Multi-phase state Al<sub>2</sub>O<sub>3</sub> model for predicting solid-roket plume infrared radiation characteristics

ZHANG Ligong; BAI Lu; LI Jinlu; GUO Lixin

doi:10.7498/aps.74.20250493

Abstract

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.

Keywords:

Authors and contacts

1.
School of Physics, Xidian University, Xi’an 710071, China
2.
Collaborative Innovation Center of Information Sensing and Understanding, Xidian University, Xi’an 710071, China

Corresponding author: BAI Lu, blu@xidian.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. U20B2059, 61875156, 62405230) and the Fundamental Research Funds for the Central Universities (Grant No. ZYTS25132).

FullText HTML

References

[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

Cited By

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

图 2 改进模型与传统模型的比较

Figure 2. Comparison of improved and classical models.

DownLoad: Full-Size Img PowerPoint

图 3 可见光实验图像^[34]

Figure 3. Images of experiments visible^[34].

DownLoad: Full-Size Img PowerPoint

图 4 羽流结果与文献[34]比较　(a)文献结果; (b)计算结果

Figure 4. Comparison of plume results with Ref. [34]: (a) Reference result; (b) calculate result.

DownLoad: Full-Size Img PowerPoint

图 5 与文献[34]中的计算结果和测量值比较

Figure 5. Comparison with measurement and calculated in the Ref. [34].

DownLoad: Full-Size Img PowerPoint

图 6 与实验结果比较　(a)波段辐射强度; (b)相对误差

Figure 6. Comparison with experimental results: (a) Band radiation intensity; (b) relative error.

DownLoad: Full-Size Img PowerPoint

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%

Figure 7. Temperature field and corresponding particle density for different aluminum contents: (a) Al-5%; (b) Al-10%; (c) Al-15%; (d) Al-20%.

DownLoad: Full-Size Img PowerPoint

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%

Figure 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%.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

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

Figure 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.

DownLoad: Full-Size Img PowerPoint

表 1 Al₂O₃相变参数^[20]

Table 1. Al₂O₃ phase transition parameter^[20].

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
E_pol/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

DownLoad: CSV

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
压强 /MPa	温度 /K	H₂O	CO₂	CO	N₂	H₂	Al₂O₃
7.4	2884	0.1084	0.2462	0.3850	0.1630	0.0140	0.0835

DownLoad: CSV

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
工况	铝含量 /%	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

DownLoad: CSV

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/%
铝含量 /%	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

DownLoad: CSV

[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

[1]	WANG Mingjun, YU Jihua, BAI Liangliang, ZHOU Yiming. Optical properties of ensemble of complex externally mixed aerosol particles under different relative humidity conditions. Acta Physica Sinica, 2025, 74(6): 064203. doi: 10.7498/aps.74.20241140
[2]	Guo Wei-Chen, Ai Bao-Quan, He Liang. Reveal flocking phase transition of self-propelled active particles by machine learning regression uncertainty. Acta Physica Sinica, 2023, 72(20): 200701. doi: 10.7498/aps.72.20230896
[3]	Qiu Zi-Yang, Chen Yan, Qiu Xiang-Gang. Infrared spectroscopic study of topological material BaMnSb₂. Acta Physica Sinica, 2022, 71(10): 107201. doi: 10.7498/aps.71.20220011
[4]	Qiu Zi-Heng, Ahmed Yousif Ghazal, Long Jin-You, Zhang Song. Theoretical studies on molecular conformers and infrared spectra of triethylamine. Acta Physica Sinica, 2022, 71(10): 103601. doi: 10.7498/aps.71.20220123
[5]	Tian Chun-Ling, Liu Hai-Yan, Wang Biao, Liu Fu-Sheng, Gan Yun-Dan. Phase transition and equation of state of dense liquid nitrogen at high temperature and high pressure. Acta Physica Sinica, 2022, 71(15): 158701. doi: 10.7498/aps.71.20220124
[6]	Wu Chen-Chen, Guo Xiang-Dong, Hu Hai, Yang Xiao-Xia, Dai Qing. Graphene plasmon enhanced infrared spectroscopy. Acta Physica Sinica, 2019, 68(14): 148103. doi: 10.7498/aps.68.20190903
[7]	Xu Bing, Qiu Zi-Yang, Yang Run, Dai Yao-Min, Qiu Xiang-Gang. Optical properties of topological semimetals. Acta Physica Sinica, 2019, 68(22): 227804. doi: 10.7498/aps.68.20191510
[8]	Lin Tong, Hu Die, Shi Li-Yu, Zhang Si-Jie, Liu Yan-Qi, Lv Jia-Lin, Dong Tao, Zhao Jun, Wang Nan-Lin. Infrared spectroscopy study of ironbased superconductor Li0.8Fe0.2 ODFeSe. Acta Physica Sinica, 2018, 67(20): 207102. doi: 10.7498/aps.67.20181401
[9]	Wang An-Jing, Fang Yong-Hua, Li Da-Cheng, Cui Fang-Xiao, Wu Jun, Liu Jia-Xiang, Li Yang-Yu, Zhao Yan-Dong. Simulation of pollutant-gas-cloud infrared spectra under plane-array detecting. Acta Physica Sinica, 2017, 66(11): 114203. doi: 10.7498/aps.66.114203
[10]	Xu Ting-Ting, Li Yi, Chen Pei-Zu, Jiang Wei, Wu Zheng-Yi, Liu Zhi-Min, Zhang Jiao, Fang Bao-Ying, Wang Xiao-Hua, Xiao Han. Infrared modulator based on AZO/VO2/AZO sandwiched structure due to electric field induced phase transition. Acta Physica Sinica, 2016, 65(24): 248102. doi: 10.7498/aps.65.248102
[11]	Wang Xiao-Wu, Xu Hai-Hong. Study of the solid-solid phase change in polyalcohol binary systems. Acta Physica Sinica, 2014, 63(13): 136501. doi: 10.7498/aps.63.136501
[12]	Li Xin, Yang Meng-Shi, Ye Zhi-Peng, Chen Liang, Xu Can, Chu Xiu-Xiang. DFT research on the IR spectrum of glycine tryptophan oligopeptides chain. Acta Physica Sinica, 2013, 62(15): 156103. doi: 10.7498/aps.62.156103
[13]	Liu Xiao-Dong, Tao Wan-Jun, Hagihala Masato, Guo Qi-Xin, Meng Dong-Dong, Zhang Sen-Lin, Zheng Xu-Guang. Mid-infrared spectroscopic properties of geometrically frustrated basic cobalt chlorides. Acta Physica Sinica, 2011, 60(3): 037803. doi: 10.7498/aps.60.037803
[14]	Wang Xiao-Wu, Xu Hai-Hong. Mechanism of polyalcohol solid—solid phase change. Acta Physica Sinica, 2011, 60(3): 030507. doi: 10.7498/aps.60.030507
[15]	Wang Zhi-Gang, Wu Liang, Zhang Yang, Wen Yu-Hua. Phase transition and coalescence behavior of fcc Fe nanoparticles: a molecular dynamics study. Acta Physica Sinica, 2011, 60(9): 096105. doi: 10.7498/aps.60.096105
[16]	Chen Bin, Peng Xiang-He, Fan Jing-Hong, Sun Shi-Tao, Luo Ji. A thermo-elastoplastic constitutive equation including phase transformation and its applications. Acta Physica Sinica, 2009, 58(13): 29-S34. doi: 10.7498/aps.58.29
[17]	Wang Hui, Liu Jin-Fang, He Yan, Chen Wei, Wang Ying, Gerward L., Jiang Jian-Zhong. Size-induced enhancement of bulk modulus and transition pressure of nanocrystalline Ge. Acta Physica Sinica, 2007, 56(11): 6521-6525. doi: 10.7498/aps.56.6521
[18]	Shi Zhu-Yi, Ji Shi-Yin. Specific heat capacity and phase transition on 148—158Sm nucleiin microscopic core plus two-quasiparticle model. Acta Physica Sinica, 2003, 52(1): 42-47. doi: 10.7498/aps.52.42
[19]	Liang Zi-Zhang, Jin Ya-Qiu. . Acta Physica Sinica, 2002, 51(10): 2239-2244. doi: 10.7498/aps.51.2239
[20]	LING ZHI-HUA. STUDY OF POLARIZED FT-IR FOR ANTIFERROELECTRIC LIQUID CRYSTAL TFMHxPOCBC-D2 IN A HOMEOTROPICALLY ALIGNED CELL. Acta Physica Sinica, 2001, 50(2): 227-232. doi: 10.7498/aps.50.227

Catalog

Vol. 74, Issue 16 - 2025-08-20

Metrics

Abstract views: 2521
PDF Downloads: 28
Cited By: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

Search

Article

留言板

Multi-phase state Al₂O₃ model for predicting solid-roket plume infrared radiation characteristics

Abstract

Authors and contacts

Corresponding author: BAI Lu, blu@xidian.edu.cn

FullText HTML

References

Cited By

Catalog

Metrics

Authors

Referees

About Journal

About

Search

Article

留言板

Multi-phase state Al2O3 model for predicting solid-roket plume infrared radiation characteristics

Abstract

Authors and contacts

Corresponding author: BAI Lu, blu@xidian.edu.cn

FullText HTML

References

Cited By

Catalog

Metrics

Publishing process

Authors

Referees

About Journal

About

Multi-phase state Al₂O₃ model for predicting solid-roket plume infrared radiation characteristics