# Numerical Evaluation of Ultrasonic Detection of Solid Occlusions in CSP Molten Salt Piping
## 5 Conclusions  
This study demonstrates the potential of ultrasonic techniques for detecting solid inclusions in molten salt piping systems used in concentrated solar power (CSP) plants. Through extensive numerical simulations, we identified key relationships between the attenuation of ultrasonic signals, the position of solid occlusions, and the degree of section porosity. The results highlight that ultrasonic wave scattering and attenuation can provide information about the spatial distribution and size of solid inclusions, enabling real-time monitoring of system conditions. By integrating statistical analysis, we established a probabilistic framework that links measured attenuation levels to likely section porosity ranges, forming the basis for operational decision making. This approach addresses the limitations of traditional temperature-based controls by reducing energy consumption and minimizing unnecessary intervention activation. However, it is important to note that this preliminary study was conducted to assess the feasibility of using this technology for detecting solid inclusions, which were geometrically simplified for the purpose of  
Figure 8: Probability map illustrating the likelihood of section porosity \(\varphi\) values for a given measured dimensionless attenuation \(\bar{\alpha}\). The map is designed as a decision-making tool, correlating attenuation levels with the probable extent of solid inclusions. Higher attenuation values correspond to lower porosity ranges, indicating more significant inclusions. This framework supports the definition of critical thresholds for triggering intervention mechanisms.  
Figure 9: Schematic representation of the intervention mechanism procedure based on the probability map.  
the numerical analysis. It must be taken into account that the actual distribution and formation of solid inclusions remain uncertain, both in terms of their locations and shapes. Nevertheless, it is crucial to emphasize that this numerical study represents an early phase in the development of an experimental prototype, which will allow for the validation of the methodology developed in this work and facilitate the calibration of the probability map designed to estimate the solid inclusion percentage. Future work could focus on experimental validation of the proposed methods and the integration of supervised machine learning techniques to improve predictive capabilities. Such advancements would pave the way for more robust, efficient, and adaptive systems capable of autonomously managing the challenges of solidification in CSP piping networks. This research underscores the transformative potential of ultrasonic technology in improving the safety and energy efficiency of industrial processes reliant on molten salts.  
Conceptualization, E.D.G., R.A.R. and R.D.; methodology, E.D.G. and R.D.; software, R.D.; validation, E.D.G., R.A.R. and R.D.; formal analysis, E.D.G.; investigation, E.D.G., R.A.R. and R.D.; resources, R.D.; data curation, E.D.G.; writing--original draft preparation, E.D.G.; writing--review and editing, E.D.G., R.A.R. and R.D.; visualization, E.D.G., R.A.R. and R.D.; supervision, R.A.R. All authors have read and agreed to the published version of the manuscript.  
This work was funded by the Italian Ministry of Environment and Energy Security through the \"National Electric System Research\" Programme-Project 1.9 \"CSP/CST technology\", 2022-2024 implementation plan.  
Not applicable.  
The data are available on request.  
The authors declare no conflicts of interest.