Non-Contact Thermophysical Property Measurements of High-Temperature Corium Through Aerodynamic Levitation

Abstract

The thermophysical properties of corium are critical for improving the predictive accuracy of severe accident analysis codes. However, due to the high melting temperature and high volatility of corium, thermophysical property measurements are extremely challenging, resulting in a significant lack of data. This study presents a non-contact measurement facility based on the aerodynamic levitation technique, enabling the measurement of the density, surface tension, and viscosity of corium components at temperatures exceeding 3000 K. Density is measured based on the axisymmetric ellipsoid assumption of levitated drops, while the surface tension and viscosity are determined using the drop oscillation method. Experimental results for key corium components, including ZrO₂ and a UO₂-ZrO₂ mixture, are presented, addressing data gaps in the thermophysical properties of UO₂-containing materials.

1. Introduction

In the event of a severe accident at a nuclear power plant, the consequences go beyond mere property damage and pose significant risks to public health and environmental safety [1]. Given the destructive potential of such incidents, ensuring nuclear power safety has become a paramount concern in advancing nuclear energy. To achieve the goal of practically eliminating large-scale radioactive releases, the design of third-generation advanced pressurized water reactors must be improved to enhance the prevention and mitigation of severe accidents. Therefore, a deeper understanding of the mechanisms and phenomena associated with severe accidents is essential for improving the safety of nuclear power plants.

Severe accidents involve a range of complex phenomena, including the interactions between the core melt (corium) with reactor structures and water, as well as the release, transport, and deposition of the fission product. These phenomena are governed by thermal hydraulics, high-temperature material science, and aerosol physics, among others [2]. Accurate predictions of severe accident progression depend on accurate experimental data and modeling, with the thermophysical properties of corium being a critical factor.

Corium primarily consists of U-Zr-O-Fe. Its high melting temperature and volatility pose significant challenges for the thermophysical property measurements, leading to limited available data. To address these challenges, two experimental devices have been developed: the VITI-MBP device by the Commissariat à l’Energie Atomique et aux Energies Alternatives (CEA) under the ALISA project [3] and the TIGEL device by the Russian Kurchatov Institute under the MASCA project [4].

The VITI-MBP device used the maximum bubble pressure method to measure the density and surface tension of C32 (composition: 54.5% UO₂, 14.5% ZrO₂, and 31% Zr in mol) [5], as well as to assess these properties of corium in severe accident scenarios such as in-vessel retention, a large break loss of coolant accident, and loss of outside power [3]. However, the measurement accuracy was affected by factors such as temperature gradients in the molten pool and the shape deformation of bubbles. The TIGEL device utilized the Archimedes method to measure the density of C32 [6] and the oscillating cup method to measure the viscosity of C22 (composition: 62% UO₂, 8.4% ZrO₂, and 29.6% Zr in mol) and C100 (composition: 62% UO₂ and 38% ZrO₂ in mol) [7]. However, challenges remained due to the influence of surface tension and the stability of the suspended system, which induced potential errors in determining the surface position in the molten pool.

Both the VITI-MBP and TIGEL devices use contact methods, which are susceptible to sample contamination due to interactions between the corium and the container wall at high temperatures. Non-contact methods are more preferred for high-temperature measurements, such as acoustic levitation (AL) [8], electromagnetic levitation (EML) [9], electrostatic levitation (ESL) [10], and aerodynamic levitation (ADL) [11,12,13]. These techniques use the acoustic radiation force, Lorentz force, Coulomb force, and gas drag force to levitate the sample, thereby eliminating the risk of contamination.

AL is mainly used at ambient temperature with few material limitations [14]. However, AL is sensitive to temperature variations and can also cause strong atomization and fragmentation for high-density drops. The application of EML is limited to samples with sufficient electrical conductivity while ESL requires samples to be charged before levitation. Therefore, EML and ESL are typically used for metallic materials. Some hybrid levitation techniques have been developed for more stable levitation at high temperatures, such as aero-acoustic levitation [15]. However, due to the exposure of the tested sample to air, the composition of gases around the sample is difficult to control. In contrast, ADL is more versatile, accommodating both metallic and non-metallic materials [16]. Given that UO₂ and ZrO₂ are key components of corium, ADL stands out as the optimal non-contact method for measuring the thermophysical properties of corium.

In this study, an ADL device was developed to measure the density, surface tension, and viscosity of key corium components, including ZrO₂ and a UO₂-ZrO₂ mixture with a U/Zr molar ratio of 0.456. Spherical samples were prepared using the laser hearth method for single components and the pressing sintering method for mixtures. Measurements were conducted at temperatures exceeding 3000 K. The resulting data address data gaps in the thermophysical properties of UO₂-containing materials.

2. Methods

2.1. Experimental Setup

The experimental setup, named ALSEE (Aerodynamic Levitation-laSEr hEating installation for melt properties), has been developed at China Nuclear Power Engineering Co., Ltd. (CNPE), Beijing, China for measuring the thermophysical properties of corium. The schematic diagram is illustrated in Figure 1. The ALSEE facility comprises an aerodynamic levitation system, laser heating system, temperature measurement system, optical imaging system, acoustic excitation system, and vacuum chamber system.

The aerodynamic levitation system stably levitates a 2–3 mm spherical sample using a converging–diverging conical nozzle, with argon gas flow precisely regulated by a flow controller. The laser heating system, consisting of two 100 W CO₂ lasers (wavelength 10.6 μm.), heats the sample into a liquid drop from both the top and bottom sides. The temperature measurement system employs two infrared dual-color pyrometers, covering the ranges of 1173–2073 K and 1873–3573 K, respectively. The measurement uncertainty for temperature is 0.5% of the measured value in °C + 1 K. The optical imaging system includes a high-speed camera, narrow-band filter, and background laser. Coupled with the filter, the background laser enables backlighting imaging, ensuring consistent image brightness even at high temperatures. The acoustic excitation system, consisting of a waveform generator and loudspeaker, transmits acoustic waves along the argon flow to induce oscillations in the levitated drop. The vacuum chamber system, equipped with a pump, allows for gas wash operations to remove oxygen and nitrogen that could otherwise affect the material composition during high-temperature measurements.

2.2. Measurement Principle

Density is determined as the ratio of mass to volume. At high temperatures, an aerodynamically levitated drop generally forms an axisymmetric ellipsoidal shape due to the combined effects of gravity and gas drag forces. Drop images captured by the high-speed camera are processed using edge detection to extract the edge position data. These data are then analyzed using an ellipse fitting algorithm to determine the drop radius, allowing for density calculation as follows:

$$\rho ={\displaystyle \frac{3m}{4\pi r_{\mathrm{h}}^2{r}_{\mathrm{v}}}}$$

(1)

where m is the sample mass, and r_h and r_v the horizontal and vertical radius. The sample mass is determined by an electric balance at room temperature with an uncertainty of 0.05 mg.

Surface tension and viscosity are measured by the drop oscillation method. For a spherical drop oscillating at a small amplitude, the surface tension is related to its resonant frequency and mass [17], as described by the following equation:

$$\gamma ={\displaystyle \frac{3\pi m{v}_{\mathrm{r}}^2}{l(l-1)(l+2)}}$$

(2)

where $v_r$ is the resonant frequency, and l is the oscillation mode. Equation (2) is known as the Rayleigh equation. When the resonant frequency for l = 2 is obtained, surface tension is calculated by the following equation:

$$\gamma ={\displaystyle \frac{3\pi m{v}_{\mathrm{r}}^2}{8}}$$

(3)

During a damped oscillation of a viscous drop oscillating around the resonant frequency, the drop horizontal or vertical radius follows a damped pattern:

$$r_{\mathrm{h}/\mathrm{v}}(t)=A\cdot \exp (-\Gamma t)\cdot \sin (2\pi vt+\varphi )+r_{\mathrm{m}}$$

(4)

where A is the oscillation amplitude, Γ is the damping constant, $v$ is the response frequency, ϕ is the oscillation phase, and r_m is the mean radius after disappearance of the damped oscillation. Viscosity is then calculated by the Lamb equation [18] as follows:

$$\eta ={\displaystyle \frac{\rho r_e^2}{5}}\Gamma$$

(5)

where r_e is the equivalent radius. By replacing equivalent radius with mass and density, viscosity can be calculated by the following equation:

$$\eta ={\displaystyle \frac{1}{5}}{({\displaystyle \frac{3}{4\pi }})}^{{\displaystyle \frac{2}{3}}}{m}^{{\displaystyle \frac{2}{3}}}{\rho }^{{\displaystyle \frac{1}{3}}}\Gamma$$

(6)

Considering the propagation law, the uncertainty of density, surface tension, and viscosity can be calculated as follows:

$${\displaystyle \frac{\Delta \rho }{\rho }}=\sqrt{{({\displaystyle \frac{\Delta m}{m}})}^2+4{({\displaystyle \frac{\Delta r_{\mathrm{h}}}{r_{\mathrm{h}}}})}^2+{({\displaystyle \frac{\Delta r_{\mathrm{v}}}{r_{\mathrm{v}}}})}^2}$$

(7)

$${\displaystyle \frac{\Delta \gamma }{\gamma }}=\sqrt{{({\displaystyle \frac{\Delta m}{m}})}^2+4{({\displaystyle \frac{\Delta v_r}{v_r}})}^2}$$

(8)

$${\displaystyle \frac{\Delta \eta }{\eta }}=\sqrt{{\displaystyle \frac{4}{9}}{({\displaystyle \frac{\Delta m}{m}})}^2+{\displaystyle \frac{1}{9}}{({\displaystyle \frac{\Delta \rho }{\rho }})}^2+{({\displaystyle \frac{\Delta \Gamma }{\Gamma }})}^2}$$

(9)

where ∆ means the uncertainty of a variable.

2.3. Sample Preparation

The ALSEE facility can stably levitate spherical samples with diameters of 2–3 mm. To maintain levitation stability during heating and melting, the sample porosity must be kept below 10% before levitation. The sample preparation process is illustrated in Figure 2. Single-component samples, such as ZrO₂, were prepared using the laser hearth method, while multi-component samples, such as the UO₂-ZrO₂ mixture, were prepared using the pressing sintering method.

In the laser hearth method, irregular raw materials are placed in the concave of a laser hearth and melted into a spherical shape under laser heating. Upon inactivation of the laser, the melt solidifies into a dense sphere [19]. In the pressing sintering method, the raw materials are first ball-milled to produce fine powders, which are then mixed and pressed into spherical embryos. These embryos are subsequently sintered at high temperatures to form dense samples [20]. It is essential to resolve inhomogeneity during the powder mixing process. To achieve this, the powders undergo wet mixing at 200 rpm for 2 h in the ball mill. The coefficient of variation, defined as the ratio of the standard deviation to the average concentration of each component, is measured to be 4.7%.

2.4. Image Analysis

Under the combined influence of gravity and levitating gas, high-temperature melts in aerodynamic levitation experiments form an axisymmetric ellipsoidal shape, with the difference between the horizontal and vertical radii typically being within 2% [21]. A commonly used ellipse-fitting algorithm is the MEST algorithm, as shown in Figure 3, with detailed principles available in the reference [22].

For each sample image, the edge detection algorithm extracts the drop contour. An ellipse is fitted to the edge through the MEST algorithm, yielding the ellipse parameters. These parameters are then used to calculate the coordinates of the ellipse center and the horizontal and vertical radii. As shown in Figure 3, the fitted ellipse closely matches the drop edge using the MEST algorithm.

Calculations including edge detection and ellipse fitting are conducted using MATLAB R2022b. Notably, image analysis outputs dimensions in pixels, requiring calibration to convert pixels to meters. Calibration is typically performed using images of standard stainless-steel spheres before measurements.

3. Results and Discussion

Analysis of the debris bed from the Three Mile Island accident revealed that fully oxidized corium was predominantly a mixture of UO₂ and ZrO₂, with elemental mass ratios of 70% U, 13.75% Zr, and 13% O [23,24]. The extreme volatility of UO₂ poses significant challenges for measuring thermophysical properties using the aerodynamic levitation technique. To expand the experimental data for the U-Zr-O system, this study focused on measuring the thermophysical properties of ZrO₂ and the UO₂-ZrO₂ mixture with a U/Zr molar ratio of 0.456.

3.1. Density of Liquid ZrO₂

Density was measured during a rapid cooling process. Figure 4 illustrates the cooling of a ZrO₂ sample. The levitated sample was initially heated to a very high temperature using lasers. Once the drop stabilized, the lasers were deactivated, causing a rapid temperature decrease. Due to the latent heat exceeding heat losses from convection and radiation, the drop entered an undercooling state before recalescence, during which the temperature rose sharply, nearing the melting temperature. After recalescence, the liquid sample transitioned to a solid state. A high-speed camera captured the drop shape throughout the cooling process to calculate its volume. Density data were derived by analyzing images taken between the start of cooling and the recalescence phase.

Measured density data for liquid ZrO₂ are presented in Figure 5, alongside published data and models. The data used in the detailed code SCDAP/RELAP [25] and the integral code MAAP5 [26] were sourced from reports by the Idaho National Lab and Electric Power Research Institute. These data are significantly higher than the experimental results, potentially leading to inaccuracies in severe accident simulations. Molecular Dynamics (MD) calculations [27,28] show better alignment with experimental data; however, their reliability still depends on experimental benchmarks, as model parameters are adjusted using experimental results.

In recent years, most of the density data for liquid ZrO₂ have been measured using ADL [29,30,31], underscoring its effectiveness for high-temperature property measurements. The majority of the values fall within the range of 4.6–5.1 g/cm³. The small discrepancies between experimental datasets demonstrate the accuracy and consistency of non-contact measurements using ADL.

Considering the uncertainties in mass and radius measurements, the density uncertainty was calculated to be 2.33% using Equation (7). A linear fitting was conducted to derive the density–temperature relationship for liquid ZrO₂ in the temperature range of 2750–3200 K with a 95% confidence level. The resulting equation is presented in

Table 1. Density equations of liquid ZrO₂.

Source	Equation (g/cm3)	Temperature (K)	Method
This study	$\rho =-(7.202\pm 0.897)\times {10}^{-4}(T-2988)+(4.716\pm 0.009)$	2750–3200	ADL
Denier	$\rho =-(1.07\pm 0.16)\times {10}^{-3}(T-2988)+(4.89\pm 0.03)$	2988–3233	ADL
Kondo	$\rho =-(4.10\pm 0.87)\times {10}^{-4}(T-2988)+(4.69\pm 0.23)$	2753–3273	ADL
Kohara	$\rho =-8.9\times {10}^{-4}(T-2988)+5.05$	2988–3273	ADL
Hong	$\rho =-4.0\times {10}^{-4}(T-2988)+4.9$	3100–3400	MD
Alderman	$\rho =-3.7\times {10}^{-4}(T-2988)+4.9$	2670–3670	MD

. The temperature coefficient is −(7.202 ± 0.897) × 10⁻⁴ g/(K·cm³), closely aligning with Kohara’s results. The density at the melting temperature (2988 K) is 4.716 ± 0.009 g/cm³, consistent with Kondo’s results.

It is worth noting that different ADL experiments used varying gas compositions. Kondo used a mixture of 15% O₂ and 85% Ar, Denier used 20% O₂ and 80% Ar, while Kohara did not specify the gas composition. In contrast, this study used pure Ar. Research by Borgard et al. [32] indicates that the gas composition may affect density measurements. The oxygen in the levitation gas could affect the oxygen stoichiometry of ZrO₂, thereby changing the sample density. Additionally, differences in the density and viscosity of gases with varying compositions may also lead to slight deviations in the drop shape.

3.2. Density of Liquid UO₂-ZrO₂ Mixture

Asmolov et al. [23] measured the density of a UO₂-ZrO₂ mixture with the U/Zr molar ratio of 1.528 using the pycnometric method. The density of the C32 melt was also measured by Asmolov et al. [33] using the modified hydrostatic weighing method and by Chikhi et al. [5] using the maximum bubble pressure method. However, no density data for UO₂-ZrO₂ mixtures with lower U/Zr molar ratios have been reported. To address this gap, the density of a UO₂-ZrO₂ mixture with a U/Zr molar ratio of 0.456 was measured in this study, expanding the density dataset for the U-Zr-O system.

The density values for the UO₂-ZrO₂ mixture (U/Zr = 0.456) measured during a rapid cooling process are presented in Figure 6. Considering the uncertainties in mass and radius measurements, the density uncertainty was calculated to be 2.14%. A linear fitting was performed to obtain the density–temperature relationship in the temperature range of 2720–3040 K with a 95% confidence level:

$$\rho =-(9.537\pm 0.163)\times {10}^{-4}T+(8.488\pm 0.046) (\mathrm{g}/\mathrm{c}{\mathrm{m}}^3)$$

(10)

Given the limited availability of density data, Figure 6 also includes data for ZrO₂, UO₂, C32, and the UO₂-ZrO₂ mixture with a U/Zr molar ratio of 1.528. The density of UO₂ was measured by Breitung and Reil [34] and was also suggested by Fink [35] in a review article. The results of this study are consistent with the observed trends in density changes as the composition varies.

The detailed code SCDAP/RELAP calculates material properties using equations provided in MATPRO [25]. The density for the U-Zr-O system can be calculated by the following equation:

$${\rho }_{\mathrm{U}\text{-}\mathrm{Zr}\text{-}\mathrm{O}}={\displaystyle \frac{0.27f_{{\mathrm{UO}}_2}+0.123f_{{\mathrm{ZrO}}_2}+0.091f_{\mathrm{Zr}}}{\frac{0.27f_{{\mathrm{UO}}_2}}{{\rho }_{{\mathrm{UO}}_2}}+\frac{0.123f_{{\mathrm{ZrO}}_2}}{{\rho }_{{\mathrm{ZrO}}_2}}+\frac{0.091f_{\mathrm{Zr}}}{{\rho }_{\mathrm{Zr}}}}}$$

(11)

where f is the molar fraction for the components UO₂, ZrO₂, and Zr.

Using the MATPRO data for UO₂ and ZrO₂, the density of the UO₂-ZrO₂ mixture (U/Zr = 0.456) was calculated and is shown in Figure 6. Significant discrepancies between the results of this study and those derived from SCDAP/RELAP are evident. The main reason is the notably higher ZrO₂ density values used in SCDAP/RELAP, as illustrated in Figure 5. Furthermore, calculating the density of a mixture by dividing the total mass by the sum of the volumes of individual components leads to substantial errors that cannot be ignored. For the density calculations of liquid mixtures, additional parameters are required. For example, in the Redlich–Kister equation, an adjustable parameter is used to determine the excess molar volume, which is defined as the difference between the mixture’s volume and the total volume of individual components [36].

3.3. Surface Tension of Liquid ZrO₂

Surface tension can be measured by the drop oscillation method in ADL experiments. In previous studies, acoustic excitation as illustrated in Figure 7 was used to induce oscillations in molten drops, such as liquid Al₂O₃. The acoustic waves from the loudspeaker cause disturbances in the levitation gas. The disturbance was then transmitted along the gas channel to the levitated drop. A frequency scan was conducted to analyze the drop response. The typical duration of measurements was 20–30 min [12]. However, ZrO₂ exhibits high volatility near its melting temperature, leading to a significant reduction in sample mass during acoustic excitation. This results in a substantial shift in the resonant frequency, compromising measurement accuracy. Therefore, this study used the self-excitation technique for surface tension measurement of liquid ZrO₂.

During the process of self-excitation, oscillations of the molten drop were induced by a pulse in the gas flow rate. The resulting disturbance was transmitted to the levitated drop via the gas channel. A frequency scan was not needed in this process. The resonant frequency was analyzed from the drop radius data. The measurement was conducted over a period of approximately 1–2 min. Therefore, the self-excitation technique was deemed an appropriate methodology for measuring the surface tension of volatile materials, such as corium.

Figure 8 shows the radius variation and the Fast Fourier Transform (FFT) analysis for a 24.17 mg ZrO₂ drop at 3178 K. Two distinct peaks were observed at 50 Hz and 170 Hz. The 170 Hz peak was identified as the resonant peak, as image analysis revealed that the vertical displacement frequency of the sample matched the 50 Hz peak. The vertical displacement was derived from the coordinates of the ellipse centroid, which were also calculated in the MEST algorithm during ellipse fitting. Using Equation (3), the surface tension at 3178 K was determined to be 0.82 N/m.

The measured surface tension values for liquid ZrO₂ at different temperatures are presented in Figure 9. The surface tension uncertainty was determined by propagating the uncertainties in mass and resonant frequency. As the resonant frequency was obtained through FFT analysis, its uncertainty was considered to be equivalent to the frequency resolution of FFT, as defined by the following equation:

$$\Delta v_r=\delta ={\displaystyle \frac{f_{\mathrm{s}}}{N}}$$

(12)

where δ is the frequency resolution, f_s is the sampling rate, and N is the number of samples.

Using Equations (8) and (12), the surface tension uncertainty at 3178 K was calculated to be 15%. By maintaining a constant sampling rate of 1000 fps and increasing the number of samples from 100 to 200, the frequency resolution improved from 10 Hz to 5 Hz, thereby reducing the surface tension uncertainty to 6%. The measured data were linearly fitted over the temperature range of 3173–3493 K with a 95% confidence level, yielding the following equation:

$$\gamma =-(6.024\pm 2.372)\times {10}^{-4}(T-2988)+(0.905\pm 0.083) (\mathrm{N}/\mathrm{m})$$

(13)

The surface tension of ZrO₂ decreases with increasing temperature, a trend consistent with other published data. In addition to ADL experiments using the drop oscillation method [31], the drop impingement method [37] was developed based on modifications to the ADL facility. This method evaluates surface tension by analyzing changes in the surface area during impingement. Notably, the surface tension used in MAAP5 is fixed at 1 N/m, likely due to the limited availability of experimental data during the software’s development. Therefore, incorporating high-temperature experimental data into severe accident codes can effectively improve calculation accuracy.

3.4. Viscosity of Liquid ZrO₂

The acoustic excitation initially induced oscillations in the levitated drop around its resonant frequency. After the acoustic excitation ceased, the drop experienced a damped oscillation. Figure 10 illustrates the radius variations during the damped oscillation. A non-linear fitting to Equation (4) was performed to determine the damping constant, which was then used to calculate viscosity.

Notably, attention should be paid to maintaining the drop temperature during both oscillating and non-oscillating states. The lasers used in our experiment provide very stable output power, with a stability of ±2% for the ti100-HS lasers produced by Synrad, Mukilteo, WA, USA which contributes to temperature stabilization. The drop was also stably levitated, with position fluctuations kept below 20 μm. The temperature fluctuation over 1–2 min was generally less than 20 K, which is close to the measurement uncertainty. However, over longer durations, the sample temperature may shift, with changes reaching up to 50 K. In such cases, the laser output power was slightly adjusted to stabilize the temperature, and the average temperature during the process was then calculated.

The measured viscosity data for liquid ZrO₂ are presented in Figure 11, alongside published data and models. The viscosity equations of ZrO₂ derived by MD calculations or used in codes are also given in

Table 2. Viscosity equations of liquid ZrO₂.

Source	Equation (mPa·s)	Temperature (K)	Method
This study	$\eta =(12.87\pm 1.03)\exp [{\displaystyle \frac{(8.035\pm 2.010)\times {10}^4}{8.314}}({\displaystyle \frac{1}{T}}-{\displaystyle \frac{1}{2988}})]$	3183–3420	ADL
Denier	$\eta =(9.02\pm 0.18)\exp [{\displaystyle \frac{(1.84\pm 0.04)\times {10}^5}{8.314T}}]$	2988–3173	ADL
Kondo	$\eta =(0.96\pm 0.69)\exp [{\displaystyle \frac{(6.4\pm 2.0)\times {10}^4}{8.314T}}]$	3170–3471	ADL
Kim	$\eta =0.32\exp ({\displaystyle \frac{8.79\times {10}^3}{T}})$	3000–5000	MD
MAAP5	$\eta =4.946\exp [{\displaystyle \frac{2.47\times {10}^5}{8.314}}({\displaystyle \frac{1}{T}}-{\displaystyle \frac{1}{2973}})]$	-	-
SCDAP/RELAP	$\eta =0.122\exp ({\displaystyle \frac{10500}{T}})$	-	-

. The temperature dependence of viscosity follows the Andrade equation [38]:

$$\eta ={\eta }_0\exp \left[{\displaystyle \frac{E_{\mathrm{a}}}{R_{\mathrm{g}}}}({\displaystyle \frac{1}{T}}-{\displaystyle \frac{1}{T_{\mathrm{m}}}})\right]$$

(14)

where ${\eta }_0$ is the viscosity at melting temperature, E_a is the activation energy for viscous flow, R_g is the gas constant (8.314 J/(mol·K)), and T_m is the melting temperature. The experimental data were fitted to Equation (14) over the temperature range of 3183–3420 K with a 95% confidence level, yielding the following equation:

$$\eta =(12.87\pm 1.03)\exp [{\displaystyle \frac{(8.035\pm 2.010)\times {10}^4}{R_{\mathrm{g}}}}({\displaystyle \frac{1}{T}}-{\displaystyle \frac{1}{2988}})] (\mathrm{mPa}\cdot \mathrm{s})$$

(15)

The uncertainty in viscosity was calculated using Equation (9) with the density uncertainty of 2.33% as reported in Section 3.1. The uncertainty in the damping constant was derived from the non-linear fitting, while the mass uncertainty was calculated by accounting for the balance precision and mass loss due to volatility. The relative uncertainty in viscosity was found to be 21% at lower temperatures and 7% at higher temperatures. These variations in uncertainty are mainly attributed to changes in the uncertainty of the damping constant. At lower temperatures, the higher viscosity results in a shorter decay process and fewer radius data for fitting, thereby leading to greater uncertainty in the damping constant.

Both the MD models proposed by Kim et al. [39] and Alderman et al. [28], as well as the empirical equations employed in MAAP5 [26] and SCDAP/RELAP [25], exhibit significant discrepancies compared to the ADL experimental results reported by Kondo et al. [29], Denier et al. [31], and this study. Given the consistency observed among the experimental results, it is necessary to apply the equations derived from these experiments when using the codes to simulate severe accidents, thereby improving simulation accuracy.

3.5. Viscosity of Liquid UO₂-ZrO₂ Mixture

The viscosity of the UO₂-ZrO₂ mixture with a U/Zr molar ratio of 0.456 was measured using the same methodology as that applied to ZrO₂, with the results presented in Figure 12. The maximum uncertainty was determined to be 10.8%. Given the scarcity of experimental data, viscosity values for other corium components, including ZrO₂, UO₂ [40], and the UO₂-ZrO₂ mixture (U/Zr = 1.632) [7], are also included for comparison. Overall, the data obtained in this study align with the observed trends in viscosity as the composition varies.

To derive a viscosity equation for the UO₂-ZrO₂ mixture (U/Zr = 0.456), a non-linear fitting to Equation (14) was conducted. The melting temperature of the mixture was determined to be 2873 K based on the phase diagram for the UO₂-ZrO₂ system reported by Romberger [41]. However, due to the limited experimental data in this study, the activation energy was calculated first to decrease the number of fitting parameters and thereby reduce the fitting uncertainty. The activation energy is determined to be 8.035 × 10⁴ J/mol for ZrO₂ as reported in Equation (15) and 3.841 × 10⁴ J/mol for UO₂ based on the viscosity equation by Woodley [40]. By applying a weighted average based on the molar proportions, the activation energy of the UO₂-ZrO₂ mixture (U/Zr = 0.456) was determined to be 6.722 × 10⁴ J/mol. The non-linear fitting over the temperature range of 2974–3093 K with a 95% confidence level yields the following equation:

$$\eta =(8.928\pm 0.418)\exp \left[{\displaystyle \frac{6.722\times {10}^4}{R_{\mathrm{g}}}}({\displaystyle \frac{1}{T}}-{\displaystyle \frac{1}{2873}})\right] (\mathrm{mPa}\cdot \mathrm{s})$$

(16)

The viscosity of the UO₂-ZrO₂ mixture (U/Zr = 0.456) was also calculated using the equations for the U-Zr-O system provided by the SCDAP/RELAP. The viscosity of the U-Zr-O system is calculated by the following equation:

$${\eta }_{\mathrm{U}\text{-}\mathrm{Zr}\text{-}\mathrm{O}}=f_{{\mathrm{UO}}_2}{\eta }_{{\mathrm{UO}}_2}+f_{{\mathrm{ZrO}}_2}{\eta }_{{\mathrm{ZrO}}_2}+f_{\mathrm{Zr}}{\eta }_{\mathrm{Zr}}$$

(17)

For the UO₂-ZrO₂ mixture (U/Zr = 0.456) with f_Zr = 0, the relevant equations for UO₂ and ZrO₂ in SCDAP/RELAP are described as follows:

$${\eta }_{{\mathrm{UO}}_2}=12.3-2.09\times {10}^{-3}T (\mathrm{mPa}\cdot \mathrm{s})$$

(18)

$${\eta }_{{\mathrm{ZrO}}_2}=0.122\exp ({\displaystyle \frac{10500}{T}}) (\mathrm{mPa}\cdot \mathrm{s})$$

(19)

The calculated viscosity values for the UO₂-ZrO₂ mixture (U/Zr = 0.456) are also shown in Figure 12. Significant discrepancies were observed between the results derived from SCDAP/RELAP and those obtained in this study, indicating that the existing equations for corium components at high temperatures lack sufficient accuracy. Incorporating the experimental results derived in this study into SCDAP/RELAP has the potential to substantially enhance the accuracy of severe accident simulations.

Notably, the viscosity data for UO₂-containing materials have traditionally been obtained through contact methods. In this study, the viscosity of the UO₂-ZrO₂ mixture (U/Zr = 0.456) was measured using a non-contact method for the first time. The measured data also address the data gap for UO₂-ZrO₂ mixtures with lower U/Zr molar ratios in the temperature range of 2974–3093 K.

4. Conclusions

This study presents a non-contact measurement device based on aerodynamic levitation, which effectively prevents sample contamination at high temperatures. To prepare samples, the laser hearth method is employed for single-component materials, while the pressing sintering method is used for mixtures. The density, surface tension, and viscosity of key corium components, including ZrO₂ and a UO₂-ZrO₂ mixture with a U/Zr molar ratio of 0.456 are measured. Equations for thermophysical property calculations are obtained through linear and non-linear fitting. The experimental results for ZrO₂ show good agreement with published data, while the results for the UO₂-ZrO₂ mixture fill the gaps in the thermophysical property data of UO₂-containing materials.