Heat transfer characteristics of supercritical CO2 in mini-type heating tube with the different flow directions

doi:10.11949/0438-1157.20230910

Abstract

Abstract:

This article focuses on the experimental study of convection heat transfer of supercritical carbon dioxide in mini-type heating tube with inner diameter of 0.75 mm under the different flow directions. The experimental results show that the local convection heat transfer coefficient has the same trends between horizontal flow and vertical upward flow when the system pressure, mass flow rate, heating power and inlet temperature remain constant, and the local convection heat transfer coefficient in horizontal flow is always higher than the local convection heat transfer coefficient in vertical upward flow. However, in vertical downward flow, the local convection heat transfer coefficient increases significantly with the increase of dimensionless temperature, and presents the best heat transfer effect at the maximum dimensionless temperature. Under the different flow directions, the local convection heat transfer coefficient increases significantly with the increase of mass flow rate, but decreases significantly with the increase of heating power and inlet temperature. However, in horizontal flow and vertical upward flow, when the fluid temperature is less than its pseudo-critical temperature, the local convection heat transfer coefficient decreases significantly with the increase of system pressure. The local convection heat transfer coefficient increases with the increase of system pressure when the fluid temperature is greater than its pseudo-critical temperature. When the fluid temperature is greater than its pseudo-critical temperature, the local convective heat transfer coefficient gradually increases with the increase of system pressure.

Key words: supercritical CO₂, different flow direction, mini-type heating tube, convection heat transfer

摘要：

针对不同流动方向上超临界CO₂流体在微型加热管（管径为0.75 mm）内的对流换热特性进行实验研究。实验结果表明，当系统压力、质量流量、加热功率以及进口温度保持恒定时，局部对流传热系数在水平流动方向和垂直向上流动方向上的变化趋势相同，并且水平流动方向上的局部对流传热系数始终大于垂直向上流动方向上的局部对流传热系数。但在垂直向下流动方向上，局部对流传热系数随无量纲温度的升高而显著增大，并在无量纲温度最大时呈现出最佳的换热效果。不同流动方向上，局部对流传热系数均随质量流量增大而显著增大，但随着加热功率、进口温度的升高而显著减小。然而，在水平流动方向和垂直向上流动方向上，当流体温度低于其假临界温度时，局部对流传热系数随系统压力的升高而显著减小。当流体温度高于其假临界温度时，局部对流传热系数则随系统压力的升高而逐渐增大。

关键词: 超临界CO₂, 不同流动方向, 微型加热管, 对流换热

CLC Number:

O 359

Lei WANG, Xiongjin CAO, Kai LUO, Yan WANG, Hua FEI. Heat transfer characteristics of supercritical CO₂ in mini-type heating tube with the different flow directions[J]. CIESC Journal, 2023, 74(11): 4535-4547.

王磊, 曹雄金, 罗凯, 王艳, 费华. 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.

Figures/Tables 17

Fig.1 Schematic diagram of experimental apparatus

Fig.2 Schematic diagram of test section

Table 1 Uncertainties analysis of experimental parameters

流动方向	P	T_w	m	q	i_f_,_z	h
水平	0.5%	0.4%~0.8%	1.7%~2.8%	6.9%~7.2%	0.1%~3.4%	7.0%~8.2%
垂直向上	0.5%	0.4%~0.7%	1.7%~2.8%	6.9%~7.2%	0.1%~3.4%	7.0%~7.9%
垂直向下	0.5%	0.4%~0.7%	1.7%~2.8%	6.9%~7.2%	0.1%~3.3%	7.0%~8.4%

Fig.3 The comparisons between the experimental results of measure temperature and theoretical values of measure temperatures in different flow directions

Fig.4 The local convective heat transfer coefficient under different system pressure and different flow direction conditions

Fig.5 Thermal properties of supercritical CO2

Fig.6 The relative percentage of local convective heat transfer coefficient under different system pressure and different flow direction conditions

Fig.7 The local convective heat transfer coefficient under different mass flow rate and different flow direction conditions

Fig.8 The relative percentage of local convective heat transfer coefficient under different mass flow rate and different flow direction conditions

Fig.9 The local convective heat transfer coefficient under different heating power and different flow direction conditions

Fig.10 The relative percentage of local convective heat transfer coefficient under different heating power and different flow direction conditions

Fig.11 The local convective heat transfer coefficient under different inlet temperature and different flow direction conditions

Fig.12 The relative percentage of local convective heat transfer coefficient under different inlet temperature and different flow direction conditions

Table 2 Heat transfer correlations for supercritical carbon dioxide under different experimental conditions

文献	Nusselt关联式	实验条件
[19]	$\begin{array}{l} N u_{b} = 0.124 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{G r}{R e_{b}^{2}})}^{0.203} {(\frac{ρ_{w}}{ρ_{b}})}^{0.842} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{0.384} \\ G r = \frac{(ρ_{b} - ρ_{w}) g ρ_{b} D^{3}}{μ_{b}^{2}}, {\bar{c}}_{p} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}} \end{array}$	压力：74~120 bar 管径：0.7~2.16 mm 水平流动方向
[19]	$\begin{array}{l} N u_{b} = 0.354 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{G r_{m}}{R e_{b}^{2.7}})}^{0.157} {(\frac{ρ_{w}}{ρ_{b}})}^{1.297} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{0.296} \\ G r_{m} = \frac{(ρ_{b} - {\bar{ρ}}_{z}) g ρ_{b} D^{3}}{μ_{b}^{2}}, {\bar{ρ}}_{z} = \frac{1}{T_{w, z} - T_{f, z}} \int_{T_{f, z}}^{T_{w, z}} ρ d T \end{array}$	压力：74~120 bar 管径：0.7~2.16 mm 垂直向上流动方向
[19]	$\begin{array}{l} N u_{b} = 0.643 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{G r_{m}}{R e_{b}^{2.7}})}^{0.186} {(\frac{ρ_{w}}{ρ_{b}})}^{2.154} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{0.751} \\ G r_{m} = \frac{(ρ_{b} - {\bar{ρ}}_{z}) g ρ_{b} D^{3}}{μ_{b}^{2}}, {\bar{ρ}}_{z} = \frac{1}{T_{w, z} - T_{f, z}} \int_{T_{f, z}}^{T_{w, z}} ρ d T \end{array}$	压力：74~120 bar 管径：0.7~2.16 mm 垂直向下流动方向
[34]	$\begin{array}{l} N u = 0.226 R e_{b}^{1.174} P r_{b}^{1.057} {(\frac{ρ_{w}}{ρ_{b}})}^{0.571} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{1.032} A c^{0.489} B u^{0.0021} \\ A c = \frac{β_{b} q_{w}^{″} D}{R e_{b}^{1.625} c_{p, b} μ_{b}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{b}}{ρ_{w}})}^{0.5} \\ B u = \frac{G r_{q}}{R e_{b}^{3.425} P r_{b}^{0.8}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{b}}{ρ_{w}})}^{0.5} \\ G r_{q} = \frac{g β_{b} ρ_{b}^{2} D^{4} q_{w}^{″}}{k_{b} μ_{b}^{2}} \\ β_{b} = - \frac{1}{ρ_{b}} (\frac{ρ_{b} - \bar{ρ}}{T_{b} - T_{w}}) \\ {\bar{ρ}}_{z} = \frac{1}{T_{w, z} - T_{f, z}} \int_{T_{f, z}}^{T_{w, z}} ρ d T \end{array}$	压力：74.6~102.6 bar 管径：4.5 mm 垂直流动方向

Table 2 Heat transfer correlations for supercritical carbon dioxide under different experimental conditions

文献	Nusselt关联式	实验条件
[19]	$\begin{array}{l} N u_{b} = 0.124 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{G r}{R e_{b}^{2}})}^{0.203} {(\frac{ρ_{w}}{ρ_{b}})}^{0.842} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{0.384} \\ G r = \frac{(ρ_{b} - ρ_{w}) g ρ_{b} D^{3}}{μ_{b}^{2}}, {\bar{c}}_{p} = \frac{i_{w} - i_{b}}{T_{w} - T_{b}} \end{array}$	压力：74~120 bar 管径：0.7~2.16 mm 水平流动方向
[19]	$\begin{array}{l} N u_{b} = 0.354 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{G r_{m}}{R e_{b}^{2.7}})}^{0.157} {(\frac{ρ_{w}}{ρ_{b}})}^{1.297} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{0.296} \\ G r_{m} = \frac{(ρ_{b} - {\bar{ρ}}_{z}) g ρ_{b} D^{3}}{μ_{b}^{2}}, {\bar{ρ}}_{z} = \frac{1}{T_{w, z} - T_{f, z}} \int_{T_{f, z}}^{T_{w, z}} ρ d T \end{array}$	压力：74~120 bar 管径：0.7~2.16 mm 垂直向上流动方向
[19]	$\begin{array}{l} N u_{b} = 0.643 R e_{b}^{0.8} P r_{b}^{0.4} {(\frac{G r_{m}}{R e_{b}^{2.7}})}^{0.186} {(\frac{ρ_{w}}{ρ_{b}})}^{2.154} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{0.751} \\ G r_{m} = \frac{(ρ_{b} - {\bar{ρ}}_{z}) g ρ_{b} D^{3}}{μ_{b}^{2}}, {\bar{ρ}}_{z} = \frac{1}{T_{w, z} - T_{f, z}} \int_{T_{f, z}}^{T_{w, z}} ρ d T \end{array}$	压力：74~120 bar 管径：0.7~2.16 mm 垂直向下流动方向
[34]	$\begin{array}{l} N u = 0.226 R e_{b}^{1.174} P r_{b}^{1.057} {(\frac{ρ_{w}}{ρ_{b}})}^{0.571} {(\frac{{\bar{c}}_{p}}{c_{p, b}})}^{1.032} A c^{0.489} B u^{0.0021} \\ A c = \frac{β_{b} q_{w}^{″} D}{R e_{b}^{1.625} c_{p, b} μ_{b}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{b}}{ρ_{w}})}^{0.5} \\ B u = \frac{G r_{q}}{R e_{b}^{3.425} P r_{b}^{0.8}} (\frac{μ_{w}}{μ_{b}}) {(\frac{ρ_{b}}{ρ_{w}})}^{0.5} \\ G r_{q} = \frac{g β_{b} ρ_{b}^{2} D^{4} q_{w}^{″}}{k_{b} μ_{b}^{2}} \\ β_{b} = - \frac{1}{ρ_{b}} (\frac{ρ_{b} - \bar{ρ}}{T_{b} - T_{w}}) \\ {\bar{ρ}}_{z} = \frac{1}{T_{w, z} - T_{f, z}} \int_{T_{f, z}}^{T_{w, z}} ρ d T \end{array}$	压力：74.6~102.6 bar 管径：4.5 mm 垂直流动方向

Fig.13 The comparisons between the experimental results of Nusselt number and predicted values of Nusselt number in horizontal flow direction

Fig.14 The comparisons between the experimental results of Nusselt number and predicted values of Nusselt number in vertical upward flow direction

Fig.15 The comparisons between the experimental results of Nusselt number and predicted values of Nusselt number in vertical downward flow direction

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Heat transfer characteristics of supercritical CO₂ in mini-type heating tube with the different flow directions

不同流动方向上微型加热管内超临界CO₂的换热特性

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