Rotary multi- crucible switching experimental device and high-temperature molten salt thermophysical parameter inversion method

Abstract

The application discloses a rotating wheel type multi-crucible switching experimental device and a high-temperature molten salt thermophysical parameter inversion method, and belongs to the technical field of high-temperature thermophysical property measurement. The device is characterized in that three graphite crucible stations are uniformly distributed on a rotating wheel in a circumferential direction, and the depths of the molten salt cavities of the stations are respectively preset as the thicknesses of a thin layer, a medium-thick layer and a thick layer. The method comprises the following steps: pouring molten salt into the three crucibles and heating the molten salt to a target temperature; controlling a stepping motor to drive the rotating wheel to sequentially switch and position the three crucibles under a laser incidence window; sequentially heating the molten salt in the three crucibles by laser with increasing matching power in the order of the thin layer, the medium-thick layer and the thick layer, and obtaining transient temperature rise curves; establishing a radiation-heat conduction coupled heat transfer forward problem model for the three thicknesses to form an observation operator; constructing a multi-thickness joint objective function, solving an optimal inversion parameter vector, and performing residual analysis and model verification.

Description

Technical Field

[0001] This application relates to a rotary multi-crucible switching experimental device and a method for inverting high-temperature molten salt thermophysical property parameters, belonging to the field of high-temperature thermophysical property measurement technology. Background Technology

[0002] High-temperature molten salts play a crucial role in solar thermal power generation, fourth-generation nuclear energy systems (molten salt reactors), and high-temperature industrial waste heat recovery due to their excellent thermal stability, low vapor pressure, high heat capacity, and favorable nuclear physics properties. Accurately obtaining the thermophysical properties (thermal conductivity, specific heat capacity) and optical parameters (refractive index, absorption coefficient) of high-temperature molten salts over a wide temperature range is essential for engineering thermophysical design, system safety assessment, and operational efficiency optimization.

[0003] In the field of high-temperature molten salt thermophysical property measurement, the laser flash analysis (LFA) method is one of the most widely used methods. A current method for inverting high-temperature molten salt thermophysical property parameters based on a high- and low-power laser heating strategy (hereinafter referred to as the "dual-condition method") is proposed. This method constructs a two-dimensional axisymmetric radiation-conduction coupled heat transfer model of a three-layer cylindrical structure of graphite-molten salt-graphite, targeting the "phonon-photon" composite heat transfer characteristics of semi-transparent high-temperature molten salt. The method generates a small temperature rise using a low-power laser, and uses the first step of inversion to lock in the thermal conductivity parameters (thermal conductivity coefficient, volumetric heat capacity) dominated by the thermal conduction mechanism. Subsequently, a large temperature rise is generated using a high-power laser, stimulating significant internal radiation effects within the medium. Using the thermal conductivity parameters obtained in the previous step as known quantities, the method focuses on analyzing the radiation parameters (refractive index, absorption coefficient) that are sensitive to high temperatures.

[0004] However, the aforementioned layered inversion strategy and the joint inversion method developed based on it still face fundamental challenges: In laser heating experiments on semi-transparent media (such as high-temperature molten salt), the transient temperature response of the sample's surface is jointly determined by the "phonon-photon" composite heat transfer mechanism. The thermal conductivity k mainly affects the rise slope and steady-state time constant of the temperature response through the thermal diffusion process; the refractive index affects the distribution of light energy entering the molten salt layer by changing the Fresnel reflection and refraction angles at the medium-graphite interface; and the absorption coefficient determines the spatial attenuation characteristics of radiant energy within the molten salt layer. The effects of these three factors in the time-domain temperature signal are highly overlapping, leading to severe parameter crosstalk in the inverse problem—different parameter combinations can produce almost identical temperature response curves within the experimental error range, making the solution of the joint inversion non-unique. Classical inversion theory points out that when the condition number of the model's sensitivity matrix is ​​too large, the inverse problem exhibits ill-posedness, and parameter estimation is extremely sensitive to measurement noise; even a small measurement error can cause the inversion result to deviate drastically from the true value.

[0005] Furthermore, the dual-condition method requires independent heating experiments at both high and low power levels, necessitating a series of operations such as laser power switching, temperature balancing, and data acquisition before each experiment. Additionally, the thickness of the molten salt layer in the existing "graphite-molten salt-graphite" three-layer structure is fixed. Improving the inversion results through multi-thickness data requires multiple disassembly and reassembly of the experimental setup, cleaning of the crucible, refilling of molten salt, and adjustment of the molten salt layer thickness—a time-consuming and labor-intensive process that introduces additional uncertainties. Under high-temperature molten salt experimental conditions (operating temperatures can reach...), ... Frequent opening and closing of the high-temperature chamber and disassembly and assembly of the graphite crucible for thickness adjustment not only seriously affect experimental efficiency, but also place high demands on the skill level of the operators. After each disassembly and assembly, the contact state between the crucible and the molten salt and the surface wetting characteristics of the graphite may change slightly, introducing additional random errors. Summary of the Invention

[0006] To address the issue that the solution for the joint inversion of thermal conductivity, refractive index, and absorption coefficient in the laser flare method for measuring the thermophysical properties of semi-transparent high-temperature molten salt is not unique, this application provides a rotary multi-crucible switching experimental device and a method for inverting the thermophysical property parameters of high-temperature molten salt.

[0007] This application discloses a rotary multi-crucible switching experimental device, comprising:

[0008] Rotating wheel, central rotating shaft, stepper motor, sealed cavity, heating and temperature control system, laser incident window, infrared detector window, and position sensor;

[0009] The rotating wheel rotates around the central rotating shaft, the central rotating shaft is connected to the stepper motor, and the stepper motor drives the rotating wheel to rotate through the central rotating shaft;

[0010] Three graphite crucible stations are evenly distributed along the circumference of the rotating wheel. Each graphite crucible station has a three-layer structure consisting of a graphite bottom, a molten salt cavity, and a graphite cover. The depth of the molten salt cavity in each of the three graphite crucible stations is one of three different thickness values.

[0011] The sealed cavity surrounds the rotating wheel, the heating and temperature control system is located inside the sealed cavity, and the laser incident window and the infrared detector window are located at the top of the sealed cavity;

[0012] The position sensor is located at the connection between the stepper motor and the central rotating shaft, and is used to monitor the rotational position of the wheel.

[0013] Preferably, the device further includes a magnetohydrodynamic seal, which is disposed at the connection between the stepper motor and the central shaft, and is used to maintain the seal of the sealing cavity when the stepper motor drives the central shaft to rotate.

[0014] This application also provides a method for inverting the thermophysical properties of high-temperature molten salt based on a rotary multi-crucible switching device, including:

[0015] Step 1: After heating the molten salt to be tested to a molten state, pour it into the molten salt chambers of the three graphite crucible stations respectively, controlling the pouring quality so that the molten salt level reaches the thickness of a thin layer. Medium and thick layer thickness and thickness of the layer The sealed cavity is heated to the target experimental temperature and maintained at a constant temperature.

[0016] Step 2: Control the stepper motor to drive the rotating wheel to rotate, and switch the three graphite crucible stations to be positioned below the laser incident window. After positioning at each station, a pulsed laser is used for irradiation, and an infrared detector is simultaneously activated to record the transient temperature rise curve of the graphite cover surface, resulting in three transient temperature rise curves. The pulsed laser powers corresponding to the three stations are respectively... , and ,and ;

[0017] Step 3: Regarding the thickness of the thin layer The thickness of the medium-thick layer and the thickness of the thick layer A radiation-conduction coupled heat transfer problem model of the three-layer structure is established respectively. The radiation transfer equation is solved by the discrete coordinate method. Fresnel reflection boundary conditions are set at the graphite-molten salt interface to form an observation operator with three thickness conditions.

[0018] Step 4: Based on the observation operators and the three transient temperature rise curves for the three thickness conditions, construct a multi-thickness joint inversion objective function, and use the ensemble Kalman inversion algorithm to solve the multi-thickness joint inversion objective function to obtain the optimal inversion parameter vector;

[0019] Step 5: Substitute the optimal inversion parameter vector into the radiation-conduction coupled heat transfer forward problem model for each thickness condition, calculate the residual between the predicted temperature rise and the transient temperature rise curve, and perform convergence diagnosis and model verification.

[0020] As a preferred embodiment, the rotation angle of the rotating wheel in step two is 120° each time, and the thickness of the thin layer... The thickness of the medium-thick layer and the thickness of the thick layer The corresponding graphite crucible station is switched and positioned sequentially in the order of thin layer, medium-thick layer, and thick layer.

[0021] As a preferred option, the steps described in step two , and satisfy The approximate proportionality principle applies, where j = 1, 2, 3.

[0022] Preferably, the multi-thickness joint inversion objective function in step four is:

[0023] ;

[0024] in, The weighting coefficients for each thickness condition satisfy... , For the first The predicted temperature response data calculated by the observation operator under the thickness condition. For the first Temperature response data obtained experimentally under thickness conditions For the first Estimated standard deviation of measurement noise under thickness conditions. For the first Number of time sampling points for thickness conditions Sampling time, The parameter vector to be inverted.

[0025] Preferably, the ensemble Kalman inversion algorithm described in step four includes:

[0026] The three transient temperature rise curves are stacked into a joint observation vector. A parameter set containing multiple particles is initialized. In each iteration, the Kalman gain is constructed using the empirical covariance of the set to update the particles until the data mismatch is reduced to the measurement noise level or a preset termination condition is met. Then, the mean of the last set is output as the optimal inversion parameter vector.

[0027] As a preferred option, construct the temperature response parameter vector under various thickness conditions. Single thickness sensitivity matrix , , Then , , Vertical splicing for multi-thickness joint sensitivity The multi-thickness joint sensitivity matrix Used to construct the Kalman gain in each iteration of the ensemble Kalman inversion algorithm, guiding the allocation of correction amounts for each parameter to reduce thermal conductivity. Refractive index and absorption coefficient Parameter crosstalk between them.

[0028] Preferably, step five also includes comparison and verification with the results of single-thickness inversion, including:

[0029] Calculate the condition number improvement factor:

[0030] ;

[0031] in Represents the matrix condition number. For the first Single thickness sensitivity matrix under thickness conditions For the multi-thickness joint sensitivity matrix, when A value greater than 1 indicates that multi-thickness joint inversion improves ill-posedness compared to single-thickness inversion;

[0032] Calculate the multi-thickness joint inversion objective function In the optimal inversion parameter vector Hessian matrix at the location The thermal conductivity is measured by inverting and normalizing the Hessian matrix, and then using the absolute value of the off-diagonal elements of the normalized inverse matrix. Refractive index and absorption coefficient The decrease in the absolute value of the off-diagonal element indicates that the multi-thickness joint inversion has suppressed parameter crosstalk.

[0033] As a preferred option, step five also includes:

[0034] The Kalman inversion algorithm is started with different random initial sets and run independently multiple times. The relative deviation between the optimal inversion parameter vectors obtained in each run is calculated. When the relative deviation is less than 5%, the inversion results are considered to be consistent.

[0035] The beneficial effects of this application are as follows: By using a rotary multi-crucible switching device, three thickness measurements can be continuously completed within minutes after a single sample loading and temperature control, improving efficiency by 5-10 times. Simultaneously, it fundamentally eliminates sample loading deviations introduced by repeated disassembly and assembly. This application uses joint constraints of multiple thickness data, such as thin-layer (thermal conductivity dominant) and thick-layer (radiation dominant), to vertically stitch together the sensitivity matrices of each thickness into a joint sensitivity matrix. This effectively decouples the three originally highly correlated parameters, obtaining a unique and accurate result. The inversion results systematically solve the parameter crosstalk problem from an information theory perspective. The power-thickness matching strategy ensures that the laser energy density absorbed per unit volume of molten salt is comparable at different thicknesses, avoiding saturation in thin layers or weak signals in thick layers. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the principle of a rotary multi-crucible switching experimental device.

[0037] Figure 2This is a flowchart illustrating the method for inverting the thermophysical properties of high-temperature molten salt in a specific implementation. Detailed Implementation

[0038] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0039] It should be noted that, unless otherwise specified, the embodiments and features described in this application can be combined with each other.

[0040] The present application will be further described below with reference to the accompanying drawings and specific embodiments, but this is not intended to limit the scope of the application.

[0041] This embodiment addresses the issue of thermal conductivity degradation caused by phonon and photon coupling heat transfer in existing high-temperature molten salt thermophysical property measurements. Refractive index absorption coefficient To address the ill-posedness and multi-valuedness issues of joint inversion, as well as the inefficiencies and uncontrollable random errors caused by repeated crucible disassembly and reassembly in traditional multi-thickness measurements, a method for inverting the thermophysical properties of high-temperature molten salt based on a rotary multi-crucible switching device is proposed. This embodiment pours the same molten salt sample into three graphite crucibles with different molten salt cavity depths on a rotary wheel, maintaining a constant temperature within the sealed cavity. A stepper motor drives the rotary wheel to rotate sequentially, switching the three crucible positions sequentially below the laser incident window. Pulsed laser heating is performed using incremental power matched to the thickness, and transient temperature rise curves under the three thickness conditions are acquired simultaneously. Then, radiation-conduction coupled heat transfer forward problem models are established for each of the three thicknesses, forming observation operators. Next, based on the multi-thickness measured data and observation operators, a multi-thickness weighted least squares joint objective function is constructed and iteratively solved using an ensemble Kalman inversion algorithm to obtain the optimal inversion parameter vector. Finally, the optimal parameter vector is substituted back into the forward problem model for residual analysis, convergence diagnosis, and comparison verification with single-thickness inversion. Specifically, this includes:

[0042] The rotary multi-crucible switching device serves as the hardware basis for implementing the above-mentioned inversion method and is implemented in the following manner.

[0043] The rotating wheel 1 is made of high-purity graphite material and is disc-shaped, rotating horizontally around the central shaft 3. The central shaft 3 passes through the bottom of the sealed cavity 5, with its lower end connected to the output shaft of the stepper motor 4 and its upper end fixedly connected to the geometric center of the rotating wheel 1. The stepper motor 4 is a high-precision two-phase hybrid stepper motor, used in conjunction with a reducer, and is installed on the lower part of the sealed cavity 5, transmitting rotational driving force to the rotating wheel 1 through the central shaft 3.

[0044] Three graphite crucible stations are evenly distributed along the circumference on the upper surface of rotor 1, with an included angle between adjacent stations. Each graphite crucible station contains a three-layer structure: a graphite base 10, a molten salt chamber 11, and a graphite cover 9. The graphite base 10 is a cylindrical base with a central concave cavity, which serves as the molten salt chamber 11 to hold the molten salt sample. The graphite cover 9 covers the graphite base 10 and has a through-hole in its center, penetrating both the upper and lower surfaces of the cover 9. This through-hole allows a pulsed laser to be perpendicularly incident on the upper surface of the molten salt, while simultaneously allowing an infrared detector to collect the infrared radiation signal from the upper surface of the cover 9. The molten salt chambers 11 of the three graphite crucible stations have three different thickness values: thin layer thickness... Medium and thick layer thickness and thickness of the layer In this embodiment, the three thickness values ​​are set respectively. for ), for , for Except for the depth of the molten salt chamber 11, the three graphite crucible stations maintain identical inner diameters, graphite cap 9 thickness, and graphite bottom 10 thickness. Thin-layer graphite crucibles are suitable for thin-layer applications where radiation effects are suppressed, with temperature response primarily driven by thermal conductivity. Medium-thickness graphite crucibles offer comparable thermal conductivity and radiation effects, providing a moderate mix of parameter sensitivities. Thick-layer graphite crucibles exhibit significant radiation effects, and their temperature response is highly sensitive to refractive index and absorption coefficient.

[0045] The sealed cavity 5 is a vacuum / inert gas sealed container made of stainless steel, surrounding the rotating wheel 1 and three graphite crucible stations. The heating and temperature control system 6 consists of a ring heater and a K-type thermocouple. The ring heater is located on the inner wall of the sealed cavity 5, and the temperature measuring end of the thermocouple extends into the cavity near the rotating wheel 1 to maintain the ambient temperature inside the cavity at the experimental target temperature above the melting point of the molten salt. The laser incident window 7 is made of quartz glass and is sealed and installed on the top of the sealed cavity 5. Its vertical projection position intersects the rotation trajectory of one of the crucible stations on the rotating wheel 1, ensuring that the window is directly below the laser beam path. The infrared detector window 8 is made of infrared-transmitting material and is sealed and installed on the top of the sealed cavity 5, adjacent to the laser incident window 7. Its optical axis forms a certain angle with the normal of the upper surface of the graphite cover 9 to ensure that the infrared detector's field of view covers the laser heating area.

[0046] The position sensor 12 is a photoelectric encoder or Hall effect sensor, located at the connection between the stepper motor 4 and the central shaft 3. Its rotor rotates synchronously with the central shaft 3 to monitor the rotation angle and position of the wheel 1 in real time and feed the position signal back to the controller of the stepper motor 4. The magnetohydrodynamic seal 13 is located at the connection between the stepper motor 4 and the central shaft 3, and is fitted around the outer circumference of the central shaft 3. Its static sealing part is fixed to the bottom of the sealing cavity 5, and its dynamic sealing part forms a magnetohydrodynamic sealing pair with the outer wall of the central shaft 3. When the stepper motor 4 drives the central shaft 3 to rotate, it maintains the vacuum / inert gas sealing integrity of the sealing cavity 5.

[0047] The drive control of the stepper motor 4, the data acquisition of the infrared detector, the triggering of the pulse laser, and the temperature regulation of the heating temperature control system 6 are all uniformly coordinated and controlled by the host industrial computer to realize the programmable automation of the measurement process.

[0048] This application presents a rotary multi-crucible switching device that enables continuous laser heating measurement of three different thicknesses of molten salt layers within a single sample loading cycle, obtaining a multi-thickness temperature response dataset. Furthermore, by utilizing a multi-thickness joint inversion framework, it fully leverages the positive complementarity of the sensitivity distribution at each thickness, significantly reducing the thermal conductivity. Refractive index absorption coefficient Ill-posedness and multi-valuedness of three-parameter joint inversion.

[0049] The high-temperature molten salt thermophysical property parameter inversion method of this embodiment includes:

[0050] Step 1: Molten salt sample loading and temperature control in the sealed cavity;

[0051] A molten salt selected from nitrate, chloride, or fluoride systems is used as the test salt. The test salt is placed in an independent heating container and heated to a temperature above its melting point, causing it to completely melt into a homogeneous liquid. Then, the operator pours the liquid molten salt into the molten salt chambers 11 of three graphite crucible stations 2a, 2b, and 2c, respectively. During the pouring process, the operator calculates the target pouring mass for each crucible based on the cross-sectional area of ​​each of the three molten salt chambers 11 and the liquid density of the test molten salt at the pouring temperature, ensuring the desired thin film thickness. The molten salt level in the corresponding graphite crucible station 2a reaches the thickness of a thin layer. To make the thickness of medium and thick layers The molten salt level in the corresponding graphite crucible station 2b reaches a medium-thickness layer thickness. To make the thickness of the thick layer The molten salt level in the corresponding graphite crucible station 2c reaches a thickness of [thickness value missing]. The molten salt poured into the three graphite crucible stations is the same molten salt system.

[0052] After the infusion is completed, the graphite caps 9 of each graphite crucible are respectively placed on the corresponding graphite bases 10, forming a complete three-layer sealed structure of graphite base 10, molten salt chamber 11, and graphite caps 9. Then, the sealed chamber 5 is closed and sealed. The heating and temperature control system 6 inside the sealed chamber 5 is activated, heating the inside of the sealed chamber 5 through a ring heater. Simultaneously, the temperature is monitored in real time by thermocouples within the chamber, raising the internal ambient temperature of the sealed chamber 5 to the preset experimental target temperature. This target temperature is higher than the melting point of the molten salt to be tested, and is around 300°C. ~800 Within the specified range. Once the thermocouple monitoring shows that the temperature has reached the experimental target temperature, the temperature is maintained constant through closed-loop control of the heating temperature control system 6, with a temperature control accuracy of ±1K.

[0053] First, the molten salt is heated to a melt, then the pouring operation is performed, and finally, the sealed cavity 5 is heated and kept at a constant temperature. During the heating process of the sealed cavity 5, the cavity is not opened, and the molten salt is heated synchronously with the cavity to the experimental target temperature.

[0054] This step enables the simultaneous loading and isothermal control of three molten salt samples of different thicknesses within the same sealed cavity 5 and at the same experimental target temperature. This provides three sets of test conditions with completely consistent initial states for subsequent continuous switching measurements, fundamentally eliminating the sample loading deviations and temperature fluctuations caused by repeated disassembly and assembly and multiple heating in traditional methods.

[0055] In this sealing operation, the magnetohydrodynamic seal 13 is located at the connection between the stepper motor 4 and the central rotating shaft 3. When the stepper motor 4 is not rotating, the magnetohydrodynamic seal 13 maintains the static seal of the sealing cavity 5, preventing external air from entering the cavity. The sealing cavity 5 remains sealed from the time the sample is loaded until all measurements are completed, and the cavity is not opened.

[0056] Step 2: Rotary wheel switching and multi-thickness continuous laser heating measurement;

[0057] Initial positioning: The stepper motor 4 drives the rotating wheel 1 to rotate via the central shaft 3, thus adjusting the thickness of the thin layer. The corresponding graphite crucible station 2a rotates to be directly below the laser incident window 7. Position sensor 12 is located at the connection between stepper motor 4 and central shaft 3, monitoring the rotational position of wheel 1 in real time; when position sensor 12 sends a feedback signal confirming the thin film thickness... When the corresponding graphite crucible station 2a is precisely aligned with the laser incident window 7, the stepper motor 4 stops rotating and locks its current position, with a repeatability accuracy better than 0.1mm. At this time, the laser pulse emitted by the pulsed laser can be perpendicularly incident through the laser incident window 7 onto the central area of ​​the upper surface of the graphite cover 9 at the current station.

[0058] First set of measurements: The output power of the pulsed laser is set to... , The value of is determined through pre-experimental calibration, corresponding to the thickness of the thin layer. To ensure that the laser energy density absorbed per unit volume of molten salt is within the optimal signal-to-noise ratio range, the laser pulse width is set to... The data acquisition system activates the high-speed infrared detector and sets the sampling rate to ≥ After the infrared detector begins sampling, a single laser pulse is emitted by the trigger laser. The laser pulse is perpendicularly incident through the laser incident window 7 onto the upper surface of the graphite cover 9 at the current workstation, forming a Gaussian spatially distributed laser heating source term on the upper surface of the graphite cover 9. The synchronously activated infrared detector is aligned with the upper surface of the graphite cover 9 through the infrared detector window 8, with a beam angle ≥ The sampling rate continuously records the transient temperature rise curve of the upper surface of the graphite cap 9. The acquisition window covers the entire process from the start of the laser pulse to the temperature dropping back to near the baseline temperature, thus obtaining the thickness of the thin layer. Transient temperature rise curve under operating conditions .

[0059] First Rotary Wheel Switching: After the thin-film working condition data is collected, the control system issues a switching command, and the stepper motor 4 drives the rotary wheel 1 to rotate via the central shaft 3. Position sensor 12 monitors the rotation angle in real time, including the thickness of the intermediate layer. Once the corresponding graphite crucible station 2b rotates to be directly below the laser incident window 7 and the position sensor 12 provides a precise positioning signal, the stepper motor 4 stops rotating and locks its position. The magnetohydrodynamic seal 13 maintains the seal of the sealed cavity 5 throughout the entire rotation of the central shaft 3 driven by the stepper motor 4, preventing external gas from entering the cavity. The rotation switching process takes 2-5 seconds. During this process, the heating and temperature control system 6 of the sealed cavity 5 continuously maintains a constant experimental target temperature, and the temperature of the molten salt samples at the three graphite crucible stations does not fluctuate with the switching operation.

[0060] Second set of measurements: The output power of the pulsed laser was set to... ,in ,and , satisfy The principle of approximate proportion is applied, meaning the laser power is approximately proportional to the thickness of the molten salt layer, so that the laser energy density absorbed per unit volume of molten salt is roughly the same for thin and medium-thick layers. The laser pulse width remains the same as in the first set of measurements. Value. The data acquisition system activates the high-speed infrared detector to begin sampling at the same sampling rate, triggering the pulsed laser to emit a single laser pulse (power). Pulse width Simultaneously record the transient temperature rise curve of the upper surface of the graphite cap 9 to obtain the thickness of the medium-thick layer. Transient temperature rise curve under operating conditions .

[0061] Second Rotor Switching: After the data acquisition for medium-thickness working conditions is completed, the control system issues another switching command, and stepper motor 4 drives rotor 1 to continue rotating. Position sensor 12 monitors in real time the thickness of the thick layer. Once the corresponding graphite crucible station 2c has rotated to a position directly below the laser incident window 7 and is precisely positioned, the stepper motor 4 stops rotating and locks its position. The magnetohydrodynamic seal 13 maintains the seal of the sealing cavity 5 throughout the entire rotation switching process.

[0062] Third set of measurements: The output power of the pulsed laser is set to... ,in ,and The principle of approximate proportion applies, meaning the laser power is approximately proportional to the thickness of the molten salt layer. The laser pulse width remains the same as that measured in the first and second groups. Value. The data acquisition system activates the high-speed infrared detector to begin sampling at the same sampling rate, triggering the pulsed laser to emit a single laser pulse (power). Pulse width Simultaneously record the transient temperature rise curve of the upper surface of the graphite cap 9 to obtain the thickness of the thick layer. Transient temperature rise curve under operating conditions .

[0063] This step involves using stepper motor 4 to drive wheel 1 to rotate precisely. Three graphite crucibles with different molten salt layer thicknesses were sequentially switched and positioned below the laser incident window 7 in the order of thin layer, medium-thick layer, and thick layer. Within a single sample loading cycle, without opening the sealed cavity 5, laser heating and temperature response data acquisition for the three thickness conditions were continuously completed, and three transient temperature rise curves were obtained. The power-thickness matching strategy ensures that the laser energy density absorbed per unit volume of molten salt is roughly the same under various thickness conditions, and ensures that the temperature response signal has a sufficient signal-to-noise ratio under various conditions.

[0064] Thin layer thickness Medium and thick layer thickness and thickness of the layer The corresponding graphite crucible stations 2a, 2b, and 2c are switched and positioned sequentially in the order of thin layer, medium-thick layer, and thick layer, with each rotation angle being [missing value]. The three workstations require two rotations to complete all measurements, with a total rotation angle of [missing value]. .

[0065] Step 3: Construct a forward problem model of a three-layer structure consisting of a graphite base, molten salt, and a graphite cap, including thickness parameters;

[0066] The computer numerical simulation system uses the finite volume method or the finite element method to numerically discretize and solve the governing equations on a discrete mesh. This step addresses the three molten salt layer thicknesses preset in step one. , , Corresponding forward problem models for radiation-conduction coupled heat transfer are established respectively.

[0067] Sub-step (3a): Establish the two-dimensional axisymmetric unsteady-state energy conservation equation:

[0068] In cylindrical coordinate system The following establishes a two-dimensional axisymmetric unsteady-state energy conservation equation, with the mathematical expression as follows:

[0069]

[0070] in, The density of the molten salt to be tested. The specific heat capacity of the molten salt to be tested is... The thermal conductivity to be inverted is For temperature field distribution, For time, The vector of radiative heat flux. For laser heating source items, It is a spatial differential operator.

[0071] Laser heating source It exhibits a Gaussian spatial distribution and is used to describe the laser energy input applied to the upper surface of the graphite layer of the sample. The energy conservation equation includes a thermal conductivity term. Radiative heat flux divergence term and laser heating source item .

[0072] Laser heating source The surface of the graphite cap 9 exhibits a Gaussian spatial distribution, and the energy conservation equation includes a heat conduction term. Radiative heat flux divergence term and laser heating source item .

[0073] Within the absorption layer of the graphite cap 9, the laser energy decays exponentially according to the Beer-Lambert law.

[0074] Sub-step (3b) solves the radiative transfer equation: for the radiative heat flux inside the molten salt translucent medium layer The radiative transfer equation is obtained by solving the radiative transfer equation. The discrete coordinate method (DOM) is used to solve the radiative transfer equation, and the spatial discretization order is adopted. The order and angle discretization scheme adopts the Carlson-Lathrop angular difference scheme. The molten salt medium is divided into two spectral bands: band 1 is... The weak absorption region has band 2. Strong absorption region. The radiative transfer equations are solved separately in the two spectral bands to obtain the radiative intensity field distribution in each band, and then the radiative heat flux vector is calculated. and its divergence .

[0075] Sub-step (3c) sets the Fresnel reflection boundary conditions at the interface: At the graphite-molten salt interface and the molten salt-graphite cap interface, the Fresnel reflection and refraction effects caused by the difference in refractive index between graphite and molten salt are considered. For radiation energy incident on the interface from the molten salt side, the refraction angle is calculated according to Snell's law, and the reflectivity and transmittance are calculated according to the Fresnel formula; for radiation energy incident on the interface from the graphite side, the same Fresnel reflection boundary conditions are applied. The radiation boundary conditions at the interface are solved in a coupled manner with the radiation intensity fields in the two spectral bands.

[0076] Sub-step (3d), forming the observation operator: with thin layer thickness Medium and thick layer thickness and thickness of the layer As the sole variable parameter, these parameters are substituted into the aforementioned energy conservation equation, radiative transfer equation, and interface Fresnel reflection boundary condition to construct three corresponding forward problem models. Except for the molten salt layer thickness parameter, the physical models, boundary conditions, material properties, and numerical discretization parameters are consistent across the three models. These three forward problem models are then organized into a set to form an observation operator encompassing the three thickness conditions. The observation operator Defined as: for any given parameter vector to be inverted Observation operator The forward problem models for the three thickness conditions are called respectively to perform calculations, and the predicted temperature rise data for the three thickness conditions are output. , , ;

[0077] This step establishes a forward problem model corresponding one-to-one with the three thickness experimental conditions in Step Two, ensuring that the differences in the three sets of temperature response data are uniquely attributed to the change in molten salt layer thickness. This provides a physically interpretable observation operator for the multi-thickness joint inversion in Step Four. .

[0078] Step 4: Construct a joint objective function for multiple thicknesses and solve it using the EKI algorithm; specifically including:

[0079] Sub-step (4a): Construct the normalized sum of squared residuals for each thickness condition: For the first... Thickness condition, defined by the observation operator under this condition. Calculated predicted temperature rise The transient temperature rise curve obtained from step two experiments Normalized residual sum of squares between The expression is:

[0080]

[0081] in, For the first The estimated standard deviation of the measurement noise under thickness conditions was obtained through multiple repeated measurements in a blank test (recording the infrared detector noise without laser pulses); For the first Number of time sampling points for thickness conditions; For the first Each sampling time; for thin-layer conditions, due to the relatively low signal-to-noise ratio... The estimated value is correspondingly greater than and For thick-layer applications, due to the large signal amplitude, The estimated value is correspondingly smaller than and .

[0082] Sub-step (4b): Constructing a joint objective function for multiple thicknesses: summing the normalized residuals squared for the three thickness conditions. , , We perform weighted summation to construct a joint objective function for multiple thicknesses. The expression is:

[0083]

[0084] in, The weighting coefficients for each thickness condition satisfy... The selection principle for the weighting coefficients is to ensure that the contributions of each thickness condition to the joint objective function are roughly balanced. In this embodiment, when the number of time sampling points for the three thickness conditions is... , , Approximately equal and the estimated standard deviation of the measurement noise , and When the difference is within one order of magnitude, take Equal weighting is performed; when the number of time sampling points or the signal-to-noise ratio differs significantly among different thickness conditions, adaptive weighting is applied based on the Fisher information content of each thickness condition. The weight coefficient is proportional to the information content of each thickness condition, giving higher weights to conditions with higher information content. The goal of multi-thickness joint inversion is to solve the following unconstrained optimization problem:

[0085]

[0086] Sub-step (4c): Constructing the joint sensitivity matrix: Before constructing the joint objective function for multiple thicknesses, first construct the temperature response vector of the parameters to be inverted under each thickness condition. Single thickness sensitivity matrix , , . No. Sensitivity matrix under thickness conditions Defined as A dimensional matrix, whose dimensional matrix is ​​the first dimensional matrix. Line number The column elements are the predicted temperature rise. Treating the inversion parameter vector Each component Partial derivatives:

[0087]

[0088] The calculation of the partial derivatives above uses the finite difference method, that is, applying a small perturbation to each parameter near the optimal parameter estimate and calling the observation operator accordingly. The predicted temperature rise after the disturbance is calculated, and the difference is used instead of the differential to obtain a numerical approximation of the sensitivity matrix.

[0089] At a single thickness, the three columns of the sensitivity matrix may exhibit a high degree of linear correlation, leading to an imbalance in the information matrix. The condition number is very large (approaching singular), making the inverse problem severely ill-posed. When different thicknesses are introduced... Subsequently, the sensitivity function exhibits different characteristics as a function of thickness:

[0090] As thickness increases, the heat diffusion path lengthens, and the temperature response increases. The sensitivity decay is relatively gradual, and the radiation weight increases in thicker layers. Its relative contribution to the total temperature rise decreases.

[0091] The light flux entering the molten salt layer is mainly affected by changing the Fresnel reflectivity of the interface. This effect is weakly related to the thickness but slightly increases with the increase of optical path length as the thickness accumulates.

[0092] The sensitivity increases exponentially with thickness; in thin layers, molten salt is nearly translucent. The changes in temperature response have a negligible effect; in thicker layers, radiative energy attenuates significantly within the molten salt layer. Changes in temperature distribution have a strong impact on temperature distribution.

[0093] Single thickness sensitivity matrix , , Vertically stitched into a multi-thickness joint sensitivity matrix :

[0094]

[0095] Obtain the joint sensitivity matrix Since the column spaces of the three sensitivity matrices are no longer collinear, the joint information matrix... The condition number is significantly reduced compared to a single thickness, thus effectively mitigating the ill-posedness of parameter inversion. This is the core mathematical theoretical foundation of the method in this application.

[0096] Sub-step (4d) uses the ensemble Kalman inversion algorithm to solve the problem: based on three transient temperature rise curves and the observation operator. The ensemble Kalman inversion (EKI) algorithm is used to solve the joint objective function for multiple thicknesses. The parameter vector that reaches the minimum value The specific execution flow of the EKI algorithm is as follows:

[0097] (4d-1) Stacked Joint Observation Vector: Transient temperature rise curves for three thickness conditions , , Stacked into joint observation vectors The mathematical expression is:

[0098]

[0099] (4d-2) Construct the noise covariance matrix: estimated from the standard deviation of the measured noise for each thickness condition. , , Construct the observation noise covariance matrix , An N×N dimensional diagonal matrix:

[0100]

[0101] in, for 3D identity matrix This indicates the construction of a block diagonal matrix with the elements within the parentheses as diagonal elements.

[0102] Each thickness channel in The relative weights in the algorithm are determined according to the weight selection principle in step 5. The variance of channels with lower signal-to-noise ratios is increased accordingly, so that the EKI update process fully inherits the multi-thickness weighted joint objective function structure of step 5: data mismatch functional. and Having the same weighted least squares form, EKI iteration is a set-based minimization process for this mismatch.

[0103] (4d-3) Initialize the particle set: Initialize the particle set within the parameter search space boundary. The parameter set of each particle , The range is 20 to 50. The boundary of the parameter search space is: , , , , . The initial sampling at It takes place within a uniformly distributed space. and Sampling is performed within their respective linearly uniform distribution spaces. The sampling method employs Latin hypercube sampling to ensure that the initial particles uniformly cover the entire parameter search space.

[0104] (4d-4) Prediction step: For the current th... Each particle in the set , Initially Call the observation operator The forward problem model was run for three different thickness conditions, resulting in three corresponding predicted temperature rise curves. These curves were then stacked into a joint prediction vector. . The prediction process for each particle is independent and is executed in parallel on the multi-core computing cluster.

[0105] (4d-5) Calculate set statistics: Calculate the mean of the parameter set. Predict the set mean Parameter-predicted cross-covariance matrix Predicting the autocovariance matrix .

[0106] (4d-6) Calculate the Kalman gain: Calculate the Kalman gain matrix In this method, matrix inversion is achieved by solving a system of linear equations after Cholesky decomposition, without explicitly inverting the matrix.

[0107] (4d-7) Update step: Apply a perturbation to the observations for each particle using the Kalman update, expressed as:

[0108]

[0109] in, is an independent and identically distributed Gaussian random perturbation vector.

[0110] (4d-8) Physical constraint projection: for each updated particle Perform a physical constraint projection to truncate particle components that exceed the boundary of the parameter search space back to the nearest boundary value. Specifically: if The amount exceeds If the range is defined, then truncate to the nearest boundary value; if The amount exceeds If the range is defined, then truncate to the nearest boundary value; if The amount exceeds If the range is limited, then truncate to the nearest boundary value. After truncation, The value is determined by the following: Obtained by taking the negative number.

[0111] (4d-9) Termination Condition Determination: Check whether one of the following termination conditions is met: ① Data mismatch is reduced to the measurement noise level, i.e. ,in ② The covariance of the set parameters shrinks to below a preset threshold; ③ The preset maximum number of iterations is reached. ,Pick If any termination condition is met, the iteration stops, and the mean of the last set is output. As the optimal inversion parameter vector If the condition is not met, return to sub-step (4d-4) to proceed to the next iteration.

[0112] When the data mismatch decreases to the level of measurement noise, that is... When the early stopping criterion is reached, the EKI algorithm terminates the iteration. This early stopping criterion is equivalent to applying iterative regularization to the ill-posed inverse problem, preventing the set from overfitting measurement noise, and is one of the mechanisms to suppress parameter multivalues.

[0113] This step uses a multi-thickness weighted least squares joint objective function. Data from three thickness conditions is fused using a joint sensitivity matrix. Positive complementarity reduces parameter crosstalk, and derivative-free, parallelizable global optimization is achieved through ensemble iteration of the EKI algorithm, ultimately obtaining the physically meaningful optimal inversion parameter vector. .

[0114] Step 5: Residual analysis, convergence diagnosis, and model validation;

[0115] The optimal inversion parameter vector obtained in step four Substitute the values ​​into the forward problem model for each thickness condition established in step three, and then execute the following sub-steps in sequence.

[0116] Sub-step (5a): Calculate the predicted temperature rise and residuals:

[0117] Will Substitute the thickness of the thin layer respectively Medium and thick layer thickness and thickness of the layer The corresponding positive problem model calls the observation operator. Calculate the predicted temperature rise under three thickness conditions. , , Then, the residual between the predicted temperature rise and the transient temperature rise curve measured in step two is calculated for each thickness condition:

[0118]

[0119] Sub-step (5b), residual statistical test:

[0120] Residual for each thickness condition Perform the following statistical tests:

[0121] (5b-1) Calculate the mean of the residuals If the value approaches 0, it indicates that there is no systematic bias in the prediction.

[0122] (5b-2) Calculate the standard deviation of the residuals Check whether it matches the estimated standard deviation of measurement noise in sub-step (4a). Consistent;

[0123] (5b-3) Calculate the autocorrelation function of the residuals and test that it is within the 95% confidence band, indicating that there are no unmodeled systematic components in the residuals;

[0124] (5b-4) Calculate the coefficient of determination ,in The average measured temperature rise under the j-th thickness condition is confirmed. A value close to 1 indicates a good fit.

[0125] Sub-step (5c), convergence diagnosis:

[0126] (5c-1) Plot the ensemble mean for each generation. Data mismatch at the location or objective function value The evolution curve confirms that the mismatch value decreases to the measurement noise level and tends to flatten out;

[0127] (5c-2) Plot the set mean Each component As the iterative algebra evolves, it is confirmed that each parameter has stabilized around a certain value.

[0128] (5c-3) Plot the decay curve of the standard deviation of the set parameters with the number of iterations. Confirm that the standard deviation continues to decrease and tends to be small, indicating that the set has collapsed and converged in the optimal parameter region.

[0129] (5c-4) Start the EKI algorithm with different random initial sets and run it independently 5 to 10 times. Calculate the relative deviation between the optimal inversion parameter vectors obtained from each run. If the relative deviation of the optimal solution between each run is less than 5%, the inversion results are considered consistent and the solution is repeatable. The relative deviation is calculated as follows: the absolute value of the difference between the optimal solution obtained from each run and the mean of the optimal solutions from multiple runs is divided by the mean, and the maximum value among the parameters is taken.

[0130] Sub-step (5d) and comparison verification with single-thickness inversion results:

[0131] (5d-1) Calculation of Condition Number Improvement Factor: Calculate the condition number improvement factor. For the three single-thickness working conditions, calculate the three... The minimum value among the possible values ​​is taken as a conservative estimate. When... When the value is greater than 1, it indicates that multi-thickness joint inversion improves ill-posedness compared to single-thickness inversion; The higher the value, the more significant the improvement.

[0132] (5d-2) Hessian matrix parameter decoupling analysis: Calculation of joint objective function for multiple thicknesses In the optimal inversion parameter vector Hessian matrix at the location The Hessian matrix is ​​a 3×3 symmetric matrix. The thermal conductivity is measured by inverting and normalizing the Hessian matrix, and then using the absolute value of the off-diagonal elements of the normalized inverse matrix. Refractive index and absorption coefficient The decrease in the absolute value of the off-diagonal element indicates that the multi-thickness joint inversion has suppressed parameter crosstalk.

[0133] Consistency verification of solution (5d-3): The optimal solution obtained by joint inversion of multiple thicknesses is... The optimal solution obtained by inversion with each individual thickness , , Compare them. If and The deviation is less than each The dispersion between them indicates that the multi-thickness joint inversion effectively integrates the information of each thickness.

[0134] This step verifies the effectiveness of the model and inversion results from the perspective of data fitting through residual statistical testing, confirms the stability and repeatability of the inversion process from the perspective of algorithm execution through convergence diagnosis, and verifies the superiority of multi-thickness joint inversion in reducing ill-posedness and suppressing parameter crosstalk from the perspective of quantitative indicators through comparison with single-thickness inversion results. The three-level verification together constitute a systematic evaluation of the reliability of the inversion results.

[0135] While this application has been described herein with reference to specific embodiments, it should be understood that these embodiments are merely examples of the principles and applications of this application. Therefore, it should be understood that many modifications can be made to the exemplary embodiments, and other arrangements can be designed without departing from the spirit and scope of this application as defined by the appended claims. It should be understood that different dependent claims and features described herein can be combined in ways different from those described in the original claims. It is also understood that features described in conjunction with individual embodiments can be used in other described embodiments.

Claims

1. A rotary multi-crucible switching experimental apparatus, characterized in that, include: Rotating wheel, central rotating shaft, stepper motor, sealed cavity, heating and temperature control system, laser incident window, infrared detector window, and position sensor; The rotating wheel rotates around the central rotating shaft, the central rotating shaft is connected to the stepper motor, and the stepper motor drives the rotating wheel to rotate through the central rotating shaft; Three graphite crucible stations are evenly distributed along the circumference of the rotating wheel. Each graphite crucible station has a three-layer structure consisting of a graphite bottom, a molten salt cavity, and a graphite cover. The depth of the molten salt cavity in each of the three graphite crucible stations is one of three different thickness values. The sealed cavity surrounds the rotating wheel, the heating and temperature control system is located inside the sealed cavity, and the laser incident window and the infrared detector window are located at the top of the sealed cavity; The position sensor is located at the connection between the stepper motor and the central rotating shaft, and is used to monitor the rotational position of the wheel.

2. The rotary multi-crucible switching experimental device according to claim 1, characterized in that, The device also includes a magnetohydrodynamic seal, which is disposed at the connection between the stepper motor and the central shaft, and is used to maintain the seal of the sealing cavity when the stepper motor drives the central shaft to rotate.

3. The method for inverting the high-temperature molten salt thermophysical property parameters based on the rotary multi-crucible switching device of claim 1, characterized in that, The method includes: Step 1: After heating the molten salt to be tested to a molten state, pour it into the molten salt chambers of the three graphite crucible stations respectively, controlling the pouring quality so that the molten salt level reaches the thickness of a thin layer. Medium and thick layer thickness and thickness of the layer The sealed cavity is heated to the target experimental temperature and maintained at a constant temperature. Step 2: Control the stepper motor to drive the rotating wheel to rotate, and switch the three graphite crucible stations to be positioned below the laser incident window. After positioning at each station, a pulsed laser is used for irradiation, and an infrared detector is simultaneously activated to record the transient temperature rise curve of the graphite cover surface, resulting in three transient temperature rise curves. The pulsed laser powers corresponding to the three stations are respectively... , and ,and ; Step 3: Regarding the thickness of the thin layer The thickness of the medium-thick layer and the thickness of the thick layer A radiation-conduction coupled heat transfer problem model of the three-layer structure is established respectively. The radiation transfer equation is solved by the discrete coordinate method. Fresnel reflection boundary conditions are set at the graphite-molten salt interface to form an observation operator with three thickness conditions. Step 4: Based on the observation operators and the three transient temperature rise curves for the three thickness conditions, construct a multi-thickness joint inversion objective function, and use the ensemble Kalman inversion algorithm to solve the multi-thickness joint inversion objective function to obtain the optimal inversion parameter vector; Step 5: Substitute the optimal inversion parameter vector into the radiation-conduction coupled heat transfer forward problem model for each thickness condition, calculate the residual between the predicted temperature rise and the transient temperature rise curve, and perform convergence diagnosis and model verification.

4. The method for inverting high-temperature molten salt thermophysical property parameters according to claim 3, characterized in that, In step two, the rotating wheel rotates 120° each time, and the thickness of the thin layer... The thickness of the medium-thick layer and the thickness of the thick layer The corresponding graphite crucible station is switched and positioned sequentially in the order of thin layer, medium-thick layer, and thick layer.

5. The method for inverting high-temperature molten salt thermophysical property parameters according to claim 3, characterized in that, The steps described in step two , and satisfy The approximate proportionality principle applies, where j = 1, 2, 3.

6. The method for inverting high-temperature molten salt thermophysical property parameters according to claim 3, characterized in that, The objective function for the multi-thickness joint inversion described in step four is: ； in, The weighting coefficients for each thickness condition satisfy... , For the first The predicted temperature response data calculated by the observation operator under the thickness condition. For the first Temperature response data obtained experimentally under thickness conditions For the first Estimated standard deviation of measurement noise under thickness conditions. For the first Number of time sampling points for thickness conditions Sampling time, The parameter vector to be inverted.

7. The method for inverting high-temperature molten salt thermophysical property parameters according to claim 2, characterized in that, The ensemble Kalman inversion algorithm described in step four includes: The three transient temperature rise curves are stacked into a joint observation vector. A parameter set containing multiple particles is initialized. In each iteration, the Kalman gain is constructed using the empirical covariance of the set to update the particles until the data mismatch is reduced to the measurement noise level or a preset termination condition is met. Then, the mean of the last set is output as the optimal inversion parameter vector.

8. The method for inverting high-temperature molten salt thermophysical property parameters according to claim 7, characterized in that, Constructing the parameter vector of temperature response under various thickness conditions Single thickness sensitivity matrix , , Then , , Vertical splicing for multi-thickness joint sensitivity The multi-thickness joint sensitivity matrix Used to construct the Kalman gain in each iteration of the ensemble Kalman inversion algorithm, guiding the allocation of correction amounts for each parameter to reduce thermal conductivity. Refractive index and absorption coefficient Parameter crosstalk between them.

9. The method for inverting high-temperature molten salt thermophysical property parameters according to claim 8, characterized in that, Step five also includes comparison and verification with the results of single-thickness inversion, including: Calculate the condition number improvement factor: ； in Represents the matrix condition number. For the first Single thickness sensitivity matrix under thickness conditions For the multi-thickness joint sensitivity matrix, when A value greater than 1 indicates that multi-thickness joint inversion improves ill-posedness compared to single-thickness inversion; Calculate the multi-thickness joint inversion objective function In the optimal inversion parameter vector Hessian matrix at the location The thermal conductivity is measured by inverting and normalizing the Hessian matrix, and then using the absolute value of the off-diagonal elements of the normalized inverse matrix. Refractive index and absorption coefficient The decrease in the absolute value of the off-diagonal element indicates that the multi-thickness joint inversion has suppressed parameter crosstalk.

10. The method for inverting high-temperature molten salt thermophysical property parameters according to claim 8, characterized in that, Step five also includes: The Kalman inversion algorithm is started with different random initial sets and run independently multiple times. The relative deviation between the optimal inversion parameter vectors obtained in each run is calculated. When the relative deviation is less than 5%, the inversion results are considered to be consistent.

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