Experimental study on convection heat transfer characteristics of supercritical carbon dioxide flowing in mini square channels

doi:10.11949/0438-1157.20241134

Abstract

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

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

CLC Number:

TK 124

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.

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.

Figures/Tables 16

Fig.1 Schematic diagram of experimental loop

Fig.2 Schematic diagram of test section

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

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

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

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

Fig.5 Heat transfer coefficients at different heat fluxes

Fig.6 Effect of pressure on heat transfer coefficients

Fig.7 Effect of mass flux on heat transfer coefficients

Fig.8 Effect of buoyancy at different mass flux

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

Fig.10 Effect of thermal acceleration at different heat flux

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]	$N u_{w} = 0.0038 R e_{w}^{0.928} {\bar{P r}}_{w}^{- 0.14} {(\frac{ρ_{w}}{ρ_{b}})}^{0.84} {(\frac{μ_{w}}{μ_{b}})}^{- 0.22} {(\frac{λ_{w}}{λ_{b}})}^{- 0.75}$	p = 8.38~8.80 MPa d = 8 mm G = 700~3200 kg/(m²·s) q = 18.40~161.12 kW/m²
[26]	$N u_{b} = 2.0514 R e_{b}^{0.928} P r_{b}^{0.742} {(\frac{ρ_{w}}{ρ_{b}})}^{1.305} {(\frac{μ_{w}}{μ_{b}})}^{- 0.669} {(\frac{c_{p, w}}{c_{p, b}})}^{- 0.888} {(q_{b}^{+})}^{0.792}$	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]	$N u_{b} = 0.124 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{ρ_{w}}{ρ_{b}})}^{1.305} {(\frac{G r}{R_{b}^{2}})}^{0.203} (\frac{{\bar{c}}_{p}}{c_{p, b}})$	p = 7.40~12.0 MPa d = 0.70~2.16 mm
[28]	$N u_{b} = 0.0858 R e_{b}^{0.846} {\bar{P r}}_{b}^{0.784} {(\frac{ρ_{w}}{ρ_{b}})}^{1.277} {(q_{b}^{+})}^{0.191}$	p = 7.40 ~ 8.44 MPa, d = 2 mm G = 600 ~ 1600 kg/(m²·s) q = 0 ~ 319 kW/m²
[29]	$N u_{w} = 0.0015 R e_{w}^{1.03} {\bar{P r}}_{w}^{0.76} {(\frac{ρ_{w}}{ρ_{b}})}^{0.46} {(\frac{μ_{w}}{μ_{b}})}^{- 0.53} {(\frac{λ_{w}}{λ_{b}})}^{- 0.43}$	p = 7.58 ~ 9.58 MPa d = 0.948 ~ 8.000 mm G = 419 ~ 1200 kg/(m²·s) q = 20 ~ 130 kW/m²

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]	$N u_{w} = 0.0038 R e_{w}^{0.928} {\bar{P r}}_{w}^{- 0.14} {(\frac{ρ_{w}}{ρ_{b}})}^{0.84} {(\frac{μ_{w}}{μ_{b}})}^{- 0.22} {(\frac{λ_{w}}{λ_{b}})}^{- 0.75}$	p = 8.38~8.80 MPa d = 8 mm G = 700~3200 kg/(m²·s) q = 18.40~161.12 kW/m²
[26]	$N u_{b} = 2.0514 R e_{b}^{0.928} P r_{b}^{0.742} {(\frac{ρ_{w}}{ρ_{b}})}^{1.305} {(\frac{μ_{w}}{μ_{b}})}^{- 0.669} {(\frac{c_{p, w}}{c_{p, b}})}^{- 0.888} {(q_{b}^{+})}^{0.792}$	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]	$N u_{b} = 0.124 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{ρ_{w}}{ρ_{b}})}^{1.305} {(\frac{G r}{R_{b}^{2}})}^{0.203} (\frac{{\bar{c}}_{p}}{c_{p, b}})$	p = 7.40~12.0 MPa d = 0.70~2.16 mm
[28]	$N u_{b} = 0.0858 R e_{b}^{0.846} {\bar{P r}}_{b}^{0.784} {(\frac{ρ_{w}}{ρ_{b}})}^{1.277} {(q_{b}^{+})}^{0.191}$	p = 7.40 ~ 8.44 MPa, d = 2 mm G = 600 ~ 1600 kg/(m²·s) q = 0 ~ 319 kW/m²
[29]	$N u_{w} = 0.0015 R e_{w}^{1.03} {\bar{P r}}_{w}^{0.76} {(\frac{ρ_{w}}{ρ_{b}})}^{0.46} {(\frac{μ_{w}}{μ_{b}})}^{- 0.53} {(\frac{λ_{w}}{λ_{b}})}^{- 0.43}$	p = 7.58 ~ 9.58 MPa d = 0.948 ~ 8.000 mm G = 419 ~ 1200 kg/(m²·s) q = 20 ~ 130 kW/m²

Fig.11 Comparison of heat transfer correlations

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

Fig.12 Prediction performance of the new correlation

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