Numerical investigation on heat transfer of supercritical CO<sub>2</sub> in solar receiver tube in high temperature region

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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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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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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

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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

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Vol. 70, Issue 3 - 2021-02-05

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