Fluid-solid Coupling Analyzing Pressure Regulation Characteristics of a Ball-seat Backpressure Valve in 2-30MPa Operating Conditions

Fluid-solid Coupling Analyzing Pressure Regulation Characteristics of a Ball-seat Backpressure Valve in 2-30MPa Operating Conditions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Fluid-solid Coupling Analyzing Pressure Regulation Characteristics of a Ball-seat Backpressure Valve in 2-30MPa Operating Conditions zhanyu Yang, Jiayi Huang, YuKuan Gu, Chunlong Jia, Qing Liu, Liping Wei This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-2058873/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract High performance backpressure valve is critical for the high-pressure fluid control technology. However, the back pressure easily suffers mechanical failure caused by the strong fluid flushing when the back pressure up to 30 MPa. This work used computational fluid dynamics and solid mechanics analysis method to analyze the basic flow and resistance characteristics of a recently developed backpressure valve. The inlet pressure, maximum flow rate, and maximum turbulent kinetic energy of the 2-30MPa backpressure valve decreases with the increasing the valve opening were analyzed in details. There is pressure suppression phenomenon in the valve chamber when the valve opening is less than 6 mm. The fluid-solid coupling results show that the existing structure of the flow channel and valve core seat can satisfy the pressure regulation requirements within the strength range, and the structure of ball spool seat improve the pressure regulation ability. Backpressure valve 30 MPa simulation fluid-solid coupling pressure curves Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 Figure 15 Figure 16 Figure 17 1. Introduction The backpressure valve is one of the key equipment for high-pressure fluid control technology, and widely used in application scenarios such as regulating and stabilizing pipeline pressure, reducing pipeline siphoning tendency, maintaining the normal delivery flow of metering pumps. The backpressure valve adjusts the high inlet pressure to the set pressure value through the throttling principle. It depends on the change of the valve core position to change the flow direction and pressure of the fluid in the valve body to realize the control of the load pressure. The present backpressure valve commonly uses the diaphragm valve core, which have insufficient pressure-bearing capacity and service life for high flow flux at high inlet-outlet pressure difference. The pressure regulating a range of the diaphragm backpressure valve is restricted [ 1 ] . Under the working environment of high backpressure, the backpressure valve bears high inlet and valve chamber pressure. Due to the severe working environment, it is easy to produce problems such as vulnerable critical valve core, valve body easy to lose efficacy, lower control accuracy, the opening and closing of the valve is easy to clamp, and frequent maintenance [ 2 ] , resulting in reduced control accuracy of the backpressure valve and shortened service life. It requires more research work focusing backpressure valve design and manufacturing technology. Computational fluid dynamics (CFD) and solid mechanics finite element analysis method provides effective tool to assist the design stage of valves. The force characteristics of the valve core and valve body can be further obtained through fluid-solid coupling research. The simulation can analyze the flow state and flow characteristics of the fluid under high-pressure flow conditions. The mechanical characteristics of the valve core and valve body can be obtained through fluid-solid coupling method. Song et al. [ 3 ] described the dynamic analysis of a spring-loaded pressure safety valve by using a moving mesh technique. Fluid-structure interaction analysis and dynamics analysis are used to improve the functionality or operational performance of the spring-loaded pressure safety valve. A transient model with a moving grid technique to observe the dynamics of the valve disc and the flow characteristics through the small chamber between the valve disc and valve seat over a remarkably short period was presented [ 4 ] . Xu et al. [ 5 ] established a flow field analysis model of an overflow valve to analyze the influence of the valve core micro modeling, valve seat flow path diameter, and gradient line chamfer depth on the flow field performance of the valve cavity. Many scholars have carried out the validation of the CFD model by comparing experimental data and simulated data. Aung et al. [ 6 ] introduced the CFD analysis of flow forces and energy loss characteristics in a flapper-nozzle pilot valve with different null clearances, compared the simulation data with experimental measurement data to verify the results, and obtained better matching results. Wu et al. [ 7 ] analyzed and predicted the nonlinear pressure-flow characteristic curve of a spring-loaded pressure relief valve, using CFD method to improve the flow characteristics, and the accuracy was validated by experimental data. Wang et al. [ 8 ] numerically optimize cone angle to reduce the erosion of a V-shape ball valve. Lin et al. [ 9 ] investigated the transient regulation performance of a V-port ball valve. Fluid-solid interaction analysis for valve static stress analysis has been applied to analyze the stress characteristics. Liu et al. [ 10 ] used the unidirectional fluid-solid coupling module of the Workbench to study the fluid flow within the butterfly valve and perform stress analysis on the butterfly plate, and optimize the design of the butterfly plate structure based on the fluid-solid coupling data. Gonzalez et al. [ 11 ] developed in-house numerical method based on a partitioned fluid-structure interaction algorithm intended to obtain high-fidelity numerical predictions and improve valve design. In their research, the differences in effective flow area and pressure drop caused by port geometry and valve speed are revealed. Hu [ 12 ] studied the cavitation phenomenon of the flow field in the ultra-supercritical steam trap, applied the CFD results to the coupling of temperature field, fluid field, and solid field, and the stress distribution of the ultra-supercritical steam trap in work conditions was analyzed, and also analyzed the valve stress types, carried out stress evaluation. Li [ 13 ] investigated the valve body stress of the feed-water valve in the opening process based on fluid-structure interaction analysis to avoid strength failure problems. Little research work has been faced on the high backpressure regulation by valve in valve design handbook or published literature [ 14 ] . Some patents show variable the brief structures of the backpressure valve for different application. Little work provide a much more detail information about the flow and stress characteristics of the backpressure value. Recently, Northwest University (NWU) designed and manufactured a backpressure valve with a spherical valve core [ 15 ] with a backpressure range of 2-30MPa. The objective of this work is to obtain the characteristics of the inlet pressure, maximum flow rate, and maximum turbulent kinetic energy of this high-performance backpressure valve with the valve opening, and the stress distribution of the backpressure valve in severeness conditions, by the fluid-solid coupling method. It hopes to explore the applicability of the backpressure valve. 2. Nwu Backpressure Valve The backpressure valve adjusts the inlet pressure to the pressure required by the working condition through the throttling principle. The flow direction and pressure in front of the valve is controlled by changing the position of the valve core. The fluid flows from the inlet to the valve core and is throttled by a narrow channel between valve core and valve seat. At the same time, the valve core receives an upward force under the action of the fluid pressure. When this force increases to a certain value balancing the pressure difference, the spring is compressed, and the fluid pushes up the valve to form a throttling channel. Then the pressure is continuously reduced when the fluid flows through the throttle channel and finally flows out from the outlet of the backpressure valve. If the fluid pressure is not enough to push up the valve core, the valve seat and the valve core will be closed, and the pressure is held inside of the valve cavity to increase the lock pressure. When the inlet pressure rises to the setting pressure, the fluid will lift the valve core to form a throttle channel. By adjusting the spring stroke to apply pressure to the stem and then adjusting the length of the spring, the setting pressure of the backpressure valve can be changed. Figure 1 shows the structure of the backpressure valve. 3. Experiment Setup A diagram of the test bench is shown in Fig. 2 . The inlet pressure and inlet flow rate of the backpressure valve can be measured experimentally. The deionized water stored in the water tank was pumped into the pipeline by a vertical multistage centrifugal pump and enters the backpressure valve. A bypass valve is installed at the pump outlet to adjust the inlet flow rate of the backpressure valve. The Orifice flowmeter and pressure gauge are installed ahead of the valve. After switching on the pump, adjust the opening of the bypass valve and record the orifice flowmeter reading. When the flow rate is adjusted to measured value, the data of pressure gauge with varying opening was recorded. 4. Numerical Simulation Method 4.1 Physical model and grid generation Due to the connecting spring, the valve core will move up and down in a small range that is difficult to predict in the actual adjustment process, and the valve core will be in a balanced position when the fluid flow is stable. In the numerical simulation, it only need to consider the opening of the balanced position of the valve core as a variable value, so it is necessary to simplify the spring. Meanwhile, parts 7–16 are used to apply pre-tightening force to the valve core of the backpressure valve by adjusting the position of the valve stem 2, then adjusting the valve opening. To simplify the calculation, parts 7–16 are simplified into an integral valve body component, and the distance between the backpressure valve core (Ruby seat) and the valve seat (sapphire) is directly given as the valve opening. The flow channel structure of the backpressure valve studied in this paper is shown in Fig. 3 . The inlet and outlet dimensions of the flow field are 10 mm. Due to the particularity of the backpressure valve structure, the valve opening is determined by the distance between the backpressure valve spool (ruby seat) and the valve seat (sapphire). Adjust the distance between the valve core and the valve seat to obtain different openings. This research considered 17 sets of openings distributed between 0.39-1.75mm, and the state at 1mm opening is shown in Fig. 3 . 4.1.1 Fluid domain To study the fluid flow characteristics in the backpressure valve, the calculation domain of the backpressure valve channel is extracted, and the geometric model of the internal flow field of the backpressure valve is obtained. Since the flow channel structure is symmetrical, 1/2 of the flow field is selected as the computational domain to save energy, computer memory, and calculation time. The geometric model of the flow field computational domain is shown in Fig. 4 . There are four types of boundaries in the computational domain, also given in Fig. 4 . Significantly, all surfaces except for the inlet, outlet, and boundary conditions of the symmetry plane are defined as fluid-solid-interaction walls (FSI_walls). Due to the complex structure at the valve core of the backpressure valve, the cross-section size of the flow channel is usually less than 1mm under the condition of a small opening, resulting in a throttling effect and significant pressure drop, and the meshing here is more complex. Therefore, it is necessary to verify the grid independence before calculating the convective domain. Due to the complex grid structure of the valve core, the grid is used at the narrow part of the valve core. The overall meshing results are shown in Fig. 5 . 4.1.2 Solid domain In the Fluid-Solid analysis, the material of the backpressure, the valve core, and the valve seat are 316 stainless steel, industrial ruby, and industrial sapphire, respectively. To ensure the sealing property, a Polytetrafluoroethylene (PTFE) pad is installed at the connection between the valve body and the valve seat. The physical parameters of the above materials are shown in Table 1 . Table 1 Physical parameter of the materials Materials Density / g·cm − 3 Elastic modulus / Pa Poisson ratio 316 stainless steel 7.98 1.93 \(\times\) 10 11 0.30 Industrial ruby 4.00 3.00 \(\times\) 10 11 0.22 Industrial sapphire 4.00 3.00 \(\times\) 10 11 0.22 PTFE 2.20 2.80 \(\times\) 10 8 0.40 Zirconia 6.05 2.10 \(\times\) 10 11 0.3 Silicon nitride ceramics 3.26 3.00 \(\times\) 10 11 0.25 Due to the complex structure, a combination of tetrahedrons and hexahedrons is used to mesh the backpressure valve. Tetrahedron elements are used to mesh parts with irregular structures such as valve cores and valve bodies, and hex dominant elements are used to divide parts with regular structures such as gaskets, valve seats, and fastening nuts to reduce the amount of calculation. Finally, the number of meshes is 475342, and the number of nodes is 847001. Figure 6 shows the results of meshing. 4.2 Numerical model and parameter settings The governing equations include continuity equation and momentum conservation equation and turbulence model. The standard k-ε model [ 16 ] was applied to describe the turbulence flow. The governing equation mentioned above is solved by using the following scheme. The volume force generated by gravity is considered because of the considerable density value of the liquid phase fluid. In pressure-velocity coupling, the SIMPLE scheme is used because it allows higher pressure corrections with relaxation factors that help accelerate convergence. To maintain the accuracy and convergence stability, momentum and standard k-ε equations adopt the second-order upwind scheme. The convergence accuracy is 10 − 3 to satisfy the continuity of mas law. 4.3 Model validation Due to the narrow flow channel between the valve core and complex structure, the tetrahedral grid is used for grid division. The fluid flew grid at the valve core is densified to varying degrees to obtain five grids with the number 430000, 730000, 1050000, 1260000, and 1470000. The five grids are simulated and calculated respectively to obtain Fig. 7 . It can be seen intuitively that the CFD model basically meets the grid independence. As can be seen from Fig. 7 that the inlet pressure of the five grids is very close, and the maximum relative error is 1.4%, which proves that the selection of grid size is reasonable. To ensure the calculation accuracy and reduce the amount of calculation, 430000 grids are selected for calculation. Then the fluid grid size at the valve core corresponding to this grid number is chosen for simulation and calculation. Figure 8 shows the simulation and experimental data at an inlet mass flow rate of 0.1389kg/s. As can be seen from Fig. 14 that both the simulated pressure value and the experimental pressure value show a trend of decreasing with the valve opening. And the curve trends of the two groups are in good agreement. Errors of the two are in the range tolerance. The simulated results can be considered reliable. Meanwhile, the rationality of the CFD mentioned above model was validated. 5. Results And Discussions 5.1 Pressure regulation characteristics 5.1.1 Effect of opening The opening greatly affect the flow area, dynamic flow and pressure characteristics [ 17 ] . The opening of different valve core shapes, such as V-shape [ 8 ] , S-shape [ 18 ] , sphere-shape, circular-shape, pyramid-shape, ellipsoid-shape [ 19 ] , circular-cone-shape [ 5 ] and Bio-inspired-shape [ 20 ] ,etc, has been focus in literature. The present reported value commonly has one throttling channel, while there are two throttling channels when the fluid flows to the valve core seat of the NWU backpressue valve, as shown in Fig. 9 . The first part is the channel between the valve core seat (ruby seat) and the fastening nut (Part 21 in Fig. 1 ), and the second part is between the valve core (ruby) and the valve seat (sapphire). The fluid flows through two throttling actions outlet channel to the outlet. Figure 9 shows the pressure distribution in the condition of the flow rate 0.1389kg/s and opening of 0.39mm. The maximum inlet pressure is observed as 28.903MPa. The cross-sectional area of the valve decreases when the fluid flows through the first throttling channel, then becomes larger when the fluid flows into the chamber after the first throttling channel, and then becomes smaller at the second throttling channel. In the chamber after the first throttling channel, the fluid pressure accumulates and the fluid velocity decrease to some extend to avoid too strong souring. Therefore, there is a local pressure increase after the fluid flows through the first throttling channel. Figure 10 a shows that high inlet pressure is decreased to ambient value when the fluid flows through the two throttling channels. Especially the pressure drop through the throttling channel between ruby and sapphire is obvious, which indicates that the purpose of decompression can be well achieved. Compared with the velocity distribution of Fig. 10 b, it can be seen that the maximum flow rate appears at the second throttling channel. The pressure and velocity distribution at the throttle with valve opening of 0.39mm, 0.43mm, 0.55mm, and 0.9mm were simulated and the calculated inlet pressure corresponding to its opening is 29.803MPa, 19.687MPa, 9.898MPa, and 2.084MPa, respectively. It can be seen that the area of the flow channel decreases with the decreasing opening. The decreasing opening increases inlet pressure. When the opening reduces to 0.39 mm, the inlet pressure achieves 30 MPa. After the fluid flows through the first throttling channel, it quickly rises to close to the inlet pressure; It can be known that the larger the inlet pressure, the greater the pressure of the space between the two throttling channels. Especially under the working condition of 29.803mpa (i.e., the opening is 0.39mm), the fluid flows through the first throttling channel and rises rapidly to near the inlet pressure. The valve opening greatly affect the local pressure and velocity distribution of the throttling area. For the situations of larger opening of 0.43 mm, 0.55 mm and 1.25 mm, the pressure gradually decrease through the two throttling channels. The pressure in the chamber after the first throttling channel is lower than the pressure in the first throttling channel and higher than that in the second throttling channel. However, the pressure in the chamber after the first throttling channel is higher than the pressure in the first throttling channel when the opening reduces to 0.39 mm. The maximum speed occurs at the second throttle channel. When the opening is 1.25mm, the corresponding working pressure is 2.084MPa, and the fluid flow rate is uniform from the first throttle channel to the top of the ruby. With the decrease of opening, the speed difference between the first throttle and the second throttle increases gradually. And the maximum flow velocity is 294.6 m/s. The pressure at the top of the valve core is higher than in other areas. Figure 11 is the local velocity around the valve core. The fluid flows through the second throttling channel at high speed, and form jet flow characteristics in the outlet pipe. The flow direction is the positive direction of the Y-axis, without fluid back-flow. 5.1.2 Effect of inlet flow rate The flow characteristics in terms of inlet pressure, maximum flow velocity, and maximum turbulent kinetic energy were analyzed in variable openings and inlet flow rates. Figure 12 shows that the pressure of the valve inlet and valve chamber continue to decrease as the increasing opening. When the valve opening is less than 0.6 mm, the inlet pressure decreases rapidly with the increase of the valve opening. When the valve opening is more significant than 0.6 mm, the inlet pressure decreases slowly with the increase of the opening, and the downward trend has decreased. The increased inlet flow rate increases the inlet pressure at the same opening, especially at the much smaller opening. When the inlet pressure is fixed, the flow rate vs. the opening shows a quick-opening characteristics [ 19 ] , although the main function of the backpressure valve is regulating the inlet pressure. Figure 13 and 14 also show the same trend as the Fig. 12 . That is, when the valve opening is less than 0.6 mm, the maximum flow velocity and maximum turbulent kinetic energy in the valve will decrease rapidly with the increase of the valve opening. When the valve opening is greater than 0.6 mm, the decreasing trend of maximum flow velocity and maximum turbulent kinetic energy decreases, decreases slowly as the opening degree increases. At the small valve opening, the distance between the valve core and the valve seat is very small, and there is a phenomenon of build-up pressure in the valve, so when the valve opening increases slightly, the valve inlet pressure and the valve cavity pressure will drop significantly. On the contrary, when the opening is bigger than 0.6 mm, the cross-sectional area of the throttling channel between ruby and sapphire will become larger, and there will be no more pressure in the chamber after the first throttling channel. Thus, the pressure of the inlet and valve chamber has no longer declines drastically with the increase of the opening. Taking the inlet flow rate of 0.1389 kg∙s − 1 as an example. When the opening is 0.6 mm, the inlet pressure value is 8.344 MPa. When the inlet pressure is more significant than 8.344 MPa, there may be a phenomenon of build-up pressure in the chamber after the first throttling channel. It has to increase the valve opening slightly to reduce the inlet pressure. However, there is no such phenomenon in the valve cavity when the valve inlet pressure is less than 8.344 MPa. The valve opening must be significantly increased to reduce the inlet pressure. 5.2 Stress distribution characteristics 5.2.1 Stress distribution The CFD simulation shows that when the inlet mass flow is 0.1389kg∙s − 1 and the valve opening is 0.39mm, the inlet pressure of the backpressure valve reaches 29.803 MPa. Meanwhile, the cross-sectional area of the second throttling channel between the valve core and the valve seat reaches the minimum value when the inlet pressure is 29.803 MPa. When the fluid passes through the throttling passage, the pressure drops sharply, and there is also a phenomenon of build-up pressure in the chamber after the first throttling channel. Further, 29.803 MPa is considered a severe working condition of the backpressure valve. The stress distribution and deformation of the backpressure valve at an inlet pressure of 29.803 MPa was analyzed, and the applicability of the valve core material and structure was evaluated. The fluid-solid coupling stress distribution results of the valve at an opening of 0.39 mm and an inlet pressure of 29.803 MPa are shown in Fig. 15 , and the deformation results are shown in Fig. 16 . The maximum stress occurs at the joint edge where is located at the PTFE pad (part 19) connecting the valve core seat and the valve body, and the value is 192.54 MPa. The maximum displacement is 0.0081 mm. In Fig. 15 , the maximum stress value at the valve seat is 121.85 MPa, the maximum stress value at the valve core is 95.763 MPa, the maximum stress value at the joint line of part 17 and part 30 is 90.35 MPa. the maximum stress value occurred in the joint of the stress value of the valve seat and the fluid, and the overall stress distribution gradually decreases from the pressure-bearing side to the outside. Because the material of the part 17 and part 30 is different, the stress transmission is discontinuous at the rigid contact, so there is a small-scale stress concentration at the joint of the valve seat in the direction of gravity (the positive direction of the Y-axis) and the valve body. The stress distribution of the valve core presents a situation where the stress in the middle and lower parts is higher than the top part of the valve core. Due to the high pressure before the fluid flows through the throttle channel and the fluid force squeezes the valve core seat, the pressure is transmitted to the valve core through the valve core seat. Because the valve core and the valve core seat are made by different materials and the structure is not continuous, a small area of stress concentration occurs at the contact point. The maximum stress value appears at the stress concentration point. If the valve core is one part and made by same material, the stress concentration may occur in the middle position and the touch edge with fluid [ 21 ] . Figure 16 shows the maximum deformation values at the valve seat, valve core, and valve core seat are 0.00405 mm, 0.00382 mm, and 0.00485 mm, respectively. The maximum stress value occurs at the connection point between the valve core seat and the valve body. 5.2.2 Effect of valve core materials Four kinds of valve core materials, namely ruby ( \({\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\) ), 316 stainless steel, zirconia and silicon nitride ceramic, are selected to analyze stress distribution and deformation. The physical parameters of materials are given in Table 1 . Figure 17 shows a stress cloud, and Table 2 summaries the calculation results. Different materials between the valve core and seat, and the discontinuous structure cause a range of stress concentration. The maximum stress value appears at the stress concentration. The fluid pressure is transmitted to the valve core through the valve seat, and the stress value at the valve core is less than that at the valve seat. However, due to the fluid flow, the fluid will give the valve core a fluid force in the negative direction along the Y-axis. The valve core squeezes the valve seat under the action of fluid force, resulting in local stress concentration, and the maximum stress value appears. The maximum stress value does not exceed the allowable stress of the material, and the overall structural design, and material selection are reasonable and can meet the requirements of working conditions. The maximum stress of the 316 stainless steel valve core at the concentration of stresses is the smallest compared with the other three materials, because the material has the lowest elastic modulus. With the increase of the elastic modulus of the material, the stress concentration value between the valve core and the gem base is larger due to the rigid connection of different materials, and the stress concentration value is the largest when the valve core material is silicon nitride ceramic. The maximum stress of the four kinds of valve core do not exceed the allowable stress. Table 2 Calculation results of maximum stress and deformation Materials Ruby ball Silicon nitride Zirconia 316 stainless steel The maximum stress value / MPa 95.763 97.106 76.619 43.288 The maximum deformation / mm 3.8231 \(\times\) 10 −3 3.7736 \(\times\) 10 −3 3.7128 \(\times\) 10 −3 3.8316 \(\times\) 10 −3 Primary stress limit* /MPa 152 140 180 164 *Calculation based on materials properties and standard given by ASME Ⅷ-2 [ 22 ] . 6. Conclusions And Prospects A recently developed backpressure valve using a valve core structure of rubble ball and gem base was numerically investigated and analyzed the characteristics of the inlet pressure, maximum flow velocity, and maximum turbulent kinetic energy. The simulation results were compared with the experiment measured data to validate the numeral model. The fluid-solid coupling method was used to analyze the stress distribution of the backpressure valve under 30 MPa. The following conclusions mainly includes: 1. The pressure value of the model predication and the experimental measurement showed a good agreement, which indicates the present model is suitable for describing the flow field in the backpressure valve. 2. The inlet pressure, maximum flow velocity, and maximum turbulent kinetic energy of the fluid in the backpressure valve reduce with the increase of valve opening. There is a more severe build-up pressure in the valve in the valve opening degree of less than 0.6 mm. The valve inlet and chamber pressure will greatly decrease when the valve opening increases slightly larger than 0.6 mm. 3. The valve core structure of structure of rubble ball and gem base can well satisfy the pressure regulation requirements of the backpressure valve within the strength range. Four kinds of valve core materials of ruby ( \({\text{Al}}_{\text{2}}{\text{O}}_{\text{3}}\) ), 316 stainless steel, zirconia and silicon nitride ceramic are suggested to make the valve core. Declarations Availability of data and materials The authors declare that data supporting the findings of this study are available within the article. Competing interests The authors declare that they have no competing interests. Funding This work was funded by The National Natural Science Foundation of China (No. 22278332), the State Key Laboratory of Clean Energy Utilization (Open Fund Project No. ZJUCEU2020020), and the Joint Laboratory for High Pressure Flow Control and Safety Technology. The views and opinions expressed are those of the authors and not necessarily those of the funding organizations. The funding organizations had no role in the design of the study, and collection, analysis, and interpretation of the data, or writing of the manuscript. Authors' contributions YZY, HJY, GYK and WLP designed the study. YZY, HJY conducted the literature search. YZY, HJY, GYK, JCL, LQ, and WLP were involved in the analysis and interpretation of data. YZY, HJY and WLP drafted the manuscript. The study was supervised by WLP. All authors read and approved the final manuscript. 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T., and Chen, J. L., 2019, “Design of a Bio-Inspired Anti-Erosion Structure for a Water Hydraulic Valve Core: An Experimental Study,” Biomimetics, 4(3), p. 63. Available at: https://doi.org/10.3390/biomimetics4030063 . Liu, Z. W., Yu, Y., and Zhai, Q., 2019, “Impact Characteristics Simulation Analysis of High Pressure Valve Based on Workbench/ls-Dyna,” 2019 International Conference on Intelligent Transportation, Big Data & Smart City (ICITBS), pp. 267–269, Available at: https://doi.org/10.1109/ICITBS.2019.00070 . ASME. ASME Boiler and Pressure Vessel Code, Section III, Division 2: Design & Fabrication of Pressure Vessel 2021. Peng, C. T., Luo, Y., Zhou, B., Huang, F. Y., and Song, M., 2021, “Fluid-Solid Coupling and Thermal Stress Analysis of Vacuum Valve Based on CFD,” Machinery, 48(03), pp. 17–22. Wang, J., and Zheng, J. H., 2013, “Stress Analysis for Electric Stop Valve of Nuclear Power Plant Considering Action of Preload and Stem Force,” Applied Mechanics and Materials, 313–314, pp. 1210–1213. Available at: https://doi.org/10.4028/www.scientific.net/AMM.313-314.1210 . Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-2058873","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":141734558,"identity":"56d604b6-9798-4e3a-b997-bca54f8a07ab","order_by":0,"name":"zhanyu Yang","email":"","orcid":"","institution":"Xibei daxue huagong xueyuan: Northwest University School of Chemical Engineering","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"zhanyu","middleName":"","lastName":"Yang","suffix":""},{"id":141734559,"identity":"8227f94d-5570-435c-93f3-1884cfe2dbbc","order_by":1,"name":"Jiayi Huang","email":"","orcid":"","institution":"Zhejiang University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Jiayi","middleName":"","lastName":"Huang","suffix":""},{"id":141734560,"identity":"44ceab94-bd7f-496c-b162-b3b5142494b3","order_by":2,"name":"YuKuan Gu","email":"","orcid":"","institution":"China National Heavy Duty Truck Group Co.,Ltd.","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"YuKuan","middleName":"","lastName":"Gu","suffix":""},{"id":141734561,"identity":"ac788d74-a902-41d1-92c6-4a46d16a85a7","order_by":3,"name":"Chunlong Jia","email":"","orcid":"","institution":"Shaanxi provincial Natural Gas Co.,Ltd","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Chunlong","middleName":"","lastName":"Jia","suffix":""},{"id":141734562,"identity":"0d72f8f6-bd19-4ea4-9960-7240c263fdc3","order_by":4,"name":"Qing Liu","email":"","orcid":"","institution":"Joint Laboratory for High Pressure Flow Control and Safety Technology, Northwest University","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Qing","middleName":"","lastName":"Liu","suffix":""},{"id":141734563,"identity":"310239b3-5553-4b16-b5d7-4321cec661d9","order_by":5,"name":"Liping Wei","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA5ElEQVRIiWNgGAWjYFACxsYDCQwSDAzMjA0HPhjYyBGjpQGihZ354MMZBWnGRNlzAEzysyUb83w4nEhQucHx5oYDD3dY5Mk785hJ2xgwJzCwHz66Aa+WMwcbDiSekSg2PAzUkmPAlsfAk5Z2A58WsxuJQC1tEokbm8FaeIoZJHjM8Gu5/xBJi4WBRGIDQS03GCFa5jMDvc9gYEBYi/2ZRLBfEjcwAwO5xyDBmI2QXyTbjz98+HNHXeL8fmA4/PjzX46f/fAxvFrAgLEBGHQHoBw2gsphWuQbiFI6CkbBKBgFIxEAAMd+UVNxG5baAAAAAElFTkSuQmCC","orcid":"","institution":"Xibei daxue huagong xueyuan: Northwest University School of Chemical Engineering","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Liping","middleName":"","lastName":"Wei","suffix":""}],"badges":[],"createdAt":"2022-09-13 03:51:20","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-2058873/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-2058873/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":27562634,"identity":"e7e06985-0f87-4f1c-8392-6d88f9063e8f","added_by":"auto","created_at":"2022-10-10 15:38:52","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":97160,"visible":true,"origin":"","legend":"\u003cp\u003eStructure of NWU backpressure valve\u003c/p\u003e","description":"","filename":"Fig1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/9605742a6cd6382731bf362d.jpg"},{"id":27562631,"identity":"7cd18381-12e1-439a-beba-a013d8635ca3","added_by":"auto","created_at":"2022-10-10 15:38:52","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":65230,"visible":true,"origin":"","legend":"\u003cp\u003eDiagram of the test bench\u003c/p\u003e","description":"","filename":"Fig2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/3857d888e3cfe14d545b8bfd.jpg"},{"id":27562632,"identity":"819841ae-b926-4774-a170-878a8916f55d","added_by":"auto","created_at":"2022-10-10 15:38:52","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":50894,"visible":true,"origin":"","legend":"\u003cp\u003eValve structure and opening definition (eg. 1mm)\u003c/p\u003e","description":"","filename":"Fig3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/6587c7259e0e7b9f410998f5.jpg"},{"id":27563416,"identity":"abc0ab53-a6ec-4f94-a698-3fd0728683f4","added_by":"auto","created_at":"2022-10-10 15:43:52","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":41701,"visible":true,"origin":"","legend":"\u003cp\u003eFluid domain of the backpressure valve\u003c/p\u003e","description":"","filename":"Fig4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/d318b2feb2314fb270bbbdf7.jpg"},{"id":27564176,"identity":"aed029a2-c58e-4f06-a864-cd7bde2cc7cf","added_by":"auto","created_at":"2022-10-10 15:48:52","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":82706,"visible":true,"origin":"","legend":"\u003cp\u003eGrid division of the fluid field\u003c/p\u003e","description":"","filename":"Fig5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/2c094cd4cf6513f5deb6640e.jpg"},{"id":27565552,"identity":"bbcf9e64-0922-408f-be1f-1f093bdd596c","added_by":"auto","created_at":"2022-10-10 15:58:52","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":62871,"visible":true,"origin":"","legend":"\u003cp\u003eGrid division of the backpressure valve\u003c/p\u003e","description":"","filename":"Fig6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/9a2a4665075fe1ff45aa9e35.jpg"},{"id":27565096,"identity":"b58da664-7ece-42bd-9f4c-13ce87fe6f80","added_by":"auto","created_at":"2022-10-10 15:53:52","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":39797,"visible":true,"origin":"","legend":"\u003cp\u003eGrid independence test\u003c/p\u003e","description":"","filename":"Fig7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/a0a57b14f96af307680d2cc3.jpg"},{"id":27565095,"identity":"853ef800-6ec0-4625-8c4b-7d7004ad6e83","added_by":"auto","created_at":"2022-10-10 15:53:52","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":58707,"visible":true,"origin":"","legend":"\u003cp\u003eModel validation by comparing experimental and simulated values\u003c/p\u003e","description":"","filename":"Fig8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/5fb336bd36a11e18dee5993c.jpg"},{"id":27562638,"identity":"bd3844c8-821a-47cf-8833-15ae1350a782","added_by":"auto","created_at":"2022-10-10 15:38:52","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":50168,"visible":true,"origin":"","legend":"\u003cp\u003ePressure distribution at opening of 0.39 mm with inlet mass flow of 0.1389kg/s\u003c/p\u003e","description":"","filename":"Fig9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/7a5d883ee640efcaf34fc57c.jpg"},{"id":27564178,"identity":"f967d369-606e-4bb6-8801-82f205e9e585","added_by":"auto","created_at":"2022-10-10 15:48:52","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":92945,"visible":true,"origin":"","legend":"\u003cp\u003eEffect of opening on pressure and velocity distribution at inlet mass flow of 0.1389 kg/s\u003c/p\u003e","description":"","filename":"Fig10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/6850d435501a5e740b0cac70.jpg"},{"id":27563417,"identity":"3aebf3e1-9c6a-4380-ae05-f189798f01c5","added_by":"auto","created_at":"2022-10-10 15:43:52","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":50025,"visible":true,"origin":"","legend":"\u003cp\u003eVelocity vector at throttling channel at opening of 0.39 mm andinlet mass flow of 0.1389kg/s\u003c/p\u003e","description":"","filename":"Fig11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/2d3b991271732dba13b61c12.jpg"},{"id":27564183,"identity":"6b5563aa-4a68-4665-a596-e372d1a550af","added_by":"auto","created_at":"2022-10-10 15:48:52","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":72870,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of inlet pressure vs. opening under different inlet flow rates\u003c/p\u003e","description":"","filename":"Fig12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/f326e8f73d33faa6f9da6f2a.jpg"},{"id":27563419,"identity":"1051b7ac-83a1-4097-8a82-a94117c60f42","added_by":"auto","created_at":"2022-10-10 15:43:52","extension":"jpg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":75270,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of maximum velocity vs. opening under different inlet flow rates\u003c/p\u003e","description":"","filename":"Fig13.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/2c062096898a776a147f7e17.jpg"},{"id":27940376,"identity":"d17a0eeb-1699-4dd8-9b37-611691c710a5","added_by":"auto","created_at":"2022-10-18 15:47:46","extension":"jpg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":85036,"visible":true,"origin":"","legend":"\u003cp\u003eVariation of maximum turbulent kinetic energy vs. opening under different inlet flow rates\u003c/p\u003e","description":"","filename":"Fig14.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/f5d527a15f593fa86f1ff59d.jpg"},{"id":27563423,"identity":"d88b1ef9-e286-412a-8b98-d107eb86a4c7","added_by":"auto","created_at":"2022-10-10 15:43:52","extension":"jpg","order_by":15,"title":"Figure 15","display":"","copyAsset":false,"role":"figure","size":60393,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution results of the backpressure valve at opening of 0.39 mm and inlet mass flow of 0.1389kg/s\u003c/p\u003e","description":"","filename":"Fig15.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/20921a4fd77f1f063e678b36.jpg"},{"id":27562647,"identity":"820c9c1d-c5a1-4e0a-bcb0-2738ba6cdac9","added_by":"auto","created_at":"2022-10-10 15:38:52","extension":"jpg","order_by":16,"title":"Figure 16","display":"","copyAsset":false,"role":"figure","size":41683,"visible":true,"origin":"","legend":"\u003cp\u003eResults of backpressure valve deformation distribution at opening of 0.39 mm and inlet mass flow of 0.1389kg/s\u003c/p\u003e","description":"","filename":"Fig16.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/211d84ca900b1fe1fb028999.jpg"},{"id":27565550,"identity":"66c6d116-5f66-4230-be59-04fbfb25753a","added_by":"auto","created_at":"2022-10-10 15:58:52","extension":"jpg","order_by":17,"title":"Figure 17","display":"","copyAsset":false,"role":"figure","size":47731,"visible":true,"origin":"","legend":"\u003cp\u003eStress distribution of different valve cores\u003c/p\u003e","description":"","filename":"Fig17.jpg","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/772e31f408e3ec2a1a3b5e83.jpg"},{"id":43179739,"identity":"38e5a199-a221-4b5d-b575-1d42698e6828","added_by":"auto","created_at":"2023-09-15 09:09:00","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":1270876,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-2058873/v1/61523e18-26e9-45a3-9b92-a2755705934b.pdf"}],"financialInterests":"","formattedTitle":"Fluid-solid Coupling Analyzing Pressure Regulation Characteristics of a Ball-seat Backpressure Valve in 2-30MPa Operating Conditions","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe backpressure valve is one of the key equipment for high-pressure fluid control technology, and widely used in application scenarios such as regulating and stabilizing pipeline pressure, reducing pipeline siphoning tendency, maintaining the normal delivery flow of metering pumps. The backpressure valve adjusts the high inlet pressure to the set pressure value through the throttling principle. It depends on the change of the valve core position to change the flow direction and pressure of the fluid in the valve body to realize the control of the load pressure. The present backpressure valve commonly uses the diaphragm valve core, which have insufficient pressure-bearing capacity and service life for high flow flux at high inlet-outlet pressure difference. The pressure regulating a range of the diaphragm backpressure valve is restricted\u003csup\u003e[\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e]\u003c/sup\u003e. Under the working environment of high backpressure, the backpressure valve bears high inlet and valve chamber pressure. Due to the severe working environment, it is easy to produce problems such as vulnerable critical valve core, valve body easy to lose efficacy, lower control accuracy, the opening and closing of the valve is easy to clamp, and frequent maintenance\u003csup\u003e[\u003cspan citationid=\"CR2\" class=\"CitationRef\"\u003e2\u003c/span\u003e]\u003c/sup\u003e, resulting in reduced control accuracy of the backpressure valve and shortened service life. It requires more research work focusing backpressure valve design and manufacturing technology.\u003c/p\u003e \u003cp\u003eComputational fluid dynamics (CFD) and solid mechanics finite element analysis method provides effective tool to assist the design stage of valves. The force characteristics of the valve core and valve body can be further obtained through fluid-solid coupling research. The simulation can analyze the flow state and flow characteristics of the fluid under high-pressure flow conditions. The mechanical characteristics of the valve core and valve body can be obtained through fluid-solid coupling method. Song et al.\u003csup\u003e[\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e]\u003c/sup\u003e described the dynamic analysis of a spring-loaded pressure safety valve by using a moving mesh technique. Fluid-structure interaction analysis and dynamics analysis are used to improve the functionality or operational performance of the spring-loaded pressure safety valve. A transient model with a moving grid technique to observe the dynamics of the valve disc and the flow characteristics through the small chamber between the valve disc and valve seat over a remarkably short period was presented\u003csup\u003e[\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e]\u003c/sup\u003e. Xu et al.\u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e established a flow field analysis model of an overflow valve to analyze the influence of the valve core micro modeling, valve seat flow path diameter, and gradient line chamfer depth on the flow field performance of the valve cavity. Many scholars have carried out the validation of the CFD model by comparing experimental data and simulated data. Aung et al.\u003csup\u003e[\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e]\u003c/sup\u003e introduced the CFD analysis of flow forces and energy loss characteristics in a flapper-nozzle pilot valve with different null clearances, compared the simulation data with experimental measurement data to verify the results, and obtained better matching results. Wu et al.\u003csup\u003e[\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e]\u003c/sup\u003e analyzed and predicted the nonlinear pressure-flow characteristic curve of a spring-loaded pressure relief valve, using CFD method to improve the flow characteristics, and the accuracy was validated by experimental data. Wang et al.\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e numerically optimize cone angle to reduce the erosion of a V-shape ball valve. Lin et al.\u003csup\u003e[\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]\u003c/sup\u003e investigated the transient regulation performance of a V-port ball valve.\u003c/p\u003e \u003cp\u003eFluid-solid interaction analysis for valve static stress analysis has been applied to analyze the stress characteristics. Liu et al.\u003csup\u003e[\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e]\u003c/sup\u003e used the unidirectional fluid-solid coupling module of the Workbench to study the fluid flow within the butterfly valve and perform stress analysis on the butterfly plate, and optimize the design of the butterfly plate structure based on the fluid-solid coupling data. Gonzalez et al.\u003csup\u003e[\u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]\u003c/sup\u003e developed in-house numerical method based on a partitioned fluid-structure interaction algorithm intended to obtain high-fidelity numerical predictions and improve valve design. In their research, the differences in effective flow area and pressure drop caused by port geometry and valve speed are revealed. Hu\u003csup\u003e[\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e]\u003c/sup\u003e studied the cavitation phenomenon of the flow field in the ultra-supercritical steam trap, applied the CFD results to the coupling of temperature field, fluid field, and solid field, and the stress distribution of the ultra-supercritical steam trap in work conditions was analyzed, and also analyzed the valve stress types, carried out stress evaluation. Li\u003csup\u003e[\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e]\u003c/sup\u003e investigated the valve body stress of the feed-water valve in the opening process based on fluid-structure interaction analysis to avoid strength failure problems.\u003c/p\u003e \u003cp\u003eLittle research work has been faced on the high backpressure regulation by valve in valve design handbook or published literature\u003csup\u003e[\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e]\u003c/sup\u003e. Some patents show variable the brief structures of the backpressure valve for different application. Little work provide a much more detail information about the flow and stress characteristics of the backpressure value. Recently, Northwest University (NWU) designed and manufactured a backpressure valve with a spherical valve core\u003csup\u003e[\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e]\u003c/sup\u003e with a backpressure range of 2-30MPa. The objective of this work is to obtain the characteristics of the inlet pressure, maximum flow rate, and maximum turbulent kinetic energy of this high-performance backpressure valve with the valve opening, and the stress distribution of the backpressure valve in severeness conditions, by the fluid-solid coupling method. It hopes to explore the applicability of the backpressure valve.\u003c/p\u003e"},{"header":"2. Nwu Backpressure Valve","content":"\u003cp\u003eThe backpressure valve adjusts the inlet pressure to the pressure required by the working condition through the throttling principle. The flow direction and pressure in front of the valve is controlled by changing the position of the valve core. The fluid flows from the inlet to the valve core and is throttled by a narrow channel between valve core and valve seat. At the same time, the valve core receives an upward force under the action of the fluid pressure. When this force increases to a certain value balancing the pressure difference, the spring is compressed, and the fluid pushes up the valve to form a throttling channel. Then the pressure is continuously reduced when the fluid flows through the throttle channel and finally flows out from the outlet of the backpressure valve. If the fluid pressure is not enough to push up the valve core, the valve seat and the valve core will be closed, and the pressure is held inside of the valve cavity to increase the lock pressure. When the inlet pressure rises to the setting pressure, the fluid will lift the valve core to form a throttle channel. By adjusting the spring stroke to apply pressure to the stem and then adjusting the length of the spring, the setting pressure of the backpressure valve can be changed. Figure\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e shows the structure of the backpressure valve.\u003c/p\u003e "},{"header":"3. Experiment Setup","content":"\u003cp\u003eA diagram of the test bench is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The inlet pressure and inlet flow rate of the backpressure valve can be measured experimentally. The deionized water stored in the water tank was pumped into the pipeline by a vertical multistage centrifugal pump and enters the backpressure valve. A bypass valve is installed at the pump outlet to adjust the inlet flow rate of the backpressure valve. The Orifice flowmeter and pressure gauge are installed ahead of the valve. After switching on the pump, adjust the opening of the bypass valve and record the orifice flowmeter reading. When the flow rate is adjusted to measured value, the data of pressure gauge with varying opening was recorded.\u003c/p\u003e "},{"header":"4. Numerical Simulation Method","content":"\u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Physical model and grid generation\u003c/h2\u003e \u003cp\u003eDue to the connecting spring, the valve core will move up and down in a small range that is difficult to predict in the actual adjustment process, and the valve core will be in a balanced position when the fluid flow is stable. In the numerical simulation, it only need to consider the opening of the balanced position of the valve core as a variable value, so it is necessary to simplify the spring. Meanwhile, parts 7\u0026ndash;16 are used to apply pre-tightening force to the valve core of the backpressure valve by adjusting the position of the valve stem 2, then adjusting the valve opening. To simplify the calculation, parts 7\u0026ndash;16 are simplified into an integral valve body component, and the distance between the backpressure valve core (Ruby seat) and the valve seat (sapphire) is directly given as the valve opening.\u003c/p\u003e \u003cp\u003eThe flow channel structure of the backpressure valve studied in this paper is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. The inlet and outlet dimensions of the flow field are 10 mm. Due to the particularity of the backpressure valve structure, the valve opening is determined by the distance between the backpressure valve spool (ruby seat) and the valve seat (sapphire). Adjust the distance between the valve core and the valve seat to obtain different openings. This research considered 17 sets of openings distributed between 0.39-1.75mm, and the state at 1mm opening is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e4.1.1 Fluid domain\u003c/h2\u003e \u003cp\u003eTo study the fluid flow characteristics in the backpressure valve, the calculation domain of the backpressure valve channel is extracted, and the geometric model of the internal flow field of the backpressure valve is obtained. Since the flow channel structure is symmetrical, 1/2 of the flow field is selected as the computational domain to save energy, computer memory, and calculation time. The geometric model of the flow field computational domain is shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. There are four types of boundaries in the computational domain, also given in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e. Significantly, all surfaces except for the inlet, outlet, and boundary conditions of the symmetry plane are defined as fluid-solid-interaction walls (FSI_walls).\u003c/p\u003e \u003cp\u003eDue to the complex structure at the valve core of the backpressure valve, the cross-section size of the flow channel is usually less than 1mm under the condition of a small opening, resulting in a throttling effect and significant pressure drop, and the meshing here is more complex. Therefore, it is necessary to verify the grid independence before calculating the convective domain. Due to the complex grid structure of the valve core, the grid is used at the narrow part of the valve core. The overall meshing results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e.\u003c/p\u003e\u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e4.1.2 Solid domain\u003c/h2\u003e \u003cp\u003eIn the Fluid-Solid analysis, the material of the backpressure, the valve core, and the valve seat are 316 stainless steel, industrial ruby, and industrial sapphire, respectively. To ensure the sealing property, a Polytetrafluoroethylene (PTFE) pad is installed at the connection between the valve body and the valve seat. The physical parameters of the above materials are shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003ePhysical parameter of the materials\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterials\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eDensity / g\u0026middot;cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eElastic modulus / Pa\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003ePoisson ratio\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e316 stainless steel\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e7.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.93\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrial ruby\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.00\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eIndustrial sapphire\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e4.00\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.00\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePTFE\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e2.20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.80\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e8\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZirconia\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e6.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.10\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSilicon nitride ceramics\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e3.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.00\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e11\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.25\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eDue to the complex structure, a combination of tetrahedrons and hexahedrons is used to mesh the backpressure valve. Tetrahedron elements are used to mesh parts with irregular structures such as valve cores and valve bodies, and hex dominant elements are used to divide parts with regular structures such as gaskets, valve seats, and fastening nuts to reduce the amount of calculation. Finally, the number of meshes is 475342, and the number of nodes is 847001. Figure\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e shows the results of meshing.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Numerical model and parameter settings\u003c/h2\u003e \u003cp\u003eThe governing equations include continuity equation and momentum conservation equation and turbulence model. The standard k-ε model\u003csup\u003e[\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]\u003c/sup\u003e was applied to describe the turbulence flow. The governing equation mentioned above is solved by using the following scheme. The volume force generated by gravity is considered because of the considerable density value of the liquid phase fluid. In pressure-velocity coupling, the SIMPLE scheme is used because it allows higher pressure corrections with relaxation factors that help accelerate convergence. To maintain the accuracy and convergence stability, momentum and standard k-ε equations adopt the second-order upwind scheme. The convergence accuracy is 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e to satisfy the continuity of mas law.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec11\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Model validation\u003c/h2\u003e \u003cp\u003eDue to the narrow flow channel between the valve core and complex structure, the tetrahedral grid is used for grid division. The fluid flew grid at the valve core is densified to varying degrees to obtain five grids with the number 430000, 730000, 1050000, 1260000, and 1470000. The five grids are simulated and calculated respectively to obtain Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. It can be seen intuitively that the CFD model basically meets the grid independence.\u003c/p\u003e\u003cp\u003eAs can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e that the inlet pressure of the five grids is very close, and the maximum relative error is 1.4%, which proves that the selection of grid size is reasonable. To ensure the calculation accuracy and reduce the amount of calculation, 430000 grids are selected for calculation. Then the fluid grid size at the valve core corresponding to this grid number is chosen for simulation and calculation.\u003c/p\u003e \u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e shows the simulation and experimental data at an inlet mass flow rate of 0.1389kg/s. As can be seen from Fig.\u0026nbsp;\u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e that both the simulated pressure value and the experimental pressure value show a trend of decreasing with the valve opening. And the curve trends of the two groups are in good agreement. Errors of the two are in the range tolerance. The simulated results can be considered reliable. Meanwhile, the rationality of the CFD mentioned above model was validated.\u003c/p\u003e \u003c/div\u003e"},{"header":"5. Results And Discussions","content":"\u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e5.1 Pressure regulation characteristics\u003c/h2\u003e \u003cdiv id=\"Sec14\" class=\"Section3\"\u003e \u003ch2\u003e5.1.1 Effect of opening\u003c/h2\u003e \u003cp\u003eThe opening greatly affect the flow area, dynamic flow and pressure characteristics\u003csup\u003e[\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]\u003c/sup\u003e. The opening of different valve core shapes, such as V-shape\u003csup\u003e[\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]\u003c/sup\u003e, S-shape\u003csup\u003e[\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e]\u003c/sup\u003e, sphere-shape, circular-shape, pyramid-shape, ellipsoid-shape\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e, circular-cone-shape\u003csup\u003e[\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]\u003c/sup\u003e and Bio-inspired-shape\u003csup\u003e[\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]\u003c/sup\u003e,etc, has been focus in literature. The present reported value commonly has one throttling channel, while there are two throttling channels when the fluid flows to the valve core seat of the NWU backpressue valve, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e. The first part is the channel between the valve core seat (ruby seat) and the fastening nut (Part 21 in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e), and the second part is between the valve core (ruby) and the valve seat (sapphire). The fluid flows through two throttling actions outlet channel to the outlet. Figure\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e shows the pressure distribution in the condition of the flow rate 0.1389kg/s and opening of 0.39mm. The maximum inlet pressure is observed as 28.903MPa. The cross-sectional area of the valve decreases when the fluid flows through the first throttling channel, then becomes larger when the fluid flows into the chamber after the first throttling channel, and then becomes smaller at the second throttling channel. In the chamber after the first throttling channel, the fluid pressure accumulates and the fluid velocity decrease to some extend to avoid too strong souring. Therefore, there is a local pressure increase after the fluid flows through the first throttling channel.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003ea shows that high inlet pressure is decreased to ambient value when the fluid flows through the two throttling channels. Especially the pressure drop through the throttling channel between ruby and sapphire is obvious, which indicates that the purpose of decompression can be well achieved. Compared with the velocity distribution of Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003eb, it can be seen that the maximum flow rate appears at the second throttling channel. The pressure and velocity distribution at the throttle with valve opening of 0.39mm, 0.43mm, 0.55mm, and 0.9mm were simulated and the calculated inlet pressure corresponding to its opening is 29.803MPa, 19.687MPa, 9.898MPa, and 2.084MPa, respectively. It can be seen that the area of the flow channel decreases with the decreasing opening. The decreasing opening increases inlet pressure. When the opening reduces to 0.39 mm, the inlet pressure achieves 30 MPa. After the fluid flows through the first throttling channel, it quickly rises to close to the inlet pressure; It can be known that the larger the inlet pressure, the greater the pressure of the space between the two throttling channels. Especially under the working condition of 29.803mpa (i.e., the opening is 0.39mm), the fluid flows through the first throttling channel and rises rapidly to near the inlet pressure. The valve opening greatly affect the local pressure and velocity distribution of the throttling area. For the situations of larger opening of 0.43 mm, 0.55 mm and 1.25 mm, the pressure gradually decrease through the two throttling channels. The pressure in the chamber after the first throttling channel is lower than the pressure in the first throttling channel and higher than that in the second throttling channel. However, the pressure in the chamber after the first throttling channel is higher than the pressure in the first throttling channel when the opening reduces to 0.39 mm. The maximum speed occurs at the second throttle channel. When the opening is 1.25mm, the corresponding working pressure is 2.084MPa, and the fluid flow rate is uniform from the first throttle channel to the top of the ruby. With the decrease of opening, the speed difference between the first throttle and the second throttle increases gradually. And the maximum flow velocity is 294.6 m/s.\u003c/p\u003e\u003cp\u003eThe pressure at the top of the valve core is higher than in other areas. Figure\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e is the local velocity around the valve core. The fluid flows through the second throttling channel at high speed, and form jet flow characteristics in the outlet pipe. The flow direction is the positive direction of the Y-axis, without fluid back-flow.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec15\" class=\"Section3\"\u003e \u003ch2\u003e5.1.2 Effect of inlet flow rate\u003c/h2\u003e \u003cp\u003eThe flow characteristics in terms of inlet pressure, maximum flow velocity, and maximum turbulent kinetic energy were analyzed in variable openings and inlet flow rates. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e shows that the pressure of the valve inlet and valve chamber continue to decrease as the increasing opening. When the valve opening is less than 0.6 mm, the inlet pressure decreases rapidly with the increase of the valve opening. When the valve opening is more significant than 0.6 mm, the inlet pressure decreases slowly with the increase of the opening, and the downward trend has decreased. The increased inlet flow rate increases the inlet pressure at the same opening, especially at the much smaller opening. When the inlet pressure is fixed, the flow rate vs. the opening shows a quick-opening characteristics\u003csup\u003e[\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e]\u003c/sup\u003e, although the main function of the backpressure valve is regulating the inlet pressure.\u003c/p\u003e\u003cp\u003eFigure\u0026nbsp;\u003cspan refid=\"Fig13\" class=\"InternalRef\"\u003e13\u003c/span\u003e and \u003cspan refid=\"Fig14\" class=\"InternalRef\"\u003e14\u003c/span\u003e also show the same trend as the Fig.\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e12\u003c/span\u003e. That is, when the valve opening is less than 0.6 mm, the maximum flow velocity and maximum turbulent kinetic energy in the valve will decrease rapidly with the increase of the valve opening. When the valve opening is greater than 0.6 mm, the decreasing trend of maximum flow velocity and maximum turbulent kinetic energy decreases, decreases slowly as the opening degree increases. At the small valve opening, the distance between the valve core and the valve seat is very small, and there is a phenomenon of build-up pressure in the valve, so when the valve opening increases slightly, the valve inlet pressure and the valve cavity pressure will drop significantly. On the contrary, when the opening is bigger than 0.6 mm, the cross-sectional area of the throttling channel between ruby and sapphire will become larger, and there will be no more pressure in the chamber after the first throttling channel. Thus, the pressure of the inlet and valve chamber has no longer declines drastically with the increase of the opening. Taking the inlet flow rate of 0.1389 kg∙s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e as an example. When the opening is 0.6 mm, the inlet pressure value is 8.344 MPa. When the inlet pressure is more significant than 8.344 MPa, there may be a phenomenon of build-up pressure in the chamber after the first throttling channel. It has to increase the valve opening slightly to reduce the inlet pressure. However, there is no such phenomenon in the valve cavity when the valve inlet pressure is less than 8.344 MPa. The valve opening must be significantly increased to reduce the inlet pressure.\u003c/p\u003e\u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e5.2 Stress distribution characteristics\u003c/h2\u003e \u003cdiv id=\"Sec17\" class=\"Section3\"\u003e \u003ch2\u003e5.2.1 Stress distribution\u003c/h2\u003e \u003cp\u003eThe CFD simulation shows that when the inlet mass flow is 0.1389kg∙s\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e and the valve opening is 0.39mm, the inlet pressure of the backpressure valve reaches 29.803 MPa. Meanwhile, the cross-sectional area of the second throttling channel between the valve core and the valve seat reaches the minimum value when the inlet pressure is 29.803 MPa. When the fluid passes through the throttling passage, the pressure drops sharply, and there is also a phenomenon of build-up pressure in the chamber after the first throttling channel. Further, 29.803 MPa is considered a severe working condition of the backpressure valve. The stress distribution and deformation of the backpressure valve at an inlet pressure of 29.803 MPa was analyzed, and the applicability of the valve core material and structure was evaluated. The fluid-solid coupling stress distribution results of the valve at an opening of 0.39 mm and an inlet pressure of 29.803 MPa are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e, and the deformation results are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e.\u003c/p\u003e \u003cp\u003eThe maximum stress occurs at the joint edge where is located at the PTFE pad (part 19) connecting the valve core seat and the valve body, and the value is 192.54 MPa. The maximum displacement is 0.0081 mm. In Fig.\u0026nbsp;\u003cspan refid=\"Fig15\" class=\"InternalRef\"\u003e15\u003c/span\u003e, the maximum stress value at the valve seat is 121.85 MPa, the maximum stress value at the valve core is 95.763 MPa, the maximum stress value at the joint line of part 17 and part 30 is 90.35 MPa. the maximum stress value occurred in the joint of the stress value of the valve seat and the fluid, and the overall stress distribution gradually decreases from the pressure-bearing side to the outside. Because the material of the part 17 and part 30 is different, the stress transmission is discontinuous at the rigid contact, so there is a small-scale stress concentration at the joint of the valve seat in the direction of gravity (the positive direction of the Y-axis) and the valve body.\u003c/p\u003e \u003cp\u003eThe stress distribution of the valve core presents a situation where the stress in the middle and lower parts is higher than the top part of the valve core. Due to the high pressure before the fluid flows through the throttle channel and the fluid force squeezes the valve core seat, the pressure is transmitted to the valve core through the valve core seat. Because the valve core and the valve core seat are made by different materials and the structure is not continuous, a small area of stress concentration occurs at the contact point. The maximum stress value appears at the stress concentration point. If the valve core is one part and made by same material, the stress concentration may occur in the middle position and the touch edge with fluid\u003csup\u003e[\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]\u003c/sup\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig16\" class=\"InternalRef\"\u003e16\u003c/span\u003e shows the maximum deformation values at the valve seat, valve core, and valve core seat are 0.00405 mm, 0.00382 mm, and 0.00485 mm, respectively. The maximum stress value occurs at the connection point between the valve core seat and the valve body.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section3\"\u003e \u003ch2\u003e5.2.2 Effect of valve core materials\u003c/h2\u003e \u003cp\u003eFour kinds of valve core materials, namely ruby (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{Al}}_{\\text{2}}{\\text{O}}_{\\text{3}}\\)\u003c/span\u003e\u003c/span\u003e), 316 stainless steel, zirconia and silicon nitride ceramic, are selected to analyze stress distribution and deformation. The physical parameters of materials are given in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig17\" class=\"InternalRef\"\u003e17\u003c/span\u003e shows a stress cloud, and Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e summaries the calculation results. Different materials between the valve core and seat, and the discontinuous structure cause a range of stress concentration. The maximum stress value appears at the stress concentration.\u003c/p\u003e \u003cp\u003eThe fluid pressure is transmitted to the valve core through the valve seat, and the stress value at the valve core is less than that at the valve seat. However, due to the fluid flow, the fluid will give the valve core a fluid force in the negative direction along the Y-axis. The valve core squeezes the valve seat under the action of fluid force, resulting in local stress concentration, and the maximum stress value appears. The maximum stress value does not exceed the allowable stress of the material, and the overall structural design, and material selection are reasonable and can meet the requirements of working conditions.\u003c/p\u003e \u003cp\u003eThe maximum stress of the 316 stainless steel valve core at the concentration of stresses is the smallest compared with the other three materials, because the material has the lowest elastic modulus. With the increase of the elastic modulus of the material, the stress concentration value between the valve core and the gem base is larger due to the rigid connection of different materials, and the stress concentration value is the largest when the valve core material is silicon nitride ceramic. The maximum stress of the four kinds of valve core do not exceed the allowable stress.\u003c/p\u003e\u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCalculation results of maximum stress and deformation\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eMaterials\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRuby ball\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSilicon nitride\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eZirconia\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003e316 stainless steel\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe maximum stress value / MPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e95.763\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e97.106\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e76.619\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e43.288\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThe maximum deformation / mm\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.8231\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.7736\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e3.7128\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.8316\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\(\\times\\)\u003c/span\u003e\u003c/span\u003e10\u003csup\u003e\u0026minus;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePrimary stress limit* /MPa\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e152\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e140\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e180\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e164\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003e*Calculation based on materials properties and standard given by ASME Ⅷ-2 \u003csup\u003e[\u003cspan citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e]\u003c/sup\u003e.\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003c/div\u003e"},{"header":"6. Conclusions And Prospects","content":"\u003cp\u003eA recently developed backpressure valve using a valve core structure of rubble ball and gem base was numerically investigated and analyzed the characteristics of the inlet pressure, maximum flow velocity, and maximum turbulent kinetic energy. The simulation results were compared with the experiment measured data to validate the numeral model. The fluid-solid coupling method was used to analyze the stress distribution of the backpressure valve under 30 MPa. The following conclusions mainly includes:\u003c/p\u003e\n\u003cp\u003e\u003cspan\u003e1. The pressure value of the model predication and the experimental measurement showed a good agreement, which indicates the present model is suitable for describing the flow field in the backpressure valve.\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e\u003cspan\u003e2. The inlet pressure, maximum flow velocity, and maximum turbulent kinetic energy of the fluid in the backpressure valve reduce with the increase of valve opening. There is a more severe build-up pressure in the valve in the valve opening degree of less than 0.6 mm. The valve inlet and chamber pressure will greatly decrease when the valve opening increases slightly larger than 0.6 mm.\u003c/span\u003e\u003c/p\u003e\n\u003cp\u003e\u003cspan\u003e3. The valve core structure of structure of rubble ball and gem base can well satisfy the pressure regulation requirements of the backpressure valve within the strength range. Four kinds of valve core materials of ruby (\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({\\text{Al}}_{\\text{2}}{\\text{O}}_{\\text{3}}\\)\u003c/span\u003e\u003c/span\u003e), 316 stainless steel, zirconia and silicon nitride ceramic are suggested to make the valve core.\u003cbr\u003e\u003c/span\u003e\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eAvailability of data and materials\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that data supporting the findings of this study are available within the article.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFunding\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis work was funded by The National Natural Science Foundation of China (No. 22278332), the State Key Laboratory of Clean Energy Utilization (Open Fund Project No. ZJUCEU2020020), and the Joint Laboratory for High Pressure Flow Control and Safety Technology. The views and opinions expressed are those of the authors and not necessarily those of the funding organizations. The funding organizations had no role in the design of the study, and collection, analysis, and interpretation of the data, or writing of the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthors\u0026apos; contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eYZY, HJY, GYK and WLP designed the study. YZY, HJY conducted the literature search. YZY, HJY, GYK, JCL, LQ, and WLP were involved in the analysis and interpretation of data. YZY, HJY and WLP drafted the manuscript. The study was supervised by WLP. All authors read and approved the final manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThis research is supported by the National Natural Science Foundation of China (No. 22278332), supported by the State Key Laboratory of Clean Energy Utilization (Open Fund Project No. ZJUCEU2020020), and Mr. Pengjun Mao from Joint Laboratory for High Pressure Flow Control and Safety Technology.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eLiu, Y. H., 2014, \u0026ldquo;Design and Performance of Pilot Operated Relief Valve of MRF,\u0026rdquo; Kunming university of science and technology, Kunming.\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eYu, Y. 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Available at: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.4028/www.scientific.net/AMM.313-314.1210\u003c/span\u003e\u003cspan address=\"10.4028/www.scientific.net/AMM.313-314.1210\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e.\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Backpressure valve, 30 MPa, simulation, fluid-solid coupling, pressure curves","lastPublishedDoi":"10.21203/rs.3.rs-2058873/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-2058873/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eHigh performance backpressure valve is critical for the high-pressure fluid control technology. However, the back pressure easily suffers mechanical failure caused by the strong fluid flushing when the back pressure up to 30 MPa. This work used computational fluid dynamics and solid mechanics analysis method to analyze the basic flow and resistance characteristics of a recently developed backpressure valve. The inlet pressure, maximum flow rate, and maximum turbulent kinetic energy of the 2-30MPa backpressure valve decreases with the increasing the valve opening were analyzed in details. There is pressure suppression phenomenon in the valve chamber when the valve opening is less than 6 mm. The fluid-solid coupling results show that the existing structure of the flow channel and valve core seat can satisfy the pressure regulation requirements within the strength range, and the structure of ball spool seat improve the pressure regulation ability.\u003c/p\u003e","manuscriptTitle":"Fluid-solid Coupling Analyzing Pressure Regulation Characteristics of a Ball-seat Backpressure Valve in 2-30MPa Operating Conditions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2022-10-10 15:38:50","doi":"10.21203/rs.3.rs-2058873/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"910246da-79f5-4fc8-ae32-68bf915d2e6b","owner":[],"postedDate":"October 10th, 2022","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[],"tags":[],"updatedAt":"2023-09-15T09:00:52+00:00","versionOfRecord":[],"versionCreatedAt":"2022-10-10 15:38:50","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-2058873","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-2058873","identity":"rs-2058873","version":["v1"]},"buildId":"cBFmMYwuxLRRLfASyISRj","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}