Turbulent Convection at Very Low Prandtl Numbers

**Principal Investigator:**

Jörg Schumacher

**Affiliation:**

Technische Universität Ilmenau (Germany)

**Local Project ID:**

hil09

**HPC Platform used:**

JUQUEEN of JSC

**Date published:**

In many turbulent convection flows in nature and technology the thermal diffusivity is much higher than the kinematic viscosity, which means that the Prandtl number is very low. Applications of this regime reach from deep solar convection, via convection in the liquid metal core of the Earth to liquid metal batteries for grid energy storage and nuclear engineering technology. Laboratory experiments in low-Prandtl-number convection for Pr < 1e-1 have to be conducted in liquid metals which are inaccessible for laser imaging techniques and require analysis by ultrasound or X-rays. Direct numerical simulations of this regime of turbulent convection at high Rayleigh numbers are the only way to reveal the full three-dimensional structure of temperature and velocity fields.

In Rayleigh-Bénard convection, a fluid cell is kept at a constant temperature difference between top and bottom plates. If the temperature difference is big enough, the fluid motion becomes turbulent. One of the fundamental questions in the field of turbulent convection is that of the turbulent transport mechanisms of heat and momentum. The thin boundary layers of the temperature and velocity fields, which form in the vicinity of the heating and cooling plates, are the key for a deeper understanding of the global transport mechanisms.

For low Prandtl number flows the velocity boundary layer is much thinner than the one of the temperature – both boundary layers are to some degree decoupled of each other. The numerical studies, conducted by researchers of the Technische Universität Ilmenau and the Occidental College Los Angeles, show highly fluctuating velocity boundary layers. Based on these simulation runs, the scientists can also predict a Rayleigh number range at which a transition to a fully turbulent velocity boundary layer and thus a crossover into the ultimate regime of turbulent convection is possible. This Rayleigh number is much smaller in liquid metal convection compared to convection in air or other gases.

In the framework of GCS Large Scale Projects, the researchers conducted high-precision spectral element simulations which resolved the fine-scale structure of turbulent RBC, in particular the statistical fluctuations of the temperature and velocity gradients in the bulk as well as close to the cooling and heating plates. The massively parallel simulations required up to 262,144 MPI tasks on the JUQUEEN supercomputer. A snapshot of a simulation in liquid mercury is shown in Figure 1 at a Rayleigh number of Ra=1e8. The highly diffusive temperature field with the coarse thermal plumes (see Fig. 1 left) turns out to be an efficient driver of fluid turbulence in the interior of the convection cell [1]. This can be seen by the very fine and filamented contours of the velocity magnitude (see Fig.1 right). The global transport of heat becomes much less efficient in liquid metals than in air or water at the same Rayleigh number. In turn, the global momentum transport is found to be increased significantly [2]. This generates the strong fluctuations in the velocity boundary layer.

Figure 2 shows a snapshot of the velocity boundary layer in a mercury cell. Streamlines of the near-wall velocity field are plotted in combination with high-amplitude vortex filaments. The complex flow structure, which can be seen in the plot, underlines the highly transient character of the velocity boundary layer. Such vortical structures are typical in transient and fully turbulent boundary layers in other flows, such as pipe flows.

Computing time for this research work was granted by GCS on HPC system JUQUEEN, hosted at the Jülich Supercomputing Centre (JSC). The project was supported by the Deutsche Forschungsgemeinschaft within the Research Training Group GRK 1567. The scientists acknowledge support by the project SBDA 003 within the Scientific Big Data Analytics (SBDA) Program of the John von Neumann Institute for Computing. Figure 1 and a corresponding movie was generated with the help of Herwig Zilken and Renate Koschmieder from the Application Support Division of the JSC.

**Publications**

[1] Jörg Schumacher, Paul Götzfried and Janet D. Scheel, Enhanced enstrophy generation for turbulent convection in low-Prandtl number fluids, Proc. Natl. Acad. Sci. USA 112, 9530-9535 (2015).

[2] Janet D. Scheel and Jörg Schumacher, Global and local statistics in turbulent convection at low Prandtl numbers, J. Fluid Mech. 802, 147-173 (2016).

**Scientific Contact:**

Prof. Dr. Jörg Schumacher

Institute of Thermodynamics and Fluid Mechanics, Department of Mechanical Engineering

Technische Universität Ilmenau

Department of Mechanical Engineering, D-98684 Ilmenau/Germany

e-mail: joerg.schumacher [at] tu-ilmenau.de

http://www.tu-ilmenau.de/tsm