Skip to main content
SpringerLink
Log in

An analytical model for maximum temperature and temperature distribution of plate structure with active cooling

主动冷却平板型结构件的最高温度及温度分布解析模型

  • Research Paper
  • Published:
Acta Mechanica Sinica Aims and scope Submit manuscript

Abstract

Plate structures with active cooling are widely used, and rapid evaluation of the temperature performance is of interest. In this paper, an analytical model is proposed for the prediction of maximum temperature and temperature distribution of plate structures with active cooling channel. The analytical model has three types of input parameters including thermal boundary conditions, material properties, and geometry parameters. Solution procedures under different thermal boundary conditions, including heat flux and convective heat transfer, are discussed respectively. The model with heat flux boundary (MHF) is established based on the principle of energy conservation. The model with convective heat transfer boundary (MCHT) is established based on the method of second-order function fitting the real heat flux distribution. The materials of the plate structures are aluminum alloy and titanium alloy. The results show that the analytical model is able to predict the maximum temperature with an error of less than 4% compared to the numerical method. The analytical model is able to quickly and accurately evaluate the thermal protection performance of the active cooling structure.

摘要

主动冷却平板型结构件应用广泛, 快速评估其温度性能具有重要意义. 本文提出了一种用于预测主动冷却平板型结构件的最高 温度和温度分布的解析模型. 解析模型有三种输入参数, 包括热边界条件、材料特性和几何参数. 分别讨论了两种热边界条件下的求 解过程, 包括热流密度边界和对流传热边界. 根据能量守恒原理, 建立了热流密度边界模型(MHF). 采用二次函数拟合真实热流密度分 布的方法, 建立了对流传热边界模型(MCHT). 结构件的材料有铝合金和钛合金. 结果表明, 与数值模型结果相比, 该解析模型能够预测 最高温度, 误差小于4%. 该模型能够快速、准确地评估主动冷却平板型结构件的热防护性能.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Abbreviations

T :

Temperature, K

q :

Heat flux, W/m2

δ :

Thickness, m

d :

Diameter, m

W :

Width of plate/channel spacing, m

k :

Thermal conductivity of coolant, W/(m K)

λ :

Thermal conductivity of solid, W/(m K)

h :

Convective heat transfer coefficient of hot gas, W/(m2 K)

MHF:

Model with heat flux boundary

MCHT:

Model with convective heat transfer boundary

RMSE:

Root mean squared error

channel:

Channel wall

f:

Fluid

max:

Maximum

hot:

Hot gas

wall:

Surface

A, B, C :

Position

References

  1. S. Zhang, X. Li, J. Zuo, J. Qin, K. Cheng, Y. Feng, and W. Bao, Research progress on active thermal protection for hypersonic vehicles, Prog. Aerosp. Sci. 119, 100646 (2020).

    Article  Google Scholar 

  2. J. J. Gou, Z. W. Yan, J. X. Hu, G. Gao, and C. L. Gong, The heat dissipation, transport and reuse management for hypersonic vehicles based on regenerative cooling and thermoelectric conversion, Aerosp. Sci. Tech. 108, 106373 (2021).

    Article  Google Scholar 

  3. Y. Zhu, W. Peng, R. Xu, and P. Jiang, Review on active thermal protection and its heat transfer for airbreathing hypersonic vehicles, Chin. J. Aeronaut. 31, 1929 (2018).

    Article  Google Scholar 

  4. S. Luo, D. Xu, J. Song, and J. Liu, A review of regenerative cooling technologies for scramjets, Appl. Thermal Eng. 190, 116754 (2021).

    Article  Google Scholar 

  5. X. Li, M. Du, and F. Zhong, Effect of dimple depth on turbulent flow and heat transfer of kerosene in rectangular duct, Acta Mech. Sin. 38, 321271 (2022).

    Article  Google Scholar 

  6. J. Dong, X. Zhuang, X. Xu, Z. Miao, and B. Xu, Numerical analysis of a multi-channel active cooling system for densely packed concentrating photovoltaic cells, Energy Convers. Manage. 161, 172 (2018).

    Article  Google Scholar 

  7. W. He, Y. Zhang, and J. Ji, Comparative experiment study on photovoltaic and thermal solar system under natural circulation of water, Appl. Thermal Eng. 31, 3369 (2011).

    Article  Google Scholar 

  8. H. A. Nasef, S. A. Nada, and H. Hassan, Integrative passive and active cooling system using PCM and nanofluid for thermal regulation of concentrated photovoltaic solar cells, Energy Convers. Manage. 199, 112065 (2019).

    Article  Google Scholar 

  9. S. Nižetić, E. Giama, and A. M. Papadopoulos, Comprehensive analysis and general economic-environmental evaluation of cooling techniques for photovoltaic panels, Part II: Active cooling techniques, Energy Convers. Manage. 155, 301 (2018).

    Article  Google Scholar 

  10. G. Zhao, X. Wang, M. Negnevitsky, and H. Zhang, A review of air-cooling battery thermal management systems for electric and hybrid electric vehicles, J. Power Sources 501, 230001 (2021).

    Article  Google Scholar 

  11. V. G. Choudhari, D. A. S. Dhoble, and T. M. Sathe, A review on effect of heat generation and various thermal management systems for lithium ion battery used for electric vehicle, J. Energy Storage 32, 101729 (2020).

    Article  Google Scholar 

  12. X. Zhang, Z. Li, L. Luo, Y. Fan, and Z. Du, A review on thermal management of lithium-ion batteries for electric vehicles, Energy 238, 121652 (2022).

    Article  Google Scholar 

  13. Q. L. Yue, C. X. He, M. C. Wu, and T. S. Zhao, Advances in thermal management systems for next-generation power batteries, Int. J. Heat Mass Transf. 181, 121853 (2021).

    Article  Google Scholar 

  14. L. Taddeo, N. Gascoin, K. Chetehouna, A. Ingenito, F. Stella, M. Bouchez, and B. Le Naour, Experimental study of pyrolysis-combustion coupling in a regeneratively cooled combustor: System dynamics analysis, Aerosp. Sci. Tech. 67, 473 (2017).

    Article  Google Scholar 

  15. L. Taddeo, N. Gascoin, K. Chetehouna, A. Ingenito, F. Stella, M. Bouchez, and B. Le Naour, Experimental study of pyrolysis-combustion coupling in a regeneratively cooled combustor: Heat transfer and coke formation, Fuel 239, 1091 (2019).

    Article  Google Scholar 

  16. M. S. Y. Ebaid, A. M. Ghrair, and M. Al-Busoul, Experimental investigation of cooling photovoltaic (PV) panels using (TiO2) nanofluid in water-polyethylene glycol mixture and (Al2O3) nanofluid in water-cetyltrimethylammonium bromide mixture, Energy Convers. Manage. 155, 324 (2018).

    Article  Google Scholar 

  17. M. Akbarzadeh, J. Jaguemont, T. Kalogiannis, D. Karimi, J. He, L. Jin, P. Xie, J. Van Mierlo, and M. Berecibar, A novel liquid cooling plate concept for thermal management of lithium-ion batteries in electric vehicles, Energy Convers. Manage. 231, 113862 (2021).

    Article  Google Scholar 

  18. Z. Huang, Y. B. Xiong, Y. Q. Liu, P. X. Jiang, and Y. H. Zhu, Experimental investigation of full-coverage effusion cooling through perforated flat plates, Appl. Thermal Eng. 76, 76 (2015).

    Article  Google Scholar 

  19. G. Cai, C. Li, and H. Tian, Numerical and experimental analysis of heat transfer in injector plate of hydrogen peroxide hybrid rocket motor, Acta Astronaut. 128, 286 (2016).

    Article  Google Scholar 

  20. P. Pu, and Y. Jiang, Analyzing the impact of nitrogen ejection on suppression of rocket base heating, Aerosp. Sci. Tech. 107, 106275 (2020).

    Article  Google Scholar 

  21. J. Wang, Y. Li, X. Liu, C. Shen, H. Zhang, and K. Xiong, Recent active thermal management technologies for the development of energy-optimized aerospace vehicles in China, Chin. J. Aeronaut. 34, 1 (2021).

    Article  Google Scholar 

  22. W. H. Fan, F. Q. Zhong, S. G. Ma, and X. Y. Zhang, Numerical study of convective heat transfer of a supersonic combustor with varied inlet flow conditions, Acta Mech. Sin. 35, 943 (2019).

    Article  Google Scholar 

  23. Y. Wan, N. Wang, L. Zhang, and Y. Gui, Applications of multidimensional schemes on unstructured grids for high-accuracy heat flux prediction, Acta Mech. Sin. 36, 57 (2020).

    Article  MathSciNet  Google Scholar 

  24. C. K. Yuan, K. Zhou, Y. F. Liu, Z. M. Hu, and Z. L. Jiang, Spectral measurements of hypervelocity flow in an expansion tunnel, Acta Mech. Sin. 35, 24 (2019).

    Article  Google Scholar 

  25. G. Tu, J. Chen, X. Yuan, Q. Yang, M. Duan, Q. Yang, Y. Duan, X. Chen, B. Wan, and X. Xiang, Progress in flight tests of hypersonic boundary layer transition, Acta Mech. Sin. 37, 1589 (2021).

    Article  Google Scholar 

  26. B. Youn, and A. F. Mills, Cooling panel optimization for the active cooling system of a hypersonic aircraft, J. Thermophys. Heat Transf. 9, 136 (1995).

    Article  Google Scholar 

  27. W. R. Wagner, and J. M. Shoji, Advanced regenerative cooling techniques for future space transportation systems, Astronaut. Aeronaut. 14, B18 (1976).

    Google Scholar 

  28. Y. Z. Li, and K. M. Lee, Thermohydraulic dynamics and fuzzy coordination control of a microchannel cooling network for space electronics, IEEE Trans. Ind. Electron. 58, 700 (2011).

    Article  Google Scholar 

  29. V. S. Arpacz, Conduction Heat Transfer (Addison-Wesley Publishing Co., Massachusetts, 1966).

    Google Scholar 

  30. S. M. Yang, and W. Q. Tao, Heat Transfer (Higher Education Press, Beijing, 2006).

    Google Scholar 

  31. V. Yakhot, and S. A. Orszag, Renormalization group and local order in strong turbulence, Nucl. Phys. B-Proc. Suppl. 2, 417 (1987).

    Article  Google Scholar 

  32. M. Wolfshtein, The velocity and temperature distribution in one-dimensional flow with turbulence augmentation and pressure gradient, Int. J. Heat Mass Tran. 12, 301 (1969).

    Article  Google Scholar 

  33. M. G. Yan, B. C. Liu, and J. G. Li, China Aeronautical Materials Handbook (Standards Press of China, Beijing, 2001).

    Google Scholar 

  34. F. Zhong, X. Fan, G. Yu, J. Li, and C. J. Sung, Heat transfer of aviation kerosene at supercritical conditions, J. Thermophys. Heat Transf. 23, 543 (2009).

    Article  Google Scholar 

  35. G. Hu, F. Zhong, M. Du, Q. Wang, and H. Kang, Coupled heat transfer properties of aluminum/titanium alloy plates with kerosene active cooling, J. Thermal Sci. Eng. Appl. 14, 091016 (2022).

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No. 12072351).

Author information

Authors and Affiliations

  1. State Key Laboratory of High Temperature Gas Dynamics, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China

    Guohao Hu  (胡国豪), Fengquan Zhong  (仲峰泉) & Keting Chen  (陈科挺)

  2. School of Engineering Science, University of Chinese Academy of Sciences, Beijing, 100049, China

    Guohao Hu  (胡国豪), Fengquan Zhong  (仲峰泉) & Keting Chen  (陈科挺)

Authors
  1. Guohao Hu  (胡国豪)
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Fengquan Zhong  (仲峰泉)
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Keting Chen  (陈科挺)
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Guohao Hu, Fengquan Zhong, and Keting Chen designed the method and created the models. Guohao Hu and Fengquan Zhong wrote the first draft of the manuscript and revised and edited the final version.

Corresponding author

Correspondence to Fengquan Zhong  (仲峰泉).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hu, G., Zhong, F. & Chen, K. An analytical model for maximum temperature and temperature distribution of plate structure with active cooling. Acta Mech. Sin. 39, 322290 (2023). https://doi.org/10.1007/s10409-022-22290-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10409-022-22290-x

Search

Navigation