A multi-field coupling thrust calculation method for the interstage aerodynamic separation system of a launch vehicle

Abstract

This invention discloses a method for calculating the thrust of a multi-field coupled interstage aerodynamic separation system in a launch vehicle. The steps are as follows: 1. Obtain the control parameters of the aerodynamic separation system under operating conditions; 2. Determine the equation of state for the actual gas in the gas cylinder; 3. Derive the dynamic changes in gas pressure, mass, and temperature in the gas cylinder; 4. Conduct dynamic modeling of valves and pipelines; 5. Establish a mathematical model of the high-speed, high-pressure cylinder; 6. Determine whether the interstage separation performance of the first and second stages meets the requirements; if it does, output the thrust time history response of the aerodynamic separation system; if it does not meet the requirements, return to step 1. This method can not only accurately obtain the thrust variation characteristics of the interstage aerodynamic separation system under the combined action of multiple fields, but also obtain the dynamic response characteristics of the separation process of the first stage and the upper stage, which has reference value for the design optimization of the interstage aerodynamic separation system.

Description

Technical Field

[0001] This invention relates to a method for calculating the multi-field coupling thrust of an interstage aerodynamic separation system of a launch vehicle, belonging to the technical field of calculation of interstage separation characteristics of launch vehicles. Background Technology

[0002] Traditionally, interstage separation of launch vehicles is achieved by using solid rockets that propel forward and backward. This technology has high reliability but lacks reusability.

[0003] As reusability becomes an inevitable direction for the development of launch vehicles, non-pyrotechnic connection and separation technologies, represented by aerodynamic separation technology, are gradually replacing traditional pyrotechnic connection and separation technologies and becoming an important way for the next generation of rockets to achieve reusability.

[0004] Interstage separation of a launch vehicle is the process of the first stage separating from the second stage after the first stage shuts down. A high-speed, high-load, long-stroke aerodynamic separation impulse system is essential to ensure the successful completion of the separation mission. During interstage aerodynamic separation, high-pressure gas enters the cylinder through pipelines, pushing the piston pusher rod. Under the thrust, the second stage separates from the first stage, causing a sharp drop in gas temperature in the gas cylinder and a sharp rise in gas temperature in the cylinder. This process involves the combined effects of complex fluid-structure-thermal multiphysics fields, directly affecting the success or failure of the separation mission. Therefore, accurately and effectively analyzing the thrust variation characteristics of the interstage aerodynamic separation system under multi-field coupling is of great significance for ensuring the safe and reliable operation of the system. Currently, no relevant technical data on interstage aerodynamic separation technology for launch vehicles has been found. Summary of the Invention

[0005] The technical problem solved by this invention is to overcome the shortcomings of the prior art and provide a method for calculating the multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle. This method can accurately obtain the multi-field coupled thrust variation characteristics of the aerodynamic separation system and can also effectively predict the interstage separation response of a launch vehicle.

[0006] The technical solution of this invention is: a method for calculating the multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle, wherein:

[0007] Step 1: Obtain the operating control parameters based on the control conditions of the pneumatic separation system;

[0008] Step 2: Determine the equation of state for the actual gas in the gas cylinder based on its geometric characteristics and operating control parameters;

[0009] Step 3: Use the gas state equation of the real gas in the gas cylinder to derive the changes in gas pressure, mass, and temperature over time.

[0010] Step 4: Based on the control parameters of the valves and pipelines in the pneumatic separation system, establish the flow continuity equations from the gas cylinder to the valve and from the valve to the high-pressure cylinder, as well as the pressure loss equations of the gas in the pipeline from the gas cylinder to the valve and from the valve to the high-pressure cylinder.

[0011] Step 5: Divide the high-pressure cylinder into a rod chamber and a rodless chamber. Based on the actual gas characteristics obtained in steps 2, 3, and 4 in the rodless chamber of the high-pressure cylinder, obtain the relationship between the gas pressure, mass, and temperature in the rodless chamber and time. Analyze the relationship between the volume, pressure, and temperature of the gas in the rodless and rod chambers and time during the interstage pneumatic separation process between the first and second stages.

[0012] Step Six: Based on the information from Steps One to Five, solve for the response of the pneumatic separation system, including the relationship between push rod thrust, relative displacement of the pneumatic push rod, pressure, and temperature over time; if the interstage separation performance of the first and second stages meets the requirements, output the response of the pneumatic separation system; if it does not meet the requirements, return to Step One and recalculate.

[0013] Preferably, the van der Waals equation is used to determine the equation of state for the real gas in the cylinder, specifically:

[0014]

[0015] Among them, p c m c V c and T c Let be the pressure, mass, volume, and absolute temperature of the gas in the cylinder, respectively; R and M be the gas constant and molar mass in the cylinder, respectively; and a and b be the van der Waals constants of the gas.

[0016] Preferably, the changes in gas pressure, mass, and temperature in the gas cylinder over time are as follows:

[0017]

[0018] in, and F represents the change in pressure, mass, and temperature of the gas inside the cylinder per unit time, and represents the equation of state for the real gas inside the cylinder.

[0019] Preferably, utilizing the principle of mass conservation during gas flow in the cylinder, valves, pipelines, and rodless chamber of the high-pressure cylinder during the operation of the pneumatic separation system, and based on the control parameters of the valves and pipelines in the pneumatic separation system, the following is obtained:

[0020] The continuity equation for the flow rate from the gas cylinder to the valve is:

[0021]

[0022] The continuity equation for the flow rate from the valve to the high-pressure cylinder is as follows:

[0023]

[0024] In the formula, m c Let m be the mass of the gas in the cylinder. no Let q be the mass of the gas in the rodless chamber of the high-pressure cylinder. m1 and q m2 The gas mass flow rates at the valve inlet and outlet are respectively, satisfying q m1 =q m2 .

[0025] Preferably, the pressure loss Δp1 generated when the gas cylinder flows out through the pipeline to the valve inlet is:

[0026]

[0027] The pressure loss Δp2 generated from the valve outlet through the pipeline to the rodless chamber of the high-pressure cylinder is:

[0028]

[0029] In the above equation, λ is the friction coefficient in laminar flow, d is the pipe diameter, v is the gas velocity, ζ is the local resistance coefficient, g is the gravitational acceleration, L1 is the length of the pipe from the gas cylinder to the valve inlet, and L2 is the length of the pipe from the valve outlet to the rodless chamber of the cylinder.

[0030] Preferably, the relationship between the gas volume change and piston motion in the rodless and rod chambers of the high-pressure cylinder is as follows:

[0031]

[0032] In the formula, x is the relative displacement of the piston, and A no and A rod V represents the effective working area of ​​the piston in the rodless chamber and the rod chamber, respectively. no and V rod These are the volumes of the rodless chamber and the rod chamber of the cylinder, respectively.

[0033] Preferably, during the pneumatic separation process between the first and second stages, when the gas in the gas cylinder is continuously pumped into the high-pressure cylinder, the movement of the piston rod in the cylinder is divided into three stages: static friction stage, dynamic friction stage, and pressure relief stage.

[0034] During the static friction phase, the pneumatic push rod has not yet moved and its initial position is at the lowest point. As the gas cylinder supplies gas to the rodless chamber, the static friction force f between the first and second stages gradually increases. The maximum value of this static friction force satisfies p. no A no -p rod A rod -f = 0, where pno and p rod These are the pressures in the rodless chamber and the rod chamber, respectively.

[0035] During the dynamic friction stage, the gas cylinder continues to supply gas to the rodless chamber, when p is satisfied. no A no -p rod A rod When -f>0, the first stage is decelerated by a force opposite to the direction of the rocket, while the second stage is accelerated by a force in the same direction as the rocket's flight, thus achieving interstage separation;

[0036] During the depressurization phase, after the piston stroke is completed, the rodless chamber is depressurized and the piston rod returns to its original position; at the same time as the depressurization valve opens, the pipeline solenoid valve closes to retain the gas in the cylinder.

[0037] Preferably, during the dynamic friction stage of the first and second stage pneumatic separation process, the relationship between the volume and pressure of the rod-side and rodless-side chambers in the cylinder and time t is as follows:

[0038]

[0039] In the formula p no and p rod The pressures in the rodless chamber and the rod chamber are respectively, A. no and A rod , respectively, represent the effective working areas of the piston in the rodless chamber and the rod chamber; f is the maximum static friction force between the piston and the high-pressure cylinder body; B1 and B2 are the viscous damping between the piston push rod and the cylinder body, and between the atmosphere and the second stage rocket body, respectively; β is the correction value considering the change in gravitational acceleration at altitude and the angle between the direction of gravity and the rocket body axis; g is the gravitational acceleration; M1 and M2 are the total mass of the first and second stages, respectively; x is the relative displacement of the piston; x1 is the displacement of the first stage; x2 is the displacement of the second stage.

[0040] Preferably, the relationship between the gas pressure in the rodless chamber during the depressurization phase and time t is as follows:

[0041]

[0042] In the formula, p no V is the pressure inside the rodless cavity. no The volume of the rodless cavity is m. no T is the mass of the gas in the rodless cavity. no Let be the temperature of the rodless cavity, R and M be the gas constants and molar masses in the gas cylinder, and a and b be the van der Waals constants of the gas.

[0043] Preferably, the operating control parameters include the initial pressure value of the gas cylinder, gas temperature, gas cylinder volume, valve diameter, pipeline diameter, and cylinder structural dimensions in the pneumatic separation system.

[0044] Compared with the prior art, the present invention has the following advantages:

[0045] (1) A complete interstage aerodynamic separation system for launch vehicles, from gas cylinders to pipelines, valves and cylinders, has been established. It includes the mass parameters of the first and second stages of the launch vehicle and can be used for interstage aerodynamic separation technology of launch vehicles, filling the gap in domestic interstage aerodynamic separation technology of launch vehicles.

[0046] (2) Based on the real gas state equation, a high-load, high-speed, high-pressure cylinder is used as the actuating element. Considering the real physical boundary conditions, a calculation equation for the interstage pneumatic separation between the first and second substages is established. The relationship between the gas volume, pressure, and temperature of the rod chamber and rodless chamber of the cylinder and the piston displacement is obtained, so that the deviation of the calculation results can be controlled within 8%.

[0047] (3) The present invention can effectively obtain the thrust load acting on the interstage separation process of the first and second stages, and can accurately obtain the dynamic performance characteristics of the interstage separation, which helps to deepen engineers’ understanding of the entire process of dynamic response of aerodynamic separation system under extreme service environment;

[0048] (4) The method of the present invention makes the analysis of the thrust response of the high load-bearing, high-speed, high-pressure pneumatic separation impulse system more economical and faster. It not only avoids the consumption of manpower and material resources in the test process, but also enables engineers to obtain the distribution of pressure in the cylinder and the characteristics of the pneumatic push rod thrust change more intuitively during the separation process.

[0049] (5) This invention has wide applicability and can be applied to the dynamic simulation of the separation mechanism under multi-field coupling in various working conditions such as general core stage binding and separation, fairing separation, and star-rocket separation of launch vehicles. Attached Figure Description

[0050] Figure 1 This is a flowchart of the method of the present invention;

[0051] Figure 2 This is a schematic diagram of the dynamic model of the pneumatic separation system according to an embodiment of the present invention;

[0052] The attached diagram is labeled as follows: 1-Gas cylinder, 2-Pipeline, 3-Solenoid valve, 4-Pressure relief valve, 5-Rodless chamber of cylinder, 6-Rod chamber of cylinder, 7-Pneumatic push rod;

[0053] Figure 3 This is a graph showing the thrust-time history of the pneumatic pusher during the interstage separation process according to an embodiment of the present invention.

[0054] Figure 4 This is a graph showing the relative displacement time history of the pneumatic push rod during the interstage separation process according to an embodiment of the present invention.

[0055] Figure 5This is a graph showing the pressure change of the gas cylinder during the interstage separation process according to an embodiment of the present invention.

[0056] Figure 6 This is a graph showing the temperature change of the gas cylinder during the interstage separation process in an embodiment of the present invention. Detailed Implementation

[0057] This invention considers the influence of flow field, structural field, and temperature field, and presents a multi-field coupled thrust calculation method for an interstage aerodynamic separation system of a launch vehicle. The proposed method can not only accurately obtain the multi-field coupled thrust variation characteristics of the aerodynamic separation system, but also effectively predict the interstage separation response of the launch vehicle.

[0058] To achieve the above objectives, the present invention adopts the following technical solution:

[0059] Step 1: Obtain the operating control parameters of the pneumatic separation system under operating conditions;

[0060] Based on the control conditions of the pneumatic separation system, obtain the basic characteristics and operating control parameters of the pneumatic separation system, such as the initial pressure value of the gas cylinder, gas temperature, gas cylinder volume, valve diameter, pipeline diameter, and cylinder structural dimensions.

[0061] Step 2: Determine the equation of state for the actual gas in the cylinder;

[0062] Based on the geometric characteristics and operating control parameters of the gas cylinder, the van der Waals equation is used to analyze the venting process of the helium cylinder. Let p... c m c 、V c and T c Let be the pressure, mass, volume, and absolute temperature of the gas in the cylinder, respectively; R and M be the gas constant and molar mass in the cylinder, respectively; and a and b be the van der Waals constants of the gas. Then the equation of state for the real gas inside the cylinder is:

[0063]

[0064] Step 3: Use the gas state equation of the real gas inside the gas cylinder to derive the dynamic changes of gas pressure, mass, and temperature in the gas cylinder;

[0065] During the gas release process from the gas cylinder, the cylinder volume is constant, while the gas pressure, gas mass, and gas temperature inside the cylinder are variables. Taking partial differential equations on both sides of equation (2), we obtain the following expressions for the changes in gas pressure, mass, and temperature inside the cylinder over time:

[0066]

[0067] in, and It characterizes the changes in gas pressure, mass, and temperature per unit time within a gas cylinder.

[0068] Step 4: Conduct dynamic modeling of valves and pipelines;

[0069] During the operation of the pneumatic separation system, the gas flow in the cylinder, valve, pipeline and rodless chamber of the high-pressure cylinder maintains mass conservation. Based on the control parameters of the valve and pipeline in the pneumatic separation system, the flow continuity equations from the cylinder to the valve and from the pipeline to the high-pressure cylinder can be obtained.

[0070] The continuity equation for the flow rate from the gas cylinder to the valve is:

[0071]

[0072] The continuity equation for the flow rate from the valve to the high-pressure cylinder is as follows:

[0073]

[0074] In the formula, m c Let m be the mass of the gas in the cylinder. no Let q be the mass of the gas in the rodless chamber of the high-pressure cylinder. m1 and q m2 The gas mass flow rates at the valve inlet and outlet are respectively, satisfying q m1 =q m2 .

[0075] Pressure loss occurs during the process of gas flowing from the cylinder to the valve and from the valve to the rodless chamber of the cylinder. The pressure loss in each process consists of two parts: one part is the friction loss along the straight section of the pipeline, and the other part is the local pressure loss caused by the sudden reduction of the cross-sectional area when the gas enters the pipeline.

[0076] The flow of gas from the cylinder through the pipeline to the valve inlet and from the valve outlet through the pipeline to the rodless chamber of the cylinder are respectively:

[0077]

[0078] Where λ is the friction factor in laminar flow, and its calculation formula is related to the Reynolds number; d is the pipe diameter; v is the gas velocity; ζ is the local resistance coefficient; g is the gravitational acceleration; L1 is the length of the pipe from the gas cylinder to the valve; L2 is the length of the pipe from the valve to the rodless chamber of the cylinder; and the subscripts “1” and “2” correspond to the two pipe sections from the gas cylinder to the valve inlet and from the valve to the rodless chamber of the high-pressure cylinder, respectively.

[0079] Step 5: Establish a mathematical model for the high-speed, high-pressure cylinder;

[0080] The high-pressure cylinder is divided into a rod chamber and a rodless chamber. In the calculation process, the van der Waals equation is first used to analyze the actual gas characteristics in the rodless and rod chambers. Then, based on the methods in steps two and three, the changes in gas pressure, mass, and temperature over time in the rodless and rod chambers are obtained. Simultaneously, according to the first law of thermodynamics, the high-pressure gas introduced into the high-pressure cylinder drives the piston, and the piston movement causes changes in the volume of the high-pressure cylinder. The relationships between the volume changes of the gas in the rodless and rod chambers and the piston movement are established as follows:

[0081]

[0082] In the formula, x is the relative displacement of the piston, and A no and A rod V represents the effective working area of ​​the piston in the rodless chamber and the rod chamber, respectively. no and V rod Volume of rodless and rod chambers in a cylinder.

[0083] During the separation process, as gas from the cylinder is continuously pumped into the high-pressure cylinder, the movement of the piston rod in the high-pressure cylinder can be divided into three stages: 1) static friction stage; 2) dynamic friction stage; and 3) depressurization stage. In the static friction stage, the pneumatic push rod has not yet moved, and its initial position is at its lowest point. As gas is supplied from the cylinder to the rodless chamber, the static friction force (f) between the first and second stages gradually increases. The maximum value of this static friction force satisfies p. no A no -p rod A rod -f = 0, where p no and p rod These represent the pressures in the rodless and rod-shaped chambers, respectively; during the dynamic friction stage, the gas cylinder continues to supply gas to the rodless chamber, when p... no A no -p rod A rod When -f > 0, the first stage is decelerated by a force opposite to the rocket's direction, while the second stage is accelerated by a force in the same direction as the rocket's flight, thus achieving stage separation. During the dynamic friction phase of the first-to-second-stage separation process, the changes in the volume and pressure of the rod-side and rodless-side chambers of the cylinder over time satisfy the following equation:

[0084]

[0085]

[0086] In the formula, f is the maximum static friction force between the piston and the high-pressure cylinder body, B1 and B2 are the viscous damping between the piston rod and the cylinder body and between the atmosphere and the second stage rocket body, respectively, β is the correction value considering the change of gravitational acceleration at altitude and the angle between the direction of gravity and the axis of the rocket body, M1 and M2 are the total mass of the first and second stages, respectively, x is the relative displacement of the piston, x1 is the displacement of the first stage, and x2 is the displacement of the second stage.

[0087] During the depressurization phase, after the piston stroke is complete, the rodless chamber is depressurized, and the piston rod returns to its original position. Simultaneously, the pressure relief valve opens, and the pipeline solenoid valve closes to retain the gas in the cylinder. At this time, the relationship between the gas pressure in the rodless chamber and time is:

[0088]

[0089] In the formula, p no V is the pressure inside the rodless cavity. no The volume of the rodless chamber of the high-pressure cylinder; m no T represents the mass of the gas in the rodless chamber of the high-pressure cylinder. no Let be the temperature of the rodless cavity, R and M be the gas constants and molar masses in the gas cylinder, and a and b be the van der Waals constants of the gas.

[0090] Solving the above equations (steps one through five) yields the response of the pneumatic separation system, including the relationships between the push rod thrust, the relative displacement of the pneumatic push rod, pressure, and temperature over time. Figures 2-6 As shown.

[0091] Step 6: Determine whether the interstage separation performance of the first and second stages meets the requirements; if it does, output the thrust of the aerodynamic separation system and the dynamic response of the separation process of the first and second stages; if it does not meet the requirements, return to Step 1.

[0092] The requirement for the separation performance between the first and second stages is that the displacement or velocity of the piston actuation must meet the requirements of the separation index between the first and second stages.

[0093] Example:

[0094] The specific implementation of the method of the present invention will be described in detail below with reference to examples:

[0095] Step 1: Obtain the control parameters of the pneumatic separation system under operating conditions;

[0096] Based on the system control conditions, obtain the basic characteristic operating control parameters of the pneumatic separation system, such as the initial pressure value of the gas cylinder, the gas cylinder volume, the valve diameter, the pipeline diameter, and the cylinder structural dimensions.

[0097] In this invention example, the initial pressure of the gas cylinder is 35 MPa, the gas cylinder volume is 60 L, the solenoid valve / pressure relief valve diameter and pipe diameter are 16 mm, the initial temperature is 293 K, the pressure relief time is 0.3 s after the solenoid valve opens, and the cylinder diameter and pneumatic push rod diameter are 140 mm and 100 mm, respectively.

[0098] Step 2: Determine the equation of state for the actual gas in the cylinder;

[0099] Based on the geometric characteristics and operating control parameters of the gas cylinder, the van der Waals equation is used to analyze the venting process of the helium cylinder. Let p... c m c V and T c Let be the pressure, mass, volume, and absolute temperature of the gas in the cylinder, respectively; R and M be the gas constant and molar mass in the cylinder, respectively; and a and b be the van der Waals constants of the gas. Then the equation of state for the real gas inside the cylinder is:

[0100]

[0101] In this invention example, based on the control parameters of the gas cylinder in step one, the actual gas state equation in the gas cylinder is determined using equations (1) and (2). The gas constant R and molar mass M in the gas cylinder are 4.0026 g / mol and 8.314 J / (mol·K), respectively, and the van der Waals constants a and b of helium are 0.034 m... 6 ·Pa / mol 2 and 2.4×10 -6 m 3 / mol.

[0102] Step 3: Derive the dynamic changes in gas pressure, mass, and temperature in the gas cylinder;

[0103] During the gas release process from the gas cylinder, the cylinder volume is constant, while the gas pressure, gas mass, and gas temperature inside the cylinder are variables. Taking partial differential equations on both sides of equation (2), we obtain the following expressions for the changes in gas pressure, mass, and temperature inside the cylinder over time:

[0104]

[0105] in, and It characterizes the changes in gas pressure, mass, and temperature per unit time within a gas cylinder.

[0106] In this invention, based on the real gas state equation obtained in step two, partial differential equations are used to obtain the dynamic changes in gas pressure, mass, and temperature in the gas cylinder. and The expression for the temperature of the gas cylinder is given, where the differential equation for the cylinder temperature satisfies the first law of thermodynamics.

[0107] Step 4: Conduct dynamic modeling of valves and pipelines;

[0108] During the operation of the pneumatic separation system, the gas flow in the cylinder, valves, pipelines, and rodless chamber of the high-pressure cylinder maintains mass conservation. Based on the control parameters of the valves and pipelines in the pneumatic separation system, the flow continuity equations from the cylinder to the valves and from the pipeline to the high-pressure cylinder can be obtained as follows:

[0109]

[0110] In the formula, m no Let q be the mass of the gas in the rodless chamber of the high-pressure cylinder. m1 and q m2 The gas mass flow rates at the valve inlet and outlet are respectively, satisfying q m1 =q m2 Pressure loss occurs as gas flows from the cylinder through the pipeline to the valve inlet (Δp1) and from the valve outlet to the rodless chamber of the cylinder (Δp2). This pressure loss consists of two parts: one is the friction loss along the straight section of the pipeline, and the other is the local pressure loss caused by the sudden reduction in the cross-sectional area when the gas enters the pipeline from the cylinder.

[0111]

[0112] Where λ is the friction coefficient in laminar flow, and its calculation formula is the same as the Reynolds number; d is the pipe diameter; v is the gas velocity; ζ is the local resistance coefficient; g is the gravitational acceleration; and the subscripts “1” and “2” correspond to the two pipe sections from the gas cylinder to the valve inlet and from the valve to the rodless chamber of the high-pressure cylinder, respectively.

[0113] The pneumatic separation system model established in this invention includes gas cylinders, valves, pipelines, and high-pressure cylinders, as shown in the example below. Figure 2 As shown, the connections between gas cylinder 1, pipeline 2, solenoid valve 3, pressure relief valve 4, rodless chamber 5 of cylinder, rod chamber 6 of cylinder, and pneumatic push rod 7 are as follows: gas cylinder 1 is connected to solenoid valve 3 via pipeline 2; the other end of pressure relief valve 4 and solenoid valve 3 are connected to the rodless chamber (rodless chamber 5) of cylinder; the piston of pneumatic push rod 7 is located inside cylinder, dividing cylinder into rodless chamber 5 and rod chamber 6. Considering the pressure loss in the pipeline before and after the valves, the local resistance coefficient ζ1 = 0.458 when gas enters the pipeline from the gas cylinder, and the local resistance coefficient ζ2 = 0.752 when gas enters the rodless chamber of cylinder.

[0114] Step 5: Establish a mathematical model for the high-speed, high-pressure cylinder;

[0115] The high-pressure cylinder is divided into a rod chamber and a rodless chamber. In the calculation process, the van der Waals equation is first used to analyze the actual gas characteristics in the rodless and rod chambers. Then, based on the methods in steps two and three, the changes in gas pressure, mass, and temperature over time in the rodless and rod chambers are obtained. Simultaneously, according to the first law of thermodynamics, the high-pressure gas introduced into the cylinder drives the piston, and this piston movement causes changes in the cylinder volume. The relationships between the volume changes of the gas in the rodless and rod chambers and the piston movement are established as follows:

[0116]

[0117] In the formula, x is the relative displacement of the piston, and A no and A rod V represents the effective working area of ​​the piston in the rodless chamber and the rod chamber, respectively. no and V rod The volumes of the rodless and rod chambers of the cylinder. During the separation process, as gas from the cylinder is continuously pumped into the cylinder, the movement of the piston rod can be divided into three stages: 1) static friction stage; 2) dynamic friction stage; and 3) pressure relief stage. In the static friction stage, the pneumatic push rod has not yet moved, and its initial position is at its lowest point. As gas is supplied from the cylinder to the rodless chamber, the static friction force (f) between the first and second stages gradually increases. The maximum value of this static friction force satisfies p. no A no -p rod A rod -f = 0, where p no and p rod These represent the pressures in the rodless and rod-shaped chambers, respectively; during the dynamic friction stage, the gas cylinder continues to supply gas to the rodless chamber, when p... no A no -p rod A rod When -f > 0, the first stage is decelerated by a force opposite to the rocket's direction, while the second stage is accelerated by a force in the same direction as the rocket's flight, thus achieving stage separation. During the separation process between the first and second stages, the changes in the volume and pressure of the rod-side and rodless-side chambers of the cylinder satisfy the following equation.

[0118]

[0119] In the formula, f is the maximum static friction force between the piston and the cylinder, B1 and B2 are the viscous damping between the piston rod and the cylinder, and between the atmosphere and the second-stage rocket body, respectively, β is the correction value considering the change in gravitational acceleration at altitude and the angle between the direction of gravity and the rocket body axis, and M1 and M2 are the total mass of the first and second stages, respectively. During the depressurization phase, after the piston stroke is completed, the rodless chamber is depressurized, and the piston rod returns to its original position. Simultaneously with the opening of the depressurization valve, the pipeline solenoid valve closes to retain the gas in the cylinder. At this time, the relationship between the gas pressure in the rodless chamber and time is:

[0120]

[0121] By combining the above equations, we can obtain the thrust of the pneumatic separation system and the dynamic response of the first and second stage separation processes.

[0122] In this invention example, the total masses of the first and second stages of the launch vehicle are 35t and 75t, respectively. A mathematical model of the high-speed, high-pressure cylinder is established based on equations (9) to (13). The variables in the equations are then combined with the equations given in steps one to five. The control equations are integrated in the mathematical calculation software to establish a multi-field coupling simulation calculation platform for the interstage aerodynamic separation system of the launch vehicle. The dynamic characteristics of the multi-field coupling thrust of the interstage aerodynamic separation system of the launch vehicle obtained through simulation in this invention example are as follows: Figure 3 As shown in the figure, it can be clearly observed that when the solenoid valve of the pneumatic separation system opens (0-0.4ms), high-pressure gas flows into the rodless chamber of the cylinder, and the pressure of the pneumatic push rod gradually increases to a maximum value of 507.8kN. From 0.4ms to 0.3s, the thrust slowly decreases, mainly due to the increase in the volume of the rodless chamber in the cylinder. After 0.3s, the pressure relief valve opens, and the push rod thrust gradually decreases. After 0.35s, after interstage separation, due to the action of the pneumatic spring pre-pressed in the rod chamber, the cylinder thrust exhibits a small oscillation. Based on steps one to five, the following can also be obtained: Figures 4-6 The diagram shows the dynamic performance characteristics of a pneumatic separation system under multi-field coupling, including the relative displacement time history of the pneumatic pusher, changes in cylinder pressure, and temperature between stages of separation. It can be seen that during the interstage separation process, the cylinder pressure eventually stabilizes at 21.24 MPa, and the cylinder temperature after stabilization is 249 K, a decrease of 44 °C compared to the initial temperature. At the separation time of 0.35 s, the relative displacement of the piston is 1.015 m, meeting the pneumatic separation performance indicators.

[0123] Step 6: Determine whether the interstage separation performance of the first and second stages meets the requirements; if it does, output the thrust time history response of the aerodynamic separation system; if it does not meet the requirements, return to Step 1.

[0124] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A method for calculating the multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle, characterized in that... include: Step 1: Obtain the operating control parameters based on the control conditions of the pneumatic separation system; Step 2: Determine the equation of state for the actual gas in the gas cylinder based on its geometric characteristics and operating control parameters; Step 3: Use the equation of state for the real gas in the gas cylinder to derive the changes in gas pressure, mass, and temperature over time. Step 4: Based on the control parameters of the valves and pipelines in the pneumatic separation system, establish the flow continuity equations from the gas cylinder to the valve and from the valve to the high-pressure cylinder, as well as the pressure loss equations of the gas in the pipeline from the gas cylinder to the valve and from the valve to the high-pressure cylinder. Step 5: Divide the high-pressure cylinder into a rod chamber and a rodless chamber. Based on the actual gas characteristics obtained in steps 2, 3, and 4 in the rodless chamber of the high-pressure cylinder, obtain the relationship between the gas pressure, mass, and temperature in the rodless chamber and time. Analyze the relationship between the volume, pressure, and temperature of the gas in the rodless and rod chambers and time during the interstage pneumatic separation process between the first and second stages. Step Six: Based on the information from Steps One to Five, solve for the response of the pneumatic separation system, including the relationship between push rod thrust, relative displacement of the pneumatic push rod, pressure, and temperature over time; if the interstage separation performance of the first and second stages meets the requirements, output the response of the pneumatic separation system; if it does not meet the requirements, return to Step One and recalculate.

2. The method for calculating multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 1, characterized in that: The van der Waals equation is used to determine the equation of state for the real gas in the cylinder, specifically: Where, p c m c 、V c and T c Let be the pressure, mass, volume, and absolute temperature of the gas in the cylinder, respectively; R and M be the gas constant and molar mass in the cylinder, respectively; and a and b be the van der Waals constants of the gas.

3. The method for calculating the multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 2, characterized in that: The changes in gas pressure, mass, and temperature in the gas cylinder over time are as follows: in, and F represents the change in pressure, mass, and temperature of the gas inside the cylinder per unit time, and represents the equation of state for the real gas inside the cylinder.

4. The method for calculating multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 2, characterized in that: Utilizing the principle of mass conservation during gas flow in the cylinder, valves, pipelines, and rodless chamber of the high-pressure cylinder during the operation of the pneumatic separation system, and based on the control parameters of the valves and pipelines in the pneumatic separation system, we obtain: The continuity equation for the flow rate from the gas cylinder to the valve is: The continuity equation for the flow rate from the valve to the high-pressure cylinder is as follows: In the formula, m c Let m be the mass of the gas in the cylinder. no Let q be the mass of the gas in the rodless chamber of the high-pressure cylinder. m1 and q m2 The gas mass flow rates at the valve inlet and outlet are respectively, satisfying q m1 =q m2 .

5. The multi-field coupling thrust calculation method for an interstage aerodynamic separation system of a launch vehicle according to claim 4, characterized in that: The pressure loss Δp1 caused by the gas flowing from the cylinder through the pipeline to the valve inlet is: The pressure loss Δp2 generated from the valve outlet through the pipeline to the rodless chamber of the high-pressure cylinder is: In the above equations, λ is the friction coefficient in laminar flow, d is the pipe diameter, v is the gas velocity, ζ1 and ζ2 are both local resistance coefficients, g is the acceleration due to gravity, L1 is the length of the pipe from the gas cylinder to the valve inlet, and L2 is the length of the pipe from the valve outlet to the rodless chamber of the cylinder.

6. The method for calculating multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 3, characterized in that: The relationship between the gas volume change and piston motion in the rodless and rod chambers of a high-pressure cylinder is as follows: In the formula, x is the relative displacement of the piston, and A no and A rod V represents the effective working area of ​​the piston in the rodless chamber and the rod chamber, respectively. no and V rod These are the volumes of the rodless chamber and the rod chamber of the cylinder, respectively.

7. The method for calculating multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 6, characterized in that: During the pneumatic separation process between the first and second stages, when the gas in the cylinder is continuously pumped into the high-pressure cylinder, the movement of the piston push rod in the cylinder is divided into three stages: static friction stage, dynamic friction stage, and pressure relief stage. During the static friction phase, the pneumatic push rod has not yet moved and its initial position is at the lowest point. As the gas cylinder supplies gas to the rodless chamber, the static friction force f between the first and second stages gradually increases. The maximum value of this static friction force satisfies p. no A no -p rod A rod -f = 0, where p no and p rod These are the pressures in the rodless chamber and the rod chamber, respectively. During the dynamic friction stage, the gas cylinder continues to supply gas to the rodless chamber, when p is satisfied. no A no -p rod A rod When -f>0, the first stage is decelerated by a force opposite to the direction of the rocket, while the second stage is accelerated by a force in the same direction as the rocket's flight, thus achieving interstage separation; During the depressurization phase, after the piston stroke is completed, the rodless chamber is depressurized and the piston rod returns to its original position; at the same time as the depressurization valve opens, the pipeline solenoid valve closes to retain the gas in the cylinder.

8. The method for calculating multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 7, characterized in that: During the dynamic friction stage of the first and second stage pneumatic separation process, the relationship between the volume and pressure of the rod-side and rodless-side chambers in the cylinder and time t is as follows: In the formula p no and p rod The pressures in the rodless chamber and the rod chamber are respectively, A. no and A rod , respectively, represent the effective working areas of the piston in the rodless chamber and the rod chamber; f is the maximum static friction force between the piston and the high-pressure cylinder body; B1 and B2 are the viscous damping between the piston push rod and the cylinder body, and between the atmosphere and the second stage rocket body, respectively; β is the correction value considering the change in gravitational acceleration at altitude and the angle between the direction of gravity and the rocket body axis; g is the gravitational acceleration; M1 and M2 are the total mass of the first and second stages, respectively; x is the relative displacement of the piston; x1 is the displacement of the first stage; x2 is the displacement of the second stage.

9. The method for calculating multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 7, characterized in that: The relationship between the gas pressure in the rodless chamber during the depressurization phase and time t is as follows: In the formula, p no V is the pressure inside the rodless cavity. no The volume of the rodless cavity is m. no T is the mass of the gas in the rodless cavity. no Let be the temperature of the rodless cavity, R and M be the gas constants and molar masses in the gas cylinder, and a and b be the van der Waals constants of the gas.

10. The method for calculating multi-field coupled thrust of an interstage aerodynamic separation system of a launch vehicle according to claim 1, characterized in that: The operating control parameters include the initial pressure value of the gas cylinder, gas temperature, gas cylinder volume, valve diameter, pipeline diameter, and cylinder structural dimensions in the pneumatic separation system.

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