A ring-shaped rod bundle fuel element flow-induced vibration test bench and a test method thereof

Abstract

An experimental rig for flow-induced vibration of an annular rod bundle fuel element and its experimental method are disclosed. Due to excessive Stokes number leading to inertial lag and significant settling velocity, the flow field cannot be followed, resulting in the inability to obtain a clear vortex shedding structure and instantaneous velocity field. Furthermore, the time correlation between helium pressure pulsation, piston phase, and fuel element vibration response cannot be synchronously acquired, leading to an unclear energy transfer mechanism for flow-induced vibration. The intermediate connecting cylinder of the experimental device is coaxially positioned between the first and second connecting end structures. The annular rod bundle fuel element is inserted through the intermediate connecting cylinder, with one end connected to the first connecting end structure and the other end connected to the second connecting end structure. A tracer particle injector and a helium gas supply source are connected to the annular rod bundle fuel element, and a laser source and a camera are respectively mounted on the annular rod bundle fuel element.

Description

Technical Field

[0001] This invention specifically relates to a test bench for flow-induced vibration of annular rod bundle fuel elements and its experimental method. Background Technology

[0002] The series of technical challenges in the simulation and experimental verification of the space nuclear reactor-Stirling power conversion system stem from the fact that existing numerical simulation theories, experimental platform hardware architectures, flow field optical measurement technologies, and multi-field coupling testing systems are all developed based on the traditional steady-state unidirectional flow and weak coupling conditions of water working fluid in nuclear power plants. This mismatch exists comprehensively, fundamentally, and systematically, and cannot be easily corrected, with the unique physical operating mechanism of this system in deep space scenarios, characterized by low-density compressible helium working fluid, high-frequency periodic reciprocating unsteady flow, complex local flow fields in the reactor core's annular rod bundles, and strong bidirectional coupling vibrations between the flow field and structure. Firstly, at the simulation level, conventional CFD tools rely on steady-state and quasi-steady-state conditions... The steady-state core assumption, abandoning the transient characteristics of the periodic compression and expansion alternating flow of helium in the core of the Stirling engine, cannot reproduce the drastic alternation of instantaneous pressure, density, and velocity of the fluid. It completely severs the dynamic coupling relationship between the flow field and the fuel element, making it impossible to accurately capture the real flow field structure and flow-induced vibration response. On the other hand, one-dimensional lumped parameter simulation simplifies the process by averaging parameters across the entire domain, sacrificing the local flow gradient, micro-vortices, and differentiated heat transfer details between the annular rod bundle fuel element gaps. It can only output macroscopic average parameters and cannot reproduce the real dynamic response of the system under non-design variable operating conditions. The underlying modeling logic of both mainstream simulation tools is strongly non-steady on the target system. The simulation results contradict the core characteristics of constant, refined local flow and multi-field bidirectional coupling, leading to significant discrepancies between simulation results and actual engineering conditions. Secondly, at the experimental platform level, existing nuclear power thermal engineering experimental platforms are designed based on high-density incompressible water working fluid and unidirectional steady-state flow. Their hardware structure, drive methods, and boundary conditions are only suitable for the steady-state operation of traditional pressurized water reactors, completely unable to adapt to the dynamic coupling working mode of helium working fluid and piston reciprocating drive. They cannot reproduce the coupled working scenario of the core annular rod bundle and Stirling power system, nor do they have an experimental support system suitable for low-density helium media. This misalignment of the platform's original design system renders modification and optimization impossible; there are no regulations... The physical bottleneck of the system lies in the inherent physical limitations of helium working medium. Helium, the heat exchange and work medium required by the system, has inherent characteristics of low density and near-vacuum refractive index. Under typical operating conditions, the extremely low fluid density forms an order of magnitude density difference with conventional tracer particles, causing the Stokes number of traditional PIV tracer particles to be seriously exceeded. This results in flow inertial lag and gravity settling problems, making it impossible to follow the high-frequency reciprocating flow field. At the same time, the extremely low refractive index of helium leads to weak laser scattering signals and blurred imaging, completely losing the conditions for observing the flow field parameters of instantaneous velocity field and vortex shedding structure. Moreover, this contradiction in physical properties is an inherent physical property of the medium and cannot be solved by conventional equipment optimization and parameter adjustment.Finally, at the level of multi-field mechanism research, existing testing technologies employ a decentralized testing mode with independent acquisition of each parameter, lacking a unified time-based synchronous triggering acquisition system. This makes it impossible to achieve millisecond-level precise timing matching of the three core coupled parameters: helium pressure pulsation, Stirling piston motion phase, and fuel element structural vibration response. It is difficult to clarify the energy transfer timing and coupling correlation between multiple physical fields, ultimately leading to the inability to analyze and verify the core mechanism of flow-induced vibration energy transfer. All technical problems are not caused by single equipment defects or algorithm errors, but rather by the fundamental technological gap between the traditional steady-state nuclear power technology system and the special deep-space dynamic characteristics of the space nuclear Stirling system, including unsteady alternating flow, low-density compressible working fluid, strong multi-field coupled vibration, and multi-parameter timing correlation. This represents a systemic incompatibility across the entire chain of theoretical models, experimental hardware, optical diagnostics, and coupled testing technologies, thus forming a complex fundamental technical challenge that is currently difficult to overcome in the field.

[0003] In summary, due to the excessive Stokes number leading to inertial lag and significant settling velocity that cannot follow the flow field, the extremely weak scattering signal causing blurred imaging under laser sheet light, and the inability to obtain clear vortex shedding structures and instantaneous velocity fields, as well as the inability to synchronously acquire the time correlation between helium pressure pulsation, piston phase, and fuel element vibration response during the experiment, the energy transfer mechanism of flow-induced vibration remains unclear. There is no corresponding standardized and precise processing structure or method. Summary of the Invention

[0004] To overcome the shortcomings of existing technologies, a test bench for flow-induced vibration of annular rod bundle fuel elements and its experimental method are provided to solve the above problems.

[0005] An experimental apparatus for flow-induced vibration of a Stirling annular rod bundle fuel element includes a first connecting end structure, an intermediate connecting cylinder, a second connecting end structure, an annular rod bundle fuel element, a tracer particle injector, a helium gas supply source, a laser source, and a camera. The first connecting end structure and the second connecting end structure are coaxially opposite each other, and the intermediate connecting cylinder is coaxially disposed between the first connecting end structure and the second connecting end structure. The middle part of the annular rod bundle fuel element passes through the intermediate connecting cylinder, one end of the annular rod bundle fuel element is connected to the first connecting end structure, and the other end of the annular rod bundle fuel element is connected to the second connecting end structure.

[0006] The first connecting end structure includes a left cylinder, a left piston rod, and a first motor. The inner cavity of the left cylinder is a hot cavity. One end of the left piston rod is located in the hot cavity, and the other end of the left piston rod is connected to the first motor. The left piston rod slides back and forth along the length of the hot cavity under the drive of the first motor. The left cylinder is connected to the end of the nearby annular rod bundle fuel element.

[0007] The second connecting end structure includes a right cylinder, a right piston rod, and a second motor. The inner cavity of the right cylinder is a cold cavity. One end of the right piston rod is located in the cold cavity, and the other end of the right piston rod is connected to the second motor. The right piston rod slides back and forth along the length of the cold cavity under the drive of the second motor. The right cylinder is connected to the end of the nearby annular rod bundle fuel element.

[0008] The annular rod bundle fuel element is connected to a tracer particle injector and a helium gas supply source. A laser source and a camera are respectively installed on the outer wall of the annular rod bundle fuel element. The emitting end of the laser source is facing the annular rod bundle fuel element, and the imaging end of the camera is facing the annular rod bundle fuel element.

[0009] As a preferred embodiment, the system further includes a meshing transmission assembly, which comprises a main drive rod, two bevel gears, and two flywheels. A bevel gear is disposed at each end of the main drive rod. One end of the main drive rod is connected to a first connecting end structure via one of the two bevel gears, and the other end of the main drive rod is connected to a second connecting end structure via the other of the two bevel gears. Each bevel gear includes a primary gear and a secondary gear, which mesh with each other. Two flywheels are mounted on the main drive rod, with each flywheel corresponding to a bevel gear and positioned close to its corresponding bevel gear. A tachometer is also provided on the meshing transmission assembly.

[0010] As a preferred embodiment: an angle sensor and a hot-wire anemometer are installed on the outer wall of the left cylinder; the helium supply source is connected to the annular rod bundle fuel element through a supply pipeline, an acceleration sensor is installed on the outer wall of the annular rod bundle fuel element, and a pressure sensor is installed on the supply pipeline.

[0011] As a preferred embodiment: a transition flange is provided at each end of the intermediate connecting cylinder, and a first exhaust valve is provided on each transition flange. The annular rod bundle fuel element is detachably connected to the intermediate connecting cylinder through the two transition flanges. A fixing plate is fitted on the outer wall of each end of the intermediate connecting cylinder, and a connecting flange is provided on each fixing plate. Each fixing plate is detachably connected to the outer wall of the intermediate connecting cylinder through its corresponding connecting flange, and a second exhaust valve is provided on each connecting flange.

[0012] As a preferred embodiment, the intermediate connecting cylinder is equipped with multiple positioning grids, which are circular plates with circular positioning holes. The multiple positioning grids are arranged on the inner wall of the intermediate connecting cylinder along the axial direction of the intermediate connecting cylinder. The inner wall of each positioning grid is close to the outer wall of the annular rod bundle fuel element, and the outer wall of each positioning grid is close to the inner wall of the intermediate connecting cylinder.

[0013] As a preferred option: the cold cavity is connected to a cooling circuit, and a coolant is installed in the cooling circuit.

[0014] A method for testing the flow-induced vibration of a Stirling annular rod bundle fuel element, implemented using the aforementioned Stirling annular rod bundle fuel element flow-induced vibration testing apparatus, includes the following steps:

[0015] Step 1: Open the first vent valve of each transition flange and the second vent valve of the connecting flange, and simultaneously open the helium supply source. The helium supplied by the helium supply source fills the sealed channel formed between the hot cavity of the first connecting end structure, the interior of the intermediate connecting cylinder, and the cold cavity of the second connecting end structure. The pressure of the sealed channel is monitored by a pressure sensor. When the pressure sensor detects that the pressure value in the sealed channel remains stable at the preset value for 60-120 seconds, it indicates that the helium filling in the sealed channel is complete and the airtightness of the sealed channel is good. Then, close the first vent valve and the second vent valve to maintain the initial pressure of the sealed channel in a continuously stable state.

[0016] Step 2: Start the meshing transmission assembly. The meshing transmission assembly synchronously drives the left and right piston rods. Adjust the tachometer and angle sensor to ensure that the Stirling cycle frequency between the first connecting end structure, the intermediate connecting cylinder, the second connecting end structure, and the annular rod bundle fuel element remains at the target operating condition within a predetermined stable time. Turn on the cooling circuit to ensure that the temperature difference between the left and right cylinders is at the predetermined temperature difference requirement, establishing the basic dynamic conditions for helium reciprocating flow. At the same time, turn on the hot-wire anemometer main unit, tracer particle injector, laser source, camera, and acceleration sensor to complete the preheating and parameter calibration process between the first connecting end structure, the intermediate connecting cylinder, the second connecting end structure, and the annular rod bundle fuel element.

[0017] Step 3: After the Stirling cycle and helium reciprocating flow field between the first connecting end structure, the intermediate connecting cylinder, the second connecting end structure, and the annular rod bundle fuel element stabilizes, silicon-based aerogel microsphere tracer particles are injected into the intermediate connecting cylinder through a tracer particle injector. The silicon-based aerogel microsphere tracer particles enter the interior of the annular rod bundle fuel element and the gap between the annular rod bundle fuel element and the intermediate connecting cylinder with the helium. Then, a laser source is turned on to form sheet illumination, and a camera continuously captures images of the tracer particle motion and the vibration displacement of the annular rod bundle fuel element. Based on the image frame sequence acquired by the camera, the instantaneous flow velocity, vortex shedding structure, and vibration displacement, amplitude, and frequency of the annular rod bundle fuel element are calculated. At the same time, the vibration acceleration signal of the annular rod bundle fuel element under helium pressure pulsation and vortex shedding excitation is collected by an accelerometer, and the phase data of the left piston rod in the left cylinder is obtained by an angle sensor, thereby completing the flow field-vibration response correlation measurement process based on the high-speed image frame sequence and piston phase reference.

[0018] Step 4: By adjusting the speed of the first motor to change the Stirling cycle frequency or by adjusting the initial pressure of the sealed channel through the helium gas supply, the debugging and measurement process of multiple working conditions is completed; observe and record the synchronous data of the pressure sensor, hot-wire anemometer host, accelerometer and camera, calculate the vibration displacement, amplitude and frequency of the fuel element, post-process the PIV flow field image to obtain the characteristic data of the velocity distribution and vortex shedding frequency of the helium reciprocating flow, and finally combine the flow field and vibration data to analyze the flow-induced vibration mechanism of the annular rod bundle fuel element under helium working medium.

[0019] As a preferred option: In the fourth step, when calculating the vibration displacement and flow field characteristics of the fuel element, the PIV velocity field calculated based on the synchronously acquired pressure pulsations and camera image sequences, as well as the vibration response data verified by the accelerometer, is used to calculate the flow-induced vibration characteristic parameters according to the following semi-empirical formula, in order to replace or verify the conventional data processing process. The calculation formula is as follows:

[0020] ;

[0021] In the above formula, This represents the amplitude of the lateral excitation force. The equivalent drag coefficient for reciprocating flow ranges from 0.05 to 0.2. The density of helium; The projected area of ​​the rod facing the airflow; The Stirling cycle frequency is obtained by measurement using a tachometer; This refers to the scavenging volume of a single cylinder; This represents the total cross-sectional area of ​​the flow channel; The length of the annular rod bundle fuel element; The hydraulic diameter; This is the end-effect correction factor, with a value ranging from 0.3 to 0.5; The piston phase angle measured by the angle sensor; This is the initial phase offset;

[0022] After calculating the flow-induced vibration characteristic parameters, the flow field-vibration phase difference and energy transfer efficiency are determined. The corresponding calculation formulas are as follows:

[0023] ;

[0024] In the above formula, The efficiency of converting fluid kinetic energy into vibrational energy; This is the coupling coefficient, with a value ranging from 0.1 to 0.3. The amplitude of helium velocity measured by PIV; The mass of a single fuel rod; ω = , The relaxation time of the vibration system; , The phase difference between the vibration acceleration and the pressure pulsation, which are measured synchronously by the accelerometer and the pressure sensor;

[0025] The unsteady model formula for the instantaneous flow distribution in the inner and outer channels of the annular rod bundle is as follows:

[0026] ;

[0027] In the above formula, The instantaneous volumetric flow rate of the internal flow channel; D is the instantaneous volumetric flow rate of the external flow channel. in D out D is the hydraulic diameter of the internal flow channel. out The hydraulic diameter of the outer flow channel; These are the friction coefficient, length, and local resistance coefficient, respectively. A pulsation coefficient is assigned to the oscillating flow, with a value ranging from 0.1 to 0.3, and is calibrated by integrating the PIV velocity field. The hysteresis angle is relative to the piston phase.

[0028] The compressibility correction formula for PIV velocity measurement is:

[0029]

[0030] In the above formula, Particle velocities calculated directly for PIV; This is the corrected actual speed; The compressibility sensitivity coefficient is calibrated by synchronous comparison between the hot-wire anemometer main unit and the PIV, with a value range of 0.4~0.6; The local pressure pulsation measured by the pressure sensor; Ma = average pressure; / c is the Mach number, and c is the speed of sound of helium. =1.67, The specific heat ratio of helium;

[0031] coefficient The calibration process involves simultaneously acquiring data from angle sensors, pressure sensors, the hot-wire anemometer main unit, the accelerometer, and the PIV under at least five different Stirling frequencies and loop pressure conditions. The least squares fitting formula is used to ensure that the relative deviation between the theoretical calculation and the measured values ​​is less than 5%. The calibration is then performed by inversely calculating the vibration response. Get , This is the amplitude of the accelerometer sensor. Estimated from measured vibration energy and fluid dynamic pressure; The instantaneous velocity measured by PIV is obtained by integrating along the flow channel; The anemometer readings are obtained from the hot-wire anemometer unit. The coefficients are updated using least-squares fitting to define the relative deviation. The corresponding calculation process is as follows:

[0032] ;

[0033] ;

[0034] ;

[0035] ;

[0036] In the above formula, The formula for calculating the amplitude of the transverse excitation force of the reciprocating flow is used. The actual excitation force is inferred from the maximum vibration acceleration measured by the accelerometer. This serves as an indicator of the accuracy of the reciprocating excitation force formula and is used to evaluate and verify the equivalent drag coefficient of the reciprocating flow. And the calibration accuracy of the end correction factor α; The efficiency is obtained in one cycle from the formula relating the flow field-vibration phase difference to the energy transfer efficiency. The efficiency is estimated by the ratio of measured vibration energy to the characteristic quantity of fluid dynamic pressure. Vibration energy is obtained by integrating the acceleration signal to calculate velocity, and the characteristic quantity of fluid dynamic pressure is obtained by... Quantitative acquisition; The unsteady model formula for the instantaneous flow distribution in the inner and outer channels of the annular rod bundle fuel element is obtained; The instantaneous velocities of the annular fuel element bundle to the inner flow channel region and the central hole of the rod are measured using a PIV (Portable Variable Induction) system with a camera and a laser source, respectively. It can also measure the instantaneous velocity of the gap between the annular fuel element bundle and the intermediate connecting cylinder. The measured flow rate ratio is then obtained by integrating the cross-sectional area. Obtained from the compressibility correction formula of PIV velocity measurement; The instantaneous true velocity of helium gas, directly measured by a hot-wire anemometer; This indicates that the PIV velocity after compressibility correction is highly consistent with the independent measurement results of the hot-wire anemometer, thus verifying the accuracy of the compressibility sensitivity coefficient ε.

[0037] As a preferred approach: utilize the phase difference in the formula relating the flow field-vibration phase difference to energy transfer efficiency. Assessing resonance risk, when When the value is 0∘, 90∘, or 180∘, the Stirling frequency or piston phase data is adjusted according to the change in energy transfer efficiency to ensure that the flow-induced vibration of the Stirling annular rod bundle fuel element is in the predetermined state.

[0038] As a preferred option, the process also includes using the compressibility correction formula of PIV velocity measurement to correct the PIV velocity field point by point. After obtaining the corrected true velocity field of helium, the corrected velocity field is substituted back into the formula for the amplitude of the transverse excitation force and the unsteady model formula for the instantaneous flow distribution of the inner and outer channels of the annular rod bundle for iterative calculation until the change is less than 1%.

[0039] The beneficial effects of this invention are as follows:

[0040] The Stirling annular rod bundle fuel element flow-induced vibration experimental device of this invention, through the coordinated operation of a first connecting end structure, an intermediate connecting cylinder, a second connecting end structure, an annular rod bundle fuel element, a tracer particle injector, a helium gas supply source, a laser source, and a camera, can accurately simulate the flow-vibration coupling relationship and reveal the flow-induced vibration mechanism of the annular rod bundle fuel element under helium working fluid. The operation process is standardized and simplified, and it can achieve simultaneous measurement of the helium reciprocating flow field and the vibration response of the fuel element. The Stirling annular rod bundle fuel element flow-induced vibration experimental device of this invention can overcome the shortcomings of CFD and one-dimensional simulation, providing realistic local flow field and vibration calibration parameters for one-dimensional simulation programs through experimental data, thereby improving their analytical accuracy.

[0041] The Stirling annular rod bundle fuel element flow-induced vibration stabilization experimental method in this invention is a standardized and precise experimental method achieved solely through the Stirling annular rod bundle fuel element flow-induced vibration experimental device of this invention. It employs silicon-based aerogel microsphere tracer technology adapted to helium working fluid, and achieves undisturbed flow field measurement through a complete four-step process. Simultaneously, it detects flow field-vibration coupling data, using a camera to continuously capture images of tracer particle motion and fuel element vibration displacement. This allows for the acquisition of flow field velocity information and fuel element vibration displacement information within the same image frame sequence, reducing time alignment errors between different measurement devices. By combining piston phase data obtained from an angle sensor, pressure pulsation data obtained from a pressure sensor, and vibration verification data obtained from an acceleration sensor, a phase correlation relationship is established between the helium reciprocating flow field, piston phase, pressure pulsation, and fuel element vibration response, providing a standardized and accurate guidance process for related experiments. Attached Figure Description

[0042] Figure 1 A schematic diagram of the front view of the experimental setup for the flow-induced vibration of Stirling annular rod bundle fuel element;

[0043] Figure 2 This is a schematic diagram of the main view structure of the first connected end structure;

[0044] In the diagram, 1-First connecting end structure; 1-1-Left cylinder; 1-2-Left piston rod; 1-3-First motor; 2-Intermediate connecting cylinder; 3-Second connecting end structure; 3-1-Right cylinder; 3-2-Right piston rod; 3-3-Second motor; 4-Annular rod bundle fuel element; 5-Tracer particle injector; 6-Helium gas supply source; 7-Laser source; 8-Camera; 9-1-Main drive rod; 9-2-Bevel gear; 9-3-Flywheel; 10-Tachometer; 11-Angle sensor; 12-Gas supply pipeline; 13-Pressure sensor; 14-Transition flange; 15-Fixing plate; 16-Connecting flange; 17-Positioning grid; 18-Hot-wire anemometer main unit; 19-Acceleration sensor. Detailed Implementation

[0045] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention.

[0046] Specific implementation method one: Combining Figure 1 and Figure 2 This embodiment describes a Stirling annular rod bundle fuel element flow-induced vibration experimental device comprising a first connecting end structure 1, an intermediate connecting cylinder 2, a second connecting end structure 3, an annular rod bundle fuel element 4, a tracer particle injector 5, a helium gas supply source 6, a laser source 7, and a camera 8. The first connecting end structure 1 and the second connecting end structure 3 are coaxially opposite each other, and the intermediate connecting cylinder 2 is coaxially disposed between the first connecting end structure 1 and the second connecting end structure 3. The middle part of the annular rod bundle fuel element 4 passes through the intermediate connecting cylinder 2, one end of the annular rod bundle fuel element 4 is connected to the first connecting end structure 1, and the other end of the annular rod bundle fuel element 4 is connected to the second connecting end structure 3.

[0047] The first connecting end structure 1 includes a left cylinder 1-1, a left piston rod 1-2, and a first motor 1-3. The inner cavity of the left cylinder 1-1 is a hot cavity. One end of the left piston rod 1-2 is located in the hot cavity, and the other end of the left piston rod 1-2 is connected to the first motor 1-3. The left piston rod 1-2 slides back and forth along the length of the hot cavity under the drive of the first motor 1-3. The left cylinder 1-1 is connected to the end of the nearby annular rod bundle fuel element 4.

[0048] The second connecting end structure 3 includes a right cylinder 3-1, a right piston rod 3-2, and a second motor 3-3. The inner cavity of the right cylinder 3-1 is a cold cavity. One end of the right piston rod 3-2 is located in the cold cavity, and the other end of the right piston rod 3-2 is connected to the second motor 3-3. The right piston rod 3-2 slides back and forth along the length direction of the cold cavity under the drive of the second motor 3-3. The right cylinder 3-1 is connected to the end of the nearby annular rod bundle fuel element 4.

[0049] The annular rod bundle fuel element 4 is connected to a tracer particle injector 5 and a helium gas supply source 6. A laser source 7 and a camera 8 are respectively installed on the outer wall of the annular rod bundle fuel element 4. The emission end of the laser source 7 is facing the annular rod bundle fuel element 4. The camera 8 is an existing high-speed camera device, and its working principle is the same as that of existing high-speed camera devices. Specifically, it can be a high-speed camera or a high-speed video camera. The camera end of the camera 8 is facing the annular rod bundle fuel element 4.

[0050] Camera 8 is a data acquisition device for realizing time correlation analysis. The configuration of camera 8 in this experimental setup can complete the same-frame / phase correlation analysis of the flow field and the vibration response of the fuel element through continuous frame images and frame time information.

[0051] Specific Implementation Method Two: This implementation method is a further limitation of Specific Implementation Method One. This implementation method also includes a meshing transmission assembly, which includes a main transmission rod 9-1, two bevel gears 9-2, and two flywheels 9-3. A bevel gear 9-2 is respectively provided at both ends of the main transmission rod 9-1. One end of the main transmission rod 9-1 is connected to the first connecting end structure 1 through one of the two bevel gears 9-2, and the other end of the main transmission rod 9-1 is connected to the second connecting end structure 3 through the other of the two bevel gears 9-2. Each bevel gear 9-2 includes a main gear and a secondary gear, which are meshed together. Two flywheels 9-3 are mounted on the main transmission rod 9-1, and each flywheel 9-3 is positioned close to its corresponding bevel gear 9-2. A tachometer 10 is also provided on the meshing transmission assembly.

[0052] Specific Implementation Method 3: This implementation method is a further limitation of Specific Implementation Method 1 or 2. In this implementation method, an angle sensor 11 and a hot-wire anemometer host 18 are provided on the outer wall of the left cylinder 1-1; the helium gas supply source 6 is connected to the annular rod bundle fuel element 4 through the gas supply pipeline 12, the annular rod bundle fuel element 4 is provided with an acceleration sensor 19 on the outer wall, and the gas supply pipeline 12 is provided with a pressure sensor 13.

[0053] In this embodiment, the angle sensor 11 is used to acquire piston phase data, the pressure sensor 13 is used to acquire helium pressure pulsation data, and the acceleration sensor 19 is used to verify the vibration displacement, amplitude, and frequency of the annular rod bundle fuel element calculated from the image sequence of the camera 8.

[0054] Specific Implementation Method Four: This implementation method is a further limitation of Specific Implementation Method One, Two or Three. In this implementation method, a transition flange 14 is provided at each end of the intermediate connecting cylinder 2. A first exhaust valve is provided on each transition flange 14. The annular rod bundle fuel element 4 is detachably connected to the intermediate connecting cylinder 2 through the two transition flanges 14. A fixing plate 15 is fitted on the outer wall of each end of the intermediate connecting cylinder 2. A connecting flange 16 is provided on each fixing plate 15. Each fixing plate 15 is detachably connected to the outer wall of the intermediate connecting cylinder 2 through its corresponding connecting flange 16. A second exhaust valve is provided on each connecting flange 16.

[0055] In this embodiment, the end of the annular rod bundle fuel element 4 that cooperates with the second connecting end structure 3 is provided with a spring telescopic section, which is an axial elastic compensation structure for the spring telescopic section. The optimal configuration position of the spring telescopic section is between the fixed plate 15 and the right cylinder 3-1, which is used to absorb axial thermal deformation and assembly errors.

[0056] Specific Implementation Method 5: This implementation method is a further limitation of Specific Implementation Methods 1, 2, 3 or 4. In this implementation method, the intermediate connecting cylinder 2 is equipped with multiple positioning grids 17. The positioning grids 17 are circular plates with circular positioning holes. The multiple positioning grids 17 are arranged on the inner wall of the intermediate connecting cylinder 2 along the axial direction. The inner wall of each positioning grid 17 is close to the outer wall of the annular rod bundle fuel element 4, and the outer wall of each positioning grid 17 is close to the inner wall of the intermediate connecting cylinder 2.

[0057] Specific Implementation Method Six: This implementation method is a further limitation of Specific Implementation Method One, Two, Three, Four or Five. In this implementation method, the cold cavity is connected to a cooling circuit, and a coolant is provided in the cooling circuit.

[0058] Specific implementation method seven: Combining Figure 1 and Figure 2This embodiment describes a Stirling annular rod bundle fuel element flow-induced vibration stabilization experimental method based on a Stirling annular rod bundle fuel element flow-induced vibration experimental device. This device includes a first connecting end structure 1, an intermediate connecting cylinder 2, a second connecting end structure 3, an annular rod bundle fuel element 4, a tracer particle injector 5, a helium gas supply source 6, a laser source 7, a camera 8, a meshing transmission assembly, an angle sensor 11, and a hot-wire anemometer host 18. The first connecting end structure 1 and the second connecting end structure 3 are coaxially opposite each other. The intermediate connecting cylinder 2 is coaxially positioned between the first connecting end structure 1 and the second connecting end structure 3. The middle portion of the annular rod bundle fuel element 4 passes through the intermediate connecting cylinder 2. One end of the annular rod bundle fuel element 4 is connected to the first connecting end structure 1, and the other end is connected to the second connecting end structure 3.

[0059] The first connecting end structure 1 includes a left cylinder 1-1, a left piston rod 1-2, and a first motor 1-3. The inner cavity of the left cylinder 1-1 is a hot cavity. One end of the left piston rod 1-2 is located in the hot cavity, and the other end of the left piston rod 1-2 is connected to the first motor 1-3. The left piston rod 1-2 slides back and forth along the length of the hot cavity under the drive of the first motor 1-3. The left cylinder 1-1 is connected to the end of the nearby annular rod bundle fuel element 4.

[0060] The second connecting end structure 3 includes a right cylinder 3-1, a right piston rod 3-2, and a second motor 3-3. The inner cavity of the right cylinder 3-1 is a cold cavity. One end of the right piston rod 3-2 is located in the cold cavity, and the other end of the right piston rod 3-2 is connected to the second motor 3-3. The right piston rod 3-2 slides back and forth along the length of the cold cavity under the drive of the second motor 3-3. The right cylinder 3-1 is connected to the end of the nearby annular rod bundle fuel element 4. The cold cavity is connected to a cooling circuit, and a coolant is provided in the cooling circuit.

[0061] Furthermore, a transition flange 14 is provided at each end of the intermediate connecting cylinder 2, and a first exhaust valve is provided on each transition flange 14. The annular rod bundle fuel element 4 is detachably connected to the intermediate connecting cylinder 2 through the two transition flanges 14. A fixing plate 15 is fitted on the outer wall of each end of the intermediate connecting cylinder 2, and a connecting flange 16 is provided on each fixing plate 15. Each fixing plate 15 is detachably connected to the outer wall of the intermediate connecting cylinder 2 through its corresponding connecting flange 16, and a second exhaust valve is provided on each connecting flange 16.

[0062] The annular rod bundle fuel element 4 is connected to a tracer particle injector 5, and a helium gas supply source 6 is connected to the annular rod bundle fuel element 4. A laser source 7 and a camera 8 are respectively arranged on the outer wall of the annular rod bundle fuel element 4. The emission end of the laser source 7 is set towards the annular rod bundle fuel element 4, and the imaging end of the camera 8 is set towards the annular rod bundle fuel element 4.

[0063] The meshing transmission assembly includes a main transmission rod 9-1, two bevel gears 9-2, and two flywheels 9-3. A bevel gear 9-2 is provided at each end of the main transmission rod 9-1. One end of the main transmission rod 9-1 is connected to the first connecting end structure 1 via one of the two bevel gears 9-2, and the other end of the main transmission rod 9-1 is connected to the second connecting end structure 3 via the other of the two bevel gears 9-2. Each bevel gear 9-2 includes a main gear and a secondary gear, which are meshed together. Two flywheels 9-3 are mounted on the main transmission rod 9-1, with each flywheel 9-3 corresponding to a bevel gear 9-2. Each flywheel 9-3 is positioned close to its corresponding bevel gear 9-2. A tachometer 10 is also provided on the meshing transmission assembly.

[0064] In a specific configuration, the main drive rod 9-1 can be a crankshaft. The motor output shaft and the horizontal crankshaft are connected by a pair of meshing bevel gears 9-2. The bevel gears 9-2 are used to convert the vertical rotational motion of the corresponding motor by 90° into the horizontal rotational motion of the horizontal crankshaft. The horizontal crankshaft is arranged parallel to the bottom of the test section pipeline. An eccentric crank is integrated on the crankshaft, which drives the left and right pistons to perform horizontal reciprocating motion through the connecting rod, so as to realize the reciprocating oscillation of helium gas in the flow channel of the annular rod bundle fuel element. A flywheel 9-3 is coaxially installed at the power input end of the horizontal crankshaft to stabilize the crankshaft speed, counteract the piston dead point impact, and ensure the stability of the oscillating flow condition.

[0065] Helium gas supply source 6 is connected to annular rod bundle fuel element 4 through gas supply pipeline 12. An acceleration sensor 19 is installed on the outer wall of annular rod bundle fuel element 4, and a pressure sensor 13 is installed on gas supply pipeline 12.

[0066] The intermediate connecting cylinder 2 is equipped with multiple positioning grids 17. Each positioning grid 17 is a circular plate with a circular positioning hole. The multiple positioning grids 17 are arranged on the inner wall of the intermediate connecting cylinder 2 along the axial direction. The inner wall of each positioning grid 17 is close to the outer wall of the annular rod bundle fuel element 4, and the outer wall of each positioning grid 17 is close to the inner wall of the intermediate connecting cylinder 2.

[0067] The Stirling annular rod bundle fuel element flow-induced vibration stabilization experiment method in this embodiment involves the coordinated operation of the first connecting end structure 1, the intermediate connecting cylinder 2, the second connecting end structure 3, the annular rod bundle fuel element 4, the tracer particle injector 5, the helium gas supply source 6, the laser source 7, the camera 8, the meshing transmission assembly, the angle sensor 11, the pressure sensor 13, the hot-wire anemometer host 18, and the acceleration sensor 19 to acquire tracer particle motion images, instantaneous flow velocity of the helium reciprocating flow field, flow field data of the vortex shedding structure, and vibration acceleration signals and phase data of the annular rod bundle fuel element under helium pressure pulsation and vortex shedding excitation. The obtained tracer particle motion images, instantaneous flow velocity of the helium reciprocating flow field, flow field data of the vortex shedding structure, and vibration acceleration signals and phase data of the annular rod bundle fuel element under helium pressure pulsation and vortex shedding excitation are used to perform related calculations to complete the time synchronization experiment of the flow field and vibration response, ensuring that the flow-induced vibration of the Stirling annular rod bundle fuel element remains in a predetermined dynamic stable state throughout the entire experiment.

[0068] The experimental method for stabilizing flow-induced vibrations of Stirling annular rod bundle fuel elements includes the following specific steps:

[0069] Step 1: Preparation and formation of the sealed channel. While opening the first exhaust valve of each transition flange 14 and the second exhaust valve of the connecting flange 16, the helium supply source 6 is opened. The helium supplied by the helium supply source 6 fills the sealed channel formed between the hot cavity of the first connecting end structure 1, the interior of the intermediate connecting cylinder 2, and the cold cavity of the second connecting end structure 3. The pressure of the sealed channel is monitored by the pressure sensor 13. When the pressure sensor 13 detects that the pressure value in the sealed channel is stable at the preset value for 60~120s, it indicates that the helium filling in the sealed channel is complete and the airtightness of the sealed channel is in good condition. Then, the first exhaust valve and the second exhaust valve are closed to maintain the initial pressure of the sealed channel in a stable state.

[0070] Step 2: Preheating and parameter calibration process. Start the meshing transmission assembly. The meshing transmission assembly synchronously drives the left piston rod 1-2 and the right piston rod 3-2. Adjust the tachometer 10 and angle sensor 11 to ensure that the Stirling cycle frequency between the first connecting end structure 1, the intermediate connecting cylinder 2, the second connecting end structure 3 and the annular rod bundle fuel element 4 remains at the target operating condition within a predetermined stable time. Turn on the cooling circuit to ensure that the temperature difference between the left cylinder 1-1 and the right cylinder 3-1 is at the predetermined temperature difference requirement, and establish the basic dynamic conditions for the reciprocating flow of helium. At the same time, turn on the hot wire anemometer host 18, tracer particle injector 5, laser source 7, camera 8 and acceleration sensor 19 to complete the preheating and parameter calibration process between the first connecting end structure 1, the intermediate connecting cylinder 2, the second connecting end structure 3 and the annular rod bundle fuel element 4.

[0071] Step 3: Data acquisition process, which involves acquiring the vibration acceleration signal of the fuel element under helium pressure pulsation and vortex excitation, and combining it with the piston phase data of angle sensor 11 to achieve time-synchronous measurement of flow field and vibration response. Specifically, after the Stirling cycle and helium reciprocating flow field between the first connecting end structure 1, the intermediate connecting cylinder 2, the second connecting end structure 3, and the annular rod bundle fuel element 4 stabilizes, silicon-based aerogel microsphere tracer particles are injected into the intermediate connecting cylinder 2 through tracer particle injector 5. The silicon-based aerogel microsphere tracer particles enter the interior of the annular rod bundle fuel element 4 and the gap between the annular rod bundle fuel element 4 and the intermediate connecting cylinder 2 with the helium. Then, the laser source 7 is turned on to form sheet illumination, and the camera 8 continuously captures images of the movement of the tracer particles and the vibration displacement images of the annular rod bundle fuel element 4; c. Based on the image frame sequence acquired by the camera 8, the instantaneous flow velocity, vortex shedding structure, and vibration displacement, amplitude, and frequency of the helium reciprocating flow field are calculated, and the vibration acceleration signal of the annular rod bundle fuel element 4 under helium pressure pulsation and vortex shedding excitation is collected by the acceleration sensor 19. Combined with the phase data of the left piston rod 1-2 in the left cylinder 1-1 obtained by the angle sensor 11, the flow field-vibration response correlation measurement process based on the high-speed image frame sequence and piston phase reference is completed.

[0072] To ensure that the silicon-based aerogel microsphere tracer particles can follow the reciprocating flow of helium gas, the particle size and density of the silicon-based aerogel microsphere tracer particles are selected based on the Stokes number of the tracer particles, which is determined by the following formula:

[0073] ;

[0074] ;

[0075] In the above formula, The Stokes number of the tracer particles; The response time of the tracer particle; The characteristic time of the helium reciprocating flow; To trace particle density; The diameter of the tracer particle; The dynamic viscosity of helium gas is used. By selecting low-density, small-particle-size silicon-based aerogel microspheres as tracer particles, and ensuring that their Stokes number is less than a preset threshold, the inertial hysteresis of the tracer particles relative to the helium gas flow field is reduced, thereby improving the tracking performance of PIV velocity field measurements.

[0076] Step 4: Measurement and Calculation Analysis Process: By adjusting the speed of the first motor 1-3 to change the Stirling cycle frequency or by adjusting the initial pressure of the sealed channel through the helium gas supply source 6, the debugging and measurement process of multiple working conditions is completed; the synchronous data of the pressure sensor 13, the hot-wire anemometer host 18, the acceleration sensor 19 and the camera 8 are observed and recorded, the vibration displacement, amplitude and frequency of the fuel element are calculated, the PIV flow field image is post-processed to obtain the characteristic data of the velocity distribution and vortex shedding frequency of the helium reciprocating flow, and finally, the flow field and vibration data are combined to analyze the flow-induced vibration mechanism of the annular rod bundle fuel element under helium working medium.

[0077] Specific Implementation Method Eight: This implementation method is a further limitation of Specific Implementation Method Seven. In the fourth step of this implementation method, when calculating the vibration displacement and flow field characteristics of the fuel element, it also includes calculating the flow-induced vibration characteristic parameters according to the following semi-empirical formula based on the synchronously acquired pressure pulsation, the PIV velocity field calculated from the image sequence of camera 8, and the vibration response data verified by acceleration sensor 19, in order to replace or verify the conventional data processing process. The calculation formula is as follows:

[0078] ;

[0079] In the above formula, This represents the amplitude of the lateral excitation force. The equivalent drag coefficient for reciprocating flow ranges from 0.05 to 0.2. The density of helium; The projected area of ​​the rod facing the airflow; The Stirling cycle frequency is obtained by measurement using tachometer 10; This refers to the scavenging volume of a single cylinder; This represents the total cross-sectional area of ​​the flow channel; The length of the annular rod bundle fuel element 4; The hydraulic diameter; This is the end-effect correction factor, with a value ranging from 0.3 to 0.5; The piston phase angle is measured and acquired by angle sensor 11; This is the initial phase offset;

[0080] After calculating the flow-induced vibration characteristic parameters, the flow field-vibration phase difference and energy transfer efficiency are determined. The corresponding calculation formulas are as follows:

[0081] ;

[0082] In the above formula, The efficiency of converting fluid kinetic energy into vibrational energy; This is the coupling coefficient, with a value ranging from 0.1 to 0.3. The amplitude of helium velocity measured by PIV; The mass of a single fuel rod; ω = , The relaxation time of the vibration system; , The phase difference between the vibration acceleration and the pressure pulsation, which are synchronously measured by the acceleration sensor 19 and the pressure sensor 13;

[0083] The unsteady model formula for the instantaneous flow distribution in the inner and outer channels of the annular rod bundle is as follows:

[0084] ;

[0085] In the above formula, The instantaneous volumetric flow rate of the internal flow channel; D is the instantaneous volumetric flow rate of the external flow channel. in D out D is the hydraulic diameter of the internal flow channel. out The hydraulic diameter of the outer flow channel; These are the friction coefficient, length, and local resistance coefficient, respectively. A pulsation coefficient is assigned to the oscillating flow, with a value ranging from 0.1 to 0.3, and is calibrated by integrating the PIV velocity field. The hysteresis angle is relative to the piston phase.

[0086] The compressibility correction formula for PIV velocity measurement is:

[0087]

[0088] In the above formula, Particle velocities calculated directly for PIV; This is the corrected actual speed; The compressibility sensitivity coefficient is calibrated by synchronous comparison between the hot-wire anemometer main unit 18 and the PIV, with a value range of 0.4~0.6; The local pressure pulsation measured by pressure sensor 13; Ma = average pressure; / Mach number, The speed of sound of helium; =1.67, The specific heat ratio of helium;

[0089] coefficient The calibration process involves simultaneously acquiring data from angle sensor 11, pressure sensor 13, hot-wire anemometer main unit 18, acceleration sensor 19, and PIV under at least five different Stirling frequencies and loop pressure conditions. The least squares fitting formula is used to ensure that the relative deviation between the theoretical calculation and the measured value is less than 5%. The calibration is then performed by inversely calculating the vibration response. Get , The amplitude of the accelerometer; Estimated from measured vibration energy and fluid dynamic pressure; The instantaneous velocity measured by PIV is obtained by integrating along the flow channel; The anemometer measured by the hot-wire anemometer main unit 18 is used to update the coefficient values ​​through least squares fitting to define the relative deviation. The corresponding calculation process is as follows:

[0090] ;

[0091] ;

[0092] ;

[0093] ;

[0094] In the above formula, The formula for calculating the amplitude of the transverse excitation force of the reciprocating flow is used. The actual excitation force is inferred from the maximum vibration acceleration measured by accelerometer 19. This serves as an indicator of the accuracy of the reciprocating excitation force formula and is used to evaluate and verify the equivalent drag coefficient of the reciprocating flow. The calibration accuracy of the end correction factor α; The efficiency is obtained in one cycle from the formula relating the flow field-vibration phase difference to the energy transfer efficiency. The efficiency is estimated by the ratio of measured vibration energy to the characteristic quantity of fluid dynamic pressure. Vibration energy is obtained by integrating the acceleration signal to calculate velocity, and the characteristic quantity of fluid dynamic pressure is obtained by... Quantitative acquisition; The unsteady model formula for the instantaneous flow distribution of the inner and outer channels of the annular rod bundle fuel element 4 is obtained; The instantaneous velocities of the annular rod bundle fuel element 4 in the inner flow channel region and the central hole of the rod are measured by the PIV (Portable Variable Imaging) camera 8 and laser source 7, respectively. The instantaneous velocity of the gap between the annular rod bundle fuel element 4 and the intermediate connecting cylinder 2 can also be measured. The measured flow rate ratio is then obtained by integrating the cross-sectional area. Obtained from the compressibility correction formula of PIV velocity measurement; The instantaneous true velocity of helium gas directly measured by the hot-wire anemometer 22; This indicates that the PIV velocity after compressibility correction is highly consistent with the independent measurement results of the hot-wire anemometer 22, thus verifying the accuracy of the compressibility sensitivity coefficient ε.

[0095] Specific Implementation Method Nine: This implementation method is a further limitation of Specific Implementation Method Seven or Eight. In this implementation method, the phase difference in the formula relating the flow field-vibration phase difference to the energy transfer efficiency is utilized. Assessing resonance risk, when When the value is 0∘, 90∘, or 180∘, the Stirling frequency or piston phase data is adjusted according to the change in energy transfer efficiency to ensure that the flow-induced vibration of the Stirling annular rod bundle fuel element is in the predetermined state.

[0096] Specific Implementation Method 10: This implementation method is a further limitation of Specific Implementation Methods 7, 8 or 9. This implementation method also includes a point-by-point correction process for the PIV velocity field using the compressibility correction formula of PIV velocity measurement. After obtaining the corrected true velocity field of helium, the corrected velocity field is substituted back into the formula for the amplitude of the transverse excitation force and the unsteady model formula for the instantaneous flow distribution of the inner and outer channels of the annular rod bundle for iterative calculation until the change is less than 1%, at which point the calculation can be stopped.

[0097] In the specific configuration experiment of this invention, the tracer particle injector 5, laser source 7, and camera 8 are coaxially arranged. Silicon-based aerogel microspheres are used as tracers combined with PIV technology to capture the reciprocating flow of helium gas, achieving visualized measurement of the flow field. The silicon-based aerogel microspheres used have a density of 5~10 kg / m³, serving as PIV tracer particles for the helium reciprocating flow, fundamentally avoiding particle sedimentation, hysteresis, and weak scattering.

Claims

1. A Stirling annular rod bundle fuel element flow-induced vibration experimental device, characterized in that: It includes a first connecting end structure (1), an intermediate connecting cylinder (2), a second connecting end structure (3), an annular rod bundle fuel element (4), a tracer particle injector (5), a helium gas supply source (6), a laser source (7), and a camera (8); the first connecting end structure (1) and the second connecting end structure (3) are coaxially opposite each other, the intermediate connecting cylinder (2) is coaxially arranged between the first connecting end structure (1) and the second connecting end structure (3), the middle part of the annular rod bundle fuel element (4) is inserted into the intermediate connecting cylinder (2), one end of the annular rod bundle fuel element (4) is connected to the first connecting end structure (1), and the other end of the annular rod bundle fuel element (4) is connected to the second connecting end structure (3); The first connecting end structure (1) includes a left cylinder (1-1), a left piston rod (1-2), and a first motor (1-3). The inner cavity of the left cylinder (1-1) is a hot cavity. One end of the left piston rod (1-2) is located in the hot cavity, and the other end of the left piston rod (1-2) is connected to the first motor (1-3). The left piston rod (1-2) slides back and forth along the length of the hot cavity under the drive of the first motor (1-3). The left cylinder (1-1) is connected to the end of the nearby annular rod bundle fuel element (4). The second connecting end structure (3) includes a right cylinder (3-1), a right piston rod (3-2), and a second motor (3-3). The inner cavity of the right cylinder (3-1) is a cold cavity. One end of the right piston rod (3-2) is located in the cold cavity, and the other end of the right piston rod (3-2) is connected to the second motor (3-3). The right piston rod (3-2) slides back and forth along the length of the cold cavity under the drive of the second motor (3-3). The right cylinder (3-1) is connected to the end of the nearby annular rod bundle fuel element (4). The annular rod bundle fuel element (4) is connected to a tracer particle injector (5), and a helium gas supply source (6) is connected to the annular rod bundle fuel element (4). A laser source (7) and a camera (8) are respectively arranged on the outer wall of the annular rod bundle fuel element (4). The emission end of the laser source (7) is set towards the annular rod bundle fuel element (4), and the imaging end of the camera (8) is set towards the annular rod bundle fuel element (4).

2. The experimental apparatus for flow-induced vibration of Stirling annular rod bundle fuel element according to claim 1, characterized in that: It also includes a meshing transmission assembly, which includes a main transmission rod (9-1), two bevel gears (9-2) and two flywheels (9-3). A bevel gear (9-2) is provided at each end of the main transmission rod (9-1). One end of the main transmission rod (9-1) is connected to the first connecting end structure (1) through one of the two bevel gears (9-2), and the other end of the main transmission rod (9-1) is connected to the second connecting end structure (3) through the other of the two bevel gears (9-2). Each bevel gear (9-2) includes a main gear and a secondary gear, which are meshed together. Two flywheels (9-3) are mounted on the main transmission rod (9-1). The flywheels (9-3) are arranged in a one-to-one correspondence with the bevel gears (9-2), and each flywheel (9-3) is arranged close to its corresponding bevel gear (9-2). A tachometer (10) is provided on the meshing transmission assembly.

3. The experimental apparatus for flow-induced vibration of Stirling annular rod bundle fuel element according to claim 2, characterized in that: An angle sensor (11) and a hot-wire anemometer host (18) are installed on the outer wall of the left cylinder (1-1); the helium gas supply source (6) is connected to the annular rod bundle fuel element (4) through the gas supply pipeline (12), the annular rod bundle fuel element (4) is installed on the outer wall of the annular rod bundle fuel element (4), and the gas supply pipeline (12) is installed with a pressure sensor (13).

4. The experimental apparatus for flow-induced vibration of Stirling annular rod bundle fuel element according to claim 3, characterized in that: A transition flange (14) is provided at each end of the intermediate connecting cylinder (2). A first exhaust valve is provided on each transition flange (14). The annular rod bundle fuel element (4) is detachably connected to the intermediate connecting cylinder (2) through the two transition flanges (14). A fixing plate (15) is fitted on the outer wall of each end of the intermediate connecting cylinder (2). A connecting flange (16) is provided on each fixing plate (15). Each fixing plate (15) is detachably connected to the outer wall of the intermediate connecting cylinder (2) through its corresponding connecting flange (16). A second exhaust valve is provided on each connecting flange (16).

5. The experimental apparatus for flow-induced vibration of Stirling annular rod bundle fuel element according to any one of claims 1 to 4, characterized in that: The intermediate connecting cylinder (2) is equipped with multiple positioning grids (17). The positioning grids (17) are circular plates with circular positioning holes. Multiple positioning grids (17) are arranged on the inner wall of the intermediate connecting cylinder (2) along the axial direction of the intermediate connecting cylinder (2). The inner wall of each positioning grid (17) is close to the outer wall of the annular rod bundle fuel element (4), and the outer wall of each positioning grid (17) is close to the inner wall of the intermediate connecting cylinder (2).

6. The experimental apparatus for flow-induced vibration of Stirling annular rod bundle fuel element according to claim 5, characterized in that: The cold cavity is connected to a cooling circuit, and a coolant is installed in the cooling circuit.

7. A method for experimentally inducing the flow-induced vibration of a Stirling annular rod bundle fuel element, implemented using the experimental apparatus for experimentally inducing the flow-induced vibration of a Stirling annular rod bundle fuel element as described in claim 6, characterized in that: The experimental method for stabilizing flow-induced vibrations of Stirling annular rod bundle fuel elements includes the following steps: Step 1: Open the first exhaust valve of each transition flange (14) and the second exhaust valve of the connecting flange (16) at the same time open the helium supply source (6). The helium supplied by the helium supply source (6) fills the sealed channel formed between the hot cavity of the first connecting end structure (1), the interior of the intermediate connecting cylinder (2), and the cold cavity of the second connecting end structure (3). The pressure of the sealed channel is monitored by the pressure sensor (13). When the pressure sensor (13) detects that the pressure value in the sealed channel is stable at the preset value for 60~120s, it indicates that the helium filling in the sealed channel is complete and the airtightness of the sealed channel is in good condition. Then close the first exhaust valve and the second exhaust valve to maintain the initial pressure of the sealed channel in a stable state. Step 2: Start the meshing transmission assembly. The meshing transmission assembly synchronously drives the left piston rod (1-2) and the right piston rod (3-2). Adjust the tachometer (10) and angle sensor (11) to ensure that the Stirling cycle frequency between the first connecting end structure (1), the intermediate connecting cylinder (2), the second connecting end structure (3), and the annular rod bundle fuel element (4) remains at the target working condition within a predetermined stable time. Turn on the cooling circuit to ensure that the temperature difference between the left cylinder (1-1) and the right cylinder (3-1) is at the predetermined temperature difference requirement, and establish the basic dynamic conditions for the reciprocating flow of helium. At the same time, turn on the hot wire anemometer host (18), tracer particle injector (5), laser source (7), camera (8), and acceleration sensor (19) to complete the preheating and parameter calibration process between the first connecting end structure (1), the intermediate connecting cylinder (2), the second connecting end structure (3), and the annular rod bundle fuel element (4). Step 3: After the Stirling cycle and helium reciprocating flow field between the first connecting end structure (1), the intermediate connecting cylinder (2), the second connecting end structure (3), and the annular rod bundle fuel element (4) stabilizes, silicon-based aerogel microsphere tracer particles are injected into the intermediate connecting cylinder (2) through the tracer particle injector (5). The silicon-based aerogel microsphere tracer particles enter the interior of the annular rod bundle fuel element (4) and the gap between the annular rod bundle fuel element (4) and the intermediate connecting cylinder (2) along with the helium. Then, the laser source (7) is turned on to form sheet illumination, and the camera (8) continuously captures the movement map of the tracer particles. The vibration displacement images of the annular rod bundle fuel element (4) are obtained from the image frame sequence acquired by the camera (8). The instantaneous flow velocity, vortex shedding structure, vibration displacement, amplitude and frequency of the helium reciprocating flow field are calculated based on the image frame sequence acquired by the camera (8). At the same time, the vibration acceleration signal of the annular rod bundle fuel element (4) under helium pressure pulsation and vortex shedding excitation is collected by the acceleration sensor (19). The phase data of the left piston rod (1-2) in the left cylinder (1-1) is obtained by the angle sensor (11), thereby completing the flow field-vibration response correlation measurement process based on the high-speed image frame sequence and piston phase reference. Step 4: Adjust the Stirling cycle frequency by adjusting the speed of the first motor (1-3) or adjust the initial pressure of the sealed channel by the helium gas supply source (6) to complete the debugging and measurement process of multiple working conditions; observe and record the synchronous data of the pressure sensor (13), the hot-wire anemometer host (18), the acceleration sensor (19) and the camera (8), calculate the vibration displacement, amplitude and frequency of the fuel element, perform post-processing on the PIV flow field image, obtain the characteristic data of the velocity distribution and vortex shedding frequency of the helium reciprocating flow, and finally combine the flow field and vibration data to analyze the flow-induced vibration mechanism of the annular rod bundle fuel element under the helium working medium.

8. The experimental method for maintaining the stability of flow-induced vibration of Stirling annular rod bundle fuel element according to claim 7, characterized in that: In the fourth step, when calculating the vibration displacement and flow field characteristics of the fuel element, it also includes calculating the flow-induced vibration characteristic parameters according to the pressure pulsation and the PIV velocity field calculated from the image sequence of the camera (8) and the vibration response data verified by the accelerometer (19) in the synchronously acquired pressure pulsation. This is done to replace or verify the conventional data processing process. The calculation formula is as follows: ； In the above formula, This represents the amplitude of the lateral excitation force. The equivalent drag coefficient for reciprocating flow ranges from 0.05 to 0.

2. The density of helium; The projected area of ​​the rod facing the airflow; The Stirling cycle frequency is obtained by measurement using a tachometer (10); This refers to the scavenging volume of a single cylinder; This represents the total cross-sectional area of ​​the flow channel; The length of the annular rod bundle fuel element (4); The hydraulic diameter; This is the end-effect correction factor, with a value ranging from 0.3 to 0.5; The piston phase angle is measured and obtained by the angle sensor (11); This is the initial phase offset; After calculating the flow-induced vibration characteristic parameters, the flow field-vibration phase difference and energy transfer efficiency are determined. The corresponding calculation formulas are as follows: ； In the above formula, The efficiency of converting fluid kinetic energy into vibrational energy; This is the coupling coefficient, with a value ranging from 0.1 to 0.

3. The amplitude of helium velocity measured by PIV; The mass of a single fuel rod; ω = , The relaxation time of the vibration system; , The phase difference between the vibration acceleration and the pressure pulsation is obtained by synchronous measurement of the acceleration sensor (19) and the pressure sensor (13); The unsteady model formula for the instantaneous flow distribution in the inner and outer channels of the annular rod bundle is as follows: ； In the above formula, The instantaneous volumetric flow rate of the internal flow channel; D is the instantaneous volumetric flow rate of the external flow channel. in D out D is the hydraulic diameter of the internal flow channel. out The hydraulic diameter of the outer flow channel; These are the friction coefficient, length, and local resistance coefficient, respectively. A pulsation coefficient is assigned to the oscillating flow, with a value ranging from 0.1 to 0.3, and is calibrated by integrating the PIV velocity field. The hysteresis angle is relative to the piston phase. The compressibility correction formula for PIV velocity measurement is: In the above formula, Particle velocities calculated directly for PIV; This is the corrected actual speed; The compressibility sensitivity coefficient is calibrated by synchronous comparison between the hot-wire anemometer main unit (18) and the PIV, with a value range of 0.4~0.6; The local pressure pulsation measured by the pressure sensor (13); Ma = average pressure; / c is the Mach number, and c is the speed of sound of helium. =1.67, The specific heat ratio of helium; coefficient The calibration process involves simultaneously acquiring data from the angle sensor (11), pressure sensor (13), hot-wire anemometer main unit (18), acceleration sensor (19), and PIV under at least five different Stirling frequencies and loop pressure conditions. The least squares fitting formula is used to ensure that the relative deviation between the theoretical calculation value and the measured value is less than 5%. The calibration is then performed by inversely calculating the vibration response. Get , The amplitude of the accelerometer; Estimated from measured vibration energy and fluid dynamic pressure; The instantaneous velocity measured by PIV is obtained by integrating along the flow channel; The anemometer is measured by the hot-wire anemometer host (18). The coefficient values ​​are updated by least squares fitting to define the relative deviation. The corresponding calculation process is as follows: ； ； ； ； In the above formula, The formula for calculating the amplitude of the transverse excitation force of the reciprocating flow is used. The actual excitation force is inferred from the maximum vibration acceleration measured by the accelerometer (19); This serves as an indicator of the accuracy of the reciprocating excitation force formula and is used to evaluate and verify the equivalent drag coefficient of the reciprocating flow. The calibration accuracy of the end correction factor α; The efficiency is obtained in one cycle from the formula relating the flow field-vibration phase difference to the energy transfer efficiency. The efficiency is estimated by the ratio of measured vibration energy to the characteristic quantity of fluid dynamic pressure. Vibration energy is obtained by integrating the acceleration signal to calculate velocity, and the characteristic quantity of fluid dynamic pressure is obtained by... Quantitative acquisition; The unsteady model formula for the instantaneous flow distribution of the inner and outer channels of the annular rod bundle fuel element (4) is obtained; The instantaneous velocities of the annular rod bundle fuel element (4) in the inner flow channel region and the central hole of the rod are measured by the camera (8) and laser source (7) respectively using PIV. The instantaneous velocity of the gap between the annular rod bundle fuel element (4) and the intermediate connecting cylinder (2) can also be measured. The measured flow rate ratio can then be obtained by integrating the cross-sectional area. Obtained from the compressibility correction formula of PIV velocity measurement; The instantaneous true velocity of helium gas directly measured by a hot-wire anemometer (22); This indicates that the PIV velocity after compressibility correction is highly consistent with the independent measurement results of the hot-wire anemometer (22), thus verifying the accuracy of the compressibility sensitivity coefficient ε.

9. The experimental method for maintaining the stability of flow-induced vibration of a Stirling annular rod bundle fuel element according to claim 8, characterized in that: The phase difference in the formula relating flow field-vibration phase difference to energy transfer efficiency Assessing resonance risk, when When the value is 0∘, 90∘, or 180∘, the Stirling frequency or piston phase data is adjusted according to the change in energy transfer efficiency to ensure that the flow-induced vibration of the Stirling annular rod bundle fuel element is in the predetermined state.

10. The experimental method for maintaining the stability of flow-induced vibration of a Stirling annular rod bundle fuel element according to claim 7, 8, or 9, characterized in that: It also includes a point-by-point correction process for the PIV velocity field using the compressibility correction formula of PIV velocity measurement. After obtaining the corrected true velocity field of helium, the corrected velocity field is substituted back into the formula for the amplitude of the transverse excitation force and the unsteady model formula for the instantaneous flow distribution of the inner and outer channels of the annular rod bundle for iterative calculation until the change is less than 1%.

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