酚醛树脂气凝胶复合材料热物性参数预测方法

doi:10.7527/S1000-6893.2023.28848

Abstract

Abstract:

The thermo-physical properties of Inorganic-organic Hybrid Phenolic Aerogel Composites （IPC） are difficult to be accurately measured， due to the dynamic changes during carbonization. A new method to predict the thermo- physical properties of IPC during carbonization is proposed based on the measured information， by solving transient nonlinear inverse heat conduction problems. The modified gradient-based algorithm is applied to solving the transient nonlinear inverse heat conduction problem， to predict the temperature-dependent thermo-physical properties. To improve the accuracy， the complex variable-differentiation method is introduced to calculate the sensitivity coefficient matrix. The results show that the proposed algorithm has better stability， accuracy and efficiency than the conventional gradient algorithm in solving transient nonlinear inverse heat conduction problems， and the calculation time is reduced from 75 s to 35 s. The relative error between the calculated temperatures and measurements is 3.279%， and the present algorithm has high accuracy in predicting the effective thermal conductivity of IPC during carbonization. This work provides an effective method for the determination of the high temperature thermo-physical properties of thermal protection materials， and provides the key parameters for the engineering design of charring thermal protection materials.

Key words: thermal protection, inorganic-organic hybrid phenolic aerogel composites, effective thermal conductivity, parameter prediction, gradient-based algorithm

CLC Number:

V250.3

Chunyun ZHANG, Xiongbin CHEN, Jian LIU, Miao CUI. Prediction of thermo⁃physical properties of inorganic⁃organic hybrid phenolic aerogel composites[J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(6): 428848.

Figures/Tables 19

Fig.1

Fig.2

Table 1

Table 2

Fig.3

Fig.4

Fig.5

Table 3

Table 4

Table 5

Fig.6

Fig.7

Fig.8

Fig.9

Fig.10

Table 6

Fig.11

Fig.12

Fig.13

References 25

1	GHOSH P， NASKAR K， DAS N C. Influence of synthetic graphite powder on tribological and thermo-mechanical properties of organic-inorganic hybrid fiber reinforced elastomer-modified phenolic resin friction composites［J］. Composites Part C： Open Access， 2020， 2： 100018.
2	刘圆圆，郭慧，刘韬，等. 酚醛树脂基纳米多孔材料的制备及结构调控［J］. 航空学报， 2019， 40（5）： 422654.
	LIU Y Y， GUO H， LIU T， et al. Preparation and structure control of phenolic resin-based nanoporous materials［J］. Acta Aeronautica et Astronautica Sinica， 2019， 40（5）： 422654 （in Chinese）.
3	NIU Z Q， CHEN B X， SHEN S， et al. Zirconium chelated hybrid phenolic resin with enhanced thermal and ablation resistance properties for thermal insulation composites［J］. Composites Communications， 2022， 35： 101284.
4	董金鑫，朱召贤，姚鸿俊，等. 酚醛气凝胶/碳纤维复合材料的结构调控及性能研究［J］. 化工学报， 2018， 69（11）： 4896-4901.
	DONG J X， ZHU Z X， YAO H J， et al. Structural control and properties of phenolic aerogel/carbon fiber composites［J］. CIESC Journal， 2018， 69（11）： 4896-4901 （in Chinese）.
5	MERRITT B， SENECA M， LARSON S， et al. Measurements of the thermal conductivity of reference liquids using a modified transient hot-wire needle probe［J］. International Journal of Heat and Mass Transfer， 2022， 189： 122674.
6	KHALIFA D， JANNOT Y， DEGIOVANNI A， et al. Thermophysical characterization of mould materials using parallel hot wire and needle probe methods at high temperatures［J］. International Journal of Thermal Sciences， 2022， 179： 107630.
7	王泽林，籍日添，惠心雨，等. 基于深度学习驱动的L型定向热疏导机理［J］. 航空学报， 2021， 42（6）： 124242.
	WANG Z L， JI R T， HUI X Y， et al. L-shaped directional heat transfer based on deep learning［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（6）： 124242 （in Chinese）.
8	TOURN B A， ÁLVAREZ HOSTOS J C， FACHINOT TI V D. A modified sequential gradient-based method for the inverse estimation of transient heat transfer coefficients in non-linear one-dimensional heat conduction problems［J］. International Communications in Heat and Mass Transfer， 2021， 127： 105488.
9	SANCHEZ-CAMARGO C M， HOR A， MABRU C. A robust inverse analysis method for elastoplastic behavior identification using the true geometry modeling of Berkovich indenter［J］. International Journal of Mechanical Sciences， 2020， 171： 105370.
10	兑红娜，刘栋梁，张志贤，等. 基于应变测量的结构载荷分布反演方法［J］. 航空学报， 2021， 42（5）： 524337.
	DUI H N， LIU D L， ZHANG Z X， et al. Distributed load recovery approach based on strain measurements［J］. Acta Aeronautica et Astronautica Sinica， 2021， 42（5）： 524337 （in Chinese）.
11	周焕林，徐兴盛，李秀丽，等. 反演二维瞬态热传导问题随温度变化的导热系数［J］. 应用数学和力学， 2014， 35（12）： 1341-1351.
	ZHOU H L， XU X S， LI X L， et al. Identification of temperature-dependent thermal conductivity for 2-D transient heat conduction problems［J］. Applied Mathematics and Mechanics， 2014， 35（12）： 1341-1351 （in Chinese）.
12	TAHMASBI V， NOORI S. Inverse identification of temperature-dependent thermal conductivity coefficients in an orthotropic charring composite［J］. Applied Thermal Engineering， 2021， 183： 116219.
13	LIU H， XIA X L， AI Q， et al. Experimental investigations on temperature-dependent effective thermal conductivity of nanoporous silica aerogel composite［J］. Experimental Thermal and Fluid Science， 2017， 84： 67-77.
14	姜贵庆，马志强，俞继军，等. 新型防热涂层热导率的参数辩识［J］. 宇航材料工艺， 2008， 38（4）： 11-13.
	JIANG G Q， MA Z Q， YU J J， et al. Parameter identification of thermal conductivity coefficient for new type coating materials［J］. Aerospace Materials & Technology， 2008， 38（4）： 11-13 （in Chinese）.
15	XIE T， HE Y L， TONG Z X， et al. An inverse analysis to estimate the endothermic reaction parameters and physical properties of aerogel insulating material［J］. Applied Thermal Engineering， 2015， 87： 214-224.
16	张红军，李海群，康宏琳，等. 纳米酚醛气凝胶材料高温热物性参数辨识方法［J］. 北京航空航天大学学报， 2023， 49（1）： 92-99.
	ZHANG H J， LI H Q， KANG H L， et al. High temperature thermal conductivity estimation method of inorganic-organic hybrid phenolic composites［J］. Journal of Beijing University of Aeronautics and Astronautics， 2023， 49（1）： 92-99 （in Chinese）.
17	林旭文，高博，易法军，等. 烧蚀炭化热防护材料热导率的贝叶斯辨识方法［J］. 空天技术， 2022（3）： 18-30， 70.
	LIN X W， GAO B， YI F J， et al. Bayesian identification of thermal conductivity for charring ablative thermal protection materials［J］. Aerospace Technology， 2022（3）： 18-30， 70 （in Chinese）.
18	WANG X M， ZHANG L S， YANG C， et al. Estimation of temperature-dependent thermal conductivity and specific heat capacity for charring ablators［J］. International Journal of Heat and Mass Transfer， 2019， 129： 894-902.
19	POURGHOLI R， DANA H， TABASI S H. Solving an inverse heat conduction problem using genetic algorithm： Sequential and multi-core parallelization approach［J］. Applied Mathematical Modelling， 2014， 38（7-8）： 1948-1958.
20	SAJEDI R， FARAJI J， KOWSARY F. A new damping strategy of Levenberg-Marquardt algorithm with a fuzzy method for inverse heat transfer problem parameter estimation［J］. International Communications in Heat and Mass Transfer， 2021， 126： 105433.
21	HAN W W， CHEN H B， LU T. Estimation of the time-dependent convective boundary condition in a horizontal pipe with thermal stratification based on inverse heat conduction problem［J］. International Journal of Heat and Mass Transfer， 2019， 132： 723-730.
22	ZHANG C Y， MEI J， BAI Y S， et al. Simultaneous identification of multi-parameter for power hardening elastoplastic problems in three-dimensional geometries［J］. Engineering Computations， 2022， 39（8）： 2990-3011.
23	杨世铭，陶文铨. 传热学［M］. 4版. 北京：高等教育出版社， 2006.
	YANG S M， TAO W Q. Heat transfer［M］. 4th ed. Beijing： Higher Education Press， 2006 （in Chinese）.
24	CUI M， ZHAO Y， XU B B， et al. A new approach for determining damping factors in Levenberg-Marquardt algorithm for solving an inverse heat conduction problem［J］. International Journal of Heat and Mass Transfer， 2017， 107： 747-754.
25	ZHANG B W， MEI J， ZHANG C Y， et al. A general method for predicting the bank thickness of a smelting furnace with phase change［J］. Applied Thermal Engineering， 2019， 162： 114219.

T/℃	ρ/（kg·m^-3）	c/（J·kg^-1·℃^-1）	λ/（W·m^-1·℃^-1）
20	1 440	840	0.20
100	1 430	893	0.30
200	1 400	960	0.35
350	1 350	1 060	0.45
400	1 200	1 093	0.50
500	1 000	1 160	0.55
800	840	1 360	0.60

方法	步长h	是否收敛	迭代步数	目标函数	计算时间/s
本文算法	1×10^-5	是	5	2.12×10^-8	35
	1×10^-20	是	5	1.90×10^-8	36
	1×10^-30	是	5	3.65×10^-8	35

传统算法	1×10^-7	是	5	2.95×10^-9	45
	1×10^-14	是	9	5.52×10^-7	75
	1×10^-16	否

T/℃	ξ=1%		ξ=2%		ξ=3%
T/℃	Y_k	E_re/%	Y_k	E_re/%	Y_k	E_re/%
20	0.200	0.512	0.201	0.681	0.196	1.448
100	0.300		0.298		0.304
200	0.349		0.351		0.344
350	0.448		0.452		0.459
400	0.510		0.491		0.487
500	0.546		0.555		0.552
800	0.600		0.597		0.601

T/℃	λ/（W·m^-1·℃^-1）
100	0.045 5
400	0.054 0
800	0.087 0
1 000	0.214 8

[1]	Xiaofeng YANG, Xingkao CAI, Lei LIU, Dong WEI, Guangming XIAO, Yanxia DU, Yewei GUI. Coupling simulation of aircraft aerothermodynamics regulated by gradient characteristics of thermal protection structure and its experimental verification [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(9): 130888-130888.
[2]	Jihong ZHU, Jiacheng HAN, Xiaojun GU, Yahui ZHANG, Jun WANG, Jie HOU, Weihong ZHANG. Advances and challenges in cross-domain vehicle structures and morphing configuration design technologies [J]. Acta Aeronautica et Astronautica Sinica, 2025, 46(18): 431686-431686.
[3]	Fei QIN, Zheng ZHAO, Guoqiang HE, Tingting JING, Xing SUN, Xianggeng WEI. Thermal structure technology development of rocket based combined cycle engine [J]. Acta Aeronautica et Astronautica Sinica, 2024, 45(11): 529572-529572.
[4]	Zhifan YE, Jin ZHAO, Zhihui LI, Xiangchun SUN, Dongsheng WEN. Multiscale coupling simulation method for thermal protection material ablation based on thermochemical interfacial reactive model [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(S2): 729469-729469.
[5]	Shengbo SHI, Bao LEI, Yuntian ZHANG, Li HU, Maoyuan LI, Jun LIANG. Prediction method of ablation and thermal response for a thermal protection coating with silicone rubber [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(23): 428141-428141.
[6]	Weimin BAO. A review of reusable launch vehicle technology development [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(23): 629555-629555.
[7]	Xun YUAN, Xin YU, Jiangbo PENG, Hui ZENG, Dongbin OU. Research and experimental verification of NO-PLIF visualization method in arc-heated wind tunnel [J]. Acta Aeronautica et Astronautica Sinica, 2023, 44(19): 128391-128391.
[8]	LI Jun, WANG Junfeng, ZHAO Yatian, LUO Shibin. Research on combinational configuration of spike and multi-jets in off-design regimes [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(9): 125949-125949.
[9]	ZHENG Hui, QIU Lei, YUAN Shenfang, YANG Xiaofei, LU Xulong, XUE Zhaopeng. Experimental method of guided wave monitoring for high temperature airflow damage of C/C thermal protection structures [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(8): 225659-225659.
[10]	TIAN Jia, ZHANG Jingzhou, TAN Xiaoming, WANG Yuanshuai. Thermal analysis model and validation for graded-composite thermal protection structure of rotating detonation combustor [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 125271-125271.
[11]	LYU Junming, LI Fei, LI Qi, CHENG Xiaoli. Modeling of Martian atmospheric high temperature spectra and prediction of non-equilibrium radiative heating [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 626551-626551.
[12]	ZHENG Kai, RAO Wei, XIANG Yanchao, ZHANG Dong, ZHANG Bingqiang, XUE Shuyan, DAI Chenghao, YE Qing. Design of aerogel-based thermal protector for Mars landing engine [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(3): 626568-626568.
[13]	ZHAO Jin, SUN Xiangchun, ZHANG Jun, TANG Zhigong, WEN Dongsheng. Research advances on heat and mass transfer coupling effect at gas-solid interface for thermal protection materials [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2022, 43(10): 527577-527577.
[14]	WANG Zelin, JI Ritian, HUI Xinyu, DING Chen, WANG Hui, BAI Junqiang. L-shaped directional heat transfer based on deep learning [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(6): 124242-124242.
[15]	AI Bangcheng, CHEN Siyuan, HAN Haitao, HU Longfei, LU Qin, CHU Min, DENG Daiying, YU Jijun. Heat transfer limit characteristics of integrated dredging thermal protection structure [J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2021, 42(2): 623989-623989.

Prediction of thermo⁃physical properties of inorganic⁃organic hybrid phenolic aerogel composites

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 19

References 25

Related Articles 15

Recommended Articles

Metrics

Comments

t/s	T₁/℃	T₂/℃
0	20	20
2	50	21
20	200	30
40	600	40
80	1 000	60
100	1 200	80