固体火箭发动机三维装药的逆向设计与形状优化

doi:10.7527/S1000-6893.2023.29089

Abstract

Abstract:

The solid rocket motor grain reverse design， an effort to seek the optimal grain shape to match a given internal ballistic curve， can be used to guide the conceptual design of brand-new grains. Grain reverse design is now progressing from the size optimization level towards the shape optimization and even topology optimization level. Shape optimization problems tend to have large degrees of freedom and high nonlinearity， placing extremely high demands on the computational efficiency of burn-back analysis. However， existing elliptic algorithms for burn-back analysis fail to meet the requirement. It is necessary to develop an efficient elliptic algorithm for burn-back analysis and apply it to the 3-dimensional （3D） grain reverse design. Firstly， the eikonal equation is linearized to a Helmholtz equation and a Poisson equation， forming a series of Fast Heat Conduction （FHC） methods for burn-back analysis. Among them， the f-FHC method， describing the grain geometry by cavity fraction distribution， uses the LDL decomposition method to solve the linear equations. With the principle of “once decomposition， back substitution everywhere”， the computational efficiency can be significantly improved. Secondly， the key issues of 3D grain reverse design are systematically analyzed， including the selection of objective function， the range of independent variables that need to be optimized， isolated holes identification， and casting requirements. With the aid of the evolutionary neural network， the Grain Reverse and Intelligent Design （GRID） system is developed. The calculation results show that the f-FHC method can reduce the calculation time of 3D grain burn-back analysis into less than 1 s. Targeting at the burning surface curve or internal ballistic curve of the dual-thrust grain， the GRID system successfully designs a series of new grains containing complex 3D internal cavities. The resulting grains meet the casting requirements， and their mandrels can be manufactured by 3D-print. The proposed algorithm and the developed software can provide support for the conceptual design of brand-new grains.

Key words: solid rocket motor, grain reverse design, shape optimization, topology optimization, burn-back analysis, eikonal equation, evolutionary neural networks

CLC Number:

V435⁺.21

Wentao LI, Yunqin HE, Wenbo LI, Yiyi ZHANG, Guozhu LIANG. 3D grain reverse design and shape optimization for solid rocket motor[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(11): 529089-529089.

Figures/Tables 22

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Fig.2

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Fig.8

Table 1

Recommended values for main parameters

项目	推荐值
径向网格数	80
隐含层的神经元数	20
种群数 $n g$	10M（N+2）
遗传代数	2.5 $n g$
变异率	0.01
交叉率	0.8
参数取值范围	见式（47）
编码位数	16
提取等值面（燃面）总数	20

Table 1

Fig.9

Fig.10

Fig.11

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Fig.13

Fig.14

Table 2

Fig.15

Fig.16

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Fig.18

Fig.19

Fig.20

References 35

1	蒋雨晴. 固体装药型面通用设计方法研究［D］. 北京：北京航空航天大学， 2018.
	JIANG Y Q. Study on general design method of solid grain internal surface［D］. Beijing： Beihang University， 2018 （in Chinese）.
2	VANDENBRANDE J. DARPA TRADES challenge problems［EB/OL］. （2020-06-03）［2023-05-31］. .
3	WU Z P， WANG D H， ZHANG W H， et al. Solid-rocket-motor performance-matching design framework［J］. Journal of Spacecraft and Rockets， 2017， 54（3）： 698-707.
4	MESGARI S， BAZAZZADEH M， MOSTOFIZADEH A. Finocyl grain design using the genetic algorithm in combination with adaptive basis function construction［J］. International Journal of Aerospace Engineering， 2019， 2019： 3060173.
5	HASHISH A， AHMED M Y， ABDALLAH H， et al. Design of solid propellant grain for predefined performance criteria： AIAA-2019-2014［R］. Reston： AIAA， 2019.
6	ALBARADO K， HARTFIELD R， HURSTON B， et al. Solid rocket motor performance matching using pattern search/particle swarm optimization： AIAA-2011-5798［R］. Reston： AIAA， 2011.
7	LI W T， LI W B， HE Y Q， et al. Reverse design of solid propellant grain for a performance-matching goal： Shape optimization via evolutionary neural network［J］. Aerospace， 2022， 9（10）： 552.
8	MAUTE K， DE S. Shape and material optimization of problems with dynamically evolving interfaces applied to solid rocket motors［J］. Structural and Multidisciplinary Optimization， 2022， 65（8）： 218.
9	YOSHIMURA M， SHIMOYAMA K， MISAKA T， et al. Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model［J］. International Journal for Numerical Methods in Engineering， 2017， 109（4）： 514-532.
10	BENDSØE M P. Optimal shape design as a material distribution problem［J］. Structural Optimization， 1989， 1（4）： 193-202.
11	BENDSØE M P， KIKUCHI N. Generating optimal topologies in structural design using a homogenization method［J］. Computer Methods in Applied Mechanics and Engineering， 1988， 71（2）： 197-224.
12	SFORZINI R H. Automated approach to design of solid rockets［J］. Journal of Spacecraft and Rockets， 1981， 18（3）： 200-205.
13	GREFEN B， BECKER J， LINKE S， et al. Design， production and evaluation of 3D-printed mold geometries for a hybrid rocket engine［J］. Aerospace， 2021， 8（8）： 220.
14	CHANDRU R A， BALASUBRAMANIAN N， OOMMEN C， et al. Additive manufacturing of solid rocket propellant grains［J］. Journal of Propulsion and Power， 2018， 34（4）： 1090-1093.
15	王璐，赵永超，苗楠，等. 复合固体推进剂直写式3D打印工艺及其性能［J］. 固体火箭技术， 2021， 44（5）： 650-655.
	WANG L， ZHAO Y C， MIAO N， et al. Direct-writing 3D printing technology and characteristics of composite solid propellant［J］. Journal of Solid Rocket Technology， 2021， 44（5）： 650-655 （in Chinese）.
16	GUIRGUIS D， AULIG N， PICELLI R， et al. Evolutionary black-box topology optimization： Challenges and promises［J］. IEEE Transactions on Evolutionary Computation， 2020， 24（4）： 613-633.
17	SETHIAN J A. Curvature and the evolution of fronts［J］. Communications in Mathematical Physics， 1985， 101（4）： 487-499.
18	LIU Y Q， YIN K X， BAO F T， et al. Efficient simulation of grain burning surface regression［J］. Advanced Materials Research， 2012， 466/467： 314-318.
19	CAPOZZOLI A， CURCIO C， LISENO A， et al. A comparison of Fast Marching， Fast Sweeping and Fast Iterative Methods for the solution of the eikonal equation［C］∥ 2013 21st Telecommunications Forum Telfor. Piscataway： IEEE Press， 2013： 685-688.
20	李文韬，何允钦，张艺仪，等.非均匀装药的复杂燃面退移与内弹道性能预示［J/OL］.北京航空航天大学学报，（2022-11-17）［2023-05-31］. .
	LI W T， HE Y Q， ZHANG Y Y， et al. Complex burning surface burn-back analysis and internal ballistic performance prediction of non-uniform grain［J］. Journal of Beijing University of Aeronautics and Astronautics，（2022-11-17）［2023-05-31］. （in Chinese）.
21	MOKRÝ P. Iterative method for solving the eikonal equation［C］∥ Optics and Measurement International Conference. 2016： 263-268.
22	CHURBANOV A G， VABISHCHEVICH P N. Numerical solving a boundary value problem for the eikonal equation［C］∥ International Conference on Finite Difference Methods. Cham： Springer， 2019： 28-34.
23	CRANE K， WEISCHEDEL C， WARDETZKY M. Geodesics in heat： A new approach to computing distance based on heat flow［J］. ACM Transactions on Graphics， 2013， 32（5）： 152.
24	PATANKAR S V. Numerical heat transfer and fluid flow［M］. New York： Hemisphere Publishing Corporation， 1980.
25	WANG M Y， WANG X M， GUO D M. A level set method for structural topology optimization［J］. Computer Methods in Applied Mechanics and Engineering， 2003， 192（1/2）： 227-246.
26	WANG M Y， ZHOU S W. Phase field： A variational method for structural topology optimization［J］. CMES - Computer Modeling in Engineering and Sciences， 2004， 6（6）： 547-566.
27	DE RUITER M J， VAN KEULEN F. Topology optimization using a topology description function［J］. Structural and Multidisciplinary Optimization， 2004， 26（6）： 406-416.
28	RENNICH S C， STOSIC D， DAVIS T A. Accelerating sparse Cholesky factorization on GPUs［J］. Parallel Computing， 2016， 59： 140-150.
29	WILLCOX M A， BREWSTER M Q， TANG K C， et al. Solid propellant grain design and burnback simulation using a minimum distance function［J］. Journal of Propulsion and Power， 2007， 23（2）： 465-475.
30	LI W B， LI W T， CHENG L， et al. Trajectory optimization with complex obstacle avoidance constraints via homotopy network sequential convex programming［J］. Aerospace， 2022， 9（11）： 720.
31	WALL M. GAlib： A C++ library of genetic algorithm components［EB/OL］. ［2023-05-31］. .
32	JACOB B， GUENNEBAUD G. Eigen［EB/OL］. （2021-08-18）［2023-05-31］. .
33	DAVIS T. Suitesparse：A suite of sparse matrix software［EB/OL］. （2022-11-12）［2023-05-31］. .
34	WELLER H， GREENSHIELDS C， DE ROUVRAY C. OpenFOAM［EB/OL］. （2022-07-28）［2023-05-31］. .
35	MARTIN P， BARRANQUERO C， SANCHEZ J， et al. OpenNN： Open neural networks library［EB/OL］. （2022-11-11）［2023-05-31］. .

参数	数值
推进剂密度/（kg·m^-3）	1 700
推进剂特征速度/（m·s^-1）	1 400
推进剂燃速系数/（m·（s·Pa^0.3）^-1）	0.000 1
推进剂压力指数	0.3
长径比	1.5

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3D grain reverse design and shape optimization for solid rocket motor

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