A unified lattice Boltzmann model for heat transfer in opacifiers-doped silica aerogel

doi:10.11949/0438-1157.20221612

Abstract

Abstract:

Aerogel is a nanoporous super-insulation material, and its internal heat transfer process involves gas-phase heat conduction, solid-phase heat conduction, gas-solid coupling heat transfer and radiation heat transfer. In the present study, the energy equation containing the radiation source and the radiation transfer equation are derived based on the lattice Boltzmann method (LBM), and a unified lattice Boltzmann model to describe multi-mode and multi-scale coupled heat transfer in SiO₂ aerogel composites is established. The effects of diameter and doping volume fraction of SiC opacifiers on the thermal insulation performance of SiO₂ aerogel composites are investigated. The temperature-dependent optimal diameter and doping volume fraction of SiC opacifiers are obtained to minimize the effective thermal conductivity of SiC-doped silica aerogel composites.

Key words: SiO₂ aerogel, coupled heat transfer, unified lattice Boltzmann model, opacifiers, equivalent thermal conductivity

摘要：

气凝胶是一种纳米多孔超级隔热材料，其内部的传热过程涉及气相导热、固相导热、气固耦合传热及辐射传热。基于格子Boltzmann方法，演化了含有辐射源项的能量方程和辐射传输方程，建立了描述SiO₂气凝胶复合材料内多模式多尺度耦合传热的统一格子Boltzmann模型，探究了SiC遮光剂粒径和掺杂量对气凝胶复合材料隔热性能的影响，获得了使得材料等效热导率最小的SiC遮光剂最优粒径和最佳掺杂量随温度的变化规律。

关键词: SiO₂气凝胶, 耦合传热, 统一格子Boltzmann模型, 遮光剂, 等效热导率

CLC Number:

TK 124

Kunyang FAN, Jingxing YANG, Haibo XU, Xingrong LIAN, Fengmei HE, Conghui CHEN, Zengyao LI. A unified lattice Boltzmann model for heat transfer in opacifiers-doped silica aerogel[J]. CIESC Journal, 2023, 74(5): 1974-1981.

范坤阳, 杨景兴, 许海波, 连兴容, 何凤梅, 陈聪慧, 李增耀. 遮光剂掺杂SiO₂气凝胶传热的统一格子Boltzmann模型研究[J]. 化工学报, 2023, 74(5): 1974-1981.

Figures/Tables 11

Fig.1 Multi-component and multi-mode coupled heat transfer inside aerogel material

Fig.2 The schematic of the opacifiers-doped silica aerogel[14]

Fig.3 Temperature dependent thermal conductivity (λa) of SiO2 aerogel matrix

Fig.4 Physical model of heat transfer in aerogel composites

Fig.5 D2Q8 lattice model for radiation heat transfer

Fig.6 Validation of the unified lattice Boltzmann model

Fig.7 Temperature dependent equivalent thermal conductivity of SiO2 aerogel

Fig.8 The effect of diameter of SiC opacifiers on the radiative thermal conductivities of SiO2 aerogel

Fig.9 The optimal diameter of SiC opacifiers vs temperature

Fig.10 The equivalent thermal conductivity of silica aerogel composites vs the volume fraction of SiC opacifiers

Fig.11 The optimal volume fraction of SiC opacifiers vs temperature

References 30

1	Aegerter M A, Leventis N, Koebel M M. Aerogels Handbook[M]. New York: Springer Science+Business Media, LLC, 2011.
2	胡子君, 李俊宁, 孙陈诚, 等. 纳米超级隔热材料及其最新研究进展[J]. 中国材料进展, 2012, 31(8): 25-32.
	Hu Z J, Li J N, Sun C C, et al. Recent developments of nano-superinsulating materials[J]. Rare Metals Letters, 2012, 31(8): 25-32.
3	段远源, 林杰, 王晓东, 等. 二氧化硅气凝胶的气相热导率模型分析[J]. 化工学报, 2012, 63(S1): 54-58.
	Duan Y Y, Lin J, Wang X D, et al. Analysis of gaseous thermal conductivity models for silica aerogels[J]. CIESC Journal, 2012, 63(S1): 54-58.
4	Dai Y J, Tang Y Q, Fang W Z, et al. A theoretical model for the effective thermal conductivity of silica aerogel composites[J]. Applied Thermal Engineering, 2018, 128: 1634-1645.
5	Wang X D, Sun D, Duan Y Y, et al. Radiative characteristics of opacifier-loaded silica aerogel composites[J]. Journal of Non-Crystalline Solids, 2013, 375: 31-39.
6	Xie T, He Y L, Hu Z J. Theoretical study on thermal conductivities of silica aerogel composite insulating material[J]. International Journal of Heat and Mass Transfer, 2013, 58(1/2): 540-552.
7	Zhao J J, Duan Y Y, Wang X D, et al. Experimental and analytical analyses of the thermal conductivities and high-temperature characteristics of silica aerogels based on microstructures[J]. Journal of Physics D: Applied Physics, 2013, 46(1): 015304.
8	方文振, 粘权鑫, 张虎, 等. 气凝胶及其纤维复合材料等效导热系数预测[J]. 西安交通大学学报, 2015, 49(7): 25-29.
	Fang W Z, Zhan Q X, Zhang H, et al. Prediction of the effective thermal conductivity of aerogel and its fiber-loaded composites[J]. Journal of Xi'an Jiaotong University, 2015, 49(7): 25-29.
9	任登凤, 宣益民, 韩玉阁. 多尺度特征对纳米多孔材料辐射特性的影响[J]. 化工学报, 2012, 63(S1): 219-224.
	Ren D F, Xuan Y M, Han Y G. Effect of multi-scale features on radiation property of nanoporous materials[J]. CIESC Journal, 2012, 63(S1): 219-224.
10	Fang W Z, Zhang H, Chen L, et al. Numerical predictions of thermal conductivities for the silica aerogel and its composites[J]. Applied Thermal Engineering, 2017, 115: 1277-1286.
11	Xie T, He Y L. Heat transfer characteristics of silica aerogel composite materials: structure reconstruction and numerical modeling[J]. International Journal of Heat and Mass Transfer, 2016, 95: 621-635.
12	Asinari P, Mishra S C, Borchiellini R. A lattice Boltzmann formulation for the analysis of radiative heat transfer problems in a participating medium[J]. Numerical Heat Transfer, Part B: Fundamentals, 2010, 57(2): 126-146.
13	Tong Z X, Li M J, Xie T, et al. Lattice Boltzmann method for conduction and radiation heat transfer in composite materials[J]. Journal of Thermal Science, 2022, 31(3): 777-789.
14	Zhu C Y, Li Z Y, Pan N. Design and thermal insulation performance analysis of endothermic opacifiers doped silica aerogels[J]. International Journal of Thermal Sciences, 2019, 145: 105995.
15	Zhu C Y, Li Z Y. Modeling of the apparent solid thermal conductivity of aerogel[J]. International Journal of Heat and Mass Transfer, 2018, 120: 724-730.
16	Bi C, Tang G H, Hu Z J, et al. Coupling model for heat transfer between solid and gas phases in aerogel and experimental investigation[J]. International Journal of Heat and Mass Transfer, 2014, 79: 126-136.
17	艾青, 刘华, 夏新林, 等. 高温复合隔热结构组成对其瞬态热特性的影响[J]. 化工学报, 2014, 65(S1): 371-376.
	Ai Q, Liu H, Xia X L, et al. Influence of high temperature composite insulation structure on its transient thermal characteristics[J]. CIESC Journal, 2014, 65(S1): 371-376.
18	Zhao J J, Duan Y Y, Wang X D, et al. Optical and radiative properties of infrared opacifier particles loaded in silica aerogels for high temperature thermal insulation[J]. International Journal of Thermal Sciences, 2013, 70: 54-64.
19	阚安康, 张婷婷, 曹丹. 基于分形理论的纳米颗粒多孔介质真空导热特性[J]. 化工学报, 2013, 64(11): 4008-4014.
	Kan A K, Zhang T T, Cao D. Vacuum thermal conduction characteristic of nano-granule porous medium using fractal theory[J]. CIESC Journal, 2013, 64(11): 4008-4014.
20	Zhao J J, Duan Y Y, Wang X D, et al. A 3-D numerical heat transfer model for silica aerogels based on the porous secondary nanoparticle aggregate structure[J]. Journal of Non-Crystalline Solids, 2012, 358(10): 1287-1297.
21	Howell J R, Siegel R, Menguc M P. Thermal Radiation Heat Transfer[M]. 5th ed. Boca Raton: CRC Press, 2010.
22	安巍. 介质辐射换热有限元法的扩散综合加速算法[J]. 化工学报, 2009, 60(5): 1087-1091.
	An W. Finite element diffusion-synthetic acceleration for radiative heat transfer in participating medium[J]. CIESC Journal, 2009, 60(5): 1087-1091.
23	Zhu C Y, Li Z Y, Pang H Q, et al. Design and optimization of core/shell structures as highly efficient opacifiers for silica aerogels as high-temperature thermal insulation[J]. International Journal of Thermal Sciences, 2018, 133: 206-215.
24	Wei G S, Liu Y S, Zhang X X, et al. Thermal conductivities study on silica aerogel and its composite insulation materials[J]. International Journal of Heat and Mass Transfer, 2011, 54(11/12): 2355-2366.
25	阚安康, 康利云, 曹丹, 等. 基于lattice-Boltzmann方法的纳米颗粒多孔介质导热特性[J]. 化工学报, 2015, 66(11): 4412-4417.
	Kan A K, Kang L Y, Cao D, et al. Thermal conduction characteristic of nano-granule porous material using lattice-Boltzmann method[J]. CIESC Journal, 2015, 66(11): 4412-4417.
26	Zhang H, Fang W Z, Wang X, et al. Thermal conductivity of fiber and opacifier loaded silica aerogel composite[J]. International Journal of Heat and Mass Transfer, 2017, 115: 21-31.
27	孙夺, 王晓东, 段远源, 等. 气凝胶-遮光剂复合材料中遮光剂的辐射特性[J]. 应用基础与工程科学学报, 2012, 20(S1): 181-189.
	Sun D, Wang X D, Duan Y Y, et al. Radiant performance of opacifiers in opcifier-loaded silica aerogel-based composites[J]. Journal of Basic Science and Engineering, 2012, 20(S1): 181-189.
28	方文振, 张虎, 屈肖迪, 等. 遮光剂对气凝胶复合材料隔热性能的影响[J]. 化工学报, 2014, 65(S1): 168-174.
	Fang W Z, Zhang H, Qu X D, et al. Influence of opacifiers on thermal insulation properties of composite aerogels[J]. CIESC Journal, 2014, 65(S1): 168-174.
29	刘鹤, 焦俊华, 田友, 等. 遮光剂复合氧化硅气凝胶材料的隔热性能优化[J]. 工程热物理学报, 2021, 42(11): 2991-3000.
	Liu H, Jiao J H, Tian Y, et al. Thermal insulation performance optimization of opacifier doped silica aerogel composites[J]. Journal of Engineering Thermophysics, 2021, 42(11): 2991-3000.
30	Jo H Y, Oh S J, Kim M N, et al. Effects of SiC particle size and inorganic binder on heat insulation of fumed silica-based heat insulation plates[J]. Journal of the Korean Ceramic Society, 2016, 53(4): 386-392.

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