Design method of ratio parameters for single-chamber double-thrust solid rocket motor considering external ballistic constraints

Abstract

The present invention belongs to the technical field of overall design of guided rockets, and specifically relates to a method for designing ratio parameters of a single-chamber dual-thrust solid rocket engine taking into account external ballistic constraints, comprising: step 1: optimizing the internal ballistics of an outer loop; step 2: optimizing the external ballistics of an inner loop; step 3: integrating the internal and external loops; the outstanding advantage of the present invention is that, when designing the internal ballistic thrust curve of the engine, the external ballistic constraints and the optimality of the range are comprehensively considered, and at the same time, the previous two-stage ratio design method relying on experience is transformed into a computer-automated optimization process. The obtained engine internal ballistic parameters can effectively reduce the external ballistic thermal environment pressure, improve the range capability, reduce the design costs such as the thermal protection of the projectile body, and improve the advancement of the overall design indicators.

Description

Technical Field

[0001] The invention belongs to the technical field of overall design of guided rockets, and in particular relates to a method for designing ratio parameters of a single-chamber dual-thrust solid rocket engine taking into account external ballistic constraints. Background Art

[0002] During the guided rocket design process, the design of the solid rocket motor has a crucial influence on the feasibility of the entire solution. With the trend toward longer-range guided rockets, the requirements for the specific impulse and total impulse of solid rocket motors are becoming increasingly stringent to meet range requirements. This series of requirements significantly impacts the external trajectory. While increasing range, it also results in excessive rocket velocity at the end of the active phase, resulting in a more severe thermal environment. To ensure the structural safety of guided rockets, thermal protection is generally required in vulnerable areas such as the nose and rudder leading edge. This increases the overall cost of the guided rocket, adds structural weight, and reduces the optimality of the solution.

[0003] A single-chamber, multi-thrust solid rocket motor (SMM) achieves multiple thrust stages within the same combustion chamber. Its primary advantage is that thrust grading significantly improves the velocity characteristics of guided rockets. Single-chamber, dual-thrust rockets are generally used. During the overall design process, parameters such as the operating time ratio and total impulse ratio of the two-stage thrust are typically determined based on engineering experience, lacking targeted design. These parameters significantly influence the acceleration process of guided rockets. Acceleration within the dense atmosphere, in turn, determines the maximum thermal environment and range capability of guided rockets, making them a key design approach for improving the overall performance of ammunition. Summary of the Invention

[0004] (1) Technical issues to be resolved

[0005] The technical problem to be solved by the present invention is: how to reduce the maximum heat flux rate at weak positions such as the head stagnation point and the leading edge of the rudder wing of the external ballistic projectile while improving the range capability by designing the ratio parameters of the two-stage working time and the two-stage total impulse under the conditions of the total impulse and total working time limitations of a single-chamber dual-thrust solid rocket engine.

[0006] (2) Technical solution

[0007] In order to solve the above technical problems, the present invention provides a method for designing the ratio parameters of a single-chamber dual-thrust solid rocket engine considering external ballistic constraints. The implementation process of the method is as follows:

[0008] Step 1: Trajectory optimization within the outer loop;

[0009] The outer loop optimization is to solve the engine's internal ballistic ratio parameters. The ratio of the first-stage working time to the total working time, k1, and the ratio of the first-stage total impulse to the two-stage total impulse, k2, are taken as optimization parameters. The outer ballistic calculation is used as the dynamic function of the optimization solution, and the optimization problem of the internal ballistic ratio parameters is transformed into a dual-parameter optimal control problem.

[0010] The optimal control problem is solved using the interior point method. The partial derivatives of the ratio k1 and the optimization parameter k2 are solved using finite differences. Initial values are pre-set at the beginning of the iteration to avoid iteration failure. At this time, the optimization problem of the ballistic ratio parameters in the outer loop is to search for k1 and k2 to minimize the performance index. The performance index of the outer loop optimization is set to the weighted value of the maximum heat flux and the maximum range:

[0011]

[0012] Where: J is the performance index; ω1∈[0,1] is the weight of the thermal environment relative to the range. A value of 1 means that only the reduction of heat flux is considered, and a value of 0 means that only the improvement of the range is considered. Q δ is the maximum heat flux at the target location on the exterior ballistic projectile; S max is the maximum range of the external trajectory; Q scale 、S scale are the normalized parameters of maximum heat flux and maximum range, respectively, taking the expected maximum heat flux and expected range;

[0013] During the solution process, two-stage thrust constraints are set, and the two-stage thrust ratio of a single-chamber dual-thrust system should not be greater than the design limit parameter k max , the parameter constraints are as follows:

[0014]

[0015] Step 2: Optimize the inner and outer trajectory;

[0016] In the process of optimizing engine parameters, the external ballistic optimization calculation serves as the inner loop of the internal ballistic optimization. Based on the Gaussian pseudospectral method, a standard model considering the complete aerodynamic environment is established in the spherical coordinate system. The corresponding dynamic model is as follows:

[0017]

[0018]

[0019]

[0020]

[0021]

[0022] In the formula: r is the distance from the center of the earth; V is the speed of the projectile; θ is the ballistic inclination; S is the range; P is the engine thrust; α is the angle of attack; X is the drag, Y is the lift; g is the acceleration of gravity; m is the total mass of the projectile; mdot is the engine flow rate per second. With r, S, V, θ, m, α as state variables, the rate of change of angle of attack is As the control variable, the relationship between the angle of attack and the rudder angle is established based on the instantaneous equilibrium assumption; the inner loop uses the range as the performance indicator, that is:

[0023] J=-S end (8)

[0024] The heat flow rate is calculated as follows:

[0025]

[0026] Where: K Q is a parameter related to the structure; ρ is the atmospheric density;

[0027] Step 3: Integration of internal and external circuits;

[0028] After the inner loop solution converges, the maximum heat flux rate and the maximum range of the entire trajectory are first weighted as the performance indicators of the outer loop; then the outer loop determines whether the inner ballistic solution has converged based on the value of this performance indicator and the iterative status of the ratio parameter. If it has not converged, the last calculation result of the inner loop is used as the initial value to update the initial value guess of the outer ballistic optimization, thereby speeding up the solution of the inner loop; when the inner ballistic optimization solution of the outer loop meets the convergence accuracy requirements, the solution ends and the optimal time ratio and optimal total impulse ratio parameters of the single-chamber dual-thrust solid rocket engine are output.

[0029] (3) Beneficial effects

[0030] The present invention proposes a simple and reliable optimization solution method for the optimal design problem of the solid rocket engine ratio parameters in the overall design process, which can effectively improve the advancement of the overall engine indicators, reduce the thermal protection cost of the entire missile, improve the ammunition range capability, and promote efficient optimization and iteration of the solution.

[0031] Compared with the existing technology, the present invention mainly adopts the method of joint optimization of internal ballistics and external ballistics to design the key ratio parameters of single-chamber dual-thrust solid rocket engine in the overall design process of guided rocket, reduce the external ballistic thermal environment constraints, reduce the structural risk of materials in the high-temperature area of the projectile, reduce the thermal protection cost, and at the same time improve the maximum range capability of the entire projectile.

[0032] This method is simple and reliable, and the solution process converges quickly. Without significantly increasing the difficulty of implementing solid rocket engine technology, it can reduce the economic cost and structural thermal protection difficulty of medium and long-range guided rockets through the optimized design of the two-stage time and total impulse ratio parameters of a single-chamber dual-thrust solid rocket engine, thereby promoting the improvement of the design level of guided rockets. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 Schematic diagram of the dual-loop optimization framework for interior and exterior ballistics;

[0034] Figure 2 It is a schematic diagram of the trajectory comparison curve;

[0035] Figure 3 Schematic diagram of the comparison curve of the maximum heat flux rate of the head and the leading edge of the rudder;

[0036] Figure 4 This is a schematic diagram of the altitude comparison curve;

[0037] Figure 5 It is a schematic diagram of the speed comparison curve. DETAILED DESCRIPTION

[0038] In order to make the purpose, content and advantages of the present invention more clear, the specific implementation methods of the present invention are further described in detail below with reference to the accompanying drawings and examples.

[0039] The present invention provides a method for designing the ratio parameters of a single-chamber, dual-thrust solid rocket engine taking into account external ballistic constraints. When designing key parameters of the engine's internal ballistics, constraints such as the external ballistic thermal environment and range are taken into account. The method is a dual-parameter optimization iterative method for solving the optimal ratio of the total impulse and time of a single-chamber, dual-thrust solid rocket engine under conditions of external ballistic constraints. The method also provides an optimal solution framework for the inner and outer loops of the joint design of the internal and external ballistics of the single-chamber, dual-thrust solid rocket engine.

[0040] In order to solve the problems in the prior art, the present invention provides a method for designing the ratio parameters of a single-chamber dual-thrust solid rocket engine considering the external ballistic constraint. The dual-loop optimization solution process of the method is as follows: Figure 1 As shown; the implementation process of the method is as follows:

[0041] Step 1: Trajectory optimization within the outer loop;

[0042] The outer loop optimization is to solve the engine's internal ballistic ratio parameters. The ratio of the first-stage working time to the total working time, k1, and the ratio of the first-stage total impulse to the two-stage total impulse, k2, are taken as optimization parameters. The outer ballistic calculation is used as the dynamic function of the optimization solution, and the optimization problem of the internal ballistic ratio parameters is transformed into a dual-parameter optimal control problem.

[0043] The optimal control problem is solved using the interior point method. The partial derivatives of the ratio k1 and the optimization parameter k2 are solved using finite differences. Initial values are pre-set at the beginning of the iteration to avoid iteration failure. At this time, the optimization problem of the ballistic ratio parameters in the outer loop is to search for k1 and k2 to minimize the performance index. The performance index of the outer loop optimization is set to the weighted value of the maximum heat flux and the maximum range:

[0044]

[0045] Where: J is the performance index; ω1∈[0,1] is the weight of the thermal environment relative to the range. A value of 1 means that only the reduction of heat flux is considered, and a value of 0 means that only the improvement of the range is considered. Q δ is the maximum heat flux at the target location on the exterior ballistic projectile; S max is the maximum range of the external trajectory; Q scale 、S scale are the normalized parameters of maximum heat flux and maximum range, respectively, and are generally taken as the expected maximum heat flux and expected range;

[0046] During the solution process, two-stage thrust constraints are set. Generally, the thrust ratio of a single-chamber dual-thrust two-stage system should not be greater than the design limit parameter k max , the parameter constraints are as follows:

[0047]

[0048] Step 2: Optimize the inner and outer trajectory;

[0049] In the process of optimizing engine parameters, the external ballistic optimization calculation serves as the inner loop of the internal ballistic optimization. Based on the Gaussian pseudospectral method, a standard model considering the complete aerodynamic environment is established in the spherical coordinate system. The corresponding dynamic model is as follows:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] In the formula: r is the distance from the center of the earth; V is the speed of the projectile; θ is the ballistic inclination; S is the range; P is the engine thrust; α is the angle of attack; X is the drag, Y is the lift; g is the acceleration of gravity; m is the total mass of the projectile; mdot is the engine flow rate per second. With r, S, V, θ, m, α as state variables, the rate of change of angle of attack is As the control variable, the relationship between the angle of attack and the rudder angle is established based on the instantaneous equilibrium assumption; the inner loop uses the range as the performance indicator, that is:

[0056] J=-S end (8)

[0057] The heat flow rate is calculated as follows:

[0058]

[0059] Where: K Q is a parameter related to the structure; ρ is the atmospheric density;

[0060] For medium and long-range guided rockets, the thermal environment is generally the worst at the leading edge of the rudder, and factors such as the sweep angle of the leading edge of the rudder must be considered during the precise calculation process.

[0061] Step 3: Integration of internal and external circuits;

[0062] After the inner loop solution converges, the maximum heat flux rate and the maximum range of the entire trajectory are first weighted as the performance indicators of the outer loop; then the outer loop determines whether the inner ballistic solution has converged based on the value of this performance indicator and the iterative status of the ratio parameter. If it has not converged, the last calculation result of the inner loop is used as the initial value to update the initial value guess of the outer ballistic optimization, thereby speeding up the solution of the inner loop; when the inner ballistic optimization solution of the outer loop meets the convergence accuracy requirements, the solution ends and the optimal time ratio and optimal total impulse ratio parameters of the single-chamber dual-thrust solid rocket engine are output.

[0063] Step 4: Numerical simulation

[0064] Taking a certain type of benchmark ammunition as the research object, the total engine impulse and total working time remain unchanged. Set k max =5, the single-chamber dual-thrust solid rocket engine ratio parameter design method proposed in the present invention is used for optimization design, and the simulation curve comparison between the original scheme and the optimal ratio scheme is shown in FIG. Figures 2 to 5 shown.

[0065] The optimal design ratio of the single-chamber dual-thrust solid rocket engine obtained by the present invention is k1 = 23.31%, k2 = 59.64%, and the corresponding average thrust ratio is 4.86, which meets the maximum thrust ratio requirement. The maximum range is increased from 346.7km to 391.2km, an increase of 12.8%; the maximum heat flux at the head stagnation point is increased from 3.04MW / m 2 Reduced to 1.74MW / m 2 , reduced by 42.8%; the maximum heat flux rate at the leading edge of the rudder blade is reduced from 9.17MW / m 2 Reduced to 3.84MW / m 2 , a decrease of 58.1%.

[0066] The above results show that adjusting the internal ballistic ratio parameters of a single-chamber, dual-thrust solid rocket motor can significantly affect external ballistic performance. The velocity comparison curve shows that the optimal ratio corresponds to a short, high-thrust acceleration process in the first stage and a long, low-thrust acceleration process in the second stage. The maximum speed corresponding to the optimal ratio is basically the same as that of the original design. The altitude comparison curve shows that the optimal ratio corresponds to a higher active segment trajectory altitude, and the air density corresponding to the maximum speed of the guided rocket is lower, thus effectively reducing the thermal environment pressure on the projectile.

[0067] The above examples fully demonstrate the superiority of the present invention. Using the method proposed in the present invention to design the engine during the overall design stage can effectively reduce the thermal protection pressure of the guided rocket structure, reduce the thermal protection cost, and at the same time improve the maximum range capability, which has a good promoting effect on improving the optimality of the overall solution.

[0068] Example 1

[0069] In order to solve the above technical problems, the present invention provides a single-chamber dual-thrust solid rocket engine ratio parameter design method considering external ballistic constraints. The optimization of the internal ballistic ratio parameters is used as the outer loop, and the optimization of the external ballistics is used as the inner loop. Through feedback iteration, the optimal ratio scheme of the engine is quickly given.

[0070] The optimization of the internal trajectory ratio parameters is solved using a dual-parameter optimization and iteration method, taking into account the maximum thrust ratio constraint. The optimization of the external trajectory is achieved using the Gaussian pseudo-spectral method, with maximum range as the performance indicator, while also considering initial values, state, and control variables. The performance indicators for the internal trajectory optimization process are obtained by weightedly combining the maximum range capability achieved with the external trajectory and the thermal environment of the entire trajectory.

[0071] The optimal engine parameters obtained by the dual-loop optimization solution can effectively improve the exterior ballistic performance, converge quickly, and have strong engineering application value.

[0072] In summary, the present invention belongs to the technical field of overall design of guided rockets, and specifically relates to a method for designing the ratio parameters of a single-chamber dual-thrust solid rocket engine taking into account external ballistic constraints. The outstanding advantage of the present invention is that when designing the engine's internal ballistic thrust curve, the external ballistic constraints and range optimality are comprehensively considered, and at the same time, the previous two-stage ratio design method based on experience is transformed into a computer-automated optimization process. The obtained engine internal ballistic parameters can effectively reduce the external ballistic thermal environment pressure, improve the range capability, reduce the design costs such as the projectile heat protection, and enhance the advancement of the overall design indicators. This method can significantly improve the optimality of the engine's internal ballistics in the overall design process of the guided rocket, and effectively improve the design performance of the overall scheme. The method is simple and reliable, and the obtained design results have been verified in large quantities, and have great room for promotion and application. The present invention adopts an inner and outer loop solution framework that combines interior ballistic optimization with exterior ballistic optimization, takes the exterior ballistic optimization as the inner loop of interior ballistic optimization, and the interior ballistic design uses the exterior ballistic optimization result as feedback, transforming the interior ballistic optimization design problem of a single-chamber dual-thrust solid rocket engine into a search problem for the optimal ratio of the two-stage total impulse and the optimal ratio of the two-stage working time. Then, a dual-parameter optimization iterative method is used to optimize the engine's interior ballistic parameters, and a design scheme for key interior ballistic parameters under the condition of optimal exterior ballistic performance is obtained.

[0073] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A method for designing the ratio parameters of a single-chamber dual-thrust solid rocket engine considering external ballistic constraints, characterized in that: The method is implemented as follows: Step 1: Trajectory optimization within the outer loop; The outer loop optimization is to solve the engine's internal ballistic ratio parameters. The ratio of the first-stage working time to the total working time, k1, and the ratio of the first-stage total impulse to the two-stage total impulse, k2, are taken as optimization parameters. The outer ballistic calculation is used as the dynamic function of the optimization solution, and the optimization problem of the internal ballistic ratio parameters is transformed into a dual-parameter optimal control problem. The optimal control problem is solved using the interior point method. The partial derivatives of the optimization parameters k1 and k2 are solved using finite differences. Initial values are preset at the beginning of the iteration to avoid iteration failure. At this time, the optimization problem of the ballistic ratio parameters in the outer loop is to search for k1 and k2 to minimize the performance index. The performance index of the outer loop optimization is set to the weighted value of maximum heat flux and maximum range: （1） Where: is a performance indicator; , is the weight of the thermal environment relative to the range. A value of 1 means that only the reduction of heat flux is considered, and a value of 0 means that only the improvement of the range is considered. The maximum heat flux at the area of interest on the exterior ballistic projectile; It is the maximum range of the exterior trajectory; 、 are the normalized parameters of maximum heat flux and maximum range, respectively, taking the expected maximum heat flux and expected range; During the solution process, two-stage thrust constraints are set, and the two-stage thrust ratio of a single-chamber dual-thrust system should not be greater than the design limit parameter k max , the parameter constraints are as follows: （2）； Step 2: Optimize the inner and outer trajectory; In the process of optimizing engine parameters, the external ballistic optimization calculation serves as the inner loop of the internal ballistic optimization. Based on the Gaussian pseudospectral method, a standard model considering the complete aerodynamic environment is established in the spherical coordinate system. The corresponding dynamic model is as follows: （3） （4） （5） （6） （7） Where: is the distance from the center of the Earth; is the bullet speed; is the ballistic inclination angle; For range; is the engine thrust; is the angle of attack; For resistance, lift; is the acceleration due to gravity; is the mass of the entire projectile; is the engine flow rate per second; by 、 、 、 、 、 is the state quantity, the rate of change of angle of attack As the control variable, the relationship between the angle of attack and the rudder angle is established based on the instantaneous equilibrium assumption; the inner loop uses the range as the performance indicator, that is: （8） The heat flow rate is calculated as follows: （9） Where: are parameters related to the structure; is the atmospheric density; Step 3: Integration of internal and external circuits; After the inner loop solution converges, the maximum heat flux rate and the maximum range of the entire trajectory are first weighted as the performance indicators of the outer loop; then the outer loop determines whether the inner ballistic solution has converged based on the value of this performance indicator and the iterative status of the ratio parameter. If it has not converged, the last calculation result of the inner loop is used as the initial value to update the initial value guess of the outer ballistic optimization, thereby speeding up the solution of the inner loop; when the inner ballistic optimization solution of the outer loop meets the convergence accuracy requirements, the solution ends and the optimal time ratio and optimal total impulse ratio parameters of the single-chamber dual-thrust solid rocket engine are output.

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