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含铝固体推进剂以其可靠性、耐久性在战略战术导弹中得到广泛应用. 作为被动探测的主要手段, 准确识别排气羽流的红外辐射特征有助于快速预警和跟踪. 本文基于高温羽流环境下燃烧产物Al2O3晶体结构的变化, 提出了含多相态Al2O3的固体火箭羽流辐射计算模型. 采用球谐离散坐标法求解两相羽流的光谱辐射特性. 与忽略Al2O3颗粒相变的传统模型相比, 新模型与实验测量数据结果更加吻合, 进一步提高了计算精度. 利用该模型研究了不同含铝比例的羽流红外光谱辐射特性. 结果表明, 在1.7—2.0 μm范围内, 传统模型明显高估了低含铝情况的羽流辐射结果, 最大差异达67.2%. 在2.5—3.0 μm范围内, 随着含铝比例的增大, 两种模型之间的差异逐渐减小; 在4.0—4.5 μm范围内的颗粒相变对整体结果影响不明显, 平均相差7%左右. 所以有必要通过考虑羽流中颗粒的相态变化实现辐射特性的精确预测. 本研究结果可为固体火箭发动机的准确检测和识别提供理论依据和参考.Aluminum-doped propellants are widely used in strategic tactical missiles for their reliability, durability and adaptability. The accurate identification of infrared radiation characteristics of exhaust plumes, as a main means of passive detection, is helpful for rapid warning and tracking. In response to the shortcomings of traditional model that ignores the evolution of particle crystal phases, this paper proposes a radiation calculation model for multiphase Al2O3 containing the solid rocket plumes based on the changes of Al2O3 crystal structure in high temperature environments. The radiative transfer equation of the gas-solid two-phase plume is solved by using spherical harmonic discrete ordinate method (SHDOM). Compared with the classical method of simplifying the Al2O3 particles as single liquid phase particles, the model is more consistent with the results of experimental measurement data, which further improves the calculation accuracy. The infrared spectral radiation characteristics of plumes with different aluminum doping ratios are investigated using the model. The results show that under low aluminum doping ratios, the classical method significantly overestimates the plume radiation in the near-infrared band. At 1.7–2.0 μm, the maximum decrease is 67.2%; in the range of 2.5–3.0 μm, the difference in results between the two methods decreases from 21.6% to 3.6% with the increase of aluminum doping rate; and the particle phase transition in the range of 4.0–4.5 μm does not have much influence on the overall results, whose difference is about 7% on average. Therefore, it is necessary to accurately predict the radiation characteristics by considering the phase change of particles in the plume. These results contribute to the accurate detection and identification of solid rocket motors.
[1] Lucas M, Brotton S J, Min A, Pantoya M L, Kaiser R I 2019 J. Phys. Chem. Lett. 10 5756
Google Scholar
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Google Scholar
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Google Scholar
[5] Orlandi O, Plaud M, Godfroy F, Larrieu S, Cesco N 2019 Acta Astronaut. 158 470
Google Scholar
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Google Scholar
[10] Boischot A, Roblin A, Hespel L, Dubois I, Prevot P, Smithson T 2006 Targets and Backgrounds XII: Characterization and Representation Orlando, Florida, USA, May 4, 2006 p195
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Shen W T, Dong C, Zhu D Q, Cai G B 2012 J. Aerosp. Power 27 1874
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[16] Zhang D M, Bai L, Wang Y K, Lü Q, Zhang T J 2022 Infrared Phys. Technol. 122 104054
Google Scholar
[17] 张腾, 牛青林, 柳云峰, 高文强, 董士奎 2024 兵工学报 45 2228
Google Scholar
Zhang T, Niu Q L, Liu Y F, Gao W Q, Dong S K 2024 Acta Armamentarii 45 2228
Google Scholar
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Google Scholar
[19] Bityukov V K, Petrov V A 2013 Appl. Phys. Res. 5 51
Google Scholar
[20] Plastinin Y, Sipatchev H, Karabadzhak G, Khmelinin B, Khlebnikov A, Shishkin Y 2000 38th Aerospace Sciences Meeting and Exhibit Reno, USA, January 10–13, 2000 p735
[21] Anfimov N, Karabadyak G, Khmelinin B, Plastinin Y, Rodionov A 1993 28th Thermophysics Conference Orlando, Florida, USA, July 6–9, 1993 p2818
[22] Xu Y Y, Lu B, Li J Y, Li J L, Gao P H 2020 Opt. Express 28 17
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[23] Li J Y, Bai L, Wu Z S, Guo L X, Gong Y 2017 J. Quant. Spectrosc. Radiat. Transfer 202 233
Google Scholar
[24] Evans K F 1998 J. Atmos. Sci. 55 429
Google Scholar
[25] Malkmus W 1967 J. Opt. Soc. Am. 57 323
Google Scholar
[26] Young S J 1977 J. Quant. Spectrosc. Radiat. Transfer 18 1
Google Scholar
[27] Rothman L S, Gordon I, Barber R, Dothe H, Gamache R R, Goldman A, Perevalov V I, Tashkun S A, Tennyson J 2010 J. Quant. Spectrosc. Radiat. Transfer 111 2139
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[28] Hulst H C, van de Hulst H C 1981 Light Scattering by Small Particles (Courier Corporation) pp4–12
[29] Bohren CF, Huffman DR 2008 Absorption and Scattering of Light by Small Particles (John Wiley & Sons) pp83–129
[30] Gossé S, Sarou K V, Véron E, Millot F, Rifflet J C, Simon P 2003 36th AIAA Thermophysics Conference Orlando, Florida, USA, June 23–26, 2003 p3649
[31] Hespel L, Delfour A, Gosse S, Millot F 2003 36th AIAA Thermophysics Conference Orlando, Florida, USA, June 23–26, 2003 p3650
[32] Dombrovsky L A, Baillis D 2010 Thermal Radiation in Disperse Systems: An Engineering Approach (New York: Begell House) pp64–221
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[34] 包醒东, 余西龙, 王振华, 毛宏霞, 肖志河 2021 推进技术 42 3
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Google Scholar
[35] Avital G, Cohen Y, Gamss L, Kanelbaum, Y, Macales J, Trieman B, Yaniv S, Lev M, Stricker J, Sternlieb A 2001 J. Thermophys. Heat Transfer 15 377
Google Scholar
[36] Hermsen R 1981 J. Spacecr. Rockets 18 483
Google Scholar
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图 1 固体推进剂羽流多相态Al2O3模型示意图 (a)羽流的主要辐射产物; (b)气固两相流的辐射传输求解; (c) Al2O3颗粒的多种相态
Fig. 1. Schematic diagram of multiphase state Al2O3 model for solid propellent plume: (a) Main radiation product of the plume; (b) radiation transfer of gas-solid two-phase flow; (c) Al2O3 particles in multiple phases.
图 6 与实验结果比较 (a)波段辐射强度; (b)相对误差
Fig. 6. Comparison with experimental results: (a) Band radiation intensity; (b) relative error.
图 7 不同含铝情况的温度场及对应的粒子总质量密度 (a) Al-5%; (b) Al-10%; (c) Al-15%; (d) Al-20%
Fig. 7. Temperature field and corresponding particle density for different aluminum contents: (a) Al-5%; (b) Al-10%; (c) Al-15%; (d) Al-20%.
图 8 不同含铝情况下多相态模型与传统模型的羽流红外光谱辐射强度对比 (a) Al-5%; (b) Al-10%; (c) Al-15%; (d) Al-20%
Fig. 8. Comparison of plume infrared spectral radiation intensity between the multiphase model and the traditional model under different aluminum contents: (a) Al-5%; (b) Al-10%; (c) Al-15%; (d) Al-20%.
图 9 不同含铝情况下多相态模型与传统模型在1.7—2.0 μm波段排气羽流的辐射亮度对比 (a)传统模型; (b)多相态模型
Fig. 9. Radiance comparison of exhaust plumes at 1.7–2.0 μm band between multiphase model and traditional model under different aluminum contents: (a) Traditional model; (b) multiphase model.
图 11 不同含铝情况下多相态模型与传统模型在4.0—4.5 μm波段排气羽流的辐射亮度对比 (a)传统模型; (b)多相态模型
Fig. 11. Radiance comparison of exhaust plumes at 4.0–4.5 μm band between multiphase model and traditional model under different aluminum contents: (a) Traditional model; (b) multiphase model.
图 10 不同含铝情况下多相态模型与传统模型在2.5—3.0 μm波段排气羽流的辐射亮度对比 (a)传统模型; (b)多相态模型
Fig. 10. Radiance comparison of exhaust plumes at 2.5–3.0 μm band between multiphase model and traditional model under different aluminum contents: (a) Traditional model; (b) multiphase model.
参数 液相 γ相 α相 a/K–2 2.1 × 10–7 2.1 × 10–7 2.1 × 10–7 E0/μm–1 4.472 6.25 6.82 f/μm–1 1.784 × 10–4 1.3 × 10–3 8.8 × 10–4 Epol/μm–1 — 0.53 0.53 b/μm–1 2.5 × 10–2 2.5 × 10–2 2.5 × 10–2 c/(K–1·μm) 6800 6800 6800 d/μm–1 2.0 2.0 1.6 e/μm–1 0.95 0.95 0.95 h/μm–1 — 7.93 × 10–4 7.93 × 10–4 ω0/μm–1 — 1333 1333 
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表 2 双基推进剂燃烧室参数
Table 2. Parameter of combustion chamber for double-base propellant.
压强
/MPa温度
/K燃烧室组分的质量分数 H2O CO2 CO N2 H2 Al2O3 7.4 2884 0.1084 0.2462 0.3850 0.1630 0.0140 0.0835
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表 3 不同含铝比例的燃烧室中各组分参数
Table 3. Mass fraction of each component in the combustion chamber at different doping ratios.
工况 铝含量
/%燃烧室组分的质量分数 H2O CO2 CO HCl Al2O3 1 5 0.24 0.13 0.17 0.244 0.09 2 10 0.20 0.09 0.18 0.235 0.17 3 15 0.16 0.06 0.19 0.225 0.24 4 20 0.12 0.04 0.20 0.216 0.31
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表 4 不同含铝情况下多相态模型与传统模型的红外波段辐射强度差异
Table 4. Difference of infrared band radiation intensity between the multiphase model and the traditional model under different aluminum contents.
铝含量
/%红外波段辐射强度差异/% 1.7—2.0 μm 2.5—3.0 μm 4.0—4.5 μm 5 47.2 18.6 2.7 10 67.2 21.6 13.1 15 3.4 10.1 7.5 20 1.8 3.6 4.8
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[1] Lucas M, Brotton S J, Min A, Pantoya M L, Kaiser R I 2019 J. Phys. Chem. Lett. 10 5756
Google Scholar
[2] Zhang W C, Fan Z M, Shu Y, Ren P, Liu P J, Li L K, Ao W 2024 Aerosp. Sci. Technol. 149 109164
Google Scholar
[3] Lee Y R, Lee J W, Shin C M, Kim J W, Myong R 2022 J. Aircr. 59 1320
Google Scholar
[4] Shi L, Zhao G J, Yang Y Y, Gao D, Qin F, Wei X G, He G Q 2019 Prog. Aeronaut. Sci. 107 30
Google Scholar
[5] Orlandi O, Plaud M, Godfroy F, Larrieu S, Cesco N 2019 Acta Astronaut. 158 470
Google Scholar
[6] Liu M Y, Xiong L, Huang H X, Cai J, Zhao D, Li S P 2024 Therm. Sci. Eng. Prog. 49 102505
Google Scholar
[7] Nelson H F 1984 J. Spacecr. Rockets 21 425
Google Scholar
[8] Laredo D, Netzer D W 1993 J. Quant. Spectrosc. Radiat. Transfer 50 511
Google Scholar
[9] Alexeenko A, Gimelshein N, Levin D, Collins R J, Rao R, Candler G V, Gimelshein S F, Hong J S, Schilling T 2002 J. Thermophys. Heat Transfer 16 50
Google Scholar
[10] Boischot A, Roblin A, Hespel L, Dubois I, Prevot P, Smithson T 2006 Targets and Backgrounds XII: Characterization and Representation Orlando, Florida, USA, May 4, 2006 p195
[11] Cai G B, Zhu D Q, Zhang X Y 2007 Aerosp. Sci. Technol. 11 473
Google Scholar
[12] Feng S J, Nie W S, Xie Q F, Duan L W 2007 39th AIAA Thermophysics Conference Miami, Florida, USA, June 25–28, 2007 p4415
[13] 申文涛, 董超, 朱定强, 蔡国飙 2012 航空动力学报 27 1874
Google Scholar
Shen W T, Dong C, Zhu D Q, Cai G B 2012 J. Aerosp. Power 27 1874
Google Scholar
[14] Zhang X Y, Chen H 2016 Chin. J. Aeronaut. 29 924
Google Scholar
[15] Rialland V, Guy A, Gueyffier D, Perez P, Roblin A, Smithson T 2016 Journal of Physics: Conference Series Albi, France, April 1–3, 2015 p12
[16] Zhang D M, Bai L, Wang Y K, Lü Q, Zhang T J 2022 Infrared Phys. Technol. 122 104054
Google Scholar
[17] 张腾, 牛青林, 柳云峰, 高文强, 董士奎 2024 兵工学报 45 2228
Google Scholar
Zhang T, Niu Q L, Liu Y F, Gao W Q, Dong S K 2024 Acta Armamentarii 45 2228
Google Scholar
[18] Bao X D, Yu X L, Wang Z H, Mao H X, Liu D 2020 Proced. Comput. Sci. 174 645
Google Scholar
[19] Bityukov V K, Petrov V A 2013 Appl. Phys. Res. 5 51
Google Scholar
[20] Plastinin Y, Sipatchev H, Karabadzhak G, Khmelinin B, Khlebnikov A, Shishkin Y 2000 38th Aerospace Sciences Meeting and Exhibit Reno, USA, January 10–13, 2000 p735
[21] Anfimov N, Karabadyak G, Khmelinin B, Plastinin Y, Rodionov A 1993 28th Thermophysics Conference Orlando, Florida, USA, July 6–9, 1993 p2818
[22] Xu Y Y, Lu B, Li J Y, Li J L, Gao P H 2020 Opt. Express 28 17
Google Scholar
[23] Li J Y, Bai L, Wu Z S, Guo L X, Gong Y 2017 J. Quant. Spectrosc. Radiat. Transfer 202 233
Google Scholar
[24] Evans K F 1998 J. Atmos. Sci. 55 429
Google Scholar
[25] Malkmus W 1967 J. Opt. Soc. Am. 57 323
Google Scholar
[26] Young S J 1977 J. Quant. Spectrosc. Radiat. Transfer 18 1
Google Scholar
[27] Rothman L S, Gordon I, Barber R, Dothe H, Gamache R R, Goldman A, Perevalov V I, Tashkun S A, Tennyson J 2010 J. Quant. Spectrosc. Radiat. Transfer 111 2139
Google Scholar
[28] Hulst H C, van de Hulst H C 1981 Light Scattering by Small Particles (Courier Corporation) pp4–12
[29] Bohren CF, Huffman DR 2008 Absorption and Scattering of Light by Small Particles (John Wiley & Sons) pp83–129
[30] Gossé S, Sarou K V, Véron E, Millot F, Rifflet J C, Simon P 2003 36th AIAA Thermophysics Conference Orlando, Florida, USA, June 23–26, 2003 p3649
[31] Hespel L, Delfour A, Gosse S, Millot F 2003 36th AIAA Thermophysics Conference Orlando, Florida, USA, June 23–26, 2003 p3650
[32] Dombrovsky L A, Baillis D 2010 Thermal Radiation in Disperse Systems: An Engineering Approach (New York: Begell House) pp64–221
[33] Mishchenko M I 2018 OSA Continuum 1 243
Google Scholar
[34] 包醒东, 余西龙, 王振华, 毛宏霞, 肖志河 2021 推进技术 42 3
Google Scholar
Bao X D, Yu X L, Wang Z H, Mao H X, Liu D, Xiao Z H 2021 J. Propul. Technol. 42 3
Google Scholar
[35] Avital G, Cohen Y, Gamss L, Kanelbaum, Y, Macales J, Trieman B, Yaniv S, Lev M, Stricker J, Sternlieb A 2001 J. Thermophys. Heat Transfer 15 377
Google Scholar
[36] Hermsen R 1981 J. Spacecr. Rockets 18 483
Google Scholar
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