A Design Method for the Burning Surface Retrogression of a Complex Charge in a Solid Rocket Motor
Through the inverse problem solving method, the geometric structure of metal wire embedded in the medicine column is designed, which solves the problem of thrust control of solid rocket engines under complex working conditions, achieves more flexible and precise thrust adjustment, and improves the adaptability of solid rocket engines.
Patent Information
- Application Number
- CN202410297425.7
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-03-15
- Publication Date
- 2025-08-01
- Estimated Expiration
- 2044-03-15
AI Technical Summary
In the prior art, the solid rocket engine drug column uses straight metal wires to meet the needs of precise thrust control under complex operating conditions, and it is difficult to adapt to complex operating conditions such as high-speed flight and temperature changes inside and outside the atmosphere.
The inverse problem solving method is adopted to design the thrust change curve of the working state of the solid rocket, and the geometric structure of the wire embedded in the medicine column is constructed. The cubic Bezier curve and PEF method are used to simulate and calculate the combustion surface retreat, and the wire geometric parameters are optimized to generate the target thrust change curve.
It improves the design freedom of the wire structure, achieves more flexible and precise thrust adjustment, and enhances the adaptability of solid rocket engines under complex operating conditions.
Smart Images
Figure CN118246270B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of solid rocket engine structure design, and particularly relates to a method for designing the burning surface recession of a complex charge in a solid rocket engine. Background Art
[0002] Due to its advantages such as simple structure and high reliability, solid rocket engines are widely used in the fields of missiles and launch vehicles. A solid rocket engine consists of a grain, a combustion chamber, a nozzle assembly, an ignition device, etc. Among them, the grain is a solid propellant with a specific geometric shape and size, which is the energy and working fluid source of the engine. The geometric shape and size of the grain determine the law of change of the combustion chamber pressure and the engine thrust over time, thus determining the performance of the engine. Therefore, the level of grain design has a great influence on the performance of the engine.
[0003] As an important part of a solid rocket engine, the combustion forms of the grain mainly include internal hole combustion, internal and external hole combustion, end combustion, etc. Among them, the end-burning grain is widely used in sustainer solid rocket engines due to its advantages such as simple shape and high loading coefficient. However, the problem with the end-burning grain is that the combustion area is relatively small, resulting in insufficient engine thrust and restricting the overload provided in its application. In response to this limitation, the geometric design of the burning surface of the grain has a very limited effect. Currently, a simple and feasible method is to add metal wires to the propellant. Utilizing the characteristic that the metal wire has a high thermal conductivity (its thermal conductivity is 300 - 500 times that of the propellant), the temperature of the propellant near the metal wire is increased, thereby greatly increasing the burning rate at this location, creating a new law of change of the burning surface, increasing the combustion area, and thus increasing the thrust.
[0004] In actual applications, solid rocket engines may face various complex working conditions, including high-speed flight, temperature changes inside and outside the atmosphere, acceleration changes, etc., and need to quickly and accurately adjust the thrust to adapt to different working conditions. Currently, related technologies use straight metal wire designs to meet the requirements. However, although straight metal wires can accelerate the end-burning grain to a certain extent, their effect on adjusting the thrust magnitude is relatively small, and it is difficult to meet the precise control requirements under complex working conditions. Summary of the Invention
[0005] The purpose of the present invention is to solve the technical problem that it is difficult for the grain of a solid rocket engine using straight metal wires to meet the precise control requirements of thrust under complex working conditions, and provides a method for designing the burning surface recession of a complex charge in a solid rocket engine. This method is a reverse metal wire structure design method for specified thrust change requirements. By applying the inverse problem solving method, through the thrust change curve required for the operation of the solid rocket, the geometric structure of the metal wire embedded in the engine grain is inversely solved, improving the design freedom of the metal wire structure and better meeting the thrust change requirements.
[0006] To achieve the above object, the technical solution provided by the present invention is as follows:
[0007] A method for designing the burning surface recession of a complex charge of a solid rocket engine, characterized in that it includes the following steps:
[0008] Step 1, design a thrust-time variation curve according to the working state of the solid rocket as the target thrust variation curve;
[0009] Step 2, use parametric curves to construct the geometry of the metal wire embedded in the solid rocket engine grain, parameterize the geometry of the metal wire, and obtain the geometric parameter model of the metal wire;
[0010] Step 3, establish a three-dimensional finite element model of the grain embedded with the constructed metal wire, use the PEF method to simulate and calculate the burning surface recession result of the grain, output the isosurface data of the burning surface, and obtain the thrust-time variation curve of the rocket;
[0011] Step 4, take the error between the thrust variation curve obtained by simulation and the target thrust variation curve as the optimization goal, solve the inverse problem of the metal wire geometric parameters, and finally obtain the metal wire geometric parameters that can generate the target thrust variation curve, so as to determine the final structure of the metal wire embedded in the grain.
[0012] Further, Step 2 includes the following sub-steps:
[0013] Step 2.1, use the cubic Bezier curve as the parametric curve to form the geometry of the metal wire, where the cubic Bezier curve is expressed as:
[0014] P(t) = P0(1 - t) 3 + 3P1t(1 - t) 2 + 3P2t 2 (1 - t) + P3t 3 , t ∈ [0, 1]
[0015] In the formula, P(t) represents any point on the curve, P0, P1, P2, and P3 respectively represent the four control points of the metal wire curve, which are the starting point, two intermediate points, and the end point respectively. The value of the parameter t from 0 to 1 represents the movement process of the point on the curve along the entire curve path;
[0016] Step 2.2, fix the control points P0 and P3, and set the control points P1 and P2 as the parameters to be optimized.
[0017] Further, in Step 2.2, fix the abscissas of the control points P1 and P2, and set their ordinates as the parameters to be optimized.
[0018] Further, Step 4 includes the following sub-steps:
[0019] Step 4.1, establish a mathematical model for solving the geometric parameters of the wire:
[0020] Find:y1,y2
[0021] Minimize:
[0022] Subject to:y min ≤y1≤y max
[0023] y min ≤y2≤y max
[0024] Wherein, J h represents the objective function, y is the ordinate of the control point of the wire parameter curve to be solved, y1 and y2 respectively represent the ordinates of the control points P1 and P2, y max and y min respectively represent the upper and lower limits of the ordinate of the control point, S i represents the isosurface area at times i = 1, 2, 3,..., N, the superscript "s" represents the simulation data, and the superscript "t" represents the target data, represents the maximum value of the target data;
[0025] Step 4.2, repeatedly optimize the ordinates of the control points P1 and P2 to minimize the error between the generated thrust change curve and the target thrust change curve.
[0026] Further, in Step 4.2, an optimization algorithm is used to optimize and solve the model established in Step 4.1 to obtain the optimal ordinates of the control points P1 and P2, so as to minimize the error between the generated thrust change curve and the target thrust change curve.
[0027] Further, the optimization algorithm uses simulated annealing, genetic algorithm, ant colony algorithm, particle swarm algorithm or GCMMA algorithm (Globally Convergent Method of Moving Asymptotes).
[0028] The advantages of the present invention are:
[0029] The method for designing the burning surface recession of a complex charge in a solid rocket engine according to the present invention first designs a target thrust change curve according to the working state of the solid rocket, then selects a parameter curve to construct the geometry of the embedded metal wire in the grain, and then establishes a grain model and uses the PEF method (Poisson equation—Eikonal equation—Finite element method) to calculate the burning surface recession result of the grain. Finally, taking the error between this result and the target thrust change curve as the optimization goal, the required geometric parameters of the metal wire are obtained. Therefore, the method of the present invention allows the reverse design of the metal wire structure by applying the inverse problem solving method according to the specific solid rocket thrust requirements under different working conditions, improves the design freedom of the metal wire structure, further optimizes the burning surface recession design of the complex charge in the solid rocket engine, can adjust the solid rocket thrust more flexibly and accurately, and improves its ability to adapt to complex working conditions. BRIEF DESCRIPTION OF THE DRAWINGS
[0030] Through the following description with reference to the drawings, the features and advantages of the present invention will become more readily understood. In the drawings:
[0031] Figure 1 is a flowchart of the method for designing the burning surface recession of a complex charge in a solid rocket engine according to the present invention;
[0032] Figure 2 is a schematic diagram of a cubic Bézier curve used in the method of the present invention;
[0033] Figure 3 is a schematic diagram of a cubic polynomial curve used in the method of the present invention;
[0034] Figure 4 is a schematic diagram of a 1 / 8 model of a cylindrical grain constructed in an example of the method of the present invention;
[0035] Figure 5 is a schematic diagram of the burning surface recession result calculated in an example of the method of the present invention;
[0036] Figure 6 is a comparison chart of the change curve of the isosurface area with time (i.e., the thrust change curve) before and after iteration in an example of the method of the present invention and the target curve. DETAILED DESCRIPTION OF THE EMBODIMENTS
[0037] The present invention will be described in detail below with reference to the accompanying drawings by means of exemplary embodiments of the present invention. It should be noted that the following detailed description of the present invention is for illustrative purposes only and does not limit the present invention.
[0038] The present invention provides a method for designing the burning surface recession of a complex charge in a solid rocket engine. This method inversely solves the geometric structure of the metal wire embedded in the engine grain according to the thrust change curve required for the operation of the solid rocket.
[0039] Referring to Figure 1 , the method for designing the burning surface recession of a complex charge in a solid rocket engine as an exemplary embodiment of the present invention may include the following steps:
[0040] Step S1: Design the thrust change curve with time according to the working state of the solid rocket as the target thrust change curve;
[0041] Step S2: Use parametric curves to construct the geometric shape of the metal wire embedded in the solid rocket engine grain, parameterize the geometric shape of the metal wire, and obtain the geometric parameter model of the metal wire;
[0042] Step S3: Establish a three-dimensional finite element model of the grain embedded with the constructed metal wire, use the PEF method to simulate and calculate the burning surface recession result of the grain, output the isosurface data of the burning surface, and obtain the thrust change curve of the rocket with time;
[0043] Step S4: Take the error between the thrust change curve obtained by simulation and the target thrust change curve as the optimization goal, solve the inverse problem of the metal wire geometric parameters, and finally obtain the metal wire geometric parameters that can generate the target thrust change curve, so as to determine the final structure of the metal wire embedded in the grain.
[0044] In step S1, design the curve of thrust changing with time according to the specific requirements of the working conditions faced by the solid rocket, divide the curve into N time points to obtain the characteristic points of the target curve. For each time point, output the corresponding thrust value to form a specific set of characteristic points of thrust changing with time.
[0045] In step S2, directly control the curve characteristics and shape of the metal wire by parameterizing the geometric shape of the metal wire. In particular, a cubic Bezier curve can be used as the parametric curve to construct the geometric shape of the metal wire. It should be understood that the parametric curve used to construct the geometric shape of the metal wire is not unique, and other parametric curve forms, such as cubic polynomial curves, can also be used to parameterize the geometric shape of the metal wire.
[0046] The expression of the metal wire constructed using a cubic Bezier curve in the Cartesian coordinate system is as shown in the following formula:
[0047] P(t) = P0(1 - t) 3 + 3P1t(1 - t) 2 + 3P2t 2 (1 - t) + P3t 3 , t ∈ [0, 1]
[0048] In the formula, P(t) represents any point on the curve, and P0, P1, P2, and P3 respectively represent the four control points of the wire curve, which are the starting point, two intermediate points, and the ending point of the curve respectively. The parameter t is a key parameter of the cubic Bézier curve, which controls the position of the points on the curve. The value range of t is [0, 1]. The value of t from 0 to 1 represents the movement process of the points on the curve along the entire curve path. The closer the value of the parameter t is to 0, the closer the point on the curve is to the starting point; the closer the value is to 1, the closer the point on the curve is to the ending point. When t takes a value in the middle position, the point on the curve will be closer to the position of the intermediate control point. As Figure 2 shown, during the solution, the endpoints P0 and P3 can be fixed, and the control points P1 and P2 can be set as parameters to be optimized, that is, both their abscissas and ordinates are set as parameters to be optimized. Preferably, the abscissas of P1 and P2 are fixed and their ordinates are set as parameters to be optimized, which can make the wire geometry change arbitrarily within a certain range. It should be noted that regardless of the form of the parametric curve selected, the number of control points is not fixed, but an increase in the number will affect the inverse solution speed and accuracy. Preferably, 2 to 3 control points are selected in addition to the starting point and the ending point. In addition, the initial values of the control points can be arbitrarily given.
[0049] The expression of the cubic polynomial curve is as follows:
[0050] P(t) = a0 + a1t + a2t 2 + a3t 3 , t ∈ [0, 1]
[0051] Similar to the cubic Bézier curve, P(t) represents any point on the curve, t is the parameter, and its value range is [0, 1]. a0, a1, a2, and a3 are the coefficients of the polynomial. a0 determines the intercept of the curve on the x-axis, a1 determines the slope of the curve, a2 determines the convexity of the curve, and a3 determines the degree of curvature of the curve. As shown in Figure 3 the figure, the coefficients a0 and a3 can be fixed, and the coefficients a1 and a2 can be set as parameters to be optimized, which can also make the wire geometry change arbitrarily within a certain range. Without affecting the convergence accuracy, the number of parameters to be optimized can also be increased.
[0052] The PEF method used in step S3 is a method that uses the finite element method to approximate the viscous solution of the eikonal equation by solving the Poisson equation. It can transform the problem of burning surface recession into a "special steady-state heat conduction problem", realizing the calculation of the burning surface recession of three-dimensional charges with irregular geometries and complex burning rate distributions. It is applicable to complex interfaces formed by various burning rate propellants and can handle the combustion problems of non-uniform charges.
[0053] In step S4, in the case of using a cubic Bezier curve, a mathematical model for solving the geometric parameters of the wire can be established as follows:
[0054] Find:y1,y2
[0055] Minimize:
[0056] Subject to:y min ≤y1≤y max
[0057] y min ≤y2≤y max
[0058] In the formula, J h represents the objective function, y is the ordinate of the control point of the wire parameter curve to be solved, y1 and y2 respectively represent the ordinates of two control points P1 and P2, y max and y min respectively represent the upper and lower limits of the ordinate of the control point; S i represents the isosurface area (i.e., the thrust magnitude) at times i = 1, 2, 3,..., N. The superscript "s" represents the simulation data, and the superscript "t" represents the target data, represents the maximum value of the target data.
[0059] Then, by repeatedly optimizing the ordinates (wire geometric parameters) of the two intermediate control points P1 and P2, the generated thrust change curve is continuously fine-tuned to minimize the error with the target thrust change curve and make it closer to the target thrust change curve. In particular, an optimization algorithm can be used to optimize and solve the above model to obtain the optimal ordinates of the control points P1 and P2. The optimization algorithms used include but are not limited to simulated annealing, genetic algorithms, ant colony algorithms, particle swarm algorithms, and GCMMA algorithms.
[0060] As described above, the method for designing the burning surface recession of the complex charge of the solid rocket engine of the present invention first designs the target thrust change curve according to the working state of the solid rocket, then selects a parameter curve to construct the geometric shape of the wire embedded in the grain, then establishes a grain model and calculates the burning surface recession result of the grain using the PEF method, and finally takes the error between this result and the target thrust change curve as the optimization objective to obtain the required wire geometric parameters. Therefore, the method of the present invention allows the reverse design of the wire structure using the inverse problem solving method according to the specific solid rocket thrust requirements under different working conditions, improves the design freedom of the wire structure, further optimizes the design of the burning surface recession of the complex charge of the solid rocket engine, and can adjust the solid rocket thrust more flexibly and accurately, improving its ability to adapt to complex working conditions.
[0061] Next, the structural design method of embedding metal wires in the grain of a solid rocket motor of the present invention will be further described with reference to examples.
[0062] After designing the target thrust variation curve, a cubic Bézier curve is selected as the parametric curve to construct the geometry of the metal wire, and as Figure 2 such, the starting point and the ending point are fixed and their ordinates are made equal, the abscissas of the two intermediate control points are fixed, and the ordinates are set as the parameters to be optimized for the metal wire.
[0063] Then, a three-dimensional finite element model of the grain is constructed. The 1 / 8 three-dimensional finite element model of the grain is as Figure 4 shown. The result of the grain burning surface recession obtained by simulation calculation is as Figure 5 shown. Then, the areas of N isosurfaces are output. The area of each isosurface corresponds to the thrust value at that moment point, thereby forming a set of characteristic points of the thrust varying with time, that is, the thrust variation curve is obtained.
[0064] Finally, an optimization design is carried out. The error between the thrust variation curve obtained by simulation and the target thrust variation curve is used as the optimization objective, and iterative calculation is performed until the target thrust variation curve is finally generated. As Figure 6 shown, the curve of the isosurface area varying with time (i.e., the thrust variation curve) at the initial iteration point, after iteration, the final curve basically coincides with the target curve.
[0065] In summary, through simulation tests, the applicability and effectiveness of the structural design method of embedding metal wires in the grain of a solid rocket motor provided by the present invention are verified.
[0066] The features mentioned and / or shown in the above description of the exemplary embodiments of the present invention can be combined in the same or similar manner into one or more other embodiments, combined with the features in other embodiments or replace the corresponding features in other embodiments. The technical solutions obtained by such combination or replacement should also be regarded as being included within the protection scope of the present invention.
Claims
1. A method for designing the burning surface recession of a complex charge in a solid rocket motor, characterized in that Including the following steps: Step 1, design a thrust variation curve with respect to time according to the working state of the solid rocket, which serves as the target thrust variation curve; Step 2, construct the geometry of the embedded metal wire in the solid rocket motor grain using parametric curves, parameterize the geometry of the metal wire, and obtain the geometric parameter model of the metal wire, including the following sub-steps: Step 2.1, use the cubic Bézier curve as the parametric curve to form the geometry of the metal wire, where the cubic Bézier curve is expressed as: P(t) = P0(1 - t) 3 + 3P1t(1 - t) 2 + 3P2t 2 (1 - t)+ P3t 3 , t ∈ [0, 1] In the formula, P(t) represents any point on the curve, and P0, P1, P2, and P3 respectively represent the four control points of the metal wire curve, which are the starting point, two intermediate points, and the end point. The value of the parameter t from 0 to 1 represents the movement process of the point on the curve along the entire curve path; Step 2.2, fix the control points P0 and P3, and set the control points P1 and P2 as the parameters to be optimized; Step 3, establish a three-dimensional finite element model of the grain embedded with the constructed metal wire, use the PEF method to simulate and calculate the burning surface recession result of the grain, output the isosurface data of the burning surface, and obtain the thrust variation curve of the rocket with respect to time; Step 4, take the error between the simulated thrust variation curve and the target thrust variation curve as the optimization objective, solve the inverse problem of the metal wire geometric parameters, and finally obtain the metal wire geometric parameters that can generate the target thrust variation curve, thereby determining the final structure of the embedded metal wire in the grain, including the following sub-steps: Step 4.1, establish a mathematical model for solving the metal wire geometric parameters: Find:y1,y2 Subject to: y min ≤ y1 ≤ y max y min ≤ y2 ≤ y max In the formula, J h represents the objective function, y is the ordinate of the control point of the wire parameter curve to be solved, y1 and y2 respectively represent the ordinates of the control points P1 and P2, y max and y min respectively represent the upper and lower limits of the ordinate of the control point, S i represents the isosurface area at times i = 1, 2, 3,..., N, the superscript "s" represents the simulation data, and the superscript "t" represents the target data, represents the maximum value of the target data; Step 4.2, repeatedly optimize the ordinates of the control points P1 and P2 to minimize the error between the generated thrust variation curve and the target thrust variation curve.
2. The burning surface recession design method for the complex charge of a solid rocket motor according to claim 1, wherein: In the said Step 2.2, fix the abscissas of the control points P1 and P2, and set their ordinates as the parameters to be optimized.
3. The design method for the burning surface recession of the complex charge of a solid rocket motor according to claim 1 or 2, characterized in that: In the said Step 4.2, use an optimization algorithm to optimize and solve the model established in Step 4.1 to obtain the optimal ordinates of the control points P1 and P2, and minimize the error between the generated thrust variation curve and the target thrust variation curve.
4. The burning surface recession design method for the complex charge of a solid rocket motor according to claim 3, characterized in that: The said optimization algorithm adopts simulated annealing, genetic algorithm, ant colony algorithm, particle swarm algorithm or GCMMA algorithm.