# Numerical Evaluation of Ultrasonic Detection of Solid Occlusions in CSP Molten Salt Piping
## 1 Introduction  
In recent decades, ultrasonic technology has emerged as a cornerstone in various fields, ranging from medical diagnostics [1, 2] to materials science and industrial process monitoring [3, 4]. This is primarily due to its unique ability to probe materials and solutions non-invasively, providing precise detection of inclusions, defects, and phase changes. By leveraging the propagation of high-frequency acoustic waves, ultrasound enables detailed characterization of a medium's internal properties, making it a versatile and effective tool across diverse applications. In medicine, for instance, ultrasound has revolutionized diagnostics and monitoring by allowing the identification of tissue anomalies, such as calcification, cysts, or tumors, with remarkable precision [5]. The technique is non-invasive and safe, relying on the differential reflection of sound waves by structures of varying densities and compositions to create high-resolution images. This capability has made ultrasound an indispensable tool in sensitive clinical scenarios. Similarly, in materials science and industrial applications, ultrasound plays a critical role in ensuring the integrity and reliability of components. Ultrasonic inspection is widely used to detect internal defectslike cracks, voids, or impurities in metals, composites, and ceramics [6; 7]. These applications are particularly important in industries such as aerospace, nuclear energy, and heavy manufacturing, where the structural integrity of materials is paramount. Ultrasonic waves interact with inhomogeneities within these materials, producing echoes and refraction that can be analyzed to accurately map internal anomalies [8]. Recently, the application of ultrasonic technology to fluid systems has garnered increasing attention, especially in challenging scenarios like the use of molten salts in concentrated solar power (CSP) plants [9; 10; 11; 12]. Molten salts, such as the widely used NaNO\({}_{3}\)-KNO\({}_{3}\) mixture, play a critical role as heat storage and transfer media in these systems [13]. However, under stagnant conditions, the salts are prone to solidification when temperatures drop below approximately 240 \({}^{\circ}\)C at ambient pressure. This solidification can result in the formation of inclusions within piping and storage sections, posing operational risks and potentially compromising efficiency [14; 15; 16]. For instance, a study by [PERSON] et al. [17] utilized a 20 kHz ultrasonic system to clean contaminants from the bottoms of ships. The research characterized the cleaning process and optimized parameters such as distance, amplitude, and duration to determine the most effective cleaning efficiency. This approach highlighted the potential of ultrasonic technology in industrial cleaning applications, which could be adapted for monitoring and detecting inclusions in molten salts [18]. Another relevant study discussed the development of an apparatus and method for ultrasonically detecting inclusions in molten bodies, including metals and glasses. The apparatus features a probe comprising an inert refractory shell, a window for carrying ultrasonic waves, and a coupling medium for transmitting ultrasonic waves between a transducer and the window. This design is suitable for detecting particulate inclusions in molten aluminum and aluminum alloys, demonstrating the versatility of ultrasonic methods in various molten materials [19]. Additionally, research on in situ sensors for liquid metal quality has led to the development of ultrasonic online systems capable of registering larger inclusion clusters in rolled steel sheets during production. These systems facilitate real-time monitoring, which is crucial for maintaining the quality of materials in industrial processes [20]. Furthermore, a study on non-invasive, in situ acoustic diagnosis and monitoring of corrosion in a model molten-salt vessel operating at 550 \({}^{\circ}\)C demonstrated the effectiveness of ultrasonic techniques in assessing the integrity of materials exposed to harsh conditions.