垂直管内高质量流速超临界CO2换热特性

doi:10.16085/j.issn.1000-6613.2023-0281

摘要/Abstract

摘要：

利用已有的流动传热实验数据，对不同湍流模型预测超临界CO₂（S-CO₂）传热能力进行了评价及选取，确定了SST k-ω 湍流模型为最优模型。分析了入口温度、热流密度、质量流速、浮升力和流动加速效应对内径为10mm的垂直加热管内S-CO₂的对流传热特性的影响。结果表明：在一些工况条件下Bu<10^-5、Bu*<5.6×10^-7和K_v<3×10^-6并不满足，表明浮升力和流动加速度效应并不能解释高质量流速下的数值模拟结果。基于超临界类沸腾理论，建立了垂直加热管内S-CO₂类沸腾传热模型，并阐述了S-CO₂传热恶化现象，径向方向上S-CO₂热物性和湍流的详细分布表明超临界传热受类气膜的厚度、类气膜的热性质和近壁区湍流动能的影响很大，成功解释了S-CO₂在高质量流速下的传热机理。最后引入超临界沸腾数SBO，提出了适用高质量流速的传热关联式。

关键词: 超临界二氧化碳, 高质量流速, 传热, 关联式, 数值计算

Abstract:

Based on the flow heat transfer experimental data, the ability of different turbulence models to predict heat transfer on supercritical CO₂(S-CO₂) was evaluated and selected, and the SST k-ω turbulence model was confirmed as the optimal model. The effects of inlet temperature, heat flux, mass flux, buoyancy and flow acceleration on the convective heat transfer characteristics of S-CO₂ were analyzed in a vertical heating tube with an inner diameter of 10mm.The results showed that Bu<10^-5, Bu*<5.6×10^-7 and K_v<3×10^-6 were not satisfied in some working conditions, indicating the effects of buoyance and flow acceleration could not explain the heat transfer characteristic at high mass flux. Based on the supercritical boiling theory, the S-CO₂ boiling heat transfer model in vertical heating tube was established, and the deterioration of S-CO₂ heat transfer was described. The detailed distribution of S-CO₂ thermophysical properties and turbulence in the radial direction showed that the supercritical heat transfer was greatly affected by the thickness of the pseudo-gas film, the thermal properties of the quasi-gas film and the turbulent kinetic energy in the near-wall region. The heat transfer mechanism of S-CO₂ at high mass flux was explained successfully. By introducing the supercritical boiling number, a heat transfer correlation formula for high quality flow rate was proposed.

Key words: supercritical CO₂, high mass flux, heat transfer, correction, numerical calculation

中图分类号:

TK124

朱兵国, 巩楷刚, 彭斌. 垂直管内高质量流速超临界CO₂换热特性[J]. 化工进展, 2024, 43(2): 937-947.

ZHU Bingguo, GONG Kaigang, PENG Bin. Heat transfer characteristics of supercritical CO₂ with high mass flux in vertical tube[J]. Chemical Industry and Engineering Progress, 2024, 43(2): 937-947.

图/表 14

图1 物理模型

图2 不同湍流模型计算结果与实验数据对比[p=8.221MPa，G=1001.5kg/(m2·s)，qw=244.33kW/m2]

图3 网格独立性验证[p=8MPa，G=1500kg/(m2·s)，qw=400kW/m2，Tin=20℃]

图4 数值模拟计算与实验数据的比较

图5 入口温度对壁温的影响数值模拟计算与实验数据的比较[p=8MPa，G=1500kg/(m2·s)，qw=400kW/m2]

图6 压力对壁温的影响[G=1000kg/(m2·s)，Tin=25℃，qw=400kW/m2]

图7 热流密度对壁温的影响[p=8MPa，G=2000kg/(m2·s)]

图8 质量流速对壁温的影响（p=8MPa，qw=400kW/m2，Tin=25℃）

图9 不同质量流速下的浮升力变化

图10 不同质量流速下的流动加速效应的变化（p=8MPa，qw=400kW/m2，Tin=25℃）

图11 超临界类沸腾传热模型

图12 特征界面径向热物性和湍流的分布

表1 超临界传热关联式

文献	公式
Winterton等^[27]	$N u = 0.023 R e_{b}^{0.8} P r_{b}^{0.4}$ , $R e_{b} = \frac{G d_{i n}}{μ_{b}}$ , $P r_{b} = \frac{μ_{b} c_{p}}{λ_{b}}$
Kim等^[28]	$N u = 0.226 R e_{b}^{1.174} P r_{b}^{1.057} {(\frac{ρ_{w}}{ρ_{b}})}^{0.571} {(\frac{c_{p, a v e}}{c_{p, b}})}^{1.032} A c^{0.489} B u^{0.0021}$ $R e_{b} = \frac{G \times d_{i n}}{μ_{b}}$ , $P r_{b, a v e} = \frac{μ_{b} \times c_{p, a v e}}{λ_{b}}$ ， $c_{p, a v e} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}}$ $A c = \frac{q^{+}}{R e_{b}^{0.625}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{w}}{ρ_{b}})}^{- 0.5}$ ， $B u = \frac{G r^{*}}{R e_{b}^{3.425} P r_{b}^{0.8}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{w}}{ρ_{b}})}^{- 0.5}$
Gupta等^[29]	$N u = 0.01 R e_{b}^{0.89} P r_{b, a v e}^{- 0.14} {(\frac{ρ_{w}}{ρ_{b}})}^{0.93} {(\frac{λ_{w}}{λ_{b}})}^{0.22} {(\frac{μ_{w}}{μ_{b}})}^{- 1.13}$
Kim等^[30]	$N u = 2.0514 R e_{b}^{0.928} P r_{b}^{0.742} {(\frac{ρ_{w}}{ρ_{b}})}^{1.305} {(\frac{c_{p, a v e}}{c_{p, b}})}^{0.0863} {(\frac{μ_{w}}{μ_{b}})}^{- 0.669} {(q^{+})}^{0.792}$ $R e_{b} = \frac{G \times d_{i n}}{μ_{b}}$ , $P r_{b, a v e} = \frac{μ_{b} \times c_{p, a v e}}{λ_{b}}$ , $c_{p, a v e} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}}$ , $q^{+} = \frac{β q_{w}}{G c_{p}}$
Mokry等^[31]	$N u = 0.0061 R e_{b}^{0.904} P r_{b, a v e}^{0.684} {(\frac{ρ_{w}}{ρ_{b}})}^{0.564}$ , $R e_{b} = \frac{G \cdot d_{i n}}{μ_{b}}$ $P r_{b, a v e} = \frac{μ_{b} \times c_{p, a v e}}{λ_{b}}$ , $c_{p, a v e} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}}$

表1 超临界传热关联式

文献	公式
Winterton等^[27]	$N u = 0.023 R e_{b}^{0.8} P r_{b}^{0.4}$ , $R e_{b} = \frac{G d_{i n}}{μ_{b}}$ , $P r_{b} = \frac{μ_{b} c_{p}}{λ_{b}}$
Kim等^[28]	$N u = 0.226 R e_{b}^{1.174} P r_{b}^{1.057} {(\frac{ρ_{w}}{ρ_{b}})}^{0.571} {(\frac{c_{p, a v e}}{c_{p, b}})}^{1.032} A c^{0.489} B u^{0.0021}$ $R e_{b} = \frac{G \times d_{i n}}{μ_{b}}$ , $P r_{b, a v e} = \frac{μ_{b} \times c_{p, a v e}}{λ_{b}}$ ， $c_{p, a v e} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}}$ $A c = \frac{q^{+}}{R e_{b}^{0.625}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{w}}{ρ_{b}})}^{- 0.5}$ ， $B u = \frac{G r^{*}}{R e_{b}^{3.425} P r_{b}^{0.8}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{w}}{ρ_{b}})}^{- 0.5}$
Gupta等^[29]	$N u = 0.01 R e_{b}^{0.89} P r_{b, a v e}^{- 0.14} {(\frac{ρ_{w}}{ρ_{b}})}^{0.93} {(\frac{λ_{w}}{λ_{b}})}^{0.22} {(\frac{μ_{w}}{μ_{b}})}^{- 1.13}$
Kim等^[30]	$N u = 2.0514 R e_{b}^{0.928} P r_{b}^{0.742} {(\frac{ρ_{w}}{ρ_{b}})}^{1.305} {(\frac{c_{p, a v e}}{c_{p, b}})}^{0.0863} {(\frac{μ_{w}}{μ_{b}})}^{- 0.669} {(q^{+})}^{0.792}$ $R e_{b} = \frac{G \times d_{i n}}{μ_{b}}$ , $P r_{b, a v e} = \frac{μ_{b} \times c_{p, a v e}}{λ_{b}}$ , $c_{p, a v e} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}}$ , $q^{+} = \frac{β q_{w}}{G c_{p}}$
Mokry等^[31]	$N u = 0.0061 R e_{b}^{0.904} P r_{b, a v e}^{0.684} {(\frac{ρ_{w}}{ρ_{b}})}^{0.564}$ , $R e_{b} = \frac{G \cdot d_{i n}}{μ_{b}}$ $P r_{b, a v e} = \frac{μ_{b} \times c_{p, a v e}}{λ_{b}}$ , $c_{p, a v e} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}}$

图13 SBO关联式和其他关联式的比较

参考文献 31

1	XU Jinliang, LIU Chao, SUN Enhui, et al. Perspective of S-CO₂ power cycles[J]. Energy, 2019, 186: 115831.
2	师亚东, 李靓. 国际能源企业低碳化转型实践研究[J]. 中国能源, 2021, 43(3): 75-79.
	SHI Yadong, LI Liang. Study on the practice of low-carbon transformation of international energy enterprises[J]. Energy of China, 2021, 43(3): 75-79.
3	王哮江, 刘鹏, 李荣春, 等. “双碳”目标下先进发电技术研究进展及展望[J]. 热力发电, 2022, 51(1): 52-59.
	WANG Xiaojiang, LIU Peng, LI Rongchun, et al. Research progress and prospects of advanced power generation technology under the goal of carbon emission peak and carbon neutrality[J]. Thermal Power Generation, 2022, 51(1): 52-59.
4	张珍珍, 吕清泉, 张健美. “双碳”目标下分布式光伏发电技术的研究进展及展望[J]. 太阳能, 2023(1): 17-21.
	ZHANG Zhenzhen, Qingquan LYU, ZHANG Jianmei. Research progress and prospect of distributed pv power generation technology under the goal of emission peak and carbon neutrality[J]. Solar Energy, 2023(1): 17-21.
5	徐进良, 刘超, 孙恩慧, 等. 超临界二氧化碳动力循环研究进展及展望[J]. 热力发电, 2020, 49(10): 1-10.
	XU Jinliang, LIU Chao, SUN Enhui, et al. Review and perspective of supercritical carbon dioxide power cycles[J]. Thermal Power Generation, 2020, 49(10): 1-10.
6	JIANG Peixue, ZHANG Yu, ZHAO Chenru, et al. Convection heat transfer of CO₂ at supercritical pressures in a vertical mini tube at relatively low Reynolds numbers[J]. Experimental Thermal and Fluid Science, 2008, 32(8): 1628-1637.
7	JIANG Peixue, ZHANG Yu, SHI Runfu. Experimental and numerical investigation of convection heat transfer of CO₂ at supercritical pressures in a vertical mini-tube[J]. International Journal of Heat and Mass Transfer, 2008, 51(11/12): 3052-3056.
8	刘生晖, 黄彦平, 刘光旭, 等. 竖直圆管内超临界二氧化碳强迫对流传热实验研究[J]. 核动力工程, 2017, 38(1): 1-5.
	LIU Shenghui, HUANG Yanping, LIU Guangxu, et al. Investigation of correlation for forced convective heat transfer to supercritical carbon dioxide flowing in a vertical tube[J]. Nuclear Power Engineering, 2017, 38(1): 1-5.
9	Oğuzhan GÖKKAYA, Efe ÖZTABAK, Hojin AHN. Experimental investigation on heat transfer characteristics of supercritical CO₂ flowing upward and downward through a microtube at low Reynolds numbers[J]. Experimental Thermal and Fluid Science, 2022, 139: 110717.
10	GUO Jiangfeng, XIANG Mengru, ZHANG Haiyan, et al. Thermal-hydraulic characteristics of supercritical pressure CO₂ in vertical tubes under cooling and heating conditions[J]. Energy, 2019, 170: 1067-1081.
11	王珂, 谢金, 刘遵超, 等. 超临界二氧化碳在微细管内的换热特性[J]. 化工学报, 2014, 65(S1): 323-327.
	WANG Ke, XIE Jin, LIU Zunchao, et al. Heat transfer characteristics of supercritical carbon dioxide in a micro-capillary tube[J]. CIESC Journal, 2014, 65(S1): 323-327.
12	KLINE Nathan, FEUERSTEIN Florian, TAVOULARIS Stavros. Onset of heat transfer deterioration in vertical pipe flows of CO₂ at supercritical pressures[J]. International Journal of Heat and Mass Transfer, 2018, 118: 1056-1068.
13	吴新明, 朱兵国, 张良, 等. 圆管内超临界CO₂的阻力特性[J]. 化工学报, 2018, 69(12): 5024-5033.
	WU Xinming, ZHU Bingguo, ZHANG Liang, et al. Resistance characteristics of supercritical CO₂ in circular tube[J]. CIESC Journal, 2018, 69(12): 5024-5033.
14	王乃心, 杨大章, 谢晶, 等. 超临界CO₂对流换热特性试验研究进展[J]. 流体机械, 2020, 48(11): 73-79.
	WANG Naixin, YANG Dazhang, XIE Jing, et al. A review on experimental studies of convection heat transfer characteristic of supercritical CO₂ [J]. Fluid Machinery, 2020, 48(11): 73-79.
15	HUANG Dan, LI Wei. A brief review on the buoyancy criteria for supercritical fluids[J]. Applied Thermal Engineering, 2018, 131: 977-987.
16	HUANG Dan, WU Zan, SUNDEN Bengt, et al. A brief review on convection heat transfer of fluids at supercritical pressures in tubes and the recent progress[J]. Applied Energy, 2016, 162: 494-505.
17	朱兵国. 超临界二氧化碳垂直管内对流换热研究[D]. 北京: 华北电力大学, 2020.
	ZHU Bingguo. Study on convective heat transfer in vertical tube of supercritical carbon dioxide[D]. Beijing: North China Electric Power University, 2020.
18	LI Zhouhang, WU Yuxin, TANG Guoli, et al. Comparison between heat transfer to supercritical water in a smooth tube and in an internally ribbed tube[J]. International Journal of Heat and Mass Transfer, 2015, 84: 529-541.
19	WANG Kaizheng, XU Xiaoxiao, WU Yangyang, et al. Numerical investigation on heat transfer of supercritical CO₂ in heated helically coiled tubes[J]. The Journal of Supercritical Fluids, 2015, 99: 112-120.
20	JIANG Peixue, LIU Bo, ZHAO Chenru, et al. Convection heat transfer of supercritical pressure carbon dioxide in a vertical micro tube from transition to turbulent flow regime[J]. International Journal of Heat and Mass Transfer, 2013, 56(1/2): 741-749.
21	闫晨帅, 朱兵国, 张海松, 等. 超临界压力CO₂在倾斜光管内换热特性数值分析[J]. 中国电机工程学报, 2020, 40(2): 583-592.
	YAN Chenshuai, ZHU Bingguo, ZHANG Haisong, et al. Numerical analysis on heat transfer characteristics of supercritical pressure CO₂ in inclined smooth tube[J]. Proceedings of the CSEE, 2020, 40(2): 583-592.
22	ZHU Bingguo, XU Jinliang, WU Xinming, et al. Supercritical “boiling” number, a new parameter to distinguish two regimes of carbon dioxide heat transfer in tubes[J]. International Journal of Thermal Sciences, 2019, 136: 254-266.
23	JACKSON J D. Fluid flow and convective heat transfer to fluids at supercritical pressure[J]. Nuclear Engineering and Design, 2013, 264: 24-40.
24	JACKSON J D, HALL W B. Influences of Buoyancy on heat transfer to fluids flowing in vertical tubes under turbulent conditions[J]. Turbulent Forced Convection in Channels and Bundles, 1979: 613-640.
25	MCELIGOT D M, COON C W, PERKINS H C. Relaminarization in tubes[J]. International Journal of Heat and Mass Transfer, 1970, 13(2): 431-433.
26	GONG Kaigang, ZHU Bingguo, PENG Bin, et al. Numerical investigation of heat transfer characteristics of scCO₂ flowing in a vertically-upward tube with high mass flux[J]. Entropy, 2022, 24(1): 79.
27	WINTERTON R H. Where did the Dittus and Boelter equation come from?[J]. International Journal of Heat and Mass Transfer, 1998, 41(4/5): 809-810.
28	KIM D E, KIM M H. Experimental study of the effects of flow acceleration and buoyancy on heat transfer in a supercritical fluid flow in a circular tube[J]. Nuclear Engineering and Design, 2010, 240(10): 3336-3349.
29	GUPTA S, SALTANOV E, MOKRY S J, et al. Developing empirical heat-transfer correlations for supercritical CO₂ flowing in vertical bare tubes[J]. Nuclear Engineering and Design, 2013, 261: 116-131.
30	KIM J K, JEON H K, LEE J S. Wall temperature measurement and heat transfer correlation of turbulent supercritical carbon dioxide flow in vertical circular/non-circular tubes[J]. Nuclear Engineering and Design, 2007, 237(15/16/17): 1795-1802.
31	MOKRY Sarah, PIORO Igor, FARAH Amjad, et al. Development of supercritical water heat-transfer correlation for vertical bare tubes[J]. Nuclear Engineering and Design, 2011, 241(4): 1126-1136.

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垂直管内高质量流速超临界CO₂换热特性

Heat transfer characteristics of supercritical CO₂ with high mass flux in vertical tube

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