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超临界CO2池式传热流固耦合传热特性数值模拟

于博文 何孝天 徐进良

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超临界CO2池式传热流固耦合传热特性数值模拟

于博文, 何孝天, 徐进良

Numerical simulation of fluid-structure coupled heat transfer characteristics of supercritical CO2 pool heat transfer

Yu Bo-Wen, He Xiao-Tian, Xu Jin-Liang
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  • 超临界类沸腾传热已有初步研究, 对类气-类液界面的定义仍不统一. 采用层流模型对超临界CO2池式传热特性进行流固耦合数值模拟研究, d = 70 μm的铂丝为加热件, 热流密度qw范围为0—2000 kW/m2, 压力P范围为8—10 MPa, 加热丝附近采用多尺度网格进行建模, 模拟值与实验数据吻合较好. 通过与亚临界传热类比通过计算导热占比Qcon/Qt沿r方向变化规律, 将超临界划分为3个区, 当T < TL时为类液区 (liquid-like, LL), TL < T < TM时为类液向类气转变的过度区 (two-phase-like, TPL), T > TM为类气区 (vapor-like, VL), 与用超临界类沸腾干度x分区规律相同; 根据通过计算导热占比确定的类气膜内平均导热λave和导热热阻RG随热流密度qw变化曲线可很好地解释类蒸发区换热系数hqw的变化规律. 本文提出了确定超临界池式传热类气-类液界面的新方法, 较好地解释了类蒸发区传热机理, 为后续超临界类沸腾池式传热的发展提供了理论基础.
    The heat transfer of supercritical pseudo-boiling has been preliminarily studied, but the definition of gas-liquid interface is still not unified. The fluid-structure coupling numerical simulation of heat transfer characteristics in supercritical CO2 pool is carried out by using laminar flow model. Platinum wire is the heating element, with diameter d = 70 μm. The heat flux density qw is in a range of 0–2000 kW/m2, and the pressure P is in a range of 8–10 MPa. Multi-scale mesh is used to model the heating wire, and simulation values accord well with the experimental data. The results show that due to the increase of the circumferential average Rayleigh number Raave of the heating filament with qw, the characteristic of the natural convection zone is that h increases with qw. The temperatures of the four characteristic working conditions in the evaporation-like zone show a downward trend along the r direction. Through analogy with subcritical heat transfer and by calculating the thermal conductivity ratio Qcon/Qt, the supercritical is divided into three regions, T < TL is liquid-like region (LL), TL < T < TM is two-phase-like region (TPL), T > TM is vapor-like region (VL). The rule is the same as that of x partition according to supercritical pseudo-boiling dryness. According to the curves of average thermal conductivity λave and thermal resistance RG versus heat flux qw, determined by calculating thermal conductivity ratio, the variation law of heat transfer coefficient h with qw in evaporation-like region can be well explained, as qw increases, the thermal conductivity thermal resistance RG increases, and the heat from the heating filament is difficult to transfer to the fluid outside the vapor-like membrane, leading the heat transfer coefficient h to decrease when qA < qw < qC, and a significant increase in λave when qw > qC, and the recovery of heat transfer when h rises again. In this paper, a new method of determining the gas-liquid interface of supercritical pool heat transfer is proposed. This method can effectively explain the heat transfer mechanism in the evaporation-like zone, and provide a theoretical basis for developing supercritical pool heat transfer in the future.
      通信作者: 徐进良, xjl@ncepu.edu.cn
    • 基金项目: 国家自然科学基金重点项目(批准号: 52130608)和国家自然科学基金创新研究群体科学基金(批准号: 51821004)资助的课题.
      Corresponding author: Xu Jin-Liang, xjl@ncepu.edu.cn
    • Funds: Project supported by the Key Program of the National Natural Science Foundation of China (Grant No. 52130608) and the Science Fund for Creative Research Groups of the National Natural Science Foundation of China (Grant No. 51821004).
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    Knez Z, Markocic E, Leitgeb M, Primozic M, Hrncic M K, Skerget M 2014 Energy 77 235Google Scholar

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    Sarkar J 2015 Renew Sust. Energ Rev. 48 434Google Scholar

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    Liu Y P, Wang Y, Huang D G 2019 Energy 189 115900Google Scholar

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    Kafengauz N L, Fedorov M I 1966 J. Eng. Phys. 11 99Google Scholar

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    Ackerman J W 1970 J. Heat Trans. 92 490Google Scholar

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    Tamba J, Takahashi T, Ohara T, Aihara T 1998 Exp. Therm. Fluid Sci. 17 248Google Scholar

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    Zhu B G, Xu J L, Yan C S, Xie J 2020 Int. J. Heat Mass Transfer 148 119080Google Scholar

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    Xu J L, Zhang H S, Zhu B G, Xie J 2020 Sol. Energy 195 27Google Scholar

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    Zhua B G, Xu J L, Wua X M, Xie J, Li M J 2019 Int. J. Therm. Sci. 136 254Google Scholar

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    Huang D, Wu Z, Sunden B, Li W 2016 Appl. Energ. 162 494Google Scholar

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    Rousselet Y, Warrier G 2012 J. Heat Transfer 135 022501Google Scholar

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    Warrier G, Rousselet Y 2012 J. Heat Transfer 135 022502Google Scholar

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    张海松, 徐进良, 朱鑫杰 2021 物理学报 70 044401Google Scholar

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    Cheng L Y, Wang Q Y, Xu J L, 2024 Int. J. Heat Mass Transfer 220 124953Google Scholar

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    He X T, Xu J L, Yu X J, Xie J 2023 Int. J. Heat Mass Transfer 214 124417Google Scholar

    [19]

    何孝天, 徐进良, 程怡玮 2023 物理学报 72 057801Google Scholar

    He X T, Xu J L, Cheng Y W 2023 Acta Phys. Sin. 72 057801Google Scholar

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    Simeoni G G, Bryk T, Gorelli F A, Krisch M, Ruocco G, Santoro M, Scopigno T 2010 Nat. Phys. 6 503Google Scholar

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    Maxi F, Contescu C, Boillat P, Niceno B, Karalis K, Testino A, Ludwig C H 2019 Nat. Commun. 19 12117Google Scholar

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    Banuti D T 2015 J. Supercrit. Fluid 98 12Google Scholar

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    Xu J L, Wang Y, Ma X J 2021 Phys. Rev. 104 014142Google Scholar

    [24]

    Wang Q Y, Ma X J, Xu J L, Li M J, Wang Y 2021 Int. J. Heat Mass Transfer 181 121875Google Scholar

    [25]

    闫晨帅, 徐进良 2020 物理学报 4 044401Google Scholar

    Yan C S, Xu J L 2020 Acta Phys. Sin. 4 044401Google Scholar

    [26]

    Tripathi P M, Basu S 2021 Phys. Fluids 33 043304Google Scholar

    [27]

    Li X L, Yu X Y, Liu P T, Fan Y H, Yang D L, Tang G H 2023 Int. J. Heat Mass Transfer 216 124563Google Scholar

    [28]

    Wang J T, Li Z L, Zhai Y L, Wang H 2023 Int. J. Heat Mass Transfer 201 123571Google Scholar

    [29]

    于博文, 何孝天, 徐进良 2023 中国科学: 技术科学 3 25Google Scholar

    Yu B W, He X T, Xu J L 2023 Sci. Sin. Tech. 3 25Google Scholar

    [30]

    杨世铭, 陶文铨 2011 传热学 (北京: 高等教育出版社)

    Yang S M, Tao W Q 2011 Heat Transfer Science (Beijing: Higher Education Press

    [31]

    He X T, Xu J L, Xie J 2024 Phys. Fluids 36 013343Google Scholar

    [32]

    Liu M, Liu S H, Xi D P, Huang S F, Huang Y P 2023 Nucl. Energy 104 2391Google Scholar

  • 图 1  几何模型和网格划分示意图

    Fig. 1.  Geometric model and grid diagram.

    图 2  模型验证 (a)热流密度随Tw-Tpc变化; (b)平均瑞利数Raave随热流密度变化; (c)热流密度随壁温变化; (d)换热系数随热流密度变化规律

    Fig. 2.  Model verification: (a) Heat flux varies with Tw-Tpc, (b) Raave varies with heat flux; (c) heat flux varies with wall temperature; (d) heat transfer coefficient varies with heat flux.

    图 3  不同工况温度和密度沿r方向变化规律 (a), (b) Case A, qw = 87.73 kW/m2; (c), (d) P = 10 MPa, Tb = 288 K; θ = 90°

    Fig. 3.  Temperature and density change in r direction under different working conditions: (a), (b) Case A, qw = 87.73 kW/m2; (c), (d) P = 10 MPa, Tb = 288 K; θ = 90°.

    图 4  Qcon计算网格二维示意图

    Fig. 4.  Two-dimensional diagram of Qcon computing grid.

    图 5  qw = 233.33 kW/m2, θ = 90°时, 亚临界与超临界导热占比Qcon/Qt沿r方向变化类比 (a) 亚临界P = 6 MPa; (b) 超临界P = 10 MPa

    Fig. 5.  Subcritical and supercritical thermal conductivity ratio Qcon/Qt changes along the r direction with qw = 233.33 kW/m2, θ = 90°: (a) Subcritical P = 6 MPa; (b) supercritical P = 10 MPa.

    图 6  不同压力下速度矢量图 (a) 亚临界P = 6 MPa; (b) 超临界P = 10 MPa

    Fig. 6.  Velocity vector diagram at different pressures: (a) Subcritical P = 6 MPa; (b) supercritical P = 10 MPa.

    图 7  Qcon/Qtr变化规律 (a) Case A工况; (b) 同一角度不同工况下Qcon/Qtr变化规律

    Fig. 7.  Qcon/Qt changes with r: (a) Case A working condition; (b) Qcon/Qt changes with r under the same angle and different working conditions.

    图 8  不同工况下Qcon/Qt随类沸腾干度x变化曲线

    Fig. 8.  Qcon/Qt curve with boiling dryness x under different working conditions.

    图 9  (a) 导热热阻RG随热流密度变化曲线; (b) 平均导热λave随热流密度变化曲线

    Fig. 9.  (a) Curve of thermal resistance RG with heat flux; (b) average thermal conductivity λave with heat flux curve.

    表 1  网格独立性验证

    Table 1.  Grid independence verification.

    Grid No. 径向节点数 周向节点数 Tw/K 网格数 误差/%
    1 100 21 310.2 407.7×104 –3.71
    2 100 41 316.0 82.6×104 –1.88
    3 100 81 321.3 169.8×104 –0.26/0.23
    4 100 121 322.1 261.4×104 0
    5 40 81 328.7 156.3×104 2.08
    6 70 81 326.1 163.1×104 1.29
    7 130 81 322.0 176.5×104 0
    下载: 导出CSV
  • [1]

    Tsai W C, Wang Y D 2019 Prog. Polym. Sci. 98 101161Google Scholar

    [2]

    Knez Z, Markocic E, Leitgeb M, Primozic M, Hrncic M K, Skerget M 2014 Energy 77 235Google Scholar

    [3]

    Sarkar J 2015 Renew Sust. Energ Rev. 48 434Google Scholar

    [4]

    Liu Y P, Wang Y, Huang D G 2019 Energy 189 115900Google Scholar

    [5]

    Kafengauz N L, Fedorov M I 1966 J. Eng. Phys. 11 99Google Scholar

    [6]

    Ackerman J W 1970 J. Heat Trans. 92 490Google Scholar

    [7]

    Knapp K K, Sabersky R H 1965 Int. J. Heat Mass Transfer 9 41Google Scholar

    [8]

    Abadzic E, Goldstein R J 1970 Int. J. Heat Mass Transfer 13 1163Google Scholar

    [9]

    Tamba J, Takahashi T, Ohara T, Aihara T 1998 Exp. Therm. Fluid Sci. 17 248Google Scholar

    [10]

    Zhu B G, Xu J L, Yan C S, Xie J 2020 Int. J. Heat Mass Transfer 148 119080Google Scholar

    [11]

    Xu J L, Zhang H S, Zhu B G, Xie J 2020 Sol. Energy 195 27Google Scholar

    [12]

    Zhua B G, Xu J L, Wua X M, Xie J, Li M J 2019 Int. J. Therm. Sci. 136 254Google Scholar

    [13]

    Huang D, Wu Z, Sunden B, Li W 2016 Appl. Energ. 162 494Google Scholar

    [14]

    Rousselet Y, Warrier G 2012 J. Heat Transfer 135 022501Google Scholar

    [15]

    Warrier G, Rousselet Y 2012 J. Heat Transfer 135 022502Google Scholar

    [16]

    张海松, 徐进良, 朱鑫杰 2021 物理学报 70 044401Google Scholar

    Zhang H S, Xu J L, Zhu X J 2021 Acta Phys. Sin. 70 044401Google Scholar

    [17]

    Cheng L Y, Wang Q Y, Xu J L, 2024 Int. J. Heat Mass Transfer 220 124953Google Scholar

    [18]

    He X T, Xu J L, Yu X J, Xie J 2023 Int. J. Heat Mass Transfer 214 124417Google Scholar

    [19]

    何孝天, 徐进良, 程怡玮 2023 物理学报 72 057801Google Scholar

    He X T, Xu J L, Cheng Y W 2023 Acta Phys. Sin. 72 057801Google Scholar

    [20]

    Simeoni G G, Bryk T, Gorelli F A, Krisch M, Ruocco G, Santoro M, Scopigno T 2010 Nat. Phys. 6 503Google Scholar

    [21]

    Maxi F, Contescu C, Boillat P, Niceno B, Karalis K, Testino A, Ludwig C H 2019 Nat. Commun. 19 12117Google Scholar

    [22]

    Banuti D T 2015 J. Supercrit. Fluid 98 12Google Scholar

    [23]

    Xu J L, Wang Y, Ma X J 2021 Phys. Rev. 104 014142Google Scholar

    [24]

    Wang Q Y, Ma X J, Xu J L, Li M J, Wang Y 2021 Int. J. Heat Mass Transfer 181 121875Google Scholar

    [25]

    闫晨帅, 徐进良 2020 物理学报 4 044401Google Scholar

    Yan C S, Xu J L 2020 Acta Phys. Sin. 4 044401Google Scholar

    [26]

    Tripathi P M, Basu S 2021 Phys. Fluids 33 043304Google Scholar

    [27]

    Li X L, Yu X Y, Liu P T, Fan Y H, Yang D L, Tang G H 2023 Int. J. Heat Mass Transfer 216 124563Google Scholar

    [28]

    Wang J T, Li Z L, Zhai Y L, Wang H 2023 Int. J. Heat Mass Transfer 201 123571Google Scholar

    [29]

    于博文, 何孝天, 徐进良 2023 中国科学: 技术科学 3 25Google Scholar

    Yu B W, He X T, Xu J L 2023 Sci. Sin. Tech. 3 25Google Scholar

    [30]

    杨世铭, 陶文铨 2011 传热学 (北京: 高等教育出版社)

    Yang S M, Tao W Q 2011 Heat Transfer Science (Beijing: Higher Education Press

    [31]

    He X T, Xu J L, Xie J 2024 Phys. Fluids 36 013343Google Scholar

    [32]

    Liu M, Liu S H, Xi D P, Huang S F, Huang Y P 2023 Nucl. Energy 104 2391Google Scholar

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出版历程
  • 收稿日期:  2023-12-11
  • 修回日期:  2024-03-17
  • 上网日期:  2024-04-02
  • 刊出日期:  2024-05-20

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