Solid rocket engine nozzle divergence ratio optimizing method with integrated inner and outer ballistic trajectories

Abstract

The invention discloses an inner and outer trajectory integrated solid rocket engine jet pipe divergence ratio optimization method. The method comprises the steps that inner and outer loop optimization calculation is carried out; optimizing the expansion ratio of the outer loop spray pipe; and optimizing the trajectory in the inner loop. According to the method, when the expansion ratio of the engine jet pipe is designed, optimization of inner trajectory parameters and the optimality of the impact mass ratio of the actual flight working condition are comprehensively considered, and engine overall parameter design conducted according to experience in the past is converted into a computer automatic optimizing process; the obtained optimal expansion ratio of the engine jet pipe and the corresponding inner ballistic parameters can effectively improve the maximum range of the guided rocket projectile and promote the improvement of the design level.

Description

Technical Field

[0001] The invention belongs to the field of rocket technology, and in particular relates to a method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics. Background Art

[0002] In the design process of guided rockets, the overall design of solid rocket engines has a crucial impact on the feasibility of the entire solution. As guided rockets develop towards long-range, in order to meet the requirements of long range, the requirements for the impulse-to-mass ratio of solid rocket engines are getting higher and higher. Using conventional overall design methods, only the impulse-to-mass ratio of sea level conditions can be calculated, but under actual flight conditions, the impulse-to-mass ratio of the engine is greatly affected by the external ballistics. Therefore, compared with the flight conditions, the impulse-to-mass ratio of sea level conditions has a larger error.

[0003] A single-chamber multi-thrust solid rocket engine is a rocket engine that achieves multi-stage thrust in the same combustion chamber. Its advantage is that the staged thrust can significantly improve the speed characteristics of the guided rocket flight. Among them, the single-chamber dual-thrust solid rocket engine is widely used. For guided rockets that pursue long range, the design of the nozzle expansion ratio is very important to the engine performance and is directly related to the utilization rate of the propellant energy. In the overall design process, the nozzle expansion ratio is often designed with the maximum sea level impulse-to-mass ratio as the goal, lacking an optimized design for actual flight conditions that integrates internal and external ballistics. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, the present invention provides a method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics, including: internal and external loop optimization solution; external loop nozzle expansion ratio optimization; internal loop internal ballistic optimization. When designing the engine nozzle expansion ratio, the present invention comprehensively considers the optimization of internal ballistic parameters and the optimality of the impulse-to-mass ratio under actual flight conditions, and transforms the overall engine parameter design that was previously based on experience into a computer automatic optimization process. The obtained engine nozzle optimal expansion ratio and corresponding internal ballistic parameters can effectively improve the maximum range of the guided rocket and promote the improvement of the design level.

[0005] The technical solution adopted by the present invention to solve the technical problem is as follows:

[0006] Step 1: Optimization and solution of internal and external loops;

[0007] The optimization of the internal and external loops is the solution of the engine nozzle expansion ratio;

[0008] The ratio of the total engine flight impulse integrated along the external trajectory to the total engine mass is used as the objective function of the optimization solution;

[0009] Input the initial geometric parameters of the nozzle in the un-ablated state as the initial values ​​of the optimization solution, input the nozzle size limit parameters as the upper and lower limits of the values ​​in the optimization solution, input the nozzle specific impulse efficiency, throat ablation rate and gas specific heat ratio as constants in the optimization solution;

[0010] Construct the initial geometric model of the nozzle as the initial parameter for optimizing the nozzle expansion ratio;

[0011] Substitute the parameters of the nozzle geometry model into the inner loop to optimize the internal ballistics. For each type of charge and M number, a series of optimal internal ballistics that vary with the charge ratio parameters are obtained and output from the inner loop to the outer loop. Combined with the input parameters, the external ballistics are calculated for the internal ballistics.

[0012] According to the outer loop optimization method, the impact-mass ratio of the flight condition of the outer trajectory corresponding to the nozzle expansion ratio is calculated; after the maximum impact-mass ratio is obtained by iterating the nozzle expansion ratio, the solution is completed and the optimal nozzle expansion ratio is output;

[0013] Step 2: Optimizing the expansion ratio of the outer loop nozzle;

[0014] The optimization of the external circuit nozzle expansion ratio is the solution of the engine nozzle expansion ratio;

[0015] Based on the known nozzle configuration, size limitation parameters and throat ablation rate, for each nozzle expansion ratio in the iteration, the optimal internal ballistics given by the inner loop with the change of the grain parameters is solved;

[0016] The external ballistics are calculated based on the input parameters and the internal ballistics. Each internal ballistics corresponds to an external ballistics. The engine thrust coefficient and the instantaneous thrust of the engine at each point on the external ballistics are calculated. The instantaneous thrust is integrated along the external ballistics over time to obtain the total impulse of the engine under the flight condition. The nozzle weight is calculated based on the nozzle configuration, expansion ratio, throat diameter and nozzle material density parameters. The engine impulse-to-mass ratio under the flight condition is calculated by combining the input engine passive mass excluding the nozzle.

[0017] For each nozzle expansion ratio, the working condition with the maximum impact-mass ratio under the expansion ratio is solved, the nozzle expansion ratio is updated and iterated, and the maximum impact-mass ratios corresponding to different nozzle expansion ratios are compared. After the maximum impact-mass ratio is obtained, the optimization of the nozzle expansion ratio is completed;

[0018] Step 3: Optimizing the trajectory within the inner loop;

[0019] The inner loop optimization is to solve the burning rate and grain ratio parameters of the two-stage propellant of the engine grain. Based on the known inner surface geometry model of the nozzle, the types of grains that need to be compared through the impulse-to-mass ratio optimization in the initial overall design plan and the corresponding M number range are input to limit the scope of the inner ballistic optimization.

[0020] On the basis of the selected charge type and M number, the burning rate of the propellant and the grain ratio parameters are used as optimization parameters, and the iterative value range of the burning rate and grain ratio parameters of the two-stage propellant is input. Within the value range, the burning rate and grain ratio parameters of the two-stage propellant are respectively taken at intervals.

[0021] Before optimizing the inner loop, input the initial propellant burning rate and grain ratio parameters as the initial values ​​of the iteration to ensure that the solution starts normally;

[0022] Keeping the charge ratio parameters unchanged, the burning rate of the interval value is updated and iterated, and the optimal internal ballistics under different charge ratio parameters are solved. The optimization judgment basis is the maximum sea level impact-mass ratio; each charge ratio parameter corresponds to an optimal internal ballistics; a series of charge ratio parameters within the value range and their corresponding optimal internal ballistics are output to the outer loop for external ballistic calculation;

[0023] After changing the drug type or M number, repeat the process of finding the optimal ballistics within the inner loop in step 3.

[0024] Preferably, the engine thrust coefficient at each point on the outer trajectory is calculated from four parameters: combustion chamber pressure, nozzle back pressure, nozzle expansion ratio and gas specific heat ratio.

[0025] Preferably, the instantaneous thrust of the engine at each point on the external ballistic trajectory is calculated from three parameters: combustion chamber pressure, thrust coefficient and nozzle throat diameter.

[0026] Preferably, when the combustion chamber pressure is the same, the burning rate of the first-stage charge is higher than that of the second-stage charge; the charge ratio parameter is the ratio of the first-stage charge length to the total charge length, and its value range is 0.15 to 0.85; the M number is the ratio of the inner hole diameter to the outer diameter of the charge.

[0027] Preferably, the graduation value of the interval value of the two-stage propellant burning rate and grain ratio parameter of the engine grain is not greater than 1% of the value range.

[0028] Preferably, the exterior ballistic calculation adopts a dynamic model of a complete aerodynamic environment established based on the Gauss pseudo-spectral method in a spherical coordinate system.

[0029] The beneficial effects of the present invention are as follows:

[0030] 1. The present invention proposes a simple and reliable optimization solution method for the design problem of nozzle geometric structure parameters such as nozzle expansion ratio in the overall design process of solid rocket engines, which can effectively improve the overall performance indicators of the engine, improve the ammunition range capability, and promote efficient optimization and iteration of the solution.

[0031] 2. Compared with the prior art, the present invention mainly adopts an integrated internal and external ballistics method in the overall design process of the guided rocket, optimizes the internal ballistic parameters and nozzle geometric structure parameters such as the nozzle expansion ratio according to the impact-to-mass ratio index of the actual flight condition, and obtains the overall design scheme of the engine with the highest impact-to-mass ratio, thereby improving the maximum range of the whole missile.

[0032] 3. The method of the present invention is simple and reliable, and the solution process converges quickly. It can promote the improvement of the design level of guided rockets by optimizing the geometric structure parameters of the nozzle with integrated internal and external ballistics without significantly increasing the design difficulty of the single-chamber dual-thrust solid rocket engine. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 It is a schematic diagram of the framework of the method of the present invention;

[0034] Figure 2 A schematic diagram of a curve showing the relationship between range and altitude before and after expansion ratio optimization in an embodiment of the present invention;

[0035] Figure 3 This is a schematic diagram of a curve showing the relationship between flight time and altitude before and after expansion ratio optimization in an embodiment of the present invention. DETAILED DESCRIPTION

[0036] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0037] The technical problem to be solved by the present invention is: in a single-chamber double-thrust solid rocket engine, how to obtain the overall design parameters that can maximize the engine impulse-to-mass ratio under flight conditions through the optimal design of the nozzle expansion ratio.

[0038] In order to solve the above technical problems, Figure 1 As shown, the present invention provides a method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics, and the implementation process is as follows:

[0039] Step 1: Optimization and solution of internal and external loops;

[0040] The internal and external loop optimization is to solve the engine nozzle expansion ratio, and the ratio of the total engine flight impulse integrated along the external ballistic trajectory to the total engine mass is used as the objective function of the optimization solution; before the internal and external loop optimization iteration, the initial geometric parameters of the nozzle in the non-ablated state are input as the initial value of the iteration, the nozzle size limit parameters are input as the upper and lower limits of the value in the iteration, and the parameters such as the nozzle specific impulse efficiency, throat ablation rate and gas specific heat ratio are input as constants in the optimization iteration to ensure that the solution can start normally;

[0041] According to the above input parameters, the initial geometric model of the nozzle can be constructed as the initial parameters for optimizing the nozzle expansion ratio; the parameters of the nozzle geometric model are substituted into the inner loop for optimizing the internal ballistics. For each type of charge and M number, a series of optimal internal ballistics that vary with the charge ratio parameters can be obtained, and output from the inner loop to the outer loop, and the external ballistics are calculated for the internal ballistics in combination with the input parameters; according to the outer loop optimization method, a series of external ballistic flight condition impulse-to-mass ratios corresponding to a nozzle expansion ratio are calculated; after the maximum impulse-to-mass ratio is obtained by iterating the nozzle expansion ratio, the solution is completed and the optimal nozzle expansion ratio is output;

[0042] Step 2: Optimizing the expansion ratio of the nozzle in the outer loop;

[0043] The outer loop optimization is to solve the engine nozzle expansion ratio; based on the known structural parameters such as nozzle configuration, size restriction parameters and throat ablation rate, for each nozzle expansion ratio in the iteration, a series of optimal internal ballistics given by the inner loop that vary with the parameters of the grain are solved;

[0044] The external ballistics is calculated based on the input parameters and the internal ballistics. Each internal ballistics corresponds to an external ballistics. The engine thrust coefficient and the instantaneous thrust of the engine at each point on the external ballistics are calculated. The instantaneous thrust is integrated along the external ballistics over time to obtain the total impulse of the engine under the flight condition. The nozzle weight can be calculated based on the parameters such as the nozzle configuration, expansion ratio, throat diameter and nozzle material density. Combined with the input engine negative mass excluding the nozzle, the engine impulse-to-mass ratio under the flight condition can be calculated.

[0045] Each nozzle expansion ratio can solve the working condition with the maximum impact-mass ratio under the expansion ratio, update the nozzle expansion ratio iteratively, compare the maximum impact-mass ratios corresponding to different nozzle expansion ratios, and complete the optimization of the nozzle expansion ratio after obtaining the maximum impact-mass ratio;

[0046] Step 3: Optimizing the trajectory within the inner loop;

[0047] The inner loop optimization is to solve the burning rate and grain ratio parameters of the two-stage propellant of the engine grain. Based on the known inner surface geometry model of the nozzle, the types of grains that need to be compared through the impulse-to-mass ratio optimization in the initial overall design plan and the corresponding M number range are input to limit the scope of the inner ballistic optimization.

[0048] On the basis of the selected charge type and M number, the propellant burning rate and grain ratio parameters are used as optimization parameters, and the iterative value range of the two-stage propellant burning rate and grain ratio parameters is input. Within the value range, the two-stage propellant burning rate and grain ratio parameters are respectively taken at intervals; before the inner loop optimization, the initial propellant burning rate and grain ratio parameters need to be input as the initial values ​​of the iteration to ensure that the solution can start normally;

[0049] Keeping the charge ratio parameters unchanged, the burning rate of the interval value is updated and iterated, and the optimal internal ballistics under different charge ratio parameters are solved. The optimization judgment basis is the maximum sea level impact-to-mass ratio; each charge ratio parameter corresponds to an optimal internal ballistics; a series of charge ratio parameters within the value range and their corresponding optimal internal ballistics are output to the outer loop for external ballistic calculation; after changing the charge type or M number, the process of optimizing the internal ballistics in the inner loop is repeated.

[0050] The engine thrust coefficient at each point on the external ballistic trajectory is calculated from four parameters: combustion chamber pressure, nozzle back pressure, nozzle expansion ratio and gas specific heat ratio.

[0051] The instantaneous thrust of the engine at each point on the external ballistic trajectory is calculated from three parameters: combustion chamber pressure, thrust coefficient and nozzle throat diameter.

[0052] Under the same combustion chamber pressure, the burning rate of the first-stage grain is higher than that of the second-stage grain. The grain ratio parameter is the ratio of the first-stage grain length to the total grain length, and its value range is 0.15 to 0.85. The M number is the ratio of the inner diameter to the outer diameter of the grain.

[0053] The graduation value of the interval value of the burning rate and grain ratio parameters of the two-stage propellant shall not exceed 1% of the value range.

[0054] The calculation of the exterior ballistics adopts a dynamic model that takes into account the complete aerodynamic environment and is established based on the Gauss pseudo-spectral method in a spherical coordinate system.

[0055] Example:

[0056] Taking a certain type of guided rocket as the research object, the nozzle expansion ratio and other nozzle geometric structure parameters are optimized by the method of the present invention, and a new overall design scheme of the engine with better performance is obtained. The comparison curves before and after optimization are as follows: Figure 2 and Figure 3 The maximum range of the whole missile of the new scheme calculated by the method of the present invention is 739.5 km, which is 16.6% higher than the original range of 634.4 km before optimization. The total impulse of the engine at sea level of the new scheme is 8.6% higher than that before optimization.

[0057] The above verifications fully demonstrate the superiority of the present invention. Using the method of the present invention to design the internal ballistic parameters and nozzle expansion ratio of the engine in the overall design stage can effectively improve the maximum range of the whole projectile and has a good promoting effect on the performance improvement of the overall engine solution.

Claims

1. A method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics, characterized in that: The steps include: Step 1: Optimization and solution of internal and external loops; The optimization of the internal and external loops is the solution of the engine nozzle expansion ratio; The ratio of the total engine flight impulse integrated along the external trajectory to the total engine mass is used as the objective function of the optimization solution; Input the initial geometric parameters of the nozzle in the un-ablated state as the initial values ​​of the optimization solution, input the nozzle size limit parameters as the upper and lower limits of the values ​​in the optimization solution, input the nozzle specific impulse efficiency, throat ablation rate and gas specific heat ratio as constants in the optimization solution; Construct the initial geometric model of the nozzle as the initial parameter for optimizing the nozzle expansion ratio; Substitute the parameters of the nozzle geometry model into the inner loop to optimize the internal ballistics. For each type of charge and M number, a series of optimal internal ballistics that vary with the charge ratio parameters are obtained and output from the inner loop to the outer loop. Combined with the input parameters, the external ballistics are calculated for the internal ballistics. According to the outer loop optimization method, the impact-mass ratio of the flight condition of the outer trajectory corresponding to the nozzle expansion ratio is calculated; after the maximum impact-mass ratio is obtained by iterating the nozzle expansion ratio, the solution is completed and the optimal nozzle expansion ratio is output; Step 2: Optimizing the expansion ratio of the nozzle of the outer loop; The optimization of the external circuit nozzle expansion ratio is the solution of the engine nozzle expansion ratio; Based on the known nozzle configuration, size limitation parameters and throat ablation rate, for each nozzle expansion ratio in the iteration, the optimal internal ballistics given by the inner loop with the change of the grain parameters is solved; The external ballistics are calculated based on the input parameters and the internal ballistics. Each internal ballistics corresponds to an external ballistics. The engine thrust coefficient and the instantaneous thrust of the engine at each point on the external ballistics are calculated. The instantaneous thrust is integrated along the external ballistics over time to obtain the total impulse of the engine under the flight condition. The nozzle weight is calculated based on the nozzle configuration, expansion ratio, throat diameter and nozzle material density parameters. The engine impulse-to-mass ratio under the flight condition is calculated by combining the input engine passive mass excluding the nozzle. For each nozzle expansion ratio, the working condition with the maximum impact-mass ratio under the expansion ratio is solved, the nozzle expansion ratio is updated and iterated, and the maximum impact-mass ratios corresponding to different nozzle expansion ratios are compared. After the maximum impact-mass ratio is obtained, the optimization of the nozzle expansion ratio is completed; Step 3: Optimizing the trajectory within the inner loop; The inner loop optimization is to solve the burning rate and grain ratio parameters of the two-stage propellant of the engine grain. Based on the known inner surface geometry model of the nozzle, the types of grains that need to be compared through the impulse-to-mass ratio optimization in the initial overall design plan and the corresponding M number range are input to limit the scope of the inner ballistic optimization. On the basis of the selected charge type and M number, the burning rate of the propellant and the grain ratio parameters are used as optimization parameters, and the iterative value range of the burning rate and grain ratio parameters of the two-stage propellant is input. Within the value range, the burning rate and grain ratio parameters of the two-stage propellant are respectively taken at intervals. Before optimizing the inner loop, input the initial propellant burning rate and grain ratio parameters as the initial values ​​of the iteration to ensure that the solution starts normally; Keeping the charge ratio parameters unchanged, the burning rate of the interval value is updated and iterated, and the optimal internal ballistics under different charge ratio parameters are solved. The optimization judgment basis is the maximum sea level impact-mass ratio; each charge ratio parameter corresponds to an optimal internal ballistics; a series of charge ratio parameters within the value range and their corresponding optimal internal ballistics are output to the outer loop for external ballistic calculation; After changing the drug type or M number, repeat the process of finding the optimal ballistics within the inner loop in step 3.

2. The method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics according to claim 1, characterized in that: The engine thrust coefficient at each point on the outer ballistic trajectory is calculated from four parameters: combustion chamber pressure, nozzle back pressure, nozzle expansion ratio and fuel gas specific heat ratio.

3. According to the method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics as described in claim 1, the instantaneous thrust of the engine at each point on the external ballistics is calculated by three parameters: combustion chamber pressure, thrust coefficient and nozzle throat diameter.

4. According to the method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics as described in claim 2 or 3, when the pressure in the combustion chamber is the same, the burning rate of the first-stage grain is higher than the burning rate of the second-stage grain; the grain ratio parameter is the ratio of the first-stage grain length to the total grain length, and its value range is 0.15 to 0.85; the M number is the ratio of the inner hole diameter to the outer diameter of the grain.

5. According to the method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics as described in claim 1, the graduation value of the interval value of the two-stage propellant burning rate and grain ratio parameter of the engine grain is not greater than 1% of the value range.

6. According to the method for optimizing the nozzle expansion ratio of a solid rocket engine with integrated internal and external ballistics as described in claim 1, the external ballistics calculation adopts a dynamic model of a complete aerodynamic environment established based on the Gauss pseudo-spectral method in a spherical coordinate system.

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