# Ultrasound Localization Microscopy in Liquid Metal Flows
## 4 Test Case: Rayleigh-Benard Convection Experiment
### Application  
To demonstrate the potential of ULM, an experiment was conducted using the RBC set-up at HZDR. The experiment was performed with a 2 K and 10 K temperature gradient, which corresponded to \(R_{a}=2\times 10^{5}\) and \(R_{a}=10\times 10^{5}\), respectively. The application of a fairly strong magnetic field of 300 mT, which corresponded to \(Q=2\times 10^{5}\), resulted in a relaminarization of the flow. Both experiments were recorded for 10 min by ULM. The time-averaged flow structures are depicted in Figure 5.  
It was shown that both flow regimes consisted of two convection rolls with an elliptic cross-section, in which the first and, partly, the second were resolved with a maximum penetration depth of 120 mm. Due to the acoustic directivity pattern of the ultrasound probe, the upper left-hand part and the small lower left-hand part were shadowed. The upper shadowed region increased due to the lower displacement of the ultrasound probe. As expected, the experiment with the lower \(R_{a}\) incorporated a decreased velocity range. The recirculation areas were not as distinct as in \(R_{a}=10\times 10^{5}\). The velocity distribution of the main roll in \(R_{a}=2\times 10^{5}\) appeared to be more regular with a decreased velocity gradient and circular streamlines almost into the center. This can also be seen in the cross  
Figure 4: Cross-sectional drawing of the experimental set-up in which the ultrasound probe was situated. The probe was attached to the medium with a thin film of high-temperature couplant agent at an acrylic glass window that had a similar speed of sound as GalInSn. The horizontal magnetic field was aligned perpendicularly to the measurement plane and caused the turbulent convection to organize itself into ordered convection rolls.  
Figure 5: Measured streamlines averaged over 10 min of the experiment with (**left**) \(R_{a}=2\times 10^{5}\) and (**right**) \(10\times 10^{5}\), for which the indicated cross-sections are shown in Figure 6 and the zoomed region is shown in Figure 7.  
sections of the velocity in Figure 6. ULM showed that the zero velocity region was larger with an increased \(R_{a}\). This indicated the transition into turbulent flow convection.  
Furthermore, an enlarged section of the recirculation area with \(R_{a}=10\times 10^{5}\) is shown in Figure 7.  
To our knowledge, this result was the first spatially resolved recirculation area with counter-rotating rolls to be taken from an liquid metal RBC experiment. Here, the sub-millimeter spatial resolution was demonstrated as the dimensions, flow gradients and the shape of the recirculation rolls were obtained.  
Although the time-averaged results revealed a clear and stable flow structure, the actual flow was also subject to significant temporal fluctuations. The temporal dynamics could be obtained from the time-resolved tracking data. An animation of a 1 min measurement period is attached as Supplementary Material to this paper. It was found that the inner regions of the main convection roll were rotating in tiny swirls with a radius of 1 mm to 2 mm in certain patches, whereas the time-averaged data show almost no velocity in that region. On the contrary, the main flow of the roll followed more static paths. Furthermore, a high-velocity gradient in the convection roll could be obtained from close trajectories. This was possible due to the high spatial resolution that was achieved with ULM.  
Figure 6: Cross-sections of both experiments in the (**a**) y direction and (**b**) x direction with both velocity components.  
Figure 7: Enlarged recirculation area with \(R_{a}=10\times 10^{5}\), shown as (**a**) the streamlines and (**b**) the x component of the velocity vector along the cross-section in the y direction.