# Simulation of Fluid Dynamics Monitoring Using Ultrasonic Measurements
## 6 Conclusions  
We designed an extensive physical and numerical simulation strategy to study the potential of ultrasonic measurements to monitor turbulent flow. The study was focused on liquid metal flows for which ultrasonic measurements are the best candidate to monitor flows. In the case of sodium flow monitoring inside SFR nuclear reactors, it is planned that transducers will be positioned in the flows. There are not many experiments being conducted on liquid sodium flows, as they are still very difficult to perform, and there are not many SFR nuclear reactors in operation worldwide. One of the main difficulties, when trying to assess measurement performance without using real experiments, lies in simulating ultrasonic propagation in a representative flow. Our simulation strategy consisted of selecting a high-level CFD simulation of a real experiment of liquid metal jet mixing. We also drew on previous studies concerning ultrasonic wave propagation in liquid sodium to define all physical parameters for the wave simulation. The novelty of this study consisted in making a wave propagation simulation for several CFD time steps to validate the potential of ultrasonic measurements to follow flow fluctuations. Our analysis of flow fluctuation enabled us to prove that the frozen-flow hypothesis was completely valid in this study. It should be underlined that such a hypothesis is rarely numerically studied. The study required the development of dedicated tools to implement the wave propagation modeling on high-performance computers. The SPECFEM3D code was chosen as the numerical calculation tool for its numerical efficiency because of matured development for massively parallelized computing on HPCs and the application of the spectral-element method. Despite significant computer resources, we had to limit the maximum frequency observed to 5 Hz in order to be able to complete the study. This limit was enough to demonstrate that the main flow fluctuation frequency of 3 Hz can be monitored using a pair of transducers in a through-transmission setup. This demonstration opens the way for developing more simulations combining CFD simulations and wave propagation for several time steps so that better ways to monitor fluctuating flows could be developed. One limitation of these studies is the huge volume of data to be stored to study wave propagation in detail. This volume could be drastically reduced when transducer positions are not a parameter of investigation. The advantage of a pair of transducers is that it makes  
Figure 10: Temperature PSD vs. time-of-flight PSD. it possible to monitor flow between the two transducers. The wave propagates from the emitter in the flow and, to some extent, transfers the flow history to the receiver. In this study, the flow history is the fluctuation of the flow temperature. This study proves that it is now possible to conduct simulations of wave propagation in a more realistic flow geometry. There is of course still a step to be taken to be able to conduct simulations in large and long flows. Conceptualization, M.N., J.M. and C.L. ; methodology, M.N. and J.M. ; software, M.N. ; validation, J.M. and C.L. ; formal analysis, M.N. ; investigation, M.N. ; resources, M.N. ; data curation, M.N. ; writing--original draft preparation, M.N. and J.M. ; writing--review and editing, M.N., J.M. and C.L. ; visualization, M.N. ; supervision, J.M. and C.L. ; project administration, J.-P.J. ; funding acquisition, J.-P.J. All authors have read and agreed to the published version of the manuscript. This study was funded by The French Alternative Energies and Atomic Energy Commission, Cadarache. Not applicable. This study was granted access to the French HPC resources of TGCC/CINES under allocations 2016107626, 2016047165 and 2016047748 made by GENCI. We also thank [PERSON] and [PERSON], from the laboratory of CEA/DES/IRESNE/DM2S/STMF, for sharing their thermal-hydraulic data of PLAJEST and their advice on how to analyze these data.