Recent Application of Advanced Temperature Sensors in Special Scenarios of Nuclear Energy Research

2.1 Principles of thermocouple

The fundamental principle of thermocouple temperature sensors is based on the thermoelectric effect, where a closed circuit formed by two different metals generates a thermoelectromotive force when the two ends of the conductors are maintained at different temperatures. This thermoelectric effect arises due to the difference in the electronic properties of the two conductor materials, particularly their electron density. During operation, one end of the thermocouple is placed in the target environment at temperature, while the other end is kept at a reference temperature t0. The resulting thermoelectric voltage consists of two components: the contact potential, caused by the difference in electron density between the two conductors, and the thermoelectric potential (also referred to as the Seebeck effect), which depends on the intrinsic properties of the conductors and the temperature difference between the two ends.

2.2 Research status and analysis

Since the discovery of the thermoelectric effect by Seebeck in 1821, over 300 materials have been used to form thermocouples, among which eight types have been standardized, such as Type S, T, N, and K. In 1957, the Dutch company Philips developed a cable-like thermocouple by combining Type K thermocouple wires with mineral insulation material (MgO) and an outer stainless steel protective sheath, processed through swaging or drawing to form an integrated thermocomposite material known as a sheathed thermocouple, as shown in Figure 1. It is widely used in aviation, aerospace, energy, chemical, mechanical, and other fields, marking a transformative advancement in the history of thermocouple materials. For temperature measurement of the coolant at the outlet of a pressurized water reactor (PWR) core, nuclear-grade Type K (NiCr-NiAl) sheathed thermocouples are typically employed, accompanied by accessories such as junction boxes and compensation cables. Sheathed thermocouples primarily consist of metal sheath material, insulation material, and thermocouple wires.

When a thermocouple is exposed to neutron irradiation, neutrons may cause transmutation of the material composition of the thermocouple elements or induce atomic displacement, altering the material structure. Both effects can change the thermoelectric properties of the material, leading to variations in the thermoelectromotive force of the thermocouple. This creates a deviation from the calibration results of the thermocouple, resulting in temperature reading drift. To address this issue, there are three main solutions: first, select materials with small neutron cross-sections to manufacture thermocouple elements, or optimize the structure of the thermocouple to reduce the probability of neutron interaction with the material; second, conduct theoretical analysis and quantitative research on transmutation to correct the thermocouple readings; third, provide in-situ calibration for the thermocouple.

The Mo–Nb thermocouple is a product developed under the first solution. Its temperature measurement schematic is shown in Figure 2, where Mo and Nb serve as the two component wires of the thermocouple. Both Mo and Nb have very small neutron absorption cross-sections, allowing them to maintain material stability even under prolonged exposure to nuclear radiation environments. In 2020, Palmer et al [1]. conducted in-reactor testing of a high-temperature irradiation-resistant thermocouple (HTIR-TC) based on Mo–Nb components in an advanced test reactor (ATR). Over 170 days of irradiation (cumulative thermal neutron fluence < 3.0 × 10²¹ n/cm²), the thermocouple exhibited low drift. One of the HTIR-TCs operated stably for 85 days at temperatures between 1,450 °C and 1,500 °C, with deviations from the actual temperature ranging from 30 °C to 50 °C.

For the second approach, nuclear reaction analysis can determine the types and quantities of transmuted elements. Using established correlation curves, the change in thermoelectromotive force caused by elemental variation can be identified and converted into a temperature error, thereby quantitatively estimating the impact of transmutation on thermocouples. Since the 1960s, researchers worldwide have continuously studied the drift behavior of common in-reactor thermocouples under irradiation. In 1962, Ross [2] investigated platinum-rhodium thermocouples by calculating the percentage change in rhodium transmutation based on average neutron energy cross-sections, neutron flux, and exposure time. Combining this with theoretically derived curves, he obtained the theoretical drift in thermoelectromotive force. A comparison between theoretical calculations and experimental results showed high consistency, proving that temperature drift caused by transmutation from nuclear reactions in thermocouples can be predicted through theoretical derivation. In 2013, Scervini et al [3]. calculated the composition changes in nickel-based thermocouples, tungsten-based thermocouples (W-5%Re/W-26%Re, W-3%Re/W-25%Re), platinum-based thermocouples (Type S, Pt/Pd), and Mo–Nb thermocouples after irradiation in PWR and Liquid Metal Fast Breeder Reactor (LMFBR) environments. The results indicated that thermocouples undergo more significant transmutation under thermal neutron irradiation compared to fast neutron irradiation. Nickel-based thermocouples exhibited the smallest compositional changes, while platinum-based and tungsten-based thermocouples experienced considerably greater transmutation. In 2022, Skifton et al [4]. developed a drift model for high-temperature irradiation-resistant Mo–Nb thermocouples, accounting for high-temperature, ultra-high-temperature, thermal neutron irradiation, and fast neutron irradiation environments. This model uses correction parameters derived from extensive thermocouple irradiation test data to predict the effects of temperature and transmutation on any metal contained in thermocouple thermometers, ultimately providing the temperature drift behavior of the thermocouple. Experimentally, many researchers have conducted irradiation tests on common in-reactor thermocouples such as nickel-based, platinum-based, tungsten-based, and Mo–Nb thermocouples. These studies found that irradiation has a relatively small impact on the measurement accuracy and stability of nickel-based and Mo–Nb thermocouples, while the effects on platinum-based and tungsten-based thermocouples are significant.

2.3 Case studies of practical applications

Mo and Nb are the most promising thermocouple wire materials for resisting thermoelectromotive force drift (i.e., calibration drift) in high-temperature irradiation environments when placed in close proximity to or within nuclear fuel for long-term testing. For quantitative evaluation, HTIR-TCs were inserted into the Advanced Gas-cooled Reactor (AGR)-5/6/7 fuel test in a high-temperature gas-cooled reactor, undergoing in-pile testing for up to 12 months under high neutron flux and high-temperature conditions. The fuel test assembly consisted of five irradiation capsules placed in the northeast flux trap of the ATR core, which has an inner diameter of 13.34 cm. Each capsule has a diameter of approximately 7 cm (2.75 inches), and the five capsules were welded together to form a test string with a total length of 1.22 meters (the orientation of the test string and the layout of the thermocouples are shown in Figure 3).

The fuel capsules are arranged in bottom-to-top order: Capsule 1 is at the bottom of the reactor active zone, and Capsule 5 is at the top. Each capsule is loaded with different amounts of test fuel, which interacts with the neutron flux to produce different temperature gradients. The thermocouple (TC) system subsequently performs temperature measurements to obtain key test data on fuel performance and the performance of the thermocouples themselves. The thermal neutron flux in the ATR generally follows a symmetric cosine-squared distribution: at the midplane of the reactor height, the perturbed thermal neutron flux peaks at approximately 2.8 × 10¹⁴ n/cm² · s, while the fast neutron flux (E > 1 MeV) reaches about 2.25 × 10¹⁴ n/cm² · s. The neutron flux decreases in a cosine-squared pattern outward from the centerline and decays rapidly toward the top and bottom of the reactor. The temperature range of each fuel capsule depends on the total irradiation dose and its position in the core, with Capsule 3, located at the midplane of the reactor height, expected to exhibit the highest temperature. Among the five fuel capsules, only Capsule 1 and Capsule 3 are equipped with HTIR-TCs for experimental temperature measurement. However, the lead conduits of each thermocouple must be routed upward through dedicated channels in the adjacent fuel capsules above to exit the core. This means that, for example, HTIR-TCs measuring the temperature of Capsule 1 must pass through high neutron flux regions of the core. Therefore, although the thermocouples in Capsule 1 operate at lower temperatures, the thermocouple drift caused by thermal and fast neutron flux is similar across all thermocouples in both Capsule 1 and Capsule 3. Using an array of innermost temperature sensors closest to the fuel, HTIR-TCs 1–12, 1–13, 1–14, and 1–15 measured the temperature in the hottest region of Capsule 1. Data acquisition lasted approximately 425 calendar days, covering the operational period of all HTIR-TCs in Capsule 1 of the AGR-5/6/7 test assembly. Figure 4 shows the daily average temperature of each HTIR-TC during operation, calculated based on the effective operating time of each thermometer combined with the duration of ATR full-power operation[5].

3.1 Measurement principle

The principle of optical fiber temperature measurement involves light waves from a source propagating through an optical fiber into a modulation region, where they are modulated by temperature, resulting in changes in optical parameters that describe the characteristics of the light wave – such as intensity, wavelength, frequency, phase, and polarization state – thereby converting it into modulated signal light. This signal is then transmitted via optical fiber to a photodetector, where a demodulator extracts the temperature-related information to ultimately determine the measured temperature. In the field of high-temperature measurement, optical fiber sensors offer advantages such as a broad temperature measurement range, fast thermal response, high accuracy, long service life, and excellent mechanical sensitivity. Furthermore, they are immune to strong electromagnetic interference and can operate in harsh environments including high temperature and high pressure. Based on their working principles, fiber optic temperature sensors are mainly divided into four categories: fiber grating sensors, which include Fiber Bragg Gratings (FBG), Long Period Fiber Gratings (LPFG), and Chirped Fiber Gratings (CFBG). These sensors rely on temperature-induced wavelength shifts or mode coupling for measurement and are suitable for applications such as transformer windings and aircraft engines, with femtosecond laser-inscribed FBGs capable of withstanding temperatures up to 1,200°C. FBGs are novel optical devices developed in the 1990s, primarily classified into short-period FBGs (Bragg FBGs) and long-period FBGs. Short-period FBGs act as reflective bandpass filters, while long-period FBGs function as transmissive bandstop filters. When an optical signal passes through an FBG, a spectral component with a central wavelength λ is separated via reflection or transmission. This wavelength λ is related to the refractive index of the medium, and changes in the external temperature cause corresponding shifts in λ. A spectrum analyzer determines the measured temperature by detecting these changes in λ [6]. The principle of FBG temperature measurement is illustrated in Figure 5 [7, 8].

The majority of research on fiber-optic temperature measurement within reactors has focused on FBG technology. FBGs are among the most representative and widely used types of fiber gratings, also referred to as short-period gratings, with typical grating periods on the sub-micron scale. In FBGs, optical coupling occurs between modes propagating in opposite directions, making them reflective bandpass filters characterized by a narrow reflection band. The peak wavelength of this band is known as the Bragg wavelength. When light passes through a Bragg grating, it is strongly reflected at wavelengths that satisfy the phase-matching condition, while exhibiting weak reflection at wavelengths that do not meet this condition. The phase-matching condition is given by:

where n₀ represents the effective refractive index in the grating region, and Λ denotes the grating period. As can be seen from Equation (1), FBGs are intrinsically sensitive to temperature and strain by virtue of induced changes in n₀ and Λ, which makes them widely employed as temperature and strain sensors.

When the temperature changes, it induces variations in both the grating period and the effective refractive index, resulting in a shift in the Bragg wavelength. Therefore, the relationship between the wavelength shift Δλ_T and the temperature change ΔT can be expressed as:

In the case of fiber gratings, temperature changes primarily induce the thermal expansion effect and the thermo-optic effect. The thermal expansion effect mainly influences the grating period, while the thermo-optic effect predominantly affects the effective refractive index. Thus, the relationship can be simplified as:

Where α is the thermal expansion coefficient of the optical fiber material, and β is the thermo-optic coefficient, representing the rate of change of the refractive index with respect to temperature. As shown in Equation (3), within a certain temperature range where both α and β can be regarded as constants, the wavelength shift exhibits a proportional relationship with the change in temperature [9].

3.2 Research status and analysis

Berghmans et al [10]. compared three types of fiber-optic temperature sensors in a gamma radiation environment (160 kGy) in 1998. Semiconductor absorption sensors exhibited stable performance with errors below 1°C, though neutron radiation altered their absorption characteristics, causing deviations. Fabry–Pérot (F–P) cavity sensors showed monotonic decreases in readings due to radiation-induced wavelength-selective attenuation, while fluorescent sensors failed completely at 250 Gy due to radiation-induced attenuation, indicating that semiconductor absorption types are most suitable for gamma environments but require optimization for neutron radiation resistance. Gerrit J. de Villiers et al. [11] addressed the need for high-temperature distributed temperature monitoring in Pebble Bed Modular Reactor (PBMR) cores, theoretically and experimentally validating the feasibility of fiber Bragg grating (FBG) technology. Key results showed that Type I silica-based FBGs had a linear sensitivity of about 10 pm/°C below 300°C, but temperature gradients caused reflection spectrum broadening, affecting multiplexing accuracy; femtosecond laser-inscribed Type II FBGs showed no degradation at 1,000°C and exhibited a quadratic wavelength-temperature relationship, breaking the conventional FBG temperature limit; although sapphire FBGs withstand 2000°C and are radiation-resistant, their multimode transmission, high attenuation, and low reflectivity (only 5%) resulted in excessive signal noise, making them impractical for 30-meter long-distance applications. It was concluded that Type II silica-based FBGs are a practical solution for high-temperature nuclear reactor temperature measurement, while sapphire FBGs require signal quality improvements. In 2008, Sang et al. [12] used Rayleigh scattering for distributed temperature measurement in a nuclear reactor, achieving 1 cm spatial resolution and a maximum temperature of 850°C; copper-clad fibers had the highest temperature sensitivity, with higher doping concentrations increasing responsiveness, demonstrating that Rayleigh scattering technology is suitable for high-resolution in-reactor temperature measurement. In 2023, Hyer et al. [13] tested metal-armored distributed optical fibers in a simulated gas-cooled reactor environment, monitoring six gas channels (275–400°C) simultaneously with a single fiber at 1.6 mm spatial resolution, suppressing vibration via spot welding; radiation-induced drift required further optimization, but distributed sensing captured local temperature transients, improving core calorimetric accuracy. Fernandez et al. [14] tested FBG temperature sensors in SCK•CEN’s BR1 (low flux) and BR2 (high flux) reactors in Belgium from 2001 to 2002. Results in the low-neutron-flux, air-cooled graphite BR1 reactor showed less than 1°C error compared to thermocouples for untreated FBGs. In the high-flux BR2 material test reactor, severe degradation occurred at 90°C with spectral broadening and decreased reflectivity, but low-temperature (50°C) FBGs remained stable under 160 MGy dose and 8 × 10¹⁸ n/cm² neutron fluence. Mixed gamma-neutron radiation induced higher sensitivity than gamma radiation alone, and hydrogen-loaded fiber FBGs showed greater radiation sensitivity. In 2004, Mihailov et al. [15] used an 800 nm femtosecond laser with a phase mask to inscribe FBGs in pure SiO₂ and germanium-doped fibers, achieving high refractive index modulation (Δn ≈ 1.9 × 10⁻³) without hydrogen loading and stability at 950°C; the femtosecond laser-inscribed FBGs had low polarization-dependent loss (PDL < 0.24 dB), making them suitable for high-temperature nuclear environment sensors. Between 2016 and 2017, Morana et al. [16] developed a patented process for radiation-resistant FBGs (femtosecond laser inscription + 750°C thermal treatment) and validated it under X-ray/gamma radiation; under 1 MGy dose and 350°C, Bragg wavelength shift was below ± 10 pm (temperature error below ± 1°C). Fluorine-doped fibers performed even better with errors under ± 0.4°C, and stability was unaffected by dose rates (1–50 Gy/s); high reliability was also verified under neutron irradiation (5 × 10¹⁹ n/cm²) and proton irradiation (63 MeV). In 2017, Kuhnhenn et al. [17] tested Morana team’s radiation-resistant FBGs under gamma radiation (Co-60 source) from room temperature to 335°C; at 200 kGy dose, Bragg wavelength shift was within ± 2 pm, temperature error below ± 0.2°C, with stable performance at 335°C, confirming process reproducibility and suitability for real-time monitoring in nuclear facilities.

3.3 Case studies of practical applications

MYRRHA [18] is a prototype Generation IV nuclear reactor system. It is an accelerator-driven system cooled by molten lead-bismuth eutectic (LBE) within a temperature range from 125°C (the melting point of LBE) to 400°C. However, during operation, the core outlet temperature is expected to reach up to 700°C. As in any nuclear reactor, temperature must be monitored and controlled in every section or component to ensure safe operation, with the fuel assembly being one of the most critical components. In MYRRHA, a fuel assembly consists of a total of 127 parallel fuel rods equipped with wire spacers. Figure 6 shows a subassembly comprising seven such fuel rods. These fuel rods are vertically arranged within the reactor. They are mechanically fixed and supported at the bottom but free at the top. The LBE coolant flows upward. A helical wire spacer is wound around each fuel rod to maintain adequate spacing during operation. These wire spacers restrict the gap between individual fuel rods to just a few millimeters. To obtain reliable temperature readings inside the fuel assembly and use them for purposes such as reactor control, the sensors must not disturb the LBE flow. Therefore, any sensor introduced into the fuel assembly must be extremely small in size.

A LBE loop was constructed to expose a simulated fuel assembly to LBE flow under conditions representative of the MYRRHA reactor. The entire setup, shown in Figure 7, measures 3.5 m × 2.5 m and comprises an LBE storage tank, the test loop, and a control system. The loop holds approximately 350 kg of LBE and operates at temperatures up to 250°C. A 5.5 kW electric motor (model FCA 132SA-2) drives a magnetically coupled triple-screw pump (model Kral K 55–118) to achieve mass flow rates up to 20.5 kg/s. Heating and control are managed via a SCADA system integrating pressure sensors, tachometers, and 35 heating circuits – each with multiple trace heating lines – along with K-type thermocouples mounted on the loop housing, using a sampling interval of 30 seconds. The vertical test section downstream of the pump is a 0.767 m-long steel cylinder with an inner diameter of 51.2 mm, topped with a 0.450 m T-piece used to divert LBE flow and serve as the optical fiber exit. Fuel rod simulators are made of 316 L stainless steel tubes with a diameter of 6.55 mm and length of 700 mm, matching the diameter of actual MYRRHA fuel rods while at half the length. Each rod is helically wound with a 1.8 mm-diameter wire spacer at a pitch of 265 mm. The rod holders are fixed in the test section with flanged connections. To mimic the hexagonal arrangement of fuel rods within the closely surrounded bundle in MYRRHA, a hexagonal housing was placed around the fuel rod bundle.

Employing a spectroscopy-based demodulation approach offers particular advantages, such as enabling the use of state-of-the-art Bragg wavelength identification techniques. Since the expected wavelength fluctuations were small and peak shape distortions were anticipated, a phase-correlation-based method was selected to analyze the acquired spectra, allowing real-time recording and processing at acquisition rates of up to 5,000 spectra per second. Using the phase-correlation method, Bragg wavelength shifts as small as 1 pm could be resolved. As the FBGs were integrated inside the fuel rods, they were sensitive to both the thermal expansion of the rod itself and the effects of the adhesive and fiber coating. After the complete loop was properly sealed, all sections were heated and any residual oxygen was removed prior to filling the circuit with LBE. These procedures were continuously monitored using the FBG sensors. As the temperature in the test section increased, the fuel rods were heated, and the FBGs measured the corresponding thermal expansion. However, once the vacuum was established, the fuel rods became effectively thermally insulated, resulting in a more uniform temperature distribution along each rod. This effect is visible in Figure 8, which shows temperature measurements over time from multiple FBGs on a single fuel rod. It should be noted that since the FBGs only measure temperature changes, absolute temperatures must be derived using a temperature reference, such as thermocouple data. In this case, the reference was obtained from thermocouples mounted on the test section wall: once vacuum was achieved and temperature distribution became more uniform, the test section interior and wall were assumed to be nearly isothermal. Therefore, the uncertainty in the absolute temperature measurement using this reference is determined by the measurement uncertainty of the K-type thermocouples, which is approximately ± 2 K. The FBG data allowed qualitative verification of the vacuum integrity inside the loop – an effect not discernible from the thermocouple readings, as they were placed externally on the test section and thus more influenced by the ambient environment.

The FBG sensors represent the first successful application of temperature sensing within an LBE-cooled nuclear fuel assembly, overcoming challenges related to extreme space constraints, high corrosion, and electromagnetic interference. With a resolution of 30 mK, they significantly outperform conventional thermocouples, which typically have an accuracy of around ± 2 °C. Furthermore, the system supports multi-parameter monitoring capabilities including temperature distribution, liquid level variation, and equipment status (e.g., vacuum integrity and fault detection). This technology is directly applicable to temperature control and safety systems in liquid metal-cooled reactors such as MYRRHA, and can be extended to monitor other high-temperature and high-radiation components.

4.1 Measurement principle

The Passive Thermoacoustic Sensor utilizes the thermoacoustic effect to convert temperature signals into acoustic waves, enabling passive temperature measurement. The thermoacoustic effect describes the mutual conversion between thermal energy and acoustic energy. Acoustic vibrations amplify when heat is supplied during the densest phase and removed during the sparsest phase; conversely, vibrations decay if heat is removed at densest phase and supplied at sparsest phase. This device applies the amplification principle from Rayleigh’s criterion [19].

The fundamental principle of the passive temperature measurement device in a PWR core is illustrated in Figure 9. During operation, the hot end absorbs heat from fuel rods, creating a temperature gradient across the stack. The cold end maintains ambient temperature. When gas moves leftward (Step ①), heat transfers to the gas; when gas moves rightward (Step ②), heat releases back. This cyclic heat exchange generates high-frequency gas vibrations, producing intense acoustic waves in the resonator. In Step ②, heat transfer from the stack to the gas increases gas temperature (T⁺⁺→ T⁺⁺⁺) and pressure. The resulting expansion under high pressure performs work (pΔV). Pressure rise pushes gas further during each cycle. During rightward movement (Step ③), heat transfers back to the stack (Step ④), reducing gas temperature (T⁺ → T₀) and pressure. This heat removal under low pressure contracts the gas, performing additional work (pΔV). Ultimately, acoustic wave amplitude stabilizes when energy dissipation balances thermoacoustic conversion, sustaining an acoustic pressure wave [20].

Figure 10 shows a nuclear fuel rod with a stack structure for thermoacoustic sensor operation. Gas oscillating in the resonator tube has frequency f determined by tube length L and gas sound speed c. For a uniform tube in fundamental half-wavelength mode, f = c/2 l. Since sound speed relates to absolute temperature T (in K) by c = √(kRT) (where k is adiabatic index, R is gas constant), the standing wave frequency correlates with temperature. This “thermoacoustic thermometer” converts reactor heat into acoustic oscillations without electrical power. Temperature data transmits remotely via coolant, making it ideal for passive-safety-critical nuclear applications [19].

4.2 Research status and analysis

Passive instrumentation fundamentally eliminates this vulnerability by operating without power supplies or complex circuits. Research into passive instruments is thus essential for enhancing the reliability of passive safety systems and overall nuclear plant security. The development of such power-independent monitoring devices will significantly strengthen the robustness of instrumentation systems [21]. Traditional thermocouples face multiple degradation mechanisms in high-ionizing-radiation environments such as nuclear reactor cores and spent fuel storage pools: Neutron bombardment induces lattice distortion in thermoelectric materials, causing Seebeck coefficient drift. For instance, K-type thermocouples exhibit measurement deviations exceeding 5°C at fast neutron fluences of 10¹⁸ n/cm². Concurrently, gamma-ray ionization degrades insulation materials. Magnesium oxide (MgO) insulation layers suffer a precipitous drop in insulation resistance by three orders of magnitude at doses of 10⁶ Gy, creating significant signal short-circuit risks. Structurally, hydrogen generated from radiolytic decomposition of water permeates metal grain boundaries, accelerating hydrogen embrittlement and cracking in sheaths. For example, 304 stainless steel experiences a 1.5% volume expansion at neutron fluences of 10²³ n/m². Radiation also accelerates corrosion processes and degrades mechanical strength, reducing thermocouple lifespan under high-temperature and high-pressure conditions to merely one-third of the design value. These combined effects lead to reduced temperature measurement accuracy, response delays, and increased unplanned reactor shutdown risks. The Fukushima accident serves as a prime example, where radiation-induced damage critically compromised temperature monitoring capabilities.

In contrast, thermoacoustic sensors utilize materials inherently immune to radiation damage while uniquely harnessing high-energy neutrons and gamma rays as an energy source. Radiation energy absorbed by the sensor materials is converted into thermal energy. Subsequent localized heating and cooling cycles within the material induce periodic thermal expansion and contraction. This periodic mechanical excitation generates detectable acoustic waves (pressure waves) in the surrounding gas medium. Crucially, the frequency of these acoustic waves correlates directly with the material’s temperature. External microphones or acoustic sensors detect these audio signals, enabling remote temperature inference within the material environment. The fundamental theory relies on the thermodynamic relationship between gas sound speed and temperature, expressed through the acoustic virial equation for gas within the resonant cavity:

where u represent sound speed, p represent pressure, R represent gas constant, T represent temperature, M represent molecular weight, γ represent specific heat ratio, β_a and γ_a represent acoustic virial coefficients.

Within a cylindrical resonator cavity, sound waves propagate as longitudinal waves. When the frequency of the incident sound wave precisely matches the natural frequency of the gaseous medium inside the cavity, the gas undergoes resonance. Under this condition, the sound wave manifests as a standing wave pattern, and its amplitude undergoes significant amplification. According to fundamental acoustic theory, the relationship between the sound speed u and the ideal resonance frequency flmn0 is expressed as:

Where a represent internal radius of cylindrical cavity; L represent internal length; l, ∣m∣, n = 0,1,2,…eigenvalues representing axial, azimuthal, and radial half-wave integers; xmn represent the n–th root of d J m ( x ) / d x   =0 ; Jm represent the m–th order cylindrical Bessel function. The fundamental axial acoustic mode (100), characterized by the minimal frequency separation interval, is employed for measurement:

The experimentally measured acoustic resonance frequency fN deviates from the ideal resonance peak f1000 under the influence of non-ideal perturbations, primarily [21].

5.1 Measurement principles

Liquid crystals represent a state of matter intermediate between solids and liquids, exhibiting characteristics of both crystals and liquids. Their appearance resembles a fluid, demonstrating mechanical properties such as flowability, continuity, and surface tension, while their molecular structure is analogous to crystals, displaying physical properties like optical anisotropy and interference typical of solids. Thermochromic liquid crystal (TLC) thermometry is a non-contact temperature measurement technique. As an optically active chiral nematic phase material, as shown in Figure 12, the molecules of TLCs are arranged in layered structures, with each layer of molecules undergoing helical rotation along the principal axis. The pitch of the helix (i.e., the distance between two adjacent layers of liquid crystal molecules) determines the wavelength of reflected light. When changes in ambient temperature alter the interlayer molecular spacing of the TLCs, the frequency of the light waves selectively reflected by the liquid crystals also changes, resulting in a corresponding shift in the color displayed on the surface. The unique property of selective light reflection characteristic of chiral nematic phase materials forms the basis of TLC thermometry. Each displayed color corresponds to a specific temperature, allowing the temperature to be determined based on the observed color of the liquid crystals.

TLCs display distinct colors at different temperatures, characterized by a transition from colorless to red upon reaching the lower threshold of the active temperature range. As the temperature increases, the colors shift sequentially through orange, yellow, green, blue, and violet. Upon reaching the upper limit of the temperature range, the liquid crystals revert to a colorless state. Each color exhibited by the TLCs corresponds to a specific temperature, and a color-temperature correlation curve can be established through calibration experiments [23]. Based on the temperature range over which color changes occur, TLCs can be categorized into broad-band and narrow-band types. Broad-band liquid crystals typically operate over an effective temperature range of 5°C to 30°C, offering advantages such as a wide measurement range, straightforward calibration, and suitability for analyzing dynamic temperature variations. In contrast, narrow-band liquid crystals function within a narrower range of 1°C to 2°C, providing higher measurement accuracy, easier data fitting, and reduced sensitivity to external lighting conditions and illumination angles [24].

5.2 Research status and analysis

TLC thermometry is a non-contact measurement technique characterized by high resolution (temperature resolution up to 0.1°C, spatial resolution up to 1 mm), rapid response, and reversible color changes of the TLCs. Consequently, numerous domestic and international scholars have conducted extensive research on the calibration and heat transfer applications of TLCs.

Since traditional thermocouple contact measurement methods may disturb flow fields and introduce measurement errors, Chyu [25] introduced a method for obtaining local heat transfer coefficients using transient liquid crystal thermography. This study used the inlet temperature as a reference and evaluated four methods for determining the local overall average temperature in turbine blade cooling. The research highlighted the potential of liquid crystals for detailed thermal measurements in complex geometries. Bunker’s team [26] utilized TLC thermometry to conduct a detailed study of the heat transfer coefficient and pressure loss in a 45° staggered ribbed cooling channel within a temperature range of 40–45°C and a Reynolds number (Re) range of 20,000–100,000. The study accurately captured temperature variations in the cooling channel and derived corresponding changes in the heat transfer coefficient. Taslim’s team [27] employed TLC technology to investigate the heat transfer coefficient in a spanwise rotating channel with rib-roughened walls, as well as the effects of rotation, aspect ratio, and rib roughness on heat transfer performance in rib-roughened channels. The study accurately obtained the heat transfer characteristics of ribbed channels under rotating conditions, demonstrating that liquid crystal thermometry is an effective and accurate method for determining heat transfer coefficients in non-stationary test sections. Kumar’s team [28] developed an innovative method using TLCs and Bayesian inference to detect hotspots and estimate the strength of heat sources in a flat-plate system. The experimental setup involved discrete strip heat sources embedded in a flat plate, with temperature distributions measured via TLC sheets. Numerical validation of the experimental data showed discrepancies within 3%, confirming the robustness of the method. Schmid’s team [29] proposed an advanced transient heated foil method using TLCs to measure local heat transfer coefficients. By employing a linearly increasing surface heat flux, the method improved accuracy and addressed challenges in low heat transfer regions. Validation was performed on a flat plate subjected to a single circular jet impingement, with results showing good agreement with established correlations in the literature. The study emphasized the adaptability of this method for applications requiring high-resolution thermal diagnostics, provided that appropriate optical access and surface geometry are maintained.

5.3 Practical application cases

Phase change materials (PCMs) play a critical role in latent heat thermal energy storage (LHTES) systems, and the optimization of their thermal performance is central to improving energy conversion efficiency. While the addition of nanofillers enhances thermal conductivity, it also alters the material’s optical properties, rendering traditional phase interface visualization methods ineffective. Therefore, developing novel temperature measurement techniques suitable for opaque nano-enhanced phase change material (NePCM) to accurately capture temperature distributions during phase change processes holds significant theoretical and engineering value for deepening the understanding of heat transfer mechanisms and optimizing energy storage performance. Current research primarily relies on thermocouples to measure heat flux and fluid flow distribution details at specific moments, but this method suffers from low spatial resolution, and its invasive nature can introduce various artifacts that affect experimental results. Li [30] employed TLC technology to measure the temperature of invisible phase interfaces, investigating the melting process of NePCM in a differentially heated rectangular cavity. This approach enabled direct observation of the transition in heat transfer mechanisms from conduction to convection during melting and accurately determined instantaneous melt fraction and total heat storage.

Figures 13(a), (b), and (c) present schematic diagrams of the external and internal structural components of the experimental setup, including a constant-temperature bath, a rectangular cavity test section, a camera with an integrated illumination source, two aluminum plates, two constant-temperature water circulators, and a data acquisition unit. Figure 13(b) details the rectangular cavity test section, which consists of multiple poly plates and two copper blocks (serving as heating and cooling boundaries) connected via flanges.

The heating and cooling boundary temperatures were controlled by aluminum plates with internal flow channels, connected to water baths with a temperature stability of 0.01°C. Thermal grease was applied between the copper blocks and aluminum plates to reduce interfacial thermal resistance. As shown in Figure 22(c), except for the front optical observation window, the test cavity was wrapped with a thick insulating sleeve to minimize heat loss. T-type thermocouples with a calibration accuracy of ± 0.2°C were inserted into the copper plates to monitor the heating and cooling boundary temperatures, while two additional thermocouples were inserted into the top insulation layer to roughly estimate heat loss from the adiabatic walls.

From the temperature variation maps derived using the TLC thermography method, which reflect the thermal response of the samples during melting, the dynamic evolution and movement of the phase interface for different NePCM samples can be observed. As shown in Figure 14, in cavities with aspect ratios of H/B = 0.8, the melting fronts of three NePCM samples with different nanoparticle loadings (0 wt.%, 1 wt.%, and 3 wt.%) exhibit significant differences.

During the initial stage of melting in NePCMs, the melting fronts of all samples exhibited a vertical morphology, indicating dominant heat conduction. Notably, the 3 wt.% high-loading sample demonstrated the fastest advancement of the melting front due to its enhanced effective thermal conductivity (101% improvement compared to pure PCM). As melting progressed, natural convection effects gradually emerged in the molten region, characterized by distinctive bending of the upper portion of the melting front (as observed in the 20-minute image). This deformation originated from the buoyant rise of thermal plumes near the heated wall, forming a clockwise vortex at the top of the cavity.