微小方形通道内近超临界压力二氧化碳流动换热特性实验研究

doi:10.11949/0438-1157.20241134

摘要/Abstract

摘要：

开展超临界二氧化碳1.6 mm × 1.6 mm水平方形管道内受热条件下流动换热特性的实验研究。实验参数为系统压力7.4～8.4 MPa（相对压力p/p_cr = 1.003~1.138），质量流速500～1500 kg/(m²·s)，热通量100～300 kW/m²。分析了热工参数、浮升力和热加速效应对方管内换热特性的影响规律，根据换热曲线分布特性，将超临界CO₂流动换热分为类液相、类两相、类气相3个区域。实验结果表明：类两相区域时，在临界温度处平均壁温与主流温度的差值存在最小值，平均对流传热系数存在峰值。类气态区域内的换热性能较类液相区域相对减弱。浮升力使底部壁面换热得到强化，相比之下顶部壁面的换热较弱，流体热加速效应对本实验对流换热影响几乎可以忽略。通过引入表征浮升力效应的无量纲热通量q⁺，提出一个适用于方形微小通道超临界CO₂换热关联式，预测误差范围为+20%～-20%。

关键词: 超临界二氧化碳, 对流, 换热, 微通道, 浮升力

Abstract:

An experimental study was conducted on the flow and heat transfer characteristics of supercritical CO₂ in a 1.6 mm × 1.6 mm horizontal square tube under heated conditions. The experimental parameters were: system pressure between 7.4 to 8.4 MPa (relative pressure p/p_cr= 1.003—1.138), mass flux ranging from 500 to 1500 kg/(m²·s), and heat flux from 100 to 300 kW/m². The influence of thermal parameters, buoyancy and thermal acceleration effect on heat transfer characteristics in square pipes is analyzed. According to the distribution characteristics of heat transfer curves, supercritical CO₂ flow heat transfer is divided into three regions: liquid-like, two-phase, and gas-like. The experimental results showed that increasing the mass flow rate and reducing the heat flux effectively enhanced the convective heat transfer coefficient, achieving improved heat transfer. In the square microchannel, buoyancy strengthened heat transfer at the bottom wall, while the top wall experienced weaker heat transfer. The effect of thermal acceleration on convective heat transfer in this experiment was found to be negligible. A new dimensionless heat flux, q⁺, was introduced based on mass flux, wall, and mainstream temperatures, and a new heat transfer correlation was derived using q⁺ and other influencing factors, with a prediction error range of +20% to -20%.

Key words: supercritical carbon dioxide, convection, heat transfer, microchannels, buoyancy

中图分类号:

TK 124

吴罗长, 杨泽宇, 颜建国, 朱旭涛, 陈阳, 王子辰. 微小方形通道内近超临界压力二氧化碳流动换热特性实验研究[J]. 化工学报, 2025, 76(4): 1583-1594.

Luochang WU, Zeyu YANG, Jianguo YAN, Xutao ZHU, Yang CHEN, Zichen WANG. Experimental study on convection heat transfer characteristics of supercritical carbon dioxide flowing in mini square channels[J]. CIESC Journal, 2025, 76(4): 1583-1594.

图/表 16

图1 实验系统图

Fig.1 Schematic diagram of experimental loop

图2 实验段示意图

Fig.2 Schematic diagram of test section

表1 参数不确定度

Table 1 Uncertainties of the experimental parameters

参数	单位	不确定度/%
压力	MPa	0.16
质量流速	kg/(m²∙s)	0.8
流体温度	°C	0.5
壁面温度	°C	0.4
热通量	kW/m²	4.32
传热系数	W/(m²∙°C)	6.6

表2 工况

Table 2 Test conditions

序号	p/MPa	G/(kg/(m²·s))	q/(kW/m²)
1	7.4	1000	100
2	7.4	1000	200
3	7.4	1000	300
4	7.4	500	100
5	7.4	1500	100
6	7.9	1000	100
7	8.4	1000	100

图3 超临界CO2热物性（p = 7.4 MPa）

Fig.3 Thermo-physical properties of supercritical CO2 （p = 7.4 MPa）

图4 方形通道内超临界CO2典型换热特性（p = 7.4 MPa）

Fig.4 Heat transfer characteristics of supercritical CO2（p = 7.4 MPa）

图5 不同热通量下的传热系数

Fig.5 Heat transfer coefficients at different heat fluxes

图6 压力对传热系数的影响

Fig.6 Effect of pressure on heat transfer coefficients

图7 质量流速对传热系数的影响

Fig.7 Effect of mass flux on heat transfer coefficients

图8 不同质量流速下浮升力的影响

Fig.8 Effect of buoyancy at different mass flux

图9 不同换热区域中浮升力准则数和Froude数变化情况

Fig.9 Variation of buoyancy criterion number and Froude number in different heat transfer regions

图10 不同热通量下热加速效应影响

Fig.10 Effect of thermal acceleration at different heat flux

表3 超临界CO2换热关联式

Table 3 Heat transfer correlations for supercritical carbon dioxide

文献	关联式	适用范围
[24]	$N u = 0.0375 R e x 0.77 P r w 0.55$	p = 8.2732 MPa d = 4.572 mm T_b= 21 ~ 48.9℃ Re_b = 3×10⁴ ~ 3×10⁵
[25]	$N u w = 0.0038 R e w 0.928 P r ¯ w - 0.14 ρ w ρ b 0.84 μ w μ b - 0.22 λ w λ b - 0.75$	p = 8.38~8.80 MPa d = 8 mm G = 700~3200 kg/(m²·s) q = 18.40~161.12 kW/m²
[26]	$N u b = 2.0514 R e b 0.928 P r b 0.742 ρ w ρ b 1.305 μ w μ b - 0.669 c p, w c p, b - 0.888 q b + 0.792$	p = 7.46~10.26 MPa d = 4.5 mm,T_b= 29~115℃ G = 208 ~ 874 kg/(m²·s) q=38 ~ 234 kW/m²
[27]	$N u b = 0.124 R e b 0.8 P r b 0.4 ρ w ρ b 1.305 G r R b 2 0.203 c ¯ p c p, b$	p = 7.40~12.0 MPa d = 0.70~2.16 mm
[28]	$N u b = 0.0858 R e b 0.846 P r ¯ b 0.784 ρ w ρ b 1.277 q b + 0.191$	p = 7.40 ~ 8.44 MPa, d = 2 mm G = 600 ~ 1600 kg/(m²·s) q = 0 ~ 319 kW/m²
[29]	$N u w = 0.0015 R e w 1.03 P r ¯ w 0.76 ρ w ρ b 0.46 μ w μ b - 0.53 λ w λ b - 0.43$	p = 7.58 ~ 9.58 MPa d = 0.948 ~ 8.000 mm G = 419 ~ 1200 kg/(m²·s) q = 20 ~ 130 kW/m²

表3 超临界CO2换热关联式

Table 3 Heat transfer correlations for supercritical carbon dioxide

文献	关联式	适用范围
[24]	$N u = 0.0375 R e x 0.77 P r w 0.55$	p = 8.2732 MPa d = 4.572 mm T_b= 21 ~ 48.9℃ Re_b = 3×10⁴ ~ 3×10⁵
[25]	$N u w = 0.0038 R e w 0.928 P r ¯ w - 0.14 ρ w ρ b 0.84 μ w μ b - 0.22 λ w λ b - 0.75$	p = 8.38~8.80 MPa d = 8 mm G = 700~3200 kg/(m²·s) q = 18.40~161.12 kW/m²
[26]	$N u b = 2.0514 R e b 0.928 P r b 0.742 ρ w ρ b 1.305 μ w μ b - 0.669 c p, w c p, b - 0.888 q b + 0.792$	p = 7.46~10.26 MPa d = 4.5 mm,T_b= 29~115℃ G = 208 ~ 874 kg/(m²·s) q=38 ~ 234 kW/m²
[27]	$N u b = 0.124 R e b 0.8 P r b 0.4 ρ w ρ b 1.305 G r R b 2 0.203 c ¯ p c p, b$	p = 7.40~12.0 MPa d = 0.70~2.16 mm
[28]	$N u b = 0.0858 R e b 0.846 P r ¯ b 0.784 ρ w ρ b 1.277 q b + 0.191$	p = 7.40 ~ 8.44 MPa, d = 2 mm G = 600 ~ 1600 kg/(m²·s) q = 0 ~ 319 kW/m²
[29]	$N u w = 0.0015 R e w 1.03 P r ¯ w 0.76 ρ w ρ b 0.46 μ w μ b - 0.53 λ w λ b - 0.43$	p = 7.58 ~ 9.58 MPa d = 0.948 ~ 8.000 mm G = 419 ~ 1200 kg/(m²·s) q = 20 ~ 130 kW/m²

图11 换热关联式对比

Fig.11 Comparison of heat transfer correlations

表4 换热关联式的预测性能

Table 4 Prediction performances of heat transfer correlations

关联式	平均误差	平均绝对误差	均方根误差
Bringer-Smith^[24]	0.088	0.051	0.224
Pioro^[25]	-0.275	0.126	0.355
Kim-Kim^[26]	-0.065	0.038	0.195
Liao^[27]	-0.208	0.066	0.257
Lyu^[28]	0.295	0.545	0.738
Preda^[29]	0.622	0.831	0.911
新关联式	-0.017	0.010	0.101

图12 新关联式预测结果

Fig.12 Prediction performance of the new correlation

参考文献 30

1	Ma T, Li L, Xu X Y, et al. Study on local thermal-hydraulic performance and optimization of zigzag-type printed circuit heat exchanger at high temperature[J]. Energy Conversion and Management, 2015, 104: 55-66.
2	Ma T, Xin F, Li L, et al. Effect of fin-endwall fillet on thermal hydraulic performance of airfoil printed circuit heat exchanger[J]. Applied Thermal Engineering, 2015, 89: 1087-1095.
3	Shi H Y, Li M J, Wang W Q, et al. Heat transfer and friction of molten salt and supercritical CO₂ flowing in an airfoil channel of a printed circuit heat exchanger[J]. International Journal of Heat and Mass Transfer, 2020, 150: 119006.
4	Shin J H, Yoon S H. Thermal and hydraulic performance of a printed circuit heat exchanger using two-phase nitrogen[J]. Applied Thermal Engineering, 2020, 168: 114802.
5	孙玉伟, 林杰, 刘小华, 等. 超临界CO₂印刷电路板式换热器动态特性研究[J]. 热科学与技术, 2024, 23(4): 379-387.
	Sun Y W, Lin J, Liu X H, et al. Study on dynamic characteristics of supercritical CO₂ printed circuit heat exchanger[J]. Journal of Thermal Science and Technology, 2024, 23(4): 379-387.
6	李占英, 王江峰, 娄聚伟, 等. 印刷电路板换热器在超临界二氧化碳布雷顿循环系统中的动态特性研究[J]. 西安交通大学学报, 2024, 58(12): 34-44.
	Li Z Y, Wang J F, Lou J W, et al. Dynamic characteristic analysis of printed circuit heat exchangers in supercritical carbon dioxide Brayton cycle systems[J]. Journal of Xi'an Jiaotong University, 2024, 58(12): 34-44.
7	颜建国, 朱凤岭, 郭鹏程, 等. 高热流低流速条件下超临界CO₂在小圆管内的对流换热特性[J]. 化工学报, 2019, 70(5): 1779-1787.
	Yan J G, Zhu F L, Guo P C, et al. Convective heat transfer of supercritical CO₂ flowing a mini circular tube under high heat flux and low mass flux conditions[J]. CIESC Journal, 2019, 70(5): 1779-1787.
8	Jiang P X, Zhang Y, Zhao C R, 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.
9	Peng R F, Lei X L, Guo Z M, et al. Forced convective heat transfer of supercritical carbon dioxide in mini-channel under low mass fluxes[J]. International Journal of Heat and Mass Transfer, 2022, 182: 121919.
10	Wang L, Pan Y C, Lee J D, et al. Convective heat transfer characteristics of supercritical carbon dioxide in vertical miniature tubes of a uniform heating experimental system[J]. International Journal of Heat and Mass Transfer, 2021, 167: 120833.
11	Li Z Z, Wang S L, Shao Y J, et al. Experimental study on convective heat transfer characteristics of supercritical carbon dioxide in a vertical tube with low mass flux[J]. Applied Thermal Engineering, 2023, 230: 120798.
12	王磊, 曹雄金, 罗凯, 等. 不同流动方向上微型加热管内超临界CO₂的换热特性[J]. 化工学报, 2023, 74(11): 4535-4547.
	Wang L, Cao X J, Luo K, et al. Heat transfer characteristics of supercritical CO₂ in mini-type heating tube with the different flow directions[J]. CIESC Journal, 2023, 74(11): 4535-4547.
13	李妮, 浦航, 周林, 等. 矩形通道内超临界压力CO₂流动换热数值研究[J]. 推进技术, 2024, 45(8): 150-160.
	Li N, Pu H, Zhou L, et al. Numerical study of flow and heat transfer characteristics of supercritical pressure CO₂ in rectangular channel[J]. Journal of Propulsion Technology, 2024, 45(8): 150-160.
14	Coleman H W, Steele W G. Engineering application of experimental uncertainty analysis[J]. AIAA Journal, 1995, 33(10): 1888-1896.
15	Yi Z M, Xu Y, Chen X L. Numerical study on heat transfer characteristics of supercritical CO₂ in a vertical heating serpentine micro-tube[J]. Applied Thermal Engineering, 2022, 212: 118609.
16	Bazargan M, Fraser D, Chatoorgan V. Effect of buoyancy on heat transfer in supercritical water flow in a horizontal round tube[J]. Journal of Heat Transfer, 2005, 127(8): 897-902.
17	Petukhov B S, Polyakov A F, Kuleshov V A, et al. Turbulent flow and heat transfer in horizontal tubes with substantial influence of thermogravitational forces[C]//Proceeding of International Heat Transfer Conference 5. Tokyo, Japan: Begellhouse, 1974.
18	Jackson J D. Fluid flow and convective heat transfer to fluids at supercritical pressure[J]. Nuclear Engineering and Design, 2013, 264: 24-40.
19	Tanimizu K, Sadr R. Experimental investigation of buoyancy effects on convection heat transfer of supercritical CO₂ flow in a horizontal tube[J]. Heat and Mass Transfer, 2016, 52(4): 713-726.
20	程亮元, 王清洋, 王庆华, 等. 基于类沸腾理论的超临界CO₂水平管内强制对流换热特性[J]. 中国电机工程学报, 2023, 43(17): 6718-6727.
	Cheng L Y, Wang Q Y, Wang Q H, et al. Heat transfer characteristics of forced convection in supercritical CO₂ horizontal tube based on pseudo-boiling theory[J]. Proceedings of the CSEE, 2023, 43(17): 6718-6727.
21	McEligot D M, Coon C W, Perkins H C. Relaminarization in tubes[J]. International Journal of Heat and Mass Transfer, 1970, 13: 431-433.
22	Murphy H D, Chambers F W, Mceligot D M. Laterally converging flow(Part 1): Mean flow[J]. Journal of Fluid Mechanics, 1983, 127: 379.
23	刘光旭, 黄彦平, 王俊峰, 等. 浮升力效应和流动加速效应对超临界二氧化碳换热影响理论分析[J]. 核动力工程, 2018, 39(6): 34-38.
	Liu G X, Huang Y P, Wang J F, et al. Theoretical analysis of effect of buoyancy and flow acceleration on heat transfer of supercritical carbon dioxide[J]. Nuclear Power Engineering, 2018, 39(6): 34-38.
24	Bringer R P, Smith J M. Heat transfer in the critical region[J]. AIChE Journal, 1957, 3(1): 49-55.
25	Pioro I, Gupta S, Mokry S. Heat-transfer correlations for supercritical-water and carbon dioxide flowing upward in vertical bare tubes[C]//Proceedings of the ASME 2012 Summer: Heat Transfer Conference. Rio Grande, Puerto Rico, USA, 2012.
26	Kim D E, Kim M H. Experimental investigation of heat transfer in vertical upward and downward supercritical CO₂ flow in a circular tube[J]. International Journal of Heat and Fluid Flow, 2011, 32(1): 176-191.
27	Liao S M, Zhao T S. An experimental investigation of convection heat transfer to supercritical carbon dioxide in miniature tubes[J]. International Journal of Heat and Mass Transfer, 2002, 45(25): 5025-5034.
28	Lyu H C, Wang H, Huang Y P, et al. Visualization experiments and piston effect of heat transfer for supercritical carbon dioxide[J]. The Journal of Supercritical Fluids, 2023, 198: 105905.
29	Preda T, Saltanov E, Pioro I, et al. Development of a heat transfer correlation for supercritical CO₂ based on multiple data sets[C]//2012 20th International Conference on Nuclear Engineering and the ASME 2012 Power Conference, Anaheim, California, USA, 2013: 211-217.
30	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.

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