# Simulation of Fluid Dynamics Monitoring Using Ultrasonic Measurements
## 1 Introduction
To improve ultrasonic systems, various designs have been studied using waveguides [16], arrays of transducers [17], arrays of electromagnetic acoustic transducers (EMATs) [18] or dedicated acoustic mirrors [19]. In addition to the development of efficient sensors, the future of inspection requires an increasing knowledge of wave propagation in such media. The flow above a reactor core is turbulent, with local speeds of several meters per second and velocity gradients of about several meters per second per centimeter [20]. Therefore, the flow profile and the fluid turbulence create uncertainties in transit-time measurements for flowmeters [21]. In the case of acoustic thermometry, this could lead to errors in the measurement of the temperature. The development of all these applications requires modeling efforts to propose more accurate measurements or new applications. Nondestructive examinations are usually planned when the flow is steady, but it is also interesting to develop in-service inspections. In such cases, the liquid metal flow is no longer steady, the flow regime becomes turbulent and temperature gradients occur. Ultrasonic devices could provide reactor monitoring and structural health monitoring functions, but signal analysis should take into account wave propagation in a heterogeneous flow. Modeling wave propagation should include an accurate flow model. In their work, [PERSON] and al. [20] investigated the importance of temperature gradients using a ray-tracing code. They demonstrated that the beam deviates under the effect of the temperature gradient and may even split when the ultrasonic wave travels through several areas with different thermal gradients [22]. For a steady fluid, temperature heterogeneity could be described using stochastic methods, which randomly generate a fluctuating temperature field using a Gaussian random process. This method has the great advantage of proposing a simplified model and of not requiring huge computer resources, but it does not model the real flow well [23]. The signals used for monitoring often include backward echoes from geometrical parts. The influence of the edges has been discussed in several studies, including a comparison of diffraction theories [32] and a comparison with experiments [24]. In this work, a qualitative modeling leap is sought, which must include precise modeling of the fluid dynamics and 4D modeling of the acoustic wave propagation so that time is included in the acoustic simulation. The use of high-performance computing (HPC) is mandatory for such a project. For the flow modeling, we selected the PLAJEST setup, with the mixing of two hot jets with a cold one in a liquid metal medium [25]. This setup was completely simulated using computational fluid dynamics tools [26; 27]. Thanks to these CFD data provided by the DES/IRESNE/DM25/STMF laboratory of the French Alternative Energies and Atomic Energy Commission (CEA), we can develop a 4D wave propagation simulation in a very realistic, temporally fluctuating medium, which is the original objective described in this work. For the ultrasonic wave simulation, we used the spectral-element numerical tool SPECFEM3D [28]. In the second section, we present the numerical models for the wave equation, and we indicate our motivations for choosing the SPECFEM3D code. In Section 2, the CFD data used to reproduce the PLAJEST experiment are detailed, and the frozen-flow hypothesis is justified. The fourth section describes a huge task of implementing the modeling of the wave propagation in a heterogeneous medium resulting from the CFD modeling. It is a very new collaborative work combining CFD simulation and wave propagation simulation. In the last section, we demonstrate that the temporal temperature fluctuations could be monitored by ultrasounds.