# Simulation of Fluid Dynamics Monitoring Using Ultrasonic Measurements
## 1 Introduction  
Flow monitoring is of importance for many applications involving various liquids and gases. There exist some methods to characterize flows using global measurements effective in many industrial situations [1]. Many technologies use pressure variations to deduce flow rate. When the fluid has conductive properties, other technologies use electromagnetic measurements. In many cases, a precise analysis of the velocity distribution in the flow is required. When optical paths are possible, a classical solution consists of making Doppler measurements with particles floating in the fluid. Major developments in three-dimensional velocity field measurements using the tomographic particle image velocimetry (PIV) technique have taken place in past years [2]. When the flow is opaque or when it cannot be optically observed directly, then ultrasonic solutions are often implemented. In the case of liquid metals, the floating particles may be impurities (such asmetallic inclusions or oxide films), and ultrasonic measurements are also used to analyze the purity of liquid metal [3,4]. There are also studies in magnetohydrodynamics (MHDs) where flows, in metallic melts, can be driven by magnetic fields. The study of turbulent melt flows requires 2D flow mapping at a frame rate of several hertz. [PERSON] et al. developed an ultrasound array doppler velocimeter (UADV) using linear arrays of large piezoelectric elements. They demonstrated they can detect the transition from laminar flow to turbulent flow [5]. In such media, simultaneously monitoring temperatures in the flow and the fluid dynamics presents the most difficulties. [PERSON] et al. proposed to combine multiple crossing ultrasound beam lines and an array of thermocouples to realize a 3D characterization of the complex dynamics in a cylindrical convection cell that is filled with the liquid metal alloy GaInSn [6]. This method makes it possible to study complex fluid dynamics (Rayleigh-Benard convection) to understand the transport processes in several turbulent convection flows such as the geodynamo in the core of the earth [7] or liquid metal batteries for renewable energy storage [8]. There is also a great interest in liquid metal plasma-facing components (LM-PFCs) within the framework of research aiming at developing the next generation of fusion reactors. They are expected to enhance plasma confinement and withstand large heat and particle fluxes better than solid components [9,10]. In this work, we are mainly concerned with fast-breeder reactors for which a liquid metal alloy is used as a coolant fluid. A number of countries, including Japan, India, Lithuania/Belgium, France, the United States of America and Germany have sought to develop ultrasonic ranging or imaging devices for liquid-metal-cooled fast reactors [11]. In his report, [PERSON] provided an extensive review of these devices. These systems are designed to inspect the reactor core region for the presence of foreign objects prior to refueling and to detect possible component degradation or damage due to normal operation. Along with imaging, there are wide-ranging investigations on the use of acoustic or ultrasonic sensors for liquid-metal-cooled reactors that include active or passive inspections using acoustic emission and boiling detection methods [11]. In her review of ultrasonic viewing systems for liquid metal reactors published in 2007, [PERSON] explained there are no other physical means but ultrasound that would make it possible to inspect inner reactor parts submerged in an opaque hot liquid metal [12]. The harsh operating conditions in liquid metal significantly restrict the possible architecture of the visualization system and materials. In their review, [PERSON] and al. developed solutions for undersodium ultrasonic viewing for fast-breeder reactors [13]. A major difficulty is obtaining a good wetting of the transducer to avoid the trapping of gas bubbles, which reduce transmitted energy [14,15].