A method and system for calculating liquid rocket-based interstage separation gaps

Abstract

The application discloses a kind of based on liquid rocket's interstage separation gap calculation method and system, including establishing the inertial coordinate system of liquid rocket launch, rocket body coordinate system and the coordinate system of storage tank;Obtain the dynamics equation of liquid rocket mass center motion in inertial coordinate system and the dynamics equation of liquid rocket rotation around mass center in rocket body coordinate system;Obtain the displacement H of liquid rocket core first stage and liquid rocket core second stage and attitude angle;Obtain the displacement L1 of liquid rocket core second stage mass center deviating from nozzle center line, the displacement L2 of liquid rocket core second stage mass center deviating from liquid rocket core first stage axis and the distance L3 of nozzle outer edge to nozzle center line;Obtain interstage separation gap as L4, L4=R-L3-(L1-L2), solve the problem that core second stage engine nozzle and interstage section sleeve may collide in the process of large-diameter liquid rocket separation, to improve the precision of separation scheme design, attitude control system design and storage tank anti-slosh structure design.

Description

Technical Field

[0001] This invention relates to the field of liquid rocket technology, and more specifically, to a method and system for calculating the interstage separation gap of a liquid rocket. Background Technology

[0002] Modern rockets typically carry large amounts of liquid fuel to complete long-duration, complex flight missions. During launch, maneuvering, rendezvous and docking, and hovering obstacle avoidance, the rocket body is subjected to varying thrust from the engines, wind shear, gusts, and movements caused by control system commands. This can cause severe sloshing of the liquid fuel, resulting in additional sloshing forces and torques that can lead to various instabilities, even causing loss of rocket attitude control or damage to the propellant tank structure. Therefore, research on significant sloshing of liquid fuel in rockets is essential.

[0003] Existing technology CN113553661B provides a method and computer-readable storage medium for obtaining rocket propellant sloshing parameters. It simulates and calculates the liquid sloshing of propellant in rocket tanks, establishing corresponding sloshing equations and curve fitting matching for the time-domain data of sloshing force, time-domain data of sloshing torque, and nth-order sloshing frequency, thus obtaining the centroid position of the nth-order sloshing mass of the propellant. This method achieves high accuracy in obtaining sloshing parameters, which in turn affects the precise control of the rocket. However, the separate calculation of the effects of liquid fuel sloshing in rockets involves multiple synergistic influences, and complex fluid-structure interaction problems and impact unsteady problems must be considered during rocket motion. Especially for heavy-lift rockets, the impact of liquid sloshing generated by remaining liquid fuel on the interstage separation attitude is non-negligible, directly affecting the design accuracy of separation schemes, attitude control systems, and tank anti-sloshing structures.

[0004] Therefore, there is an urgent need to provide a method and system for calculating the interstage separation gap of liquid rockets that can be efficiently calculated with high accuracy. Summary of the Invention

[0005] In view of this, the present invention provides a method for calculating the interstage separation gap of a liquid rocket, establishing the inertial coordinate system of the liquid rocket launch, the rocket body coordinate system, and the coordinate system of the propellant tanks in the liquid rocket.

[0006] Based on the coordinate systems of the inertial coordinate system, the rocket body coordinate system, and the propellant tank, the dynamic equations for the motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system are obtained respectively.

[0007] Based on the dynamic equations of the liquid rocket's center of mass motion in the inertial coordinate system and the dynamic equations of the liquid rocket's rotation around the center of mass in the rocket body coordinate system, the displacements H and attitude angles of the first and second stages of the liquid rocket core are obtained, including the pitch angle. Yaw angle ψ and roll angle γ;

[0008] Based on the displacement H and attitude angle of the first and second stages of the liquid rocket core, the displacement L1 of the second stage mass center of gravity from the nozzle centerline, the displacement L2 of the second stage mass center of gravity from the axis of the first stage, and the distance L3 from the outer edge of the nozzle to the nozzle centerline are obtained.

[0009] The interstage separation gap is obtained as L4, where L4 = R - L3 - (L1 - L2), and R is the radius of the interstage sleeve, which is located between the first stage and the second stage of the rocket core.

[0010] Preferably, the dynamic equations for the motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system are further defined as follows:

[0011]

[0012] Where M is the mass of the liquid rocket excluding liquid, V is the velocity of the center of mass of the liquid rocket in the inertial coordinate system, t is the flight time, P is the thrust of the liquid rocket, F is the force of liquid sloshing, and g is the gravitational acceleration.

[0013] The dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system are as follows:

[0014]

[0015] Where I is the moment of inertia of the liquid rocket without liquid, Ω is the angular velocity of the rocket body coordinate system relative to the inertial coordinate system, and T is the torque acting on the liquid rocket.

[0016] Preferred pitch angle Let ψ be the angle between the longitudinal axis O1X1 of the launch vehicle and the plane OXZ; let ψ be the angle between the longitudinal axis O1X1 of the launch vehicle and the plane OXY; let γ be the angle between the longitudinal axis O1Y1 of the launch vehicle and the plane OXY; let n1 be the unit vector along the axis of the first stage and n2 be the unit vector along the axis of the second stage. Then, the dihedral angle α formed between the two stages due to attitude changes is α = arccos(n1·n2).

[0017] Preferably, the displacement L1 of the second-stage center of mass of the liquid rocket core from the nozzle centerline, the displacement L2 of the second-stage center of mass of the liquid rocket core from the axis of the first stage of the liquid rocket core, and the distance L3 from the outer edge of the nozzle to the nozzle centerline are obtained. Further,

[0018] The displacement L1 of the second-stage center of mass of the liquid rocket core from the nozzle centerline is:

[0019] L1 = X E *sinα

[0020] Among them, X E It is the distance from the center of mass of the second stage core to the bottom surface of the nozzle, and α is the dihedral angle between the axis of the first stage core and the axis of the second stage core.

[0021] The displacement L2 of the second-stage center of mass of the liquid rocket core from the axis of the first stage is:

[0022]

[0023] Among them, H y and H z These are the Y-axis and Z-axis coordinates of the second-order centroid in the first-order coordinate system.

[0024] The distance L3 from the outer edge of the nozzle to the center line of the nozzle is:

[0025] L3 = X P *cosα

[0026] Among them, X P It is the distance from the center of the nozzle to the outer edge of the nozzle.

[0027] Preferably, the origin O of the inertial coordinate system is defined at the launch point, the Y-axis direction is the direction opposite to the gravity at the launch point and points out of the ground, the X-axis direction is perpendicular to the Y-axis direction and points in the launch direction, and the Z-axis direction is determined according to the right-hand screw rule.

[0028] Preferably, the origin O1 of the rocket body coordinate system is defined at the center of mass of the liquid rocket, the X1 axis is the direction from the tail of the rocket body to the head of the rocket body, the Y1 axis is perpendicular to the X1 axis and is within the longitudinal symmetry plane of the liquid rocket, and the Z1 axis is determined according to the right-hand screw rule.

[0029] Preferably, the origin O2 of the coordinate system of the propellant tank is defined at the center of the propellant tank, the X2 axis is the direction from the tail of the rocket body to the head of the rocket body, the Y2 axis is perpendicular to the X2 axis and is within the longitudinal symmetry plane of the liquid rocket, and the Z2 axis is determined according to the right-hand screw rule.

[0030] Preferably, the nozzle centerline is a line parallel to the axis of the first stage of the liquid rocket core, where the nozzle center is the point where the axis of the second stage of the liquid rocket core intersects the plane containing the bottom surface of the nozzle; the outer edge of the nozzle is a point on the engine nozzle of the second stage of the liquid rocket core that is prone to collision with the interstage sleeve; and the interstage separation gap is the distance from the outer edge of the nozzle to the interstage sleeve.

[0031] Preferably, the displacement H and attitude angle of the first and second stages of the liquid rocket core are established in the coordinate system of the first stage of the liquid rocket core; the origin O3 of the coordinate system of the first stage of the liquid rocket core is defined at the center of mass of the first stage of the liquid rocket core, the X3 axis is the direction from the tail of the first stage of the liquid rocket core to the head of the first stage of the liquid rocket core, the Y3 axis is perpendicular to the X3 axis and is in the longitudinal symmetry plane of the liquid rocket, and the Z3 axis is determined according to the right-hand screw rule.

[0032] This invention also provides a calculation system for the interstage separation gap of a liquid rocket, and a liquid rocket basic parameter acquisition module that assigns values ​​to various parameters of the liquid rocket and the liquid.

[0033] The module for obtaining initial values ​​at the moment of separation between liquid rocket stages calculates the initial values ​​of displacement, attitude, velocity, and angular velocity during the separation between liquid rocket stages.

[0034] The coordinate system establishment and transformation module establishes the inertial coordinate system for liquid rocket launch, the rocket body coordinate system, and the coordinate system of the propellant tanks in the liquid rocket, and transforms the inertial coordinate system, rocket body coordinate system, and propellant tank coordinate system.

[0035] The data initialization module obtains the dynamic equations of the liquid rocket's center of mass motion in the inertial coordinate system, the rocket body coordinate system, and the tank coordinate system, respectively, as well as the dynamic equations of the liquid rocket's rotation around the center of mass in the rocket body coordinate system.

[0036] The data processing module, based on the dynamic equations of motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations of rotation of the liquid rocket around its center of mass in the rocket body coordinate system, obtains the displacement H and attitude angles of the first and second stages of the liquid rocket core, respectively. The attitude angles include pitch angles. Yaw angle ψ and roll angle γ;

[0037] The data generation module obtains the displacement L1 of the second stage mass of the liquid rocket core from the nozzle centerline, the displacement L2 of the second stage mass from the axis of the first stage mass of the liquid rocket core, and the distance L3 from the outer edge of the nozzle to the nozzle centerline based on the displacement and attitude of the first and second stages of the liquid rocket core. The interstage separation gap L4 is then calculated as L4 = R - L3 - (L1 - L2), where R is the radius of the interstage sleeve, which is located between the first and second stages of the rocket core.

[0038] The output shows the interstage separation gap L4 in an image format.

[0039] Compared with existing technologies, the method and system for calculating the interstage separation gap of a liquid rocket provided by this invention achieves at least the following beneficial effects:

[0040] This invention provides a method and system for calculating the interstage separation gap of a liquid rocket. It establishes an inertial coordinate system for the launch of the liquid rocket to describe its motion in inertial space, and establishes coordinate systems for the rocket body and the propellant tanks within the liquid rocket to describe the forces and torques acting on it. From this, the dynamic equations for the motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system can be obtained. Based on these dynamic equations, the displacements H and attitude angles of the first and second stages of the liquid rocket core are obtained. Finally, based on the displacements H and attitude angles of the first and second stages of the liquid rocket core, the displacement L1 of the second stage's center of mass from the nozzle centerline, the displacement L2 of the second stage's center of mass from the axis of the first stage, and the distance L3 from the nozzle's outer edge to the nozzle centerline are obtained. Thus, the interstage separation gap L4 can be obtained, where L4 = R - L3 - (L1 - L2). The calculation results can quantify the corresponding indicators, solving the problem of potential collisions between the core second-stage engine nozzle and the interstage sleeve during the interstage separation process of large-diameter liquid rockets, thereby improving the accuracy of separation scheme design, attitude control system design, and tank anti-sway structure design.

[0041] Of course, any product implementing this invention does not necessarily need to achieve all of the technical effects described above at the same time.

[0042] Other features and advantages of the invention will become clear from the following detailed description of exemplary embodiments of the invention with reference to the accompanying drawings. Attached Figure Description

[0043] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments of the invention and, together with their description, serve to explain the principles of the invention.

[0044] Figure 1 This is a flowchart of a method for calculating the interstage separation gap of a liquid rocket provided by the present invention;

[0045] Figure 2 This is a schematic diagram of a liquid rocket, based on a method for calculating the interstage separation gap of a liquid rocket provided by the present invention.

[0046] Figure 3 This is a schematic diagram of the geometric relationship of a liquid rocket, based on a method for calculating the interstage separation gap of a liquid rocket provided by the present invention.

[0047] Figure 4 This is a schematic diagram of the normal force and frictional force on the liquid sloshing, based on a calculation method for the interstage separation gap of a liquid rocket provided by this invention.

[0048] Figure 5 This is a schematic diagram of the coordinate system establishment method for a calculation method of interstage separation gap in a liquid rocket provided by the present invention;

[0049] Figure 6 This is a block diagram of a calculation system for the interstage separation gap of a liquid rocket, provided by the present invention. Detailed Implementation

[0050] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that, unless otherwise specifically stated, the relative arrangement, numerical expressions, and values ​​of the components and steps set forth in these embodiments do not limit the scope of the invention.

[0051] The following description of at least one exemplary embodiment is merely illustrative and is in no way intended to limit the invention or its application or use.

[0052] Techniques, methods, and equipment known to those skilled in the art may not be discussed in detail, but where appropriate, such techniques, methods, and equipment should be considered part of the specification.

[0053] In all the examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not as limitations. Therefore, other examples of exemplary embodiments may have different values.

[0054] It should be noted that similar labels and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be discussed further in subsequent figures.

[0055] Please refer to Figures 1 to 5 , Figure 1 This is a flowchart of a method for calculating the interstage separation gap of a liquid rocket, provided by the present invention. Figure 2 This is a schematic diagram of a liquid rocket, illustrating a method for calculating interstage separation gaps in liquid rockets, as provided by this invention. Figure 3 This is a schematic diagram of the rocket geometry provided by the present invention, which describes a method for calculating the interstage separation gap of a liquid rocket. Figure 4 This is a schematic diagram of the normal force and frictional force acting on liquid sloshing, based on a calculation method for interstage separation gap in a liquid rocket provided by this invention. Figure 5This is a schematic diagram illustrating the coordinate system establishment method for a method of calculating the interstage separation gap of a liquid rocket provided by the present invention. In this embodiment, a method for calculating the interstage separation gap of a liquid rocket includes:

[0056] S1. Establish the inertial coordinate system for liquid rocket launch, the rocket body coordinate system, and the coordinate system for the propellant tanks in the liquid rocket;

[0057] S2. Based on the inertial coordinate system, the rocket body coordinate system, and the tank coordinate system, obtain the dynamic equations of the liquid rocket's center of mass motion in the inertial coordinate system and the dynamic equations of the liquid rocket's rotation around the center of mass in the rocket body coordinate system, respectively.

[0058] S3. Based on the dynamic equations of the liquid rocket's center of mass motion in the inertial coordinate system and the dynamic equations of the liquid rocket's rotation around the center of mass in the rocket body coordinate system, obtain the displacement H and attitude angles of the first and second stages of the liquid rocket core, respectively. The attitude angles include pitch angles. Yaw angle ψ and roll angle γ;

[0059] S4. Based on the displacement H and attitude angle of the first and second stages of the liquid rocket core, obtain the displacement L1 of the second stage mass center of the liquid rocket core from the nozzle centerline, the displacement L2 of the second stage mass center of the liquid rocket core from the axis of the first stage of the liquid rocket core, and the distance L3 from the outer edge of the nozzle to the nozzle centerline.

[0060] S5. Obtain the interstage separation gap as L4, L4 = R - L3 - (L1 - L2), where R is the radius of the interstage sleeve, which is located between the first stage and the second stage of the liquid rocket core.

[0061] In this embodiment, the interstage separation gap of the liquid rocket refers to the first and second stages of the liquid rocket core. Since the first and second stages of the core are subjected to different forces during the separation process, this embodiment assumes that the first stage of the rocket core is subjected to thrust, liquid sloshing force and gravity, while the second stage of the core is subjected to gravity. Because the first and second stages of the core are subjected to different forces, different displacements and attitudes will occur.

[0062] Specifically, the method for calculating the interstage separation gap of a liquid rocket provided in this embodiment includes:

[0063] S1. The specific methods for establishing the inertial coordinate system for liquid rocket launch, the rocket body coordinate system, and the coordinate system of the propellant tanks in the liquid rocket are as follows:

[0064] S101. Establish an inertial coordinate system for the launch of the liquid rocket. The origin O of the inertial coordinate system is defined at the launch point. The Y-axis is the direction pointing outward from the Earth's surface in the opposite direction of gravity at the launch point. The X-axis is perpendicular to the Y-axis and points in the launch direction. The Z-axis is determined according to the right-hand screw rule. Based on the real-time thrust, mass, flight altitude, velocity, and other parameters of the liquid rocket, obtain the trajectory of the liquid rocket in inertial space in the inertial coordinate system.

[0065] S102. Establish the body coordinate system of the liquid rocket, where the origin O1 of the body coordinate system is defined at the center of mass of the liquid rocket, the X1 axis is the direction from the tail of the rocket to the head of the rocket, the Y1 axis is perpendicular to the X1 axis and is in the longitudinal symmetry plane of the liquid rocket, and the Z1 axis is determined according to the right-hand screw rule. Obtain the forces and torques on the liquid rocket in the body coordinate system.

[0066] S103. Establish the coordinate system for the propellant tanks in the liquid rocket. The propellant tanks include fuel tanks and oxidizer tanks. The origin O2 of the coordinate system is defined at the center of the tank. The X2 axis points from the tail of the rocket to the nose. The Y2 axis is perpendicular to the X2 axis and lies within the longitudinal plane of symmetry of the liquid rocket. The Z2 axis is determined according to the right-hand screw rule. Obtain the force and torque of the liquid sloshing in the propellant tank coordinate system. Please refer to... Figure 4 The force of liquid sloshing includes the normal force F of liquid sloshing. N The shaking friction force F experienced by the storage tank f ;

[0067] S2. Based on the inertial coordinate system, rocket body coordinate system, and propellant tank coordinate system obtained in steps S101, S102, and S103 above, the dynamic equations for the motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system are obtained respectively, specifically:

[0068] The dynamic equations for the motion of the center of mass of a liquid rocket in the inertial coordinate system are as follows:

[0069]

[0070] Where M is the mass of the liquid rocket excluding liquid, V is the velocity of the center of mass of the liquid rocket in the inertial coordinate system, t is the flight time, P is the thrust of the liquid rocket, F is the force of liquid sloshing, and g is the gravitational acceleration.

[0071] S202, The dynamic equations of the liquid rocket rotating around its center of mass in the rocket body coordinate system are:

[0072]

[0073] Where I is the moment of inertia of the liquid rocket without liquid, Ω is the angular velocity of the rocket body coordinate system relative to the inertial coordinate system, and T is the torque acting on the liquid rocket.

[0074] It should be noted that the establishment of the dynamic equations for the motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system in steps S201 and S202 is not sequential. Furthermore, the mass and moment of inertia of the liquid rocket in the dynamic equations for the motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system do not include the corresponding values ​​for the liquid component.

[0075] S3. Based on the dynamic equations of the liquid rocket's center of mass motion in the inertial coordinate system and the dynamic equations of the liquid rocket's rotation around the center of mass in the rocket body coordinate system obtained in steps S201 and S202 above, calculate the displacement H and attitude angles of the first stage and second stage of the liquid rocket core, respectively. The attitude angles include pitch angles. The yaw angle ψ and roll angle γ are as follows:

[0076] S301. Establish the first-stage coordinate system of the liquid rocket core. The origin O3 of the first-stage coordinate system of the liquid rocket core is defined at the center of mass of the first-stage liquid rocket core. The X3 axis is the direction from the tail of the first-stage liquid rocket core to the head of the first-stage liquid rocket core. The Y3 axis is perpendicular to the X3 axis and is in the longitudinal symmetry plane of the liquid rocket. The Z3 axis is determined according to the right-hand screw rule.

[0077] S302. In the first-stage coordinate system of the liquid rocket core obtained in step S301 above, and based on the velocity V of the liquid rocket's center of mass in the inertial coordinate system obtained in step S201, the displacements H of the first and second stages of the liquid rocket core are calculated.

[0078] S303. In the liquid rocket core first-stage coordinate system obtained in step S301 above, and based on the angular velocity Ω of the rocket body coordinate system relative to the inertial coordinate system obtained in step S202, calculate the pitch angle between the longitudinal axis O1X1 of the liquid rocket core first stage and the liquid rocket core second stage and the plane OXZ. The yaw angle ψ between the longitudinal axis O1X1 of the launch liquid rocket and the plane OXY, and the roll angle γ between the longitudinal axis O1Y1 of the launch liquid rocket and the plane OXY;

[0079] S304. The unit vector along the axis of the first core is n1, and the unit vector along the axis of the second core is n2. Due to the change in attitude angle in step S303, a dihedral angle α = arccos(n1·n2) is formed between the two stages.

[0080] S4. Based on the displacements H and attitude angles of the first and second stages of the liquid rocket core obtained in steps S301, S302, S303, and S304 above, calculate the displacement L1 of the second stage's center of mass from the nozzle centerline, the displacement L2 of the second stage's center of mass from the axis of the first stage, and the distance L3 from the outer edge of the nozzle to the nozzle centerline, respectively. Specifically:

[0081] S401, the displacement L1 of the second stage mass center of mass of the liquid rocket core from the nozzle centerline is:

[0082] L1 = X E *sinα

[0083] Among them, X E It is the distance from the center of mass of the second stage core to the bottom surface of the nozzle, and α is the dihedral angle between the axis of the first stage core and the axis of the second stage core.

[0084] S402, the displacement L2 of the second-stage centroid of the liquid rocket core from the axis of the first stage of the liquid rocket core is:

[0085]

[0086] Among them, H y and H z These are the Y-axis and Z-axis coordinates of the second-order centroid in the first-order coordinate system.

[0087] S403, the distance L3 from the outer edge of the nozzle to the centerline of the nozzle is:

[0088] L3 = X P *cosα

[0089] Among them, X P It is the distance from the center of the nozzle to the outer edge of the nozzle.

[0090] It should be noted that the calculations of L1, L2, and L3 in steps S401, S402, and S403 are not sequential. L1 and L3 are determined by the rocket's characteristics, geometric dimensions, and the angle α between the first-stage and second-stage axes. L2 is determined by the motion of the first and second stages of the rocket core. Furthermore, the nozzle centerline is the line parallel to the axis of the first stage of the liquid rocket core, with the nozzle center being the point where the axis of the second stage of the liquid rocket core intersects the plane containing the nozzle's bottom surface. The outer edge of the nozzle is the point on the engine nozzle of the second stage of the liquid rocket core where collisions with the interstage sleeve are likely to occur.

[0091] S5. Obtain the interstage separation gap as L4, L4 = R - L3 - (L1 - L2), where R is the radius of the interstage sleeve, which is located between the first stage and the second stage of the liquid rocket core.

[0092] It should be noted that the interstage separation gap is the distance from the outer edge of the nozzle to the interstage sleeve.

[0093] The above describes a method for calculating the interstage separation gap of a liquid rocket according to the present invention. For some optional embodiments, please refer to... Figure 6 , Figure 6 This is a block diagram of a calculation system for interstage separation gap in a liquid rocket provided by the present invention. This embodiment of the calculation system for interstage separation gap in a liquid rocket includes:

[0094] The liquid rocket basic parameter acquisition module 10 is used to assign values ​​to the real-time thrust, rocket mass, flight altitude, velocity status, and various parameters of the liquid rocket.

[0095] The initial value acquisition module 20 for the interstage separation of the liquid rocket calculates the initial values ​​of displacement, attitude, velocity and angular velocity of the interstage separation of the liquid rocket using the parameters in the basic parameters acquisition module 10 of the liquid rocket.

[0096] The coordinate system establishment and transformation module 30 includes a coordinate system establishment module 301, which is used to establish the inertial coordinate system for the launch of the liquid rocket, the rocket body coordinate system, and the coordinate system of the propellant tank in the liquid rocket; and a coordinate system transformation module 302, which is used to determine the transformation matrix A between the inertial coordinate system, the rocket body coordinate system, and the propellant tank coordinate system, and to transform the inertial coordinate system, the rocket body coordinate system, and the propellant tank coordinate system.

[0097] The transformation matrix A is as follows:

[0098]

[0099] in, ψ is the angle between the longitudinal axis O1X1 of the launch vehicle and the plane OXZ; ψ is the angle between the longitudinal axis O1X1 of the launch vehicle and the plane OXY; γ is the angle between the longitudinal axis O1Y1 of the launch vehicle and the plane OXY.

[0100] The coordinate system establishment module 301 includes the following functions:

[0101] An inertial coordinate system is established, with its origin O defined at the launch point. The Y-axis points outward from the Earth's surface in the opposite direction of gravity at the launch point. The X-axis is perpendicular to the Y-axis and points in the launch direction. The Z-axis is determined according to the right-hand screw rule. Based on the real-time thrust, mass, altitude, and velocity of the liquid rocket, the trajectory of the liquid rocket in inertial space is obtained in the inertial coordinate system.

[0102] Establish a rocket body coordinate system. The origin O1 of the rocket body coordinate system is defined at the center of mass of the liquid rocket. The X1 axis is the direction from the tail of the rocket body to the head of the rocket body. The Y1 axis is perpendicular to the X1 axis and is in the longitudinal symmetry plane of the liquid rocket. The Z1 axis is determined according to the right-hand screw rule. The forces and torques acting on the liquid rocket are obtained in the rocket body coordinate system.

[0103] Establish a coordinate system for the propellant tanks, which include fuel and oxidizer tanks. The origin O2 of the coordinate system is defined at the center of the tank. The X2 axis points from the tail to the nose of the rocket. The Y2 axis is perpendicular to the X2 axis and lies within the longitudinal plane of symmetry of the liquid rocket. The Z2 axis is determined according to the right-hand screw rule. Obtain the forces and torques of the liquid sloshing within the tank's coordinate system. (Please refer to...) Figure 4 The force of liquid sloshing includes the liquid sloshing force F. N The shaking friction force F experienced by the storage tank f .

[0104] Establish a coordinate system for the first stage of the liquid rocket core. The origin O3 of the coordinate system is defined at the center of mass of the first stage of the liquid rocket core. The X3 axis is the direction from the tail of the first stage of the liquid rocket core to the head of the first stage of the liquid rocket core. The Y3 axis is perpendicular to the X3 axis and lies within the longitudinal symmetry plane of the liquid rocket. The Z3 axis is determined according to the right-hand screw rule.

[0105] The data initialization module 40 obtains the dynamic equations of the liquid rocket's center of mass motion in the inertial coordinate system and the dynamic equations of the liquid rocket's rotation around the center of mass in the rocket body coordinate system, respectively, based on the inertial coordinate system, rocket body coordinate system and tank coordinate system after transformation in the coordinate system establishment and transformation module 30.

[0106] The dynamic equations for the motion of the center of mass of a liquid rocket in an inertial coordinate system are as follows:

[0107]

[0108] Where M is the mass of the liquid rocket excluding liquid, V is the velocity of the center of mass of the liquid rocket in the inertial coordinate system, t is the flight time, P is the thrust of the liquid rocket, F is the force of liquid sloshing, and g is the gravitational acceleration.

[0109] The dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system are as follows:

[0110]

[0111] Where I is the moment of inertia of the liquid rocket without liquid, Ω is the angular velocity of the rocket body coordinate system relative to the inertial coordinate system, and T is the torque acting on the liquid rocket.

[0112] It should be noted that the mass and moment of inertia of the liquid rocket in the dynamic equations of motion of the center of mass in the inertial coordinate system and the dynamic equations of rotation of the liquid rocket around the center of mass in the rocket body coordinate system do not include the corresponding values ​​of the liquid part.

[0113] The data processing module 50 includes a displacement acquisition module 501, an attitude angle acquisition module 502, and a dihedral angle acquisition module 503. The displacement acquisition module 501 includes the following functions: Under the liquid rocket core first-stage coordinate system established in the coordinate system establishment and transformation module 30, and based on the dynamic equations of the liquid rocket's center of mass motion in the inertial coordinate system in the data initialization module 40, it obtains the velocity V of the liquid rocket's center of mass in the inertial coordinate system and calculates the displacement H of the liquid rocket core first stage and the liquid rocket core second stage. The attitude angle acquisition module 502 includes the following functions: Under the liquid rocket core first-stage coordinate system established in the coordinate system establishment and transformation module 30, and based on the dynamic equations of the liquid rocket's rotation around its center of mass in the rocket body coordinate system, it obtains the angular velocity Ω of the rocket body coordinate system relative to the inertial coordinate system and calculates the pitch angle between the longitudinal axis O1X1 of the launch liquid rocket core first stage and the plane OXZ. The yaw angle ψ between the longitudinal axis O1X1 of the launch liquid rocket and the plane OXY, and the roll angle γ between the longitudinal axis O1Y1 of the launch liquid rocket and the plane OXY; the dihedral angle acquisition module 503 includes the following functions: the unit vector along the axis of the first stage core is n1, the unit vector along the axis of the second stage core is n2, and the dihedral angle α = arccos(n1·n2) is formed between the two stages due to the change in attitude angle in step S303.

[0114] The data generation module 60 obtains the displacement L1 of the second stage of the liquid rocket core from the nozzle centerline, the displacement L2 of the second stage of the liquid rocket core from the axis of the first stage of the liquid rocket core, and the distance L3 from the outer edge of the nozzle to the nozzle centerline based on the displacement H and attitude of the first and second stages of the liquid rocket core, and calculates the interstage separation gap L4.

[0115] The displacement L1 of the second-stage center of mass of the liquid rocket core from the nozzle centerline is:

[0116] L1 = X E *sinα

[0117] Among them, X E It is the distance from the center of mass of the second stage core to the bottom surface of the nozzle, and α is the dihedral angle between the axis of the first stage core and the axis of the second stage core.

[0118] The displacement L2 of the second-stage center of mass of the liquid rocket core from the axis of the first stage is:

[0119]

[0120] Among them, Hy and H z These are the Y-axis and Z-axis coordinates of the second-order centroid in the first-order coordinate system.

[0121] The distance L3 from the outer edge of the nozzle to the center line of the nozzle is:

[0122] L3 = X P *cosα

[0123] Among them, X P It is the distance from the center of the nozzle to the outer edge of the nozzle.

[0124] The interstage separation gap is obtained as L4, where L4 = R - L3 - (L1 - L2), and R is the radius of the interstage sleeve, which is located between the first stage and the second stage of the liquid rocket core.

[0125] It should be noted that the nozzle centerline is the line parallel to the axis of the first stage of the liquid rocket core, with the nozzle center being the point where the axis of the second stage of the liquid rocket core intersects the plane containing the bottom surface of the nozzle; the outer edge of the nozzle is the point on the engine nozzle of the second stage of the liquid rocket core that is prone to collision with the interstage sleeve; and the interstage separation gap is the distance from the outer edge of the nozzle to the interstage sleeve.

[0126] The output 70 presents the interstage separation gap L4 obtained by the data generation module 60 in an image format.

[0127] It should be noted that the results for the interstage separation gap L4 can also be presented in tabular form.

[0128] As can be seen from the above embodiments, the method and system for calculating the interstage separation gap of a liquid rocket provided by the present invention achieves at least the following beneficial effects:

[0129] This invention provides a method and system for calculating the interstage separation gap of a liquid rocket. It establishes an inertial coordinate system for the launch of the liquid rocket to describe its motion in inertial space, and establishes coordinate systems for the rocket body and the propellant tanks within the liquid rocket to describe the forces and torques acting on it. From this, the dynamic equations for the motion of the liquid rocket's center of mass in the inertial coordinate system and the dynamic equations for the rotation of the liquid rocket around its center of mass in the rocket body coordinate system can be obtained. Based on these dynamic equations, the displacements H and attitude angles of the first and second stages of the liquid rocket core are obtained. Finally, based on the displacements H and attitude angles of the first and second stages of the liquid rocket core, the displacement L1 of the second stage's center of mass from the nozzle centerline, the displacement L2 of the second stage's center of mass from the axis of the first stage, and the distance L3 from the nozzle's outer edge to the nozzle centerline are obtained. Thus, the interstage separation gap L4 can be obtained, where L4 = R - L3 - (L1 - L2). The calculation results can quantify the corresponding indicators, solving the problem of potential collisions between the core second-stage engine nozzle and the interstage sleeve during the interstage separation process of large-diameter liquid rockets, thereby improving the accuracy of separation scheme design, attitude control system design, and tank anti-sway structure design.

[0130] While specific embodiments of the invention have been described in detail by way of examples, those skilled in the art should understand that the examples are for illustrative purposes only and not intended to limit the scope of the invention. Those skilled in the art should understand that modifications can be made to the above embodiments without departing from the scope and spirit of the invention. The scope of the invention is defined by the appended claims.

Claims

1. A method for calculating the interstage separation gap of a liquid rocket, characterized in that: establishing an inertial coordinate system of a liquid rocket launch, a rocket body coordinate system of the liquid rocket, and a coordinate system of a tank in the liquid rocket; obtaining a dynamic equation of the mass center motion of the liquid rocket in the inertial coordinate system, and a dynamic equation of the rotation of the liquid rocket around the mass center in the rocket body coordinate system according to the inertial coordinate system, the rocket body coordinate system, and the coordinate system of the tank; obtaining a displacement L1 of the mass center of the second stage of the liquid rocket core from the center line of the nozzle, a displacement L2 of the mass center of the second stage of the liquid rocket core from the axis of the first stage of the liquid rocket core, and a distance L3 from the outer edge of the nozzle to the center line of the nozzle according to the displacement H and the attitude angle of the first stage and the second stage of the liquid rocket core; obtaining an interstage separation gap L4, L4 = R-L3-(L1-L2), wherein R is the radius of an interstage section sleeve located between the first stage of the rocket core and the second stage of the rocket core. The dynamic equation of the mass center motion of the liquid rocket in the inertial coordinate system, and the dynamic equation of the rotation of the liquid rocket around the mass center in the rocket body coordinate system are further, The dynamic equation of the mass center motion of the liquid rocket in the inertial coordinate system is: According to the dynamic equation of liquid rocket center of mass motion in the inertial coordinate system and the dynamic equation of liquid rocket rotation around the center of mass in the rocket body coordinate system, the displacement H of liquid rocket core first stage and liquid rocket core second stage and the attitude angle, including the pitch angle the yaw angle ψ and the roll angle γ, are obtained respectively. wherein M is the mass of the liquid rocket excluding liquid, V is the velocity of the mass center of the liquid rocket in the inertial coordinate system, t is the flight time, P is the thrust received by the liquid rocket, F is the force of liquid sloshing, and g is the gravitational acceleration; The dynamic equation of the rotation of the liquid rocket around the mass center in the rocket body coordinate system is:

2. The method of claim 1, wherein: wherein I is the moment of inertia of the liquid rocket excluding liquid, Ω is the angular velocity of the rocket body coordinate system relative to the inertial coordinate system, and T is the moment received by the liquid rocket. The displacement L1 of the mass center of the second stage of the liquid rocket core from the center line of the nozzle, the displacement L2 of the mass center of the second stage of the liquid rocket core from the axis of the first stage of the liquid rocket core, and the distance L3 from the outer edge of the nozzle to the center line of the nozzle are further, The displacement L1 of the mass center of the second stage of the liquid rocket core from the center line of the nozzle is: The displacement L2 of the mass center of the second stage of the liquid rocket core from the axis of the first stage of the liquid rocket core is: The distance L3 from the outer edge of the nozzle to the center line of the nozzle is:

3. The method of claim 1, wherein: Pitch angle The pitch angle is the angle between the longitudinal axis of the carrier rocket O1X1 and the plane OXZ; the yaw angle ψ is the angle between the longitudinal axis of the carrier rocket O1X1 and the plane OXY; the roll angle γ is the angle between the longitudinal axis of the carrier rocket O1Y1 and the plane OXY; the unit vector along the direction of the first-stage core axis is n1, and the unit vector along the direction of the second-stage core axis is n2. The dihedral angle α formed between the two stages due to the change in attitude is α = arccos(n1·n2).

4. The method of claim 3, wherein: The origin O of the inertial coordinate system is defined at the launch point, the Y-axis direction is directed outward from the ground along the direction opposite to the gravity at the launch point, the X-axis direction is perpendicular to the Y-axis direction and directed in the launch direction, and the Z-axis direction is determined according to the right-hand screw rule. The origin O1 of the rocket body coordinate system is defined at the mass center of the liquid rocket, the X1-axis direction is directed from the tail of the rocket body to the head of the rocket body, the Y1-axis direction is perpendicular to the X1-axis and in the longitudinal symmetry plane of the liquid rocket, and the Z1-axis direction is determined according to the right-hand screw rule. L1 = X E *sin alpha where X E is the distance from the core second centroid to the nozzle base, and a is the dihedral angle between the core first axis and the core second axis. The origin O2 of the coordinate system of the tank is defined at the center of the tank, the X2-axis direction is directed from the tail of the rocket body to the head of the rocket body, the Y2-axis direction is perpendicular to the X2-axis direction and in the longitudinal symmetry plane of the liquid rocket, and the Z2-axis direction is determined according to the right-hand screw rule. wherein H y and H z are the coordinates of the Y and Z axes of the core secondary centroid in the core primary coordinate system; ​ L3 = X P *cos a where X P is the distance from the center of the nozzle to the outer edge of the nozzle.

5. The method of claim 1, wherein: ​ 6. The method of claim 1, wherein: ​ 7. The method of claim 1, wherein: ​ 8. The method of claim 1, wherein: The nozzle center line is a line parallel to the liquid rocket core first stage axis and passing through the nozzle center, wherein the nozzle center is the intersection point of the liquid rocket core second stage axis and the plane on which the nozzle bottom surface lies; the nozzle outer edge is the point on the engine nozzle of the liquid rocket core second stage which is likely to collide with the interstage section sleeve; and the interstage separation gap is the distance from the nozzle outer edge to the interstage section sleeve.

9. The method of claim 1, wherein: The displacement H and attitude angle of the liquid rocket core first stage and the liquid rocket core second stage are established in the liquid rocket core first stage coordinate system; the origin O3 of the liquid rocket core first stage coordinate system is defined at the liquid rocket core first stage centroid; the direction of the X3 axis is the direction from the tail of the liquid rocket core first stage vehicle body to the head of the liquid rocket core first stage vehicle body; the direction of the Y3 axis is perpendicular to the X3 axis and in the longitudinal symmetry plane of the liquid rocket; and the direction of the Z3 axis is determined according to the right-hand screw rule.

10. A liquid rocket-based interstage separation gap calculation system, characterized in that: a liquid rocket basic parameter obtaining module assigns values to various parameters of the liquid rocket and the liquid; a liquid rocket interstage separation time initial value obtaining module calculates initial values of displacement, attitude, velocity, and angular velocity of the liquid rocket interstage separation; a coordinate system establishing and converting module establishes an inertial coordinate system of the liquid rocket launch, a vehicle body coordinate system of the liquid rocket, and a coordinate system of a tank in the liquid rocket, and converts the inertial coordinate system, the vehicle body coordinate system, and the tank coordinate system; a data initialization module obtains a dynamics equation of liquid rocket centroid motion in the inertial coordinate system and a dynamics equation of liquid rocket rotation around the centroid in the vehicle body coordinate system according to the inertial coordinate system, the vehicle body coordinate system, and the tank coordinate system; The data processing module obtains displacement H and attitude angle of the liquid rocket core first stage and the liquid rocket core second stage respectively according to the dynamic equation of the liquid rocket mass center motion in the inertial coordinate system and the dynamic equation of the liquid rocket rotation around the mass center in the rocket body coordinate system, wherein the attitude angle includes pitch angle yaw angle ψ and roll angle γ. a data generation module obtains a displacement L1 of the liquid rocket core second stage centroid from the nozzle center line, a displacement L2 of the liquid rocket core second stage centroid from the liquid rocket core first stage axis, and a distance L3 from the nozzle outer edge to the nozzle center line according to the displacement and attitude of the liquid rocket core first stage and the liquid rocket core second stage, and calculates an interstage separation gap L4, L4 = R - L3 - (L1 - L2), wherein R is the radius of the interstage section sleeve located between the liquid rocket core first stage and the liquid rocket core second stage; a result output presents the interstage separation gap L4 in an image mode.

Images