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摘要

研究超临界CO ₂在高温吸热管内的传热特性是将其应用于聚光太阳能热发电技术中的基础. 本文对此进行了数值模拟研究, 分析了流体温度、流动方向、系统压力、质量流率和热流密度对对流传热系数和 Nu数的影响. 结果表明: 高温区 (800—1050 K) 的对流传热系数和 Nu数受流动方向和系统压力的影响均很小, 但都随着质量流率的增大以及热流密度的减小而明显增大; 而随着流体温度的升高, 对流传热系数近似线性增大, Nu数则近似线性减小. 另外, 本文研究发现在高温区可忽略浮升力对传热的影响, 而由高热流密度引起的流动加速效应会明显恶化传热. 最后, 选取了八种管内超临界流体传热关联式与模拟结果进行对比, 发现使用基于热物性修正的关联式对高温区传热数据预测的结果优于使用基于无量纲数修正的关联式得到的结果, 且其中预测效果最优的关联式得到的计算结果与模拟结果之间的平均绝对相对偏差为8.1%.

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Abstract

Supercritical CO ₂can be used as a heat transfer fluid in a solar receiver, especially for a concentrating solar thermal power tower system. Such applications require better understanding of the heat transfer characteristics of supercritical CO ₂in the solar receiver tube in a high temperature region. However, most of the existing experimental and numerical studies of the heat transfer characteristics of supercritical CO ₂in tubes near the critical temperature region, and the corresponding heat transfer characteristics in the high temperature region are conducted. In this paper, a three-dimensional steady-state numerical simulation with the standard k- εturbulent model is established by using ANSYS FLUENT for the flow and heat transfer of supercritical CO ₂in a heated circular tube with an inner diameter of 6 mm and a length of 500 mm in the high temperature region. The effects of the fluid temperature (823–1023 K), the flow direction (horizontal, downward and upward), the pressure (7.5–9 MPa), the mass flux (200–500 kg·m ^–2·s ^–1) and the heat flux (100–800 kW·m ^–2) on the convection heat transfer coefficient and Nusselt number are discussed. The results show that the convection heat transfer coefficient increases while Nusselt number decreases nearly linearly with fluid temperature increasing. Both fluid direction and pressure have negligible effects on the convection heat transfer coefficient and Nusselt number. Moreover, the convective heat transfer coefficient and Nusselt number are enhanced greatly with the increasing of mass flux and the decreasing of heat flux, which is more obvious at a higher heat flux. The influences of buoyancy and flow acceleration on the heat transfer characteristics are also investigated. The buoyancy effect can be ignored within the present parameter range. However, the flow acceleration induced by the high heat flux significantly deteriorates the heat transfer preformation. Moreover, eight heat transfer correlations of supercritical fluid in tubes are evaluated and compared with the present numerical data. The comparison indicates that the correlations based on the thermal property modification show better performance in the heat transfer prediction in the high temperature region than those based on the dimensionless number modification. And Nusselt number predicted by the best correlation has a mean absolute relative deviation of 8.1% compared with the present numerical results, with all predicted data points located in the deviation bandwidth of ±20%. The present work can provide a theoretical guidance for the optimal design and safe operation of concentrating solar receivers where supercritical CO ₂is used as a heat transfer fluid.

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通信作者:余鹏,yup6@sustech.edu.cn

基金项目:国家自然科学基金 (批准号: 51706048) 和中国科学院低温工程学重点实验室 (理化技术研究所) (批准号: CRYO202002) 资助的课题

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Corresponding author:Yu Peng,yup6@sustech.edu.cn

Funds:Project supported by the National Natural Science Foundation of China (Grant No. 51706048) and CAS Key Laboratory of Cryogenics, Technical Institute of Physics and Chemistry (Grant No. CRYO202002)

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参考文献

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施引文献

下载: 全尺寸图片幻灯片

算例	网格数量	T_w,o/K	T_w,o的相对偏差/%	h_o/(kW·m^–2·K^–1)	h_o的相对偏差/%
1	2652250	1441.9	0	1236.7	0
2	1332250	1442.2	0.02	1236.4	0.02
3	841000	1442.9	0.07	1235.0	0.14
4	462250	1445.1	0.22	1230.1	0.54
5	196000	1448.8	0.48	1223.3	1.09

下载: 导出CSV

作者	关联式和工况条件	MARD/%	η/%
基于热物性修正
Bishop 等^[23]	$Nu = 0.0069Re_{\rm{b} }^{0.9}\overline {Pr} _{\rm{b} }^{0.66}{\left( { { { {\rho _{\rm{w} } } } }/{ { {\rho _{\rm{b} } } } } } \right)^{0.43} }\left[ {1 + 2.4({D}/{L}) } \right]$	22.2	22.3
	工质: 水
	p= 22.6—27.5 MPa,G= 680—3600 kg·m^–2·s^–1,q= 310—3500 kW·m^–2
Krasnoshchekov和 Protopopov^[24]	$Nu = 0.023Re_{\rm{b} }^{0.8}Pr_{\rm{b} }^{0.5}{\left( {{ { {\rho _{\rm{w} } } } }/{ { {\rho _{\rm{b} } } } } } \right)^{0.3} }{\left( {{ {\overline { {c_{\rm{p} } } } } }/{ { {c_{ {\rm{p,b} } } } } } } \right)^{0.4} }$	8.1	100
	工质: CO₂
	p= 8—12 MPa,G= 2971 kg·m^–2·s^–1,q= 235—500 kW·m^–2,T_in= 301.7—472 K
	流动方向: 水平
Jackson^[25]	$Nu = 0.023Re_{\rm{b} }^{0.8}\overline {Pr} _{\rm{b} }^{0.5}{\left( { { { {\rho _{\rm{w} } } } }/{ { {\rho _{\rm{b} } } } } } \right)^{0.3} }$	9.0	100
	工质: CO₂
	p= 7.8—9.8 MPa,Re_b=8×10⁴—5×10⁵,q≤ 2600 kW·m^–2
基于无量纲数修正
Liao和Zhao^[26]	垂直向上:	18.1	60.7
	$Nu = 0.354Re_{\rm{b} }^{0.8}Pr_{\rm{b} }^{0.4}{\left( {{ { {\rho _{\rm{w} } } } }/{ { {\rho _{\rm{b} } } } } } \right)^{1.297} }{\left( {{ {\overline { {c_{\rm{p} } } } } }/{ { {c_{ {\rm{p,b} } } } } } } \right)^{0.296} }Bo_{\rm{m} }^{ {\rm{0} }{\rm{.157} } }$
	垂直向下:
	$Nu = 0.643Re_{\rm{b} }^{0.8}Pr_{\rm{b} }^{0.4}{\left( { { { {\rho _{\rm{w} } } } }/{ { {\rho _{\rm{b} } } } } } \right)^{2.154} }{\left( { { {\overline { {c_{\rm{p} } } } } }/{ { {c_{ {\rm{p,b} } } } } } } \right)^{0.751} }Bo_{\rm{m} }^{ {\rm{0} }{\rm{.186} } }$
	水平:
	$Nu = 0.124Re_{\rm{b} }^{0.8}Pr_{\rm{b} }^{0.4}{\left( {{ { {\rho _{\rm{w} } } } }/{ { {\rho _{\rm{b} } } } } } \right)^{0.842} }{\left( {{ {\overline { {c_{\rm{p} } } } } }/{ { {c_{ {\rm{p,b} } } } } } } \right)^{0.384} }Bo_{\rm{b} }^{ {\rm{0} }{\rm{.203} } },~ Bo = { {Gr} }/{ {Re_{\rm{b} }^{2.7} } }$
	工质: CO₂
	p= 7.4—12 MPa,G= 236—1179 kg·m^–2·s^–1,q= 10—200 kW·m^–2,T_in= 295—385 K
Kim 等^[10]	$Nu = 0.226Re_{\rm{b}}^{1.174}Pr_{\rm{b}}^{1.057}{\left( {{{{\rho _{\rm{w}}}}}/{{{\rho _{\rm{b}}}}}} \right)^{0.571}}{\left( {{{\overline {{c_{\rm{p}}}} }}/{{{c_{{\rm{p,b}}}}}}} \right)^{1.032}}A{c^{0.489}}B{u^{0.0021}}$	42.3	11.0
	$Ac = \dfrac{ { {q^ + } } }{ {Re_{\rm b}^{0.625} } }{\left( {\dfrac{ { {\rho _{\rm{b} } } }}{ { {\rho _{\rm{w} } } } } } \right)^{0.5} }\left( {\dfrac{ { {\mu _{\rm{w} } } }}{ { {\mu _{\rm{b} } } } } } \right), ~Bu = \dfrac{ {G{r_{\rm{q} } } }}{ {Re_{\rm{b} }^{3.425}Pr_{}^{0.8} } }{\left( {\dfrac{ { {\rho _{\rm{b} } } }}{ { {\rho _{\rm{w} } } } } } \right)^{0.5} }\left( {\dfrac{ { {\mu _{\rm{w} } } }}{ { {\mu _{\rm{b} } } } } } \right)$
	工质: CO₂
	p= 7.46—10.29 MPa,G= 208—874 kg·m^–2·s^–1,q= 38—234 kW·m^–2,T_in= 302—388 K
	流动方向: 垂直向上
Bovard 等^[11]	$Nu = 0.040063Re_{\rm{b}}^{1.40418}Pr_{\rm{b}}^{0.97767359}{\left( {\dfrac{{{\rho _{\rm{w}}}}}{{{\rho _{\rm{b}}}}}} \right)^{0.573108}}{\left( {\dfrac{{\overline {{c_{\rm{p}}}} }}{{{c_{{\rm{p,b}}}}}}} \right)^{0.11577}}A{c^{0.396203}}B{u^{0.13746}}$	82.8	0
	$Ac = \dfrac{{{q^ + }}}{{Re_b^{0.625}}}{\left( {\dfrac{{{\rho _{\rm{b}}}}}{{{\rho _{\rm{w}}}}}} \right)^{0.5}}\left( {\dfrac{{{\mu _{\rm{w}}}}}{{{\mu _{\rm{b}}}}}} \right),~ Bu = \dfrac{{G{r_{\rm{m}}}}}{{Re_{\rm{b}}^{3.425}Pr_{}^{0.8}}}{\left( {\dfrac{{{\rho _{\rm{b}}}}}{{{\rho _{\rm{w}}}}}} \right)^{0.5}}\left( {\dfrac{{{\mu _{\rm{w}}}}}{{{\mu _{\rm{b}}}}}} \right)$
	工质: CO₂
	p= 6.5—8.335 MPa,G= 51—236 kg·m^–2·s^–1,q= 52—85 kW·m^–2,T_in= 302 K
	流动方向: 垂直向上
Liu 等^[17]	$Nu = 0.00075Re_{\rm{b}}^{0.93}\overline {Pr} _{\rm{b}}^{0.68}{\left( {\dfrac{{{\rho _{\rm{w}}}}}{{{\rho _{\rm{b}}}}}} \right)^{0.42}}\exp \left( {B{u^{ - 0.023}}} \right)\exp \left( {A{c^{0.079}}} \right)\left[ {1 + 2.63/\left( {L/D} \right)} \right]$	28.7	3.5
	$Bu = \dfrac{{G{r_{\rm{m}}}}}{{Re_{\rm{b}}^{2.625}Pr_{\rm{w}}^{0.4}}}{\left( {\dfrac{{{\rho _{\rm{b}}}}}{{{\rho _{\rm{w}}}}}} \right)^{0.5}}\left( {\dfrac{{{\mu _{\rm{w}}}}}{{{\mu _{\rm{b}}}}}} \right),~ Ac = \dfrac{{4{q^ + }}}{{Re_b^{0.625}}}{\left( {\dfrac{{{\rho _{\rm{b}}}}}{{{\rho _{\rm{w}}}}}} \right)^{0.5}}\left( {\dfrac{{{\mu _{\rm{w}}}}}{{{\mu _{\rm{b}}}}}} \right)$
	工质: CO₂
	p= 7.4—10.6 MPa,G= 298.8—1506.5 kg·m^–2·s^–1,q= 4.7—296 kW·m^–2,T_in= 257—322 K
	流动方向: 垂直向上
Zhang等^[19]	$Nu = \left\{ \begin{gathered} 0.00672Re_{\rm{b} }^{1.414}\overline {Pr} _{\rm{b} }^{ - 0.005}{\left( {\dfrac{ { {\rho _{\rm{w} } } } }{ { {\rho _{\rm{b} } } } } } \right)^{0.448} }{\left( {\dfrac{ {\overline { {c_{\rm{p} } } } } }{ { {c_{ {\rm{p,b} } } } } } } \right)^{0.218} }Bo_{\rm{m} }^{ {\rm{0} }{\rm{.586} } },\quad {H_{\rm{b} } } < 0.9{H_{ {\rm{pc} } } } \\ 0.056Re_{\rm{b} }^{0.829}\overline {Pr} _{\rm{b} }^{0.35}{\left( {\dfrac{ { {\rho _{\rm{w} } } } }{ { {\rho _{\rm{b} } } } } } \right)^{ - 0.095} }{\left( {\dfrac{ {\overline { {c_{\rm{p} } } } } }{ { {c_{ {\rm{p,b} } } } } } } \right)^{0.214} }Bo_{\rm{m} }^{ {\rm{0} }{\rm{.142} } }, \quad {H_{\rm{b} } } \geqslant 0.9{H_{ {\rm{pc} } } } \\\end{gathered} \right.$	64.9	0
	工质: CO₂
	p= 7.5—10.5 MPa,G= 50—500 kg·m^–2·s^–1,q= 5—100 kW·m^–2,T_in= 266—313 K
	流动方向: 垂直向上

下载: 导出CSV

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