Key Laboratory of Advanced Reactor Engineering and Safety of the Ministry of Education, Institute of Nuclear and New Energy Technology, Tsinghua University, Beijing 100084, China
Abstract：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.
杨林清, 秦本科, 薄涵亮. 结合部耦合的能量分析方法[J]. 清华大学学报（自然科学版）, 2023, 63(5): 840-848.
YANG Linqing, QIN Benke, BO Hanliang. Energy analysis method of junction coupling. Journal of Tsinghua University(Science and Technology), 2023, 63(5): 840-848.
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2023, Vol. 63 
