Paper Submission
ETC2019 17th European Turbulence Conference





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14:00   Turbulent Convection 4
14:00
15 mins

#44
Convection in liquid sodium: A direct comparison of DNS and experiments
Lukas Zwirner, Ruslan Khalilov, Ilya Kolesnichenko, Alexander Pavlinov, Andrey Mamykin, Alexander Shestakov, Peter Frick, Olga Shishkina
Abstract: State of the art experimental and numerical techniques enable us to study turbulent thermal convection in liquid sodium inside an inclined Rayleigh-Bénard convection cell of the diameter-to-height aspect ratio one. Liquid sodium is a low-Prandtl number fluid (Pr = 0.0094) where the thermal diffusivity is much larger than the viscous diffusivity. We present the results of direct numerical simulations (DNS), using the computational code goldfish [2], for Rayleigh number Ra = 1.67 × 10^7 and compare them with the measurements for similar Rayleigh number [1]. We find a good agreement of the experiments and simulations. One of the main focuses of our investigation is the dynamics of the large scale circulation (LSC) in a cell, tilted by an angle β/π ∈ [0, 0.5] with respect to gravity. We find that for low Prandtl numbers the ratio of the diffusive time scale tκ and the free-fall time scale tf determines the morphology of the flow structures. Since tκ/tf ~ (RaPr)^(1/2), we show that the flow structures are similar if one decreases Prandtl number by one order of magnitude and simultaneously increases Rayleigh number by one order of magnitude. In figure 1 we show, from our DNS data, vertical slices of the temperature fields through the plane of the LSC. The time-averaged fields (c) and (d) display a remarkable similarity, although the small-grained structures of high-Rayleigh and low-Prandtnumber flows can be seen in the instantaneous temperature field (a), while for lower Rayleigh and higher Prandtl number the instantaneous temperature field is more smooth (b). Quantitative analysis of the DNS data and measurements will be presented as well. [1] R. Khalilov, I. Kolesnichenko, A. Pavlinov, A. Mamykin, A. Shestakov, and P. Frick. Thermal convection of liquid sodium in inclined cylinders. Phys. Rev. Fluids, 3:043503, 2018. [2] L. Zwirner and O. Shishkina. Confined inclined thermal convection in low-Prandtl-number fluids. J. Fluid Mech., 850:984–1008, 2018.
14:15
15 mins

#57
The evolution of the large-scale flow in magnetoconvection
Till Zürner, Felix Schindler, Tobias Vogt, Sven Eckert, Jörg Schumacher
Abstract: Rayleigh-Bénard convection (RBC) in electrically conducting fluids can be influenced by applying external magnetic fields. It is known that a vertical magnetic field suppresses convective flows [1]. Experimental investigations on this topic are scarce [5], since the most suitable working fluids are liquid metals. These pose a considerable challenge for the measurement of the flow structure due to their opaque nature. We present experimental data on the large-scale flow structure as well as the heat and momentum transport in a RBC system using the liquid metal alloy gallium-indium-tin (Prandtl number Pr = 0.029). The set-up consists of a cylindrical cell of height 180mm and aspect ratio 1. The bottom plate is made of copper and is heated by an electrical heating pad. The top is cooled by water in a copper heat exchanger. The external magnetic field is generated by the MULTIMAG facility [4] which produces a vertical magnetic field up to 140mT. With this set-up Rayleigh numbers 106 ≤ Ra ≤ 6 × 107 and Hartmann numbers 0 ≤ Ha ≤ 1000 can be covered. The flow structure is reconstructed from direct flow measurements using ultrasound Doppler velocimetry (UDV) and an array of temperature sensors distributed in a semi-circle at half-height of the cell. Without an applied magnetic field, the convective flow is turbulent and consists of a single large-scale circulation roll (LSC). This flow structure exhibits periodic and coherent deformations, the so-called torsion and sloshing modes, which are well known from experiments in water [6]. By increasing the Hartmann number we find that the overall flow intensity is continually decreased. At first the LSC is stabilised by the suppression of turbulent fluctuations and regular oscillation. Once the magnetic field crosses a critical value, the LSC breaks down into a complex structure comprised of multiple convection cells. This indicates a transition towards laminar convection. A further increase of Ha fully suppresses the flow in the centre of the cell but not near the side walls. Even beyond the theoretical onset of convection for an infinite layer [1] a flow can still be detected. This destabilising effect of electrically insulating side walls on magnetoconvection has been predicted in theory [2] and direct numerical simulations [3], but is now shown experimentally for the first time. [1] S. Chandrasekhar. Hydrodynamic and Hydromagnetic Stability. Dover Publications, Inc., New York, 3 edition, 1961. [2] B. C. Houchens, L. M. Witkowski, and J. S. Walker. Rayleigh–Bénard instability in a vertical cylinder with a vertical magnetic field. J. Fluid Mech., 469:189–207, 2002. [3] W. Liu, D. Krasnov, and J. Schumacher. Wall modes in magnetoconvection at high Hartmann numbers. J. Fluid Mech., 849:R2, 2018. [4] J. Pal, A. Cramer, T. Gundrum, and G. Gerbeth. MULTIMAG-A MULTIpurpose MAGnetic system for physical modelling in magnetohydrodynamics. Flow Meas. Instrum., 20(6):241–251, 2009. [5] T. Zürner, W. Liu, D. Krasnov, and J. Schumacher. Heat and momentum transfer for magnetoconvection in a vertical external magnetic field. Phys. Rev. E, 94(4):043108, 2016. [6] T. Zürner, F. Schindler, T. Vogt, S. Eckert, and J. Schumacher. Coherent large-scale flow in turbulent liquid metal convection. submitted, 2018.
14:30
15 mins

#59
Transition of the flow reversal in Turbulent thermal convection
Xin Chen, Shi-Di Huang, Ke-Qing Xia, Heng-Dong Xi
Abstract: In this presentation we report an experimental study of flow reversals in quasi-2D rectangular cells. A surprise finding of our study is a sharp transition in the Ra-dependence of the flow reversal rate, which coincides with a change in the LSC topology from the usual single-roll structure to a new abnormal single-roll structure with substructures. Detailed analysis reveals that this transition is controlled by the instability of the LSC, rather than its competition with the corner rolls. Based on the balance between advection and viscous dissipation of thermal plumes, we find the critical condition for the transition and it agrees nicely with our experimental result. Our finding thus bring important insights towards a general understanding of the reversal phenomena.
14:45
15 mins

#385
Direct measurements of the thermal dissipation rate in turbulent Rayleigh-Bénard convection
Anna Hertlein, Ronald du Puits
Abstract: We will discuss the thermal dissipation rate in turbulent Rayleigh-Bénard convection at large aspect ratio. Since the definition of the thermal dissipation rate includes the gradient field of the temperature, the challenge is to measure the three-dimensional temperature gradient instantaneously. Therefore, we developed a multi-thermistor probe with four micro-thermistors, which are arranged in a Cartesian coordinate system. The measurements are undertaken in a large-scale Rayleigh-Bénard cell. This enables us to determine even the smallest dissipative structures.
15:00
15 mins

#414
Velocimetry in a radiatively driven convection experiment
Vincent Bouillaut, Simon Lepot, Benjamin Miquel, Sébastien Aumaître, Basile Gallet
Abstract: I will describe velocity measurements in a radiatively driven convection experiment. The experimental setup is described in Lepot et al. [4]: an experimental cell with a transparent bottom plate contains a mixture of water and dye. A powerful spotlight shines at the cell from below, and the absorption of light by the dye induces local heating and turbulent convec- tion. By tuning the concentration of the dye, the scaling-law relating the heat flux to the internal temperature gradients corresponds either to the one measured in standard Rayleigh-Bénard convection experiments, or to the mixing-length or « ultimate » scaling regime predicted by Spiegel and Kraichnan [5][3] , and retained in e.g. astrophysical models [1]. Using an infrared camera, I will show how one can extract the velocity field by tracking the temperature fronts with standard PIV algorithms. I will then present the resulting scaling-laws for the Reynolds number as a function of the Rayleigh number, in both the standard Rayleigh-Bénard regime and the ultimate one. I will compare these measurements to the free-fall velocity estimate [5] and discuss the existence of an energy dissipation anomaly [2] . References [1] V. Bouillaut, S. Lepot, S. Aumaître, and B. Gallet. Transition to the ultimate regime in a radiatively driven convection experiment. Journal of Fluid Mechanics, 861:R5, 2019. [2] U. Frisch and A.N. Kolmogorov. Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press, 1995. [3] R.H. Kraichnan. Turbulent thermal convection at arbitrary prandtl number. Phys. Fluids, 5, 1962. [4] S. Lepot, S. Aumaître, and B. Gallet. Radiative heating achieves the ultimate regime of thermal convection. Proceedings of the National Academy of Sciences, 115(36):8937–8941, 2018. [5] E.A. Spiegel. A generalization of the mixing-length theory of thermal convection. ApJ, 138:216, 1963.
15:15
15 mins

#437
EXPERIMENTAL INVESTIGATION OF A SHEARED THERMALLY UNSTABLE BOUNDARY LAYER
Gabriele Nunnari, Stephan Weiss
Abstract: In many natural and industrial systems heat is transported by mixed convection. There, the flow is driven not only by buoyancy due to temperature differences but also by an external pressure gradient. Prominent examples are atmospheric boundary layers in nature or active cooling devices in numerous engineering applications. We investigate experimentally the turbulent boundary layer that develops on top of a heated horizontal plate that is subject to a colder mean wind. In the experiment, we use a three-meter long (streamwise) and one meter wide (spanwise) plate that consists of a 1 m long adiabatic section, followed by a 2 m long heated section. The heated section consists of two aluminum plates (25 mm and 35 mm thick) with a Lexan plate (5 mm) sandwiched in between them. Heat is supplied by an electrical heater at the bottom plate. The heat transported away by the flow is quantified by measuring the temperature drop across the Lexan plate at 21 different lateral positions. The plate is placed inside an open wind tunnel with a cross-section 1.2 m height and wide and a 9 m long test section. Wind speeds can reach up to 12 m/s. Next to heat flux measurements, we use constant temperature anemometry (CTA) and thermistors to measure velocity and temperature profiles. We try to determine scaling relations for the heat flux as functions of the thermal driving and the applied wind speed. In particular we study the transition from fully forced to dominantly free convection [1, 2]. Furthermore, we hope to gain a better understanding of the difference between a shear-turbulent boundary layer and a laminar boundary layer which is perturbed by thermal plumes. The later question is of great importance for understanding the ultimate regime [3, 5, 4] of Rayleigh-Bénard convection.
15:30
15 mins

#142
Convective Turbulence in Liquid Sodium
Janet Scheel, Joerg Schumacher
Abstract: We report on the results of well-resolved Direct Numerical Simulations (DNS) of turbulent Rayleigh-Benard convection (RBC) for Liquid Sodium at a Prandtl number of 0.005. We study the flow in a cylindrical container of aspect ratio 1.0 (diameter= depth) and cover Rayleigh numbers from 3e5 to 5e7. Our efforts are based on the Nek5000 spectral element software package, which was developed for solving the flow equations on massively parallel supercomputers. We will make a comprehensive comparison of statistical quantities such as Nusselt number, Reynolds number, energy dissipation rates and boundary layer thickness scales. The flow patterns in the bulk of the container and their relationship to the boundary layes will also be discussed. This work is supported by the Priority Programme SPP 1881 of the Deutsche Forschungsgemeinschaft. We also acknowledge an award of computer time provided by the INCITE program. This research used resources of the ALCF at ANL, which is supported by the DOE under contract DE-AC02-06CH11357.