 383815, 398058). To eliminate NOB effects we have proposed a new method for data evaluation. In the first step of our new method we show that for 1012 < Ra < 1015, the Nusselt number closely follows Nu ~ Ra1/3, which corresponds to theoretical models. In the second step of our analysis we show that evaluation of Nu(Ra) scaling on the basis of NOB data can lead to incorrect conclusions that the ultimate regime has been reached (ASEP 430597). Observation of transition to the ultimate regime has been claimed several times. Our analysis strongly suggests that such claims are not justified and that the observed transitions are spurious, caused by the NOB properties of the working fluids used in the experiments. We believe that consistent application of our new method of data processing will lead to unification of all contradictory data. Our findings have led to very important physical results which have been published in two papers in the high-impact physical journal Phys. Rev. Lett. (11 citations in total).

The statistical properties of turbulent Rayleigh-Bénard convection were investigated experimentally in a cylindrical cell of aspect ratio one. We specifically analyzed the large-scale circulation of RBC based on measurements of temperature fluctuations by small Ge sensors placed inside our cell. The resulting dependencies of Reynolds numbers on Rayleigh number within six orders of magnitude of Ra of up to 2.1014 were identified and compared to available theoretical models and experimental results for similar geometries. The results have been serially presented at international conferences and published in the respective proceedings.

The experimentally observed effect of the anomalous heat transfer against the temperature drop via the two-phase liquid-vapour system of cryogenic helium has been described and published in a prestigious journal (ASEP 397714). The phenomenon was investigated with the use of our Rayleigh-Bénard convection cell specially designed to minimize the influence of its structure on the convective flow studied. The technical properties of our cell were crucial for the observation of this effect.

All theoretical investigations were done in cooperation or consulted with colleagues from Charles University in Prague.

Our next aim was directed towards thermally excited electromagnetic near field (NF), which is responsible for van der Waals forces and radiative heat transfer enhanced beyond the validity of Planck’s law. In connection with the development of applications of micro- and nanoscale objects, NF interactions have attracted attention of theorists and also experimenters during last two decades. The reach of thermally generated NF is on the scale of micrometres at room temperature and tens of micrometres at 30 K. Relevant experimental results are by far not as numerous as theoretical papers. Under a supported project (Grant Agency of the Academy of Sciences of the Czech Republic, Grant No. IAA10065080) we constructed a precise apparatus (ASEP 368238, 386093) enabling measurement of NF radiative heat transfer between plane parallel surfaces (geometry advantageous for direct comparison with theory but highly difficult for experiment) and compared the results with the theoretical model (ASEP 385282). Owing to the well-defined geometry and material properties of our sample surfaces (produced by magnetron sputtering at our institute) and previous experience with measurement of radiative heat transfer at low temperatures, we obtained experimental data in a wide range of temperatures and distances. The range of transferred heat power was unique, covering four orders of magnitude, starting from far field and exceeding 100 times the black-body limit.


Research plan

A new helium cryostat for new precise measurements on Nu(Ra,Pr) scaling and LSC with modified cell/s (e.g. change of the aspect ratio G, change of the location of small Ge temperature sensors in the cell) is being designed. The impact of the cell geometry on RBC will be studied. Moreover, anomalous heat transfer efficiency and its phenomenological model will be analysed in detail. We will also examine the possibility of optical visualization of RBC flow and of the development of very small temperature sensors for the study of turbulent flow structure with the support of the Czech Science Foundation grant GA14-02005S as of 2014.

We will continue our research of near-field effects under the Czech Science Foundation project GA14-07397S, including NF heat transfer between superconducting surfaces. Experimental studies on NF heat transfer are still limited in types of material, span of temperatures and distances between bodies, and super-conductors have not been explored yet. We expect to find a measurable effect of the transition to superconducting state on NF heat flow. By adjusting the distance between surfaces we will vary the wavelengths of the NF heat radiation from millimetres at the onset of the NF effect (at distances of tens of micrometers) to the far infrared wavelengths (at a distance of ~1 micrometer). The experimentally detected dependence of NF heat flux on both the superconductor temperature and the distance between surfaces will enable us to obtain information about superconductor optical constants. Vice versa, the knowledge of optical constants from independent measurements will enable us to test the theory.