The control rod drive mechanism (CRDM) actuates the control rods to perform critical operational functions such as holding rod positions, incremental upward (step-up), downward (step-down) movements, and rapid drops (scram). Control rod assemblies typically include neutron-absorbing materials. By the precise adjustment of the axial positions of these assemblies within the reactor core, a nuclear reactor's reactivity can be effectively regulated. Therefore, the positions of the control rods serve as key indicators of the reactor's reactivity state and constitute one of the primary parameters requiring continuous real-time monitoring during operation. Rod position detectors are critical components that directly measure the actual positions of control rods, providing essential signals to the reactor control and protection system. Consequently, the accuracy and reliability of these detectors directly influence the safety performance of reactor operation.

Inductive rod position detectors are the most widely used type in pressurized water reactors (PWRs) and small modular reactors (SMRs). Their configuration typically includes a primary coil and multiple secondary coil groups. As the control rod's measuring rod advances in discrete mechanical steps, the magnetic coupling between the primary and secondary coils varies, modulating the output voltage signals from the secondary coils. These detectors are specifically designed to interface with step-driven CRDMs. By encoding the voltage outputs from individual secondary coil groups, the detector produces discrete rod position "step" signals, each representing an integer multiple of the control rod's fundamental mechanical step distance. Accordingly, inductive rod position detectors provide only discrete positional information and cannot deliver continuous analog data. For reactors requiring precise rod position control, inductive detectors are inadequate due to their limited measurement accuracy. However, capacitance sensing technology has the potential to achieve continuous recognition of control rod positions, thus serving as a benchmark for precise regulation of nuclear reactor reactivity.

The nonuniformity of the sensitivity field is the key factor affecting the accuracy of capacitive rod position detectors. Measurement errors in detectors designed for SMRs are proportional to the product of the sensitivity field's nonuniformity and the insertion depth of the measuring rod. The nonuniformity of the sensitivity field depends on the radial displacement and the deflection angle of the measuring rod. Thus, to ensure the accuracy of capacitive control rod position detectors, the sensitivity fields must be properly designed and regulated. The sensitivity mechanism and rod position recognition model of the detectors are described herein, and the characteristics of the sensitivity fields are summarized. In addition, the design strategies for the sensitivity field are discussed. Future research directions for this technology are also proposed.

The control rod hydraulic drive system (CRHDS) is an innovative internal control rod drive technology developed by Tsinghua University for the low-temperature nuclear heating reactor NHR200-Ⅱ, in which the drive pump serves as the critical hydraulic power equipment. Its operational reliability is directly linked to reactor safety. However, the bypass circuit of the drive pump suffers from significant vibration and noise induced by the throttling of the control valve. Consequently, developing a high-efficiency multi-stage bypass energy dissipation and vibration reduction component is essential. This study aims to reduce pipeline vibration and enhance the operational reliability and safety of the CRHDS bypass loop through an optimization approach, thereby providing robust design criteria and theoretical guidance for bypass energy dissipation equipment.

This study employed an integrated approach combining fluid-structure interaction (FSI) experiments, machine learning, multi-objective evolutionary optimization, and computational fluid dynamics (CFD) simulations. First, an FSI experimental loop simulating the CRHDS bypass was constructed, comprising a water tank, a centrifugal pump, adjustable flow resistance components, and pipe supports. Three series-connected ball valves were used to simulate a multi-stage flow resistance component, with system parameters recorded at a sampling frequency of 4 000 Hz using four fast-response pressure sensors, a three-axis pipe accelerometer, and an ultrasonic flow meter. A 125-group full-factorial FSI experiment was conducted using characteristic valve closing angles of 20°, 30°, 40°, 50°, and 60°. Second, a physics-informed neural network (PINN) surrogate model, evaluated via 5-fold cross-validation, was developed to predict the total pressure drop and synthetic vibration acceleration using the three-stage resistance coefficients. To improve prediction accuracy, a physical constraint stipulating that the total pressure drop increases monotonically with the sum of the resistance coefficients was integrated into the network's loss function. Third, the PINN surrogate was coupled with the non-dominated sorting genetic algorithm Ⅱ (NSGA-Ⅱ) to perform multi-objective optimization, targeting minimized synthetic vibration acceleration under rated pressure drop constraints. Based on the resulting Pareto optimal front, an optimized design was selected to fabricate a physical three-stage orifice component for experimental validation. Finally, CFD simulations were carried out to analyze the internal flow fields of the optimized component under high-temperature operating conditions.

The experimental, optimization, and simulation results indicated the following: 1) The loop vibration acceleration exhibited a non-monotonic trend, initially increasing and subsequently decreasing with increasing valve closing angles, with the final-stage valve angle exerting a dominant influence; 2) The prediction accuracy of the PINN model for the total pressure drop and synthetic acceleration improved by 27.9% and 29.4%, respectively, compared with the conventional radial basis function model; 3) The optimized multistage orifice component achieved an 84.9% reduction in synthetic vibration acceleration compared with the initial FSI tests while successfully satisfying the loop pressure-drop requirements; 4) Under the 230 ℃ high-temperature condition, the minimum pressure in the flow field was 3.58 MPa, which was considerably above the saturation vapor pressure of water (2.7 MPa), thereby ensuring an ample cavitation margin.

By implementing an integrated framework of FSI experiments and multi-objective optimization, the optimal flow resistance configuration of multi-stage throttling components can be systematically determined to achieve vibration reduction and energy dissipation, thereby mitigating pipeline vibration induced by single-stage throttling. The optimized multi-stage orifice component achieved an 84.9% reduction in loop vibration acceleration under rated driving pressure and was verified to possess a sufficient cavitation margin under high-temperature reactor conditions.

Based on 5-MW hydraulic drive technology and commercial pressurized water reactor magnetic drive technology, Tsinghua University has developed a control rod hydraulic drive system (CRHDS). CRHDS is a new type of built-in control rod drive technology primarily utilized in integrated reactors, such as the 200-MW nuclear heating reactor (NHR200). CRHDS uses three hydraulic cylinders to drive two sets of latch assemblies to move in a predefined sequence and achieve the control rod step-up, step-down, and scram functions. Water hammer occurs during the operation of CRHDS. It can trigger a large fluctuation of fluid pressure, causing vibration in the driving system and equipment, interfering with the instruments, and endangering the safety of the system. Therefore, the transient flow process needs to be analyzed through experimental and theoretical studies.

Theoretical modeling and experiments were performed at the system level. The transient flow mechanism of CRHDS was illustrated, and the key characteristic parameters were analyzed with driving pressure at high temperature. Most importantly, the composition and principle of CRHDS are described. The structure of the hydraulic cylinder was described in detail because it was a key component of the theoretical model. Combined with the structure of CRHDS, a full-scale transient flow performance test rig was built, and the experiments were completed. Based on the displacement and hydraulic cylinder pressure test results, the transient flow process of CRHDS was analyzed at different stages. Based on the mechanism analysis, a step-down transient flow model incorporating the trend and water hammer models was innovatively established. The trend model comprised the fluid continuity equation, fluid momentum equation, leakage flow relationship, and dynamic and kinematic equations. The trend model was solved using the finite difference method. The water hammer model was solved using the method of characteristics. The boundary conditions included a hydraulic cylinder, straight junction, integrated valve, and test vessel. The step-down transient flow model results were verified using experimental data. In the NHR200, CRHDS operates under high temperature and pressure conditions. Finally, the step-down transient flow model of CRHDS was applied to the high-temperature condition, and the fluid physical properties were changed accordingly. The driving pressure was set at 800, 850, and 950 kPa. Variations in key parameters with driving pressure are explained.

(1) The step-down transient flow model of CRHDS comprises the trend and water hammer models. The trend model represents the overall change in hydraulic cylinder pressure, while the water hammer model illustrates the water hammer phenomenon in the system. The step-down transient flow process is analyzed by superimposing the solution results of these two models. (2) Combined with the motion of the inner cylinder, the step-down process can be divided into pre-step, step-down, and post-step stages. Pressure decreases rapidly in the pre-step and post-step stages but slowly in the step-down stage. (3) The rapid movement of the hydraulic cylinder and the sudden change in the leakage flowrate cause the water hammer phenomenon, and the water hammer pressure decays rapidly. The hydraulic cylinder acts as a water hammer source and fluid energy damper during the entire transient flow process. (4) The variation rules of the key parameters of CRHDS at high temperature are obtained. As the driving pressure increases, the pre-step stage duration increases, the step-down time decreases, and the average step-down velocity and water hammer pressure amplitude increase.

The research results illustrate the transient flow mechanism of the step-down process of CRHDS, guide the design of vibration reduction, and provide a basis for the operation monitoring of CRHDS.

The pipeline system is widely used in various fields of industrial production. In the pipeline system, water hammer is a transient flow process triggered by flow regulation, fast closing valves, or accidents, possibly leading to large fluctuations of fluid pressure and threatening the normal operation of the pipeline and equipment. Thus, evaluating the transient flow characteristics of water hammer is necessary.

Based on the fluid-structure interaction (FSI) water hammer theory, the energy analysis method was established, and the variation laws of fluid and pipeline energies were discussed to describe the influence of junction coupling on the transient flow characteristics of water hammer. First, the FSI four-equation model was solved by the method of characteristics (MOC) and verified. A variety of energy, including fluid internal energy, fluid kinetic energy, axial strain energy and axial kinetic energy of pipelines, was introduced. On this basis, the model was mathematically derived and transformed, and the physical expressions, governing equations of the pipeline and fluid energy were obtained. Combined with the initial and boundary conditions, the fluid pressure, fluid mean velocity, pipeline stress, and pipeline velocity of all nodes at different times were calculated by the FSI model. Next, according to the expressions of fluid and pipeline energy, the composite Simpson's integral method was used to integrate the physical quantities of each node numerically, and the energy of the entire pipeline at all times was obtained. The energy analysis method based on FSI water hammer theory was established, and the energy transfer and conversion process in the system were comprehensively analyzed. On this basis, the boundary conditions at the valve were changed, and the influence of the junction coupling was described quantitatively with the help of the maximum fluctuation amplitude of energy and the dimensionless factors.

The following research results are presented: 1) The energy analysis method explains the energy transfer and conversion in the water hammer process from the system level and provides a natural and direct perspective to understand the dynamic response process of the system, which is difficult to demonstrate in the traditional wave transmission and reflection theory. The relationship between fluid and pipeline energy is described, and the dominant energy is fluid internal and pipeline strain energy. Simultaneously, the relationship between the total fluid and pipeline energy is revealed, and their energy sources are clarified. 2) Considering the junction coupling, the energy transfer and conversion are intensified, and the fluid and pipeline energy slightly increase. Consequently, the fluid-structure coupling factor increases, the pipeline vibration factor significantly rises, and the hydraulic pulsation factor slightly decreases. Taking three energy factors as safety evaluation indexes, the protective measures of pipeline systems are proposed. 3) The energy equation is derived from the FSI water hammer model; therefore, this equation is linearly related to the FSI water hammer model.

The research results provide a new method to understand and compare the dynamic response of the water hammer process of different systems and provide a direction and basis for quantifying the response characteristics of the FSI water hammer process.