Method for predicting transient throttling temperature of solenoid valve

Abstract

The application discloses a solenoid valve transient throttling temperature prediction method, comprising the following steps: step 1, according to the isentropic flow model and the choked flow theory, a valve port minimum temperature calculation model is established; step 2, the valve port flow coefficient is introduced, the valve port minimum temperature calculation model is optimized, and a high-precision calculation model is obtained; step 3, a test system is constructed, the solenoid valve is subjected to multi-condition air release test through the test system, and test data are acquired; step 4, the valve port flow coefficient is inverted through the test data, multi-level verification of the high-precision calculation model is completed, and the valve port transient temperature is calculated according to the high-precision calculation model. The solenoid valve transient throttling temperature prediction method disclosed by the application solves the problem that the extreme minimum temperature of a valve port in a transient opening and closing process of an existing superhigh-pressure solenoid valve is difficult to directly observe and accurately predict.

Description

Technical Field

[0001] This invention belongs to the field of ultra-high pressure solenoid valve technology, specifically relating to a method for predicting the transient throttling temperature of solenoid valves. Background Technology

[0002] Solenoid valves, as key actuators in fluid control systems, are widely used in high-pressure pneumatic circuits in aerospace, defense equipment, energy, and chemical industries, undertaking important functions such as rapid pipeline opening and closing, and pilot control. In pilot-operated ultra-high-pressure solenoid valves, when the valve opens rapidly under a pressure difference of tens of megapascals, the gas undergoes a violent adiabatic throttling expansion process, generating a significant transient cryogenic effect in a localized area of ​​the valve orifice. This transient cryogenic effect poses a severe challenge to the reliability of the solenoid valve. On the one hand, the low temperature reduces the toughness of the internal metal materials, causing brittleness and increasing the risk of component breakage; on the other hand, non-metallic sealing materials harden and shrink at low temperatures, leading to decreased sealing performance or even failure. More seriously, if the gas contains trace amounts of moisture, the low temperature at the valve orifice can easily cause ice blockage, preventing the valve from closing properly. Therefore, accurately predicting and evaluating the cryogenic characteristics of solenoid valves during transient throttling is of significant engineering importance for ensuring their reliable operation under extreme conditions.

[0003] Existing research on the temperature drop problem during gas throttling is largely based on classical thermodynamics and gas dynamics. For the isentropic expansion of an ideal gas, its temperature change can be directly calculated using the isentropic relationship. Regarding the cryogenic throttling problem of solenoid valves, scholars both domestically and internationally have conducted research from theoretical, component, and experimental perspectives. However, most existing studies treat cryogenicity as a stable boundary condition or consider the flow as a steady-state process. For the high-speed, non-equilibrium heat-fluid coupling problem induced by the transient opening and closing of valves under ultra-high pressure differentials—that is, the extremely low-temperature impact effect of adiabatic expansion at the valve orifice within milliseconds and its direct impact on the valve's dynamic function—specific experimental observations and mechanism verification are still lacking. This results in a cognitive gap between the theoretically predicted minimum valve orifice temperature and the actual engineering tolerance.

[0004] In practical engineering applications, choked flow theory is often used to describe the mass flow rate through a constricted channel under high pressure differentials and serves as the basis for analyzing valve orifice flow. Existing research often treats low temperature as a stable boundary condition or considers the flow as a steady-state process. For high pressure differentials, especially under ultra-high pressure conditions >23 MPa, the high-speed, non-equilibrium heat-fluid coupling problem induced by transient valve opening and closing—that is, the extremely low-temperature impact effect of adiabatic expansion at the valve orifice within milliseconds and its direct impact on the valve's dynamic function—lacks targeted and verifiable theoretical prediction methods and experimental observation means. This leads to doubts about the applicability and accuracy of theoretical models under extreme transient conditions. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the transient throttling temperature of a solenoid valve, which solves the problem that the extreme minimum temperature at the valve orifice is difficult to directly observe and accurately predict during the transient opening and closing process of existing ultra-high pressure solenoid valves.

[0006] The technical solution adopted in this invention is a method for predicting the transient throttling temperature of a solenoid valve, comprising the following steps:

[0007] Step 1: Based on the isentropic flow model and choke flow theory, establish a calculation model for the minimum temperature at the valve orifice; Step 2: Introduce the valve orifice flow coefficient and optimize the calculation model for the minimum valve orifice temperature to obtain a high-precision calculation model; Step 3: Construct a test system and conduct multi-condition venting tests on the solenoid valve using the test system to obtain test data; Step 4: Invert the valve orifice flow coefficient through experimental data to complete the multi-level verification of the high-precision calculation model. Based on the high-precision calculation model, calculate the transient temperature of the valve orifice.

[0008] The invention is further characterized by: Step 1 isentropic flow model is a gas state change model inside the gas cylinder; The mass of the gas in the gas cylinder is calculated according to the gas state change model in the gas cylinder according to equation (1); (1); in, This refers to the mass of the gas inside the cylinder. The density of the gas; This refers to the volume of the gas cylinder; Calculate the gas density inside the gas cylinder according to the gas state change model in equation (2); (2); in, This refers to the cylinder pressure. is the gas constant of air; For temperature.

[0009] The critical pressure ratio of the choke flow theory in step 1 is calculated according to equation (3); (3); in, The adiabatic index of air; Calculate the gas mass flow rate according to equation (4) based on the choke flow theory; (4); in, The effective area of ​​the valve port; This is the valve orifice flow coefficient.

[0010] The pressure and density of the gas state change model inside the gas cylinder are shown in equation (5); (5).

[0011] The relationship between the gas state changes inside the gas cylinder in the gas cylinder state change model is shown in equation (6); (6); in, For time step.

[0012] The gas pressure at the valve port of the calculation model for the lowest valve port temperature is shown in equation (7). (7); According to equations (5), (6) and (7), the temperature at the valve port is obtained as shown in equation (8); (8).

[0013] The test system in step 3 includes a gas cylinder, a shut-off valve, a safety valve, a voltage transformer, the solenoid valve under test, an exhaust port, a high-precision timer, and connecting pipes. The working medium of the test system is clean compressed air that has undergone three-stage filtration to remove water, oil, and dust. A safety valve is installed on the outlet pipe of the gas cylinder. The diameter of all connecting pipes and shut-off valves in the test system is not less than 1.5 times the diameter of the solenoid valve under test. The solenoid valve under test is installed in series at the outlet of the gas cylinder. The on / off state of the solenoid valve under test is controlled by a solid-state relay via a digital I / O module by a host computer. The controller of the test system consists of a host computer, a data acquisition system, and measurement and control software.

[0014] Step 3 involves conducting a multi-condition venting test on the solenoid valve using a testing system to obtain test data. The specific process is as follows: S3.1. The gas cylinder in the test system is filled with gas using a high-pressure gas source to reach the preset initial pressure value; S3.2 After inflation, allow the test system to stand still and stabilize the pressure to ensure that the gas temperature in the gas cylinder reaches thermal equilibrium with the ambient temperature and the pressure gauge reading is stable. S3.3 The host computer controls the relay to momentarily open the solenoid valve under test, and simultaneously starts a high-precision timer. The solenoid valve under test remains open until the predetermined venting time is reached, after which it closes. Throughout the venting process, the data acquisition system records the dynamic change curve of the gas cylinder pressure in real time and extracts the initial pressure. Final pressure and the corresponding opening time ; S3.4, repeat S3.1~S3.3, conduct multiple sets of experiments, and obtain experimental data.

[0015] The initial pressure value is 1~30 MPa, the static pressure stabilization time is not less than 1800 seconds, and the interval between multiple tests is not less than 600 seconds.

[0016] The beneficial effects of this invention are: The transient throttling temperature prediction method for solenoid valves provided by this invention demonstrates a clear pressure dependence in the flow coefficient derived from experimental data, verifying the physical rationality of the model. Even under operating conditions with calculated valve temperatures as low as -90 °C, the solenoid valve can still open and close normally, and experiments observed frost formation on the pipe wall, with no ice blockage detected during disassembly. These results, from both parameter regularity and functional tolerance perspectives, jointly confirm the reliability of the theoretical model in predicting the transient cooling trend at the valve orifice, providing data and theoretical reference for the reliability assessment and application of similar solenoid valves under extreme expansion and low-temperature conditions. Attached Figure Description

[0017] Figure 1 This is a schematic diagram of the ultra-high pressure solenoid valve structure in Embodiment 6 of the transient throttling temperature prediction method for solenoid valves of the present invention; Figure 2 This is a schematic diagram of the core iterative process in Embodiment 6 of the present invention; Figure 3 This is a schematic diagram of the overall layout of the test system in Embodiment 6 of the present invention; Figure 4 This is a schematic diagram of the temperature and pressure curve of the DN15 valve in Embodiment 6 of the present invention; Figure 5 This is a schematic diagram of the five exhaust tests of the DN15 valve in Embodiment 6 of the present invention; Figure 6 This is a schematic diagram comparing the cooling rates of DN15 and DN6 in Embodiment 6 of the present invention; Figure 7 This is a schematic diagram showing the relationship between valve temperature and time for DN15 and DN6 in Embodiment 6 of the present invention; Figure 8 This is a schematic diagram of flow coefficient fitting and model correction in Embodiment 6 of the present invention. Detailed Implementation

[0018] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0019] Example 1 The transient throttling temperature prediction method for solenoid valves proposed in this embodiment includes the following steps: Step 1: Based on the isentropic flow model and choke flow theory, establish a calculation model for the minimum temperature at the valve orifice; Step 2: Introduce the valve orifice flow coefficient and optimize the calculation model for the minimum valve orifice temperature to obtain a high-precision calculation model; Step 3: Construct a test system and conduct multi-condition venting tests on the solenoid valve using the test system to obtain test data; Step 4: Invert the valve orifice flow coefficient through experimental data to complete the multi-level verification of the high-precision calculation model. Based on the high-precision calculation model, calculate the transient temperature of the valve orifice.

[0020] Example 2 The transient throttling temperature prediction method for solenoid valves proposed in this embodiment includes the following steps: Step 1: Based on the isentropic flow model and choke flow theory, establish a calculation model for the minimum temperature at the valve orifice; The isentropic flow model is a model for the change of gas state inside the gas cylinder; The mass of the gas in the gas cylinder is calculated according to the gas state change model in the gas cylinder according to equation (1); (1); in, This refers to the mass of the gas inside the cylinder. The density of the gas; This refers to the volume of the gas cylinder; Calculate the gas density inside the gas cylinder according to the gas state change model in equation (2); (2); in, This refers to the cylinder pressure. is the gas constant of air; For temperature; Step 2: Introduce the valve orifice flow coefficient and optimize the calculation model for the minimum valve orifice temperature to obtain a high-precision calculation model; Step 3: Construct a test system and conduct multi-condition venting tests on the solenoid valve using the test system to obtain test data; Step 4: Invert the valve orifice flow coefficient through experimental data to complete the multi-level verification of the high-precision calculation model. Based on the high-precision calculation model, calculate the transient temperature of the valve orifice.

[0021] Example 3 The transient throttling temperature prediction method for solenoid valves proposed in this embodiment includes the following steps: Step 1: Based on the isentropic flow model and choke flow theory, establish a calculation model for the minimum temperature at the valve orifice; The isentropic flow model is a model for the change of gas state inside the gas cylinder; The mass of the gas in the gas cylinder is calculated according to the gas state change model in the gas cylinder according to equation (1); (1); in, This refers to the mass of the gas inside the cylinder. The density of the gas; This refers to the volume of the gas cylinder; Calculate the gas density inside the gas cylinder according to the gas state change model in equation (2); (2); in, This refers to the cylinder pressure. is the gas constant of air; For temperature; The critical pressure ratio of the choke flow theory is calculated according to equation (3); (3); in, The adiabatic index of air; Calculate the gas mass flow rate according to equation (4) based on the choke flow theory; (4); in, The effective area of ​​the valve port; The valve orifice flow coefficient; Step 2: Introduce the valve orifice flow coefficient and optimize the calculation model for the minimum valve orifice temperature to obtain a high-precision calculation model; Step 3: Construct a test system and conduct multi-condition venting tests on the solenoid valve using the test system to obtain test data; Step 4: Invert the valve orifice flow coefficient through experimental data to complete the multi-level verification of the high-precision calculation model. Based on the high-precision calculation model, calculate the transient temperature of the valve orifice.

[0022] Example 4 The transient throttling temperature prediction method for solenoid valves proposed in this embodiment includes the following steps: Step 1: Based on the isentropic flow model and choke flow theory, establish a calculation model for the minimum temperature at the valve orifice; The isentropic flow model is a model for the change of gas state inside the gas cylinder; The mass of the gas in the gas cylinder is calculated according to the gas state change model in the gas cylinder according to equation (1); (1); in, The mass of the gas inside the cylinder; The density of the gas; This refers to the volume of the gas cylinder; Calculate the gas density inside the gas cylinder according to the gas state change model in equation (2); (2); in, This refers to the cylinder pressure. is the gas constant of air; For temperature; The critical pressure ratio of the choke flow theory is calculated according to equation (3); (3); in, The adiabatic index of air; Calculate the gas mass flow rate according to equation (4) based on the choke flow theory; (4); in, The effective area of ​​the valve port; The valve orifice flow coefficient; The pressure and density of the gas state change model inside the gas cylinder are shown in equation (5); (5); The relationship between the gas state changes inside the gas cylinder in the gas cylinder state change model is shown in equation (6); (6); in, For time step; The gas pressure at the valve port of the calculation model for the lowest valve port temperature is shown in equation (7). (7); According to equations (5), (6) and (7), the temperature at the valve port is obtained as shown in equation (8); (8); Step 2: Introduce the valve orifice flow coefficient and optimize the calculation model for the minimum valve orifice temperature to obtain a high-precision calculation model; Step 3: Construct a test system and conduct multi-condition venting tests on the solenoid valve using the test system to obtain test data; Step 4: Invert the valve orifice flow coefficient through experimental data to complete the multi-level verification of the high-precision calculation model. Based on the high-precision calculation model, calculate the transient temperature of the valve orifice.

[0023] Example 5 The transient throttling temperature prediction method for solenoid valves proposed in this embodiment includes the following steps: Step 1: Based on the isentropic flow model and choke flow theory, establish a calculation model for the minimum temperature at the valve orifice; The isentropic flow model is a model for the change of gas state inside the gas cylinder; The mass of the gas in the gas cylinder is calculated according to the gas state change model in the gas cylinder according to equation (1); (1); in, This refers to the mass of the gas inside the cylinder. The density of the gas; This refers to the volume of the gas cylinder; Calculate the gas density inside the gas cylinder according to the gas state change model in equation (2); (2); in, This refers to the cylinder pressure. is the gas constant of air; For temperature; The critical pressure ratio of the choke flow theory is calculated according to equation (3); (3); in, The adiabatic index of air; Calculate the gas mass flow rate according to equation (4) based on the choke flow theory; (4); in, The effective area of ​​the valve port; The valve orifice flow coefficient; The pressure and density of the gas state change model inside the gas cylinder are shown in equation (5); (5); The relationship between the gas state changes inside the gas cylinder in the gas cylinder state change model is shown in equation (6); (6); in, For time step; The gas pressure at the valve port of the calculation model for the lowest valve port temperature is shown in equation (7). (7); According to equations (5), (6) and (7), the temperature at the valve port is obtained as shown in equation (8); (8); Step 2: Introduce the valve orifice flow coefficient and optimize the calculation model for the minimum valve orifice temperature to obtain a high-precision calculation model; Step 3: Construct a test system and conduct multi-condition venting tests on the solenoid valve using the test system to obtain test data; The test system includes a gas cylinder, a shut-off valve, a safety valve, a voltage transformer, a solenoid valve under test, an exhaust port, a high-precision timer, and connecting pipes. The working medium of the test system is clean compressed air that has undergone three-stage filtration to remove water, oil, and dust. A safety valve is installed on the outlet pipe of the gas cylinder. The diameter of all connecting pipes and shut-off valves in the test system is not less than 1.5 times the diameter of the solenoid valve under test. The solenoid valve under test is installed in series at the outlet of the gas cylinder. The on / off state of the solenoid valve under test is controlled by a solid-state relay via a digital I / O module by a host computer. The controller of the test system consists of a host computer, a data acquisition system, and measurement and control software. The specific process of obtaining test data by conducting multi-condition venting tests on the solenoid valve using a test system is as follows: S3.1. The gas cylinder in the test system is filled with gas using a high-pressure gas source to reach the preset initial pressure value; the initial pressure value is 1~30 MPa. S3.2 After inflation, allow the test system to stand still and stabilize the pressure to ensure that the gas temperature inside the gas cylinder reaches thermal equilibrium with the ambient temperature and the pressure gauge reading is stable; the stabilization time shall not be less than 1800 seconds. S3.3 The host computer controls the relay to momentarily open the solenoid valve under test, and simultaneously starts a high-precision timer. The solenoid valve under test remains open until the predetermined venting time is reached, after which it closes. Throughout the venting process, the data acquisition system records the dynamic change curve of the gas cylinder pressure in real time and extracts the initial pressure. Final pressure and the corresponding opening time ; S3.4 Repeat S3.1 to S3.3 to conduct multiple sets of experiments and obtain experimental data; the interval between multiple sets of experiments shall not be less than 600 seconds; Step 4: Invert the valve orifice flow coefficient through experimental data to complete the multi-level verification of the high-precision calculation model. Based on the high-precision calculation model, calculate the transient temperature of the valve orifice.

[0024] Example 6 The transient throttling temperature prediction method for solenoid valves proposed in this embodiment includes the following steps: 1. Physical models and numerical methods; 1.1 Working principle of solenoid valve; The ultra-high pressure two-position two-way solenoid valve used in this application has a pilot-operated structure, such as... Figure 1 As shown, the opening and closing logic of the solenoid valve relies on the differential pressure control of the internal air circuit, rather than the electromagnet directly driving the main valve core; this design enables it to respond to high differential pressure conditions, but also introduces key structures and processes closely related to transient throttling cooling. When the valve is normally closed, the high-pressure gas at the inlet fills the lower chamber of the main valve core and enters the feedback chamber above the main valve core through the internal flow channel. At this time, the gas force acting on the lower end face of the main valve core, the preload of the main spring, and the gas pressure in the feedback chamber are in balance, pressing the main valve core tightly against the lower stop of the valve body to form a seal. When the electromagnet is energized, the auxiliary valve core opens, and the gas is discharged from the exhaust port. The gas in the feedback chamber is rapidly released, causing a sudden drop in pressure at the upper end of the main valve core. The pressure balance between the upper and lower end faces is broken. Driven by the high pressure at the inlet, the main valve core is quickly lifted, the valve opens, and the high-pressure gas begins to flow through the throttling area of ​​the valve port. During this opening and closing process, the valve port area through which the gas flows is the core part where throttling expansion and transient low temperature occur. The gas adiabatic expansion and temperature drop effect that this application is concerned with occurs here. At the same time, whether the main valve core sealing structure exposed to this low temperature airflow can maintain its sealing and operating functions under extreme temperature drop is a key link in the experimental verification of this application. 1.2 Theoretical model of adiabatic venting and valve port temperature; To predict the minimum temperature in the valve port region during the transient venting process of an ultra-high pressure solenoid valve, a mathematical model describing the gas state changes inside the cylinder and the obstructed flow at the valve port is established. The derivation is based on the following basic assumptions: the venting process inside the cylinder is an adiabatic isentropic process; when the gas flows through the valve port, the flow reaches an obstructed state due to the extremely large pressure difference, and the outlet velocity is the local speed of sound; the working fluid is ideal air, and its physical properties are constant. 1) Basic governing equations; The gas cylinder is a rigid, constant-volume container; the mass of the gas inside the high-pressure gas cylinder; (1); in, The mass of the gas inside the cylinder. For gas density, This refers to the volume of the gas cylinder; The gas density inside the cylinder is derived from the ideal gas law; (2); in, The pressure of the gas cylinder. Let be the gas constant of air. For temperature; 2) Congested flow and mass flow rate; When gas flows through a constricting nozzle, if the upstream-to-downstream pressure ratio is below the critical pressure value, the outlet velocity will reach the speed of sound, i.e., choked flow will occur. Critical pressure ratio: (3); in, The adiabatic index of air; When the ratio of the pressure inside the bottle to the external pressure is greater than the critical pressure ratio, the flow rate depends only on the upstream (inside the bottle) conditions and the throat area. The formula for the gas mass flow rate under choked flow conditions is as follows: (4); in, The effective area of ​​the valve port; The valve orifice flow coefficient; Valve orifice flow coefficient These are empirical parameters in the model and need to be determined by back-calculation using experimental data; 3) Changes in isentropic state within the gas cylinder; For the assumed adiabatic isentropic release process, the gas state inside the cylinder satisfies the isentropic relationship, that is, the pressure and density satisfy: (5); As gas is expelled, the density, pressure, and temperature inside the cylinder change. The state changes inside the cylinder during an isentropic process are as follows: (6); in, For time step; 4) Theoretical model for valve orifice temperature; The valve port is the area where gas expansion is most intense and where the temperature is lowest. Under clogging conditions, the gas pressure at the valve port is the critical value of the upstream pressure, that is: (7); Substituting (6) and (7) into (5) yields the temperature at the valve opening: (8); This indicates that the minimum temperature at the valve orifice depends only on the current cylinder temperature and the critical pressure ratio, which is the core of the model's prediction of transient low temperatures; 5) Numerical solution process; Based on the above model, a time-stepping method is used for numerical solution. The core iterative process is as follows: Figure 2 As shown, given the initial conditions, , , After fixing the parameters, at each time step Within, solve in the following order; Iterate until the preset termination condition is met, namely, the valve port temperature is lower than the preset limit or the time reaches the preset value, and finally output the dynamic curve of pressure-time versus valve port temperature-time. The core output of this model is the transient temperature at the valve orifice. The accuracy of its predictions will be verified through indirect measurement results from experiments; 2. Experimental System and Methods; 2.1 Test System; To accurately reproduce the transient throttling and cooling conditions faced by ultra-high pressure solenoid valves in actual engineering, this application constructs a transient venting test system with a maximum working pressure of 30 MPa. The overall layout of the test system is as follows Figure 3 As shown; The system uses clean compressed air with three-stage filtration (water removal, oil removal, and dust removal) as the working medium. After being boosted to a preset pressure of 25~30 MPa by a booster pump, it is stored in a fixed-volume high-pressure gas cylinder. The outlet pipeline of the gas cylinder is equipped with a safety valve with a set pressure of 33~35 MPa to ensure the system's overpressure safety. To minimize the interference of pipeline throttling on the test, the diameter of all connecting pipes and shut-off valves is not less than 1.5 times the diameter of the solenoid valve under test, ensuring that the main pressure drop and temperature drop occur at the valve port under test. The solenoid valve under test, model and parameters are shown in Table 1. It is installed in series at the outlet of the high-pressure gas cylinder. Its on / off state is controlled by the host computer through the digital I / O module to execute the solid-state relay, realizing the instantaneous opening and closing with millisecond-level precision, accurately simulating the rapid response requirements in actual working conditions. Table 1 Data of the tested solenoid valve

[0025] The system's "nerve center" consists of a host computer (industrial control computer), a multi-functional data acquisition card, and customized measurement and control software. A pressure transmitter with an accuracy of ±0.5% FS monitors the cylinder pressure in real time, and the signal is converted to digital value by an A / D module and recorded synchronously. The host computer simultaneously sends control commands to precisely control the opening and closing sequence of the solenoid valves and automatically records the initial pressure of each test. Final pressure and precise on / off duration ; The entire test was conducted at an ambient temperature of 15±3°C; the electrical components of the system were designed to be explosion-proof and isolated to meet the safety specifications for high-pressure gas testing; the test system was built on-site according to the overall layout of the test system. The high-pressure, fast-response, and precise control capabilities of this test system ensure that the test conditions can effectively cover the extreme transient conditions that the theoretical model is concerned with. 2.2 Test methods; To systematically study the low-temperature characteristics of ultra-high pressure solenoid valves during transient throttling, this application designs a venting test method based on dynamic pressure monitoring. The test follows a standardized process of "charging-stabilizing-transient venting-recording-recovery" to ensure the consistency and comparability of boundary conditions between various operating conditions. The specific experimental steps are as follows: First, the gas cylinder in the test system is filled with gas using a high-pressure gas source until it reaches the preset initial pressure value, ranging from 1 to 30 MPa. After filling, the system is allowed to stand still for 1800 seconds to ensure that the gas temperature inside the cylinder reaches thermal equilibrium with the ambient temperature and that the pressure gauge reading is stable. Then, the host computer controls the relay to instantaneously open the solenoid valve under test, and simultaneously starts a high-precision timer. The solenoid valve remains open until the predetermined venting time is reached, after which it closes. Throughout the venting process, the data acquisition system records the dynamic change curve of the cylinder pressure in real time and accurately extracts the initial pressure. Final pressure and the corresponding opening time After each set of tests, the system was allowed to stand for more than 600 seconds to ensure that the temperature of the valve body and pipelines had fully recovered to the ambient temperature before the next set of tests was conducted, in order to eliminate the influence of residual heat on the test results. Record-based , and Using the data and the established isentropic flow model, numerical methods are employed for iterative calculations to deduce the valve orifice flow coefficient. And further calculate the final temperature of the gas cylinder. With the lowest temperature of the valve port ; In the experimental system, the opening and closing of the solenoid valve is digitally controlled by the host computer via a solid-state relay; the host computer program sends a pulse signal: the rising edge triggers the valve to open, and after a preset delay... Then, the falling edge triggers the valve to close. This delay... This refers to the opening time defined in this application, with a setting and recording accuracy of up to 0.1 milliseconds. Although the solenoid valve's mechanical mechanism has an inherent action delay of approximately tens of milliseconds, this delay exhibits good consistency and symmetry during the opening and closing processes, thus not affecting the effective flow time. Precise control and characterization; 2.3 Explanation and limitations of the measurement method; One of the core objectives of this application is to obtain the lowest temperature at the valve orifice during transient throttling. However, direct measurement faces the following technical challenges: 1) The shortest opening time of the solenoid valve is 0.15 seconds, and the temperature drop mainly occurs within the first 0.01 seconds. The response time constant of commercial thermocouples or resistance thermometers is usually tens to hundreds of milliseconds, and their dynamic response lag will cause the measured values ​​to fail to accurately capture the transient temperature trough. 2) The valve port is the area where gas expansion is most intense and temperature is lowest, and it is also the narrowest and most confined part of the flow channel. Implanting a sensor here will significantly change the local flow field, produce additional throttling effects, interfere with the actual physical process, and there is a risk of damage from high-pressure airflow or seal failure. Given the difficulties of direct measurement, this application adopts an "indirect calculation, multiple cross-validation" method: by collecting high-precision pressure-time series data and combining it with the isentropic choke flow theoretical model established in Section 1.2, the valve orifice temperature is calculated by inversion. The logical consistency of this method is supported by the following two points: (a) high pressure measurement accuracy, fast response, and reliable dynamic data; (b) the inverted flow coefficient. The trend of pressure change is consistent with the expectations of choke flow theory, indirectly proving the rationality of the entire calculation method; 3. Results and Discussion; To comprehensively evaluate the low-temperature characteristics of ultra-high pressure solenoid valves during transient throttling, this application conducted multiple venting tests on solenoid valves with DN6 and DN15 diameters under different initial pressures. The initial pressure of the gas cylinder was recorded during the tests. Cylinder final pressure Solenoid valve opening time Initial temperature The valve orifice flow coefficient was calculated back based on the isentropic flow model. Cylinder final temperature and the lowest temperature at the valve port The experimental data are summarized in Table 2; Table 2 Transient venting test data of ultra-high pressure solenoid valve

[0026] 3.1 Comparison of model predictions and experimental data; Based on the theoretical model and program in Section 1.2, a numerical simulation was performed on the single pressure relief process of the DN15 valve under an initial pressure of 5.8 MPa. The calculation results are as follows: Figure 4 As shown.

[0027] Depend on Figure 4 It can be seen that the pressure decay curve measured in the experiment is in high agreement with the theoretical calculation value, with a maximum deviation of less than 5%. The precise matching of the pressure curve measured in the experiment proves the overall applicability of the isentropic venting assumption and the choke flow model in this experimental system, and completes the verification of the basic framework of the model. The pressure decreased from an initial 5.8 MPa to a final value of 2.7 MPa, exhibiting a typical nonlinear decay characteristic throughout the process. The decay rate was highest in the initial stage, then gradually slowed down. The valve port temperature plummeted from an initial 10°C to approximately -50°C within the first 0.2 seconds, and continued to decrease, reaching the theoretical minimum of approximately -90°C at the end of the depressurization phase. In contrast, the overall cylinder temperature only dropped to approximately -45°C, indicating that the throttling cooling effect is highly concentrated locally at the valve port. 3.2 Multi-cycle operation and repeatability verification; To evaluate the repeatability of the test and the consistency of valve body performance, the DN15 valve underwent five consecutive venting tests, and the results are as follows: Figure 5 As shown in the diagram. During the experiment, after the previous venting, sufficient time was allowed for the cylinder temperature to rise before the next venting was performed; Figure 5 shows the pressure and temperature response of the DN15 valve during five consecutive pressure relief tests. As can be seen from the figure, the minimum valve port temperature decreased with increasing test number. This phenomenon stems from the significantly prolonged valve opening time (from 0.15 seconds to 2.37 seconds) caused by the gradual decrease in initial pressure. The longer valve opening time extends the time the cryogenic gas flow acts on the valve body, resulting in a more pronounced cumulative cooling effect, ultimately reaching a minimum temperature of -90°C under the conditions of the lowest initial pressure (5.8 MPa) and the longest valve opening time (2.3706 seconds). The valve port temperature curve shows that as the initial cylinder pressure decreases, although the valve opening time increases, the rate of temperature change at the valve port gradually slows down. This indicates that when evaluating the cryogenic tolerance of solenoid valves, not only the influence of the valve opening time on the final temperature should be considered, but also the instantaneous cooling rate.

[0028] 3.3 Correlation between cooling rate and pressure; To quantify the severity of transient cooling and analyze its dominant mechanism, the instantaneous cooling rate at the valve orifice was defined. This is the absolute value of the segment with the maximum slope in the temperature-time curve. This rate reflects the instantaneous intensity of the Joule-Thomson effect. Average pressure is defined as the arithmetic mean of the initial and final pressures of the cylinder during a single venting process, characterizing the average driving potential energy of a single venting process. For example... Figure 6 As shown, Figure 6 The study demonstrates the variation of cooling rate of two types of solenoid valves with average pressure.

[0029] It can be seen that, In the high-pressure section, the cooling rates of the two valves differed significantly. The cooling rate of the DN15 valve decreased sharply from 230°C / s in the high-pressure section to 50°C / s in the low-pressure section, while the cooling rate of the DN6 valve was generally lower, with a maximum value of approximately 107°C / s. The cooling rate decay characteristic of the DN15 valve followed an exponential function, with a coefficient of determination R² > 0.95. The decay trend of the DN6 valve was closer to a power function. This difference mainly stems from the strong dependence of mass flow rate on nozzle size under choked flow conditions: under the same pressure differential, the larger nozzle size of the DN15 valve can maintain a higher initial mass flow rate, thus producing a more intense initial throttling cooling. As the pressure decreases, the difference in cooling rates between the two valves decreases significantly, and the curves gradually converge. In the low-pressure section, the cooling rates of the two valves are already on the same order of magnitude, approximately The sensitivity to nozzle size decreases significantly. This convergence phenomenon indicates that when the driving pressure drops to a certain level, the critical pressure difference and mass flow rate conditions required to maintain a high-intensity Joule-Thomson effect are no longer met, leading to the end of the drastic cooling phase dominated by this effect, and the flow enters a phase where the remaining cold energy is released at a lower and more stable rate.

[0030] 3.4 Performance comparison across different pressure ranges; like Figure 7 As shown, the correlation between valve port temperature and valve opening time was compared for solenoid valves with two diameters, DN15 and DN6, in different pressure ranges.

[0031] As shown in the figure, in the high-pressure range (>20 MPa), the opening time of the DN15 valve is concentrated between 0.15 and 0.37 seconds, corresponding to a valve orifice temperature of -50 to -57°C; the opening time of the DN6 valve extends to 0.42 to 1.16 seconds, with an orifice temperature of -22 to -64°C. This difference stems from the direct impact of the nozzle diameter on the mass flow rate: under the same pressure differential, a smaller nozzle diameter leads to a smaller flow area, resulting in a lower mass flow rate and a longer depressurization time. In the medium-pressure range (10 to 20 MPa), the performance difference between the two valves narrows, and the overlap in their opening time ranges increases, indicating a change in flow state within this range. Data in the low-pressure range (<10 MPa) shows that the opening time further extends to 1.29 to 3.92 seconds, but the minimum temperature does not continue to decrease, indicating a limiting cooling effect. This difference also stems from the direct impact of the nozzle diameter on the mass flow rate: under the same pressure differential, a smaller nozzle diameter leads to a smaller flow area, resulting in a lower mass flow rate and a longer depressurization time.

[0032] 3.5 Analysis of the dependence of valve orifice flow coefficient on pressure; Valve orifice flow coefficient These are key parameters that connect theoretical models with experimental data. For example... Figure 8 As shown, Figure 8 reveal The pattern of changes with pressure.

[0033] As shown in the figure, the flow coefficient of the DN15 valve monotonically decreases from 0.46 in the high-pressure section to 0.085 in the low-pressure section, with the decrease rate decreasing as the pressure decreases. The form is... The power function fit is better than the exponential fit, where the negative value of the exponent b reflects the sensitivity of the flow coefficient to pressure. The DN6 valve shows a similar trend but with a higher overall coefficient value, averaging about 68% higher than the DN15 at the same pressure. Notably, in the range of approximately 18-22 MPa, the flow coefficient curves of both valves show an inflection point. This inflection point pressure is basically consistent with the theoretical critical pressure, indicating that the flow state may undergo a transition from subsonic to critical flow in this range. The pressure dependence of the flow coefficient mainly stems from the coupling effect of gas compressibility and flow congestion. The traditional constant flow coefficient assumption can lead to a maximum flow prediction error of 40% within the pressure range covered in this study. 3.6 Verification and discussion of the temperature calculation model; Although this application does not directly measure the valve orifice temperature, the rationality of the theoretical model is indirectly verified through the following methods: 1) Valve orifice flow coefficient calculated from experimental data The pressure change trend is consistent with the expectations of congestion flow theory.

[15] This strongly confirms that the physical mechanisms (congestion effect, compressibility) described by this theoretical model are real and dominant. If the basic assumptions of the model were wrong, it would be impossible to deduce such physically intuitive parametric laws.

[0034] 2) The theoretically calculated pressure decay curve is in high agreement with the experimental measurement (as shown in Figure 6).

[0035] 3) During the experiment, especially under the conditions of high initial pressure and long opening time, obvious frost was observed on the outer wall of the pipe near the shut-off valve. This phenomenon directly proves that the pipe near the shut-off valve reaches a temperature below freezing point during the gas release process. Since the pipe diameter is not less than 1.5 times the diameter of the solenoid valve, the gas expansion is the greatest at the valve port, which further illustrates that the temperature in the valve port area reaches an extremely low temperature far below freezing point, providing intuitive physical evidence for the theoretically calculated low temperature trend.

[0036] 4) To confirm the actual condition of the valve after the extreme low-temperature impact, the solenoid valve was quickly disassembled after the test. Observation of the valve core and flow channel from the inlet revealed that the interior was dry and clean, with no signs of ice crystals or condensation, and the structure was intact. This preliminarily indicates that, provided the air source cleanliness is guaranteed, this type of valve can withstand the theoretically predicted extreme low-temperature impact. This result provides an important positive reference for evaluating its engineering application feasibility under similar extreme expansion and low-temperature conditions.

[0037] 4. Conclusion; This application proposes and verifies a temperature analysis method applicable to the transient opening and closing process of ultra-high pressure solenoid valves. By integrating isentropic flow and choke flow theories, a prediction model for the minimum valve orifice temperature is constructed, and the dynamic law of flow coefficient variation with pressure is revealed. The conclusions are as follows: 1. The computational model based on the isentropic congestion flow theory can effectively predict the variation trend of the minimum valve orifice temperature with initial pressure and opening time. The experimentally measured pressure decay dynamic process is in high agreement with the theoretical calculation curve, proving the applicability of the model in describing the pressure decay and valve orifice temperature drop during ultra-high pressure transient venting.

[0038] 2. Inversion analysis shows that the valve orifice flow coefficient It is not a constant, but decreases as the upstream pressure decreases. In the high-pressure range (>20 MPa), the flow is congested, and the flow coefficient is high and relatively stable; the inflection point observed in the approximately 18-22 MPa range, consistent with the theoretical critical pressure ratio, indicates a possible change in the flow state; in the low-pressure range (<10 MPa), the flow coefficient drops significantly. Ignoring this pressure dependence will lead to significant flow prediction errors.

[0039] 3. Under the same initial pressure, valves with smaller diameters (DN6) may have a lower minimum orifice temperature than valves with larger diameters (DN15) due to their smaller flow area and longer depressurization time. Furthermore, the longer opening time leads to a more significant cumulative cooling effect, resulting in extremely low orifice temperatures even at lower initial pressures.

Claims

1. A method for predicting the transient throttling temperature of a solenoid valve, characterized in that, Includes the following steps: Step 1: Based on the isentropic flow model and choke flow theory, establish a calculation model for the minimum temperature at the valve orifice; Step 2: Introduce the valve orifice flow coefficient and optimize the calculation model for the minimum valve orifice temperature to obtain a high-precision calculation model; Step 3: Construct a test system and conduct multi-condition venting tests on the solenoid valve using the test system to obtain test data; Step 4: Invert the valve orifice flow coefficient through experimental data to complete the multi-level verification of the high-precision calculation model. Based on the high-precision calculation model, calculate the transient temperature of the valve orifice.

2. The method for predicting the transient throttling temperature of a solenoid valve according to claim 1, characterized in that, The isentropic flow model mentioned in step 1 is a gas state change model inside the gas cylinder; The mass of the gas in the gas cylinder is calculated according to the gas state change model in the gas cylinder according to equation (1); （1）； in, This refers to the mass of the gas inside the cylinder. The density of the gas; This refers to the volume of the gas cylinder; Calculate the gas density inside the gas cylinder according to the gas state change model in equation (2); （2）； in, This refers to the cylinder pressure. is the gas constant of air; For temperature.

3. The method for predicting the transient throttling temperature of a solenoid valve according to claim 2, characterized in that, The critical pressure ratio of the choke flow theory mentioned in step 1 is calculated according to equation (3); （3）； in, The adiabatic index of air; Calculate the gas mass flow rate according to equation (4) based on the choke flow theory; （4）； in, The effective area of ​​the valve port; This is the valve orifice flow coefficient.

4. The method for predicting the transient throttling temperature of a solenoid valve according to claim 3, characterized in that, The pressure and density of the gas state change model inside the gas cylinder are shown in equation (5); （5）。 5. The method for predicting the transient throttling temperature of a solenoid valve according to claim 4, characterized in that, The relationship between the gas state changes inside the gas cylinder in the gas cylinder state change model is shown in equation (6); （6）； in, For time step.

6. The method for predicting the transient throttling temperature of a solenoid valve according to claim 5, characterized in that, The gas pressure at the valve port of the calculation model for the lowest temperature at the valve port is as described in equation (7); （7）； According to equations (5), (6) and (7), the temperature at the valve port is obtained as shown in equation (8); （8）。 7. The method for predicting the transient throttling temperature of a solenoid valve according to claim 6, characterized in that, The test system described in step 3 includes a gas cylinder, a shut-off valve, a safety valve, a voltage transformer, a solenoid valve under test, an exhaust port, a high-precision timer, and connecting pipes. The working medium of the test system is clean compressed air that has undergone three-stage filtration to remove water, oil, and dust. A safety valve is installed on the outlet pipe of the gas cylinder. The diameter of all connecting pipes and shut-off valves in the test system is not less than 1.5 times the diameter of the solenoid valve under test. The solenoid valve under test is installed in series at the outlet of the gas cylinder. The on / off state of the solenoid valve under test is controlled by a solid-state relay via a digital I / O module by a host computer. The controller of the test system consists of a host computer, a data acquisition system, and measurement and control software.

8. The method for predicting the transient throttling temperature of a solenoid valve according to claim 7, characterized in that, The specific process for obtaining test data by conducting multi-condition venting tests on the solenoid valve using the test system in step 3 is as follows: S3.

1. The gas cylinder in the test system is filled with gas using a high-pressure gas source to reach the preset initial pressure value; S3.2 After inflation, allow the test system to stand still and stabilize the pressure to ensure that the gas temperature in the gas cylinder reaches thermal equilibrium with the ambient temperature and the pressure gauge reading is stable. S3.3 The host computer controls the relay to momentarily open the solenoid valve under test, and simultaneously starts a high-precision timer. The solenoid valve under test remains open until the predetermined venting time is reached, after which it closes. Throughout the venting process, the data acquisition system records the dynamic change curve of the gas cylinder pressure in real time and extracts the initial pressure. Final pressure and the corresponding opening time ; S3.4, repeat S3.1~S3.3, conduct multiple sets of experiments, and obtain experimental data.

9. The method for predicting the transient throttling temperature of a solenoid valve according to claim 8, characterized in that, The initial pressure value is 1~30 MPa, the static pressure stabilization time is not less than 1800 seconds, and the interval between multiple test groups is not less than 600 seconds.

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