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Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides
Annals of Nuclear Energy xxx (xxxx) xxx
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Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides Mingrui Li, Wenzhen Chen ⇑, Jianli Hao, Xi Chu College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
a r t i c l e
i n f o
Article history: Received 1 April 2019 Received in revised form 19 August 2019 Accepted 15 September 2019 Available online xxxx Keywords: U-tube Reverse flow Preheating section Single channel
a b s t r a c t Under natural circulation conditions, the reverse flow phenomenon may occur within some U-tubes. This will result in the flow resistance coefficient of the steam generator (SG) obviously larger than that under forced circulation conditions, and the decrease of nature circulation capability in the primary circuit (PC). The heat transfer characteristics between the secondary circuit (SC) and PC in the SG are very complicated. Expressly, there is an obvious preheating section due to a certain fluid under-heat degree at the inlet of the ascending passage in the SC. In this paper, a type of marine SG is studied and a theoretical model of the SC single channel is established for the preheating sections (PS) corresponding to the ascending section (AS) and the descending section (DS) of U-tubes. Based on this model, the reverse flow characteristics of U-tubes are researched, and the influence of SC operating pressure, U-tubes pitch and circulation ratio on the U-tube reverse flow characteristics are calculated and analyzed. The results show that compared with the existing reverse flow calculation methods, the temperature distribution in the PS of SC increases exponentially and remains unchanged in the boiling section, and the critical flow rate is relatively higher. The increase of SC operating pressure and U-tubes pitch will decrease the mass flow rate of reverse flow, and the influence of circulation ratio has the opposite conclusion. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The natural circulation is an important indicator of the inherent safety of the reactor, which can derive the core decay heat without the external driving force and effectively reduce the inhomogeneity of the flow distribution in core. Related natural circulation studies have shown that with the reverse flow phenomenon occurred in the some inverted U-tubes of the steam generator (SG), the lower temperature coolant in the primary circuit (PC) will inversely flow from the outlet cavity to the inlet cavity (Hao et al., 2014a; Loomis and Soda, 1982). Under natural circulation conditions, the emergence of reverse flow can reduce the effective heat transfer area of the SG, and the reverse flow fluid is mixed and dissipated with the thermal fluid in the inlet cavity. Therefore, the flow resistance coefficient in the SG under the natural circulation conditions is greater than that under forced circulation conditions, which results in the decrease of the system natural circulation flow mass. Most of the existing researches on the U-tube reverse flow in the SG aimed to analyze the influence of PC conditions (Kukita ⇑ Corresponding author at: Faculty 304, College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China. E-mail address: [email protected] (W. Chen).
et al., 1988; Sanders, 1988). Jeong et al. (2004) established a mathematical model to analyze the single phase and two phase natural circulations in the vertical inverted U-tubes. The research showed that there was a negative slope region in the curve of U-tube’s pressure drop with mass flow, and the flow drift may occurred in the U-tube when the low mass flow is inside the region. Yang et al (2010) analyzed the flow and heat transfer characteristics of single-phase water in the parallel U-tubes of SG by establishing mathematical models and corresponding numerical calculation methods, and the calculated results were in good agreement with the experimental results. Based on the one-dimensional heat transfer model established by Sanders (1988), Watanabe et al. (2014) concluded that the reverse flow occurred more easily in the long tube than in the short tube by coupling the CFD software and system program. Hao and Chen (2014a,b) obtained the universal reverse flow judgment criterion and comprehensively analyzed the development mechanism of reverse flow through the combination of theoretical derivation, numerical simulation and proportional modeling experiment for the reverse flow in the SG U-tubes under natural circulation conditions. Hu et al. (2016) proposed to employ the critical curve to judge and evaluate the occurrence of reverse flow phenomenon, and obtained the reverse flow critical curve by the experimental research. Chu et al. (2018) used RELAP5/MOD 3.3 program to study the influence factors of the
https://doi.org/10.1016/j.anucene.2019.107064 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
2
M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
two-phase reverse flow in U-tubes under low steam quality conditions. The existing researches on the U-tube reverse flow phenomenon in the SG are under the assumptions that the secondary working conditions remained unchanged. But in the actual operation, the secondary working conditions have an important effect on the development of U-tube reverse flow in the SG. The research showed that the heat transfer characteristics in the U-tubes and the secondary circuit (SC) were very complicated (Ding and Ba, 1982). The fluid in SC had a certain subcooling at the inlet of the ascending passage, which results in an obvious preheating process. The heat transfer characteristics of vapor-liquid two-phase flow in the secondary circuit of SG have been extensively studied. Cong et al. (2014) established the threedimensional physical models for the SG to calculate the two-phase flow and steady thermohydraulics characteristics in the SC based on CFX software. Sun et al. (2015) established a simplified physical model for an actual SG, and simulated the coupled system of fluid and heat transfer characteristics in the PC and SC by CFD software. The calculated results were consistent with that by the measurement and published literature. Razmara et al. (2016) introduced an optimal control method for the transient and steady state operations of internal combustion engines based on exergy, and the calculated results show that the new optimal method can save 6.7% fuel compared with the first law of thermodynamics method. Aiming at the limitations of the existing heat transfer methods, the nanofluid (Hajmohammadi, 2017) and multi-scale annular fins (Hajmohammadi, 2018) were employed to enhance the thermal performance of the assembly. These works were useful in the design of variant cooling devices in the practical engineering applications. Hajmohammadi and Rezaei (2019a) presented a new fast algorithm based on the recursive localization for the optimization to maximize the thermal performance, and it is promising and efficient. Summarizing the literature, it could be found that the characteristics and influence factors of reverse flow in the SG have been well studied. But these researchers simply considered the fluid operating conditions of PC, and assumed that the temperature of U-tube outer wall was always equal to the saturation temperature of SC. Obviously, it was inconsistent with the actual operation conditions of SGs, and the calculation result would not be accurate. In this paper, a single-channel model is established to study the thermo-hydraulic characteristics and the phenomenon of U-tube reverse flow by coupling the PC and SC in the SG. The research conclusion has important guiding significance for the actual SG to slow down the occurrence of the reverse flow under the natural circulation conditions. It also provide a theoretical basis for improving the natural circulation capacity of the marine nuclear power plant system.
2. Theoretical models 2.1. Physical model Fig. 1 shows a simplified single-channel physical model coupling the primary and secondary sides in the natural circulation SG, which consists of four adjacent U-shaped heat transfer tubes, the tube wall and secondary fluid domain. The length of U-tube is 4.0–5.0 m, and the height of straight tube is 2.0 m. The thermal single-phase fluid of PC flows into the inlet of U-tubes, then through the U-tubes by exchanging heat with the cold fluid of SC, finally the cooled PC fluid flows out from the outlet of U-tubes. The cold fluid of SC will be heated to a saturation temperature and changed to the steam. The flow heat transfer process between the PC and SC is divided into the preheating section (PS)
Single-channel Primary flow direction U-tubes
Secondary flow direction
Secondary Wall Secondary inlet Steam Generator Primary inlet Primary outlet
Fig. 1. Single-channel model of PC and SC.
and boiling section along the normal flow direction of U-tube (NFDU). According to the SG-operation conditions, it is assumed that (1) the homogenous flow model is accepted to the SC fluid, so the velocity and temperature of vapor phase are equal to those of liquid phase; (2) the parameter variations of the PC, SC and tube wall are considered only along the axial direction; (3) the inlet mass flow is equivalent to the average mass flow (Hajmohammadi et al., 2019b). 2.2. Heat transfer coefficient equations The convection heat transfer in the U-tube is calculated using the Dittus-Boelter formula as follows (Chen et al., 2013):
h1 ¼ 0:023
k1 0:8 0:3 Re Pr d1
ð1Þ
where k1 is the fluid thermal conductivity in the tube, W/(m.°C); Re is the Reynolds number; Pr is the Prandtl number. Considering the horizontal and longitudinal flow of SC fluid in the PS through the outer wall of U-tubes, the effective surface heat transfer coefficient is given as follows (Chen et al., 2013):
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðC H ReAH Pr BH k2 =De Þ þ ðC L ReAL Pr BL k2 =De Þ h2 ¼ 2
ð2Þ
where k2 is the thermal conductivity of the SC fluid, W/(m.°C); De is the equivalent diameter of the SC flow channel, m; P is the U-tubes pitch, m; d2 is the outer diameter of U-tubes, m; A, B, C are the coefficients shown in Table 1. The heat transfer in the SC boiling section is more complicated. For the large-volume nucleate boiling on the clean heat transfer surface, the Rohsenow formula is mostly used for the heat transfer calculation, and the relationship equation is as follows (Rohsenow et al., 1985; Incropera and DeWitt, 2002): 0
h ¼
cpl rPr l C w
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi0:33
ll r g ql qg =r
Q ðsÞ0:67
ð3Þ
The heat flux density in the boiling section can be expressed as: 0
Q ðsÞ ¼ h ðT w T 2out Þ
ð4Þ
Substituting equation (4) into equation (3), the heat transfer coefficient in the boiling section is given by:
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx Table 1 The value of coefficients. Direction Arrangement
Horizontal
Triangle
0
h ¼
cpl rPrl C w
Longitudinal
A
B
C
A
B
C
0.563
0.333
0.547
0.8
0.4
0.26P/d2-0.006
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
3
ll r g ql qg =r ðT w T 2out Þ2
ð5Þ
where Cw is the empirical coefficient of the heating surface, which can be 0.013 for the outer surface of the heat transfer tube; cpl is the specific heat capacity of the saturated liquid, J/(kg ); r is the latent heat of vaporization, J/kg; g is the gravity acceleration, m/ s2;Q2(s) is the heat flux density, W/m2; ll is the dynamic viscosity of the saturated liquid, kg/(ms); ql and qg are the density corresponding to the saturated liquid and vapor, kg/m3; r is the surface tension of liquid-vapor interface, N/m; Tw is the temperature of Utube outer wall, °C; T2out is the fluid saturation temperature in the SC, °C. The experimental study shows that the heat transfer coefficient calculated by Eq. (5) is 30% higher than the experimental value. Therefore, we take a coefficient to corrected the result by Eq. (5), and the value is 0.7 in this paper (Ding and Ba, 1982). 2.3. Heat transfer equations in the PC and SC The energy conservation equation of fluid in the U-tube is:
_ 1 cp1 m
@T 1 ¼ qðsÞ @s
ð6Þ
_ 1 is the mass flow rate in U-tube, kg/s; q is the linear heat where: m flux density, W/m; s is the coordinate in the normal flow direction along the U-tube, m; the subscripts 1 and 2 mean the parameters in the PC and SC, respectively. According to the heat transfer analysis in a single U-tube, we can obtain:
T 1 ðsÞ ¼ T 2 ðsÞ þ
hsp ¼
qðsÞ pd1 hsp
1 1 h1
þ 2kd1w ln dd21 þ hd2 1d2
ð8Þ
T 1 ð0Þ ¼ T 1in T 2 ð0Þ ¼ T 2in ;
ð10Þ
T 2 xup ¼ T 2 ðxdown Þ ¼ T 2out
T 2 ðsÞ ¼ T 2in
ð11Þ
where Tin and Tout are the temperature of inlet and outlet, respectively, °C; the subscripts up and down mean the AS and DS, respectively. Based on the energy conservation equation, we have:
ð12Þ
_ 1 cp1 m ðT ðsÞ T 1in Þ _ 2 cp2 1 m
ð13Þ
According to the countercurrent heat transfer characteristics, when L-xdown s L, the SC fluid temperature in the PS can be obtained from Eq. (9) as follows:
T 2 ðsÞ ¼ T 2out þ
_ 1 cp1 m ðT ðsÞ T 1 ðL xdown ÞÞ _ 2 cp2 1 m
ð14Þ
Combining Eqs. (6), (7) and (13), results in the differential expressions of the fluid temperature in the U-tube as follows:
@T 1 ðsÞ pd1 hsp pd1 hsp pd1 hsp T 1 ð sÞ þ þ T ¼ _ 1 cp1 _ 2 cp2 _ 2 cp2 1in @s m m m pd1 hsp þ T 0 s < xup _ 1 cp1 2in m @T 1 ðsÞ pd1 hsp pd1 hsp ¼ T ðsÞ þ T _ 1 cp1 1 _ 1 cp1 2out @s m m @T 1 ðsÞ ¼ @s
pd1 hsp _ 2 cp2 m
þ
pd1 hsp _ 1 cp1 m
ð15Þ
xup s < L xdown
ð16Þ
pd1 hsp T 1 ðsÞ T ðL xdown Þ _ 1 cp1 _ 2 cp2 1 m m
pd1 hsp
T 2out
ðL xdown s < LÞ
ð17Þ
Integrating Eqs. (15)–(17) along the NFDU, the fluid temperature can be calculated by:
_ 2 cp2 T 2in _ 2 cp2 T 1in m m T 1 ð sÞ ¼ e _ 2 cp2 _ 1 cp1 þ m m _ 2 cp2 T 2in _ 1 cp1 T 1in þ m m þ _ 2 cp2 _ 1 cp1 þ m m
pd1 hsp pd1 hsp _ c þm _ c m 1 p1
_ 2 cp2 T 2in _ 2 cp2 T 1in m m _ 1 cp1 þm _ 2 cp2 m pd1 hsp
e m_ 1 cp1
ðxup sÞ
e
pd1 hsp pd1 hsp _ c þm _ c m 1 p1
þ T 2out
2 p2
s
0 s < xup
T 1 ðsÞ ¼
ð9Þ
It is assumed that xup and xdown denote the PS heights corresponding to the ascending section (AS) and descending section (DS) of the PC, respectively, then there are the boundary conditions as follows:
_ 2 cp2 m ðT T 2in Þ _ 1 cp1 2out m
where L is the total length of the U-tube, m. When 0 s < xup, the SC fluid temperature in the PS can be obtained from Eq. (9) as follows:
ð7Þ
where hsp is the overall heat transfer coefficient between the primary and secondary sides, W/(m2.K); kw is the U-tube wall thermal conductivity, W/(m.K); d1 and d2 are the inner and outer diameter of the U-tube, respectively, m. Based on the thermodynamic equilibrium theory, the heat transfer equation between the primary and secondary sides can be obtained as follows:
_ 2 cp2 DT 2 _ 1 cp1 DT 1 ¼ m m
T 1 ðL xdown Þ ¼ T 1out þ
2 p2
ð18Þ
xup
! þ
_ 2 cp2 T 2in _ 1 cp1 T 1in þm m _ 1 cp1 þm _ 2 cp2 m
T 2out
xup s < L xdown ð19Þ
_ 2 cp2 T 1 ðL xdown Þ pm_d1chsp pm_d1chsp ðLxdown sÞ _ 2 cp2 T 2out m m 1 p1 2 p2 e T 1 ð sÞ ¼ _ 2 cp2 _ 1 cp1 m m þ
_ 2 cp2 T 2out _ 1 cp1 T 1 ðL xdown Þ m m _ 2 cp2 _ 1 cp1 m m
ðL xdown s < LÞ ð20Þ
From Eqs. (18), (19) and (20), the change of fluid temperature in the U-tube can be written as follows:
T 1 ðsÞ ¼ DTens þ T 0
ð21Þ
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
Combining Eqs. (13) and (18), the SC fluid temperature can be evaluated by:
_ 1 cp1 ðT 1in T 2in Þ m T 2 ðsÞ ¼ T 2in þ 1e _ 2 cp2 _ 1 cp1 þ m m
pd1 hsp pd1 hsp _ c þm _ c m 1 p1
2 p2
! s
0 s < xup
L 2
ð22Þ When xup s < L-xdown, the SC fluid reaches the saturation temperature. Combining Eqs. (14) and (20), we can obtain:
_ 1 cp1 T 1 ðL xdown Þ pm_d1chsp pm_d1chsp ðLxdown sÞ _ 1 cp1 T 2out m m 1 p1 2 p2 T 2 ðsÞ ¼ e _ 2 cp2 _ 1 cp1 m m þ
_ 2 cp2 T 2out _ 1 cp1 T 1 ðL xdown Þ m m _ _ m1 cp1 m2 cp2
ðL xdown s LÞ
According to Eqs. (22) and (23), when s = xup and s = L, the heights of the PS corresponding to the AS and DS of U-tube can be obtained as follows, respectively:
_ 2 cp2 ðT 2out T 2in Þ _ 1 cp1 ðT 1in T 2out Þ m m ln ¼ pd1 hsp pd h _ 1 cp1 ðT 1in T 2in Þ m þ 1 sp 1
_ 1 cp1 m
_ 2 cp2 m
ð24Þ xdown
_ 2 cp2 ðT 2in T 2out Þ _ 1 cp1 ðT 2in T 1 ðL xdown ÞÞ m m ln ¼ pd1 hsp pd h _ 1 cp1 ðT 2out T 1 ðL xdown ÞÞ m 1 sp 1
_ 1 cp1 m
_ 2 cp2 m
ð25Þ
The actual operation conditions show that the height ratio of AD to DS in the secondary side PS of SG U-tube is a constant z’, which can be obtained by a large number of modeling calculations and experiments (Cong et al., 2013). It is found that the PS height is related to the increase rate of temperature. Therefore, the reciprocal SC temperature loss coefficients kup and kdown can be expressed as follows:
kup ¼
@T 02up ðsÞ=@s @T 2up ðsÞ=@s
kdown ¼
@T 02down ðsÞ=@s @T 2down ðsÞ=@s
ð26Þ
where the superscript ’ indicates the parameter after the transverse heat transfer. Considering the transverse heat transfer of fluid in PS, we found that the ratio of the temperature increase rate of AD to DS in the secondary side PS of SG U-tube is equal to z’, that is:
z¼
0
z ¼
@T 2down ðsÞ=@s @T 2up ðsÞ=@s @T 02down ðsÞ=@s @T 02up ðsÞ=@s
_ 1 d1 0:25 0:3164 m ¼ 0:3164 Re0:25 A1 l
ð28Þ
3:5 d1 K ¼ 0:262 þ 0:326 ru
ð32Þ
where ru is the bend radius, m; Based on the Boussinesq equation, the fluid density in U-tubes satisfies:
qðT Þ ¼ q0 ½1 bðT T 2out Þ
ð33Þ
where q0 is the reference density, kg/m ; b is the thermal expansion coefficient, K1. Integrating the density along the NFDU, the relationship between the pressure drop of U-tube and the mass flow rate under steady-state conditions can be obtained as follows: 3
_ 21 m fL þ K d1 2A2 q 3 2 L DT 1 n1 xup ð1 e Þ þ DnT22 en2 xup 2en2 2 þ en2 ðLxdown Þ n1 5 q0 gb4 þ DnT33 en3 L ð1 en3 x2 Þ þ T 01 xup xup xdown T 02 T 03 xdown
Dp ¼ pin pout ¼
ð34Þ where:
_ 2 cp2 T 2in _ 2 cp2 T 1in m m _ 2 cp2 _ 1 cp1 þ m m
_ 2 cp2 T 1in m _ 2 cp2 T 2in pm_d1chsp þpm_d1chsp kup xup m 1 p1 2 p2 DT 2 ¼ e _ 1 cp1 þ m _ 2 cp2 m pd1 hsp _ 1 cp1 T 1in þ m _ 2 cp2 T 2in kup xup m T 2out e m_ 1 cp1 þ _ 1 cp1 þ m _ 2 cp2 m
ð35Þ
ð36Þ
_ 2 cp2 T 1 ðL xdown Þ pm_d1chsp pm_d1chsp kdown ðLxdown Þ _ 2 cp2 T 2out m m DT 3 ¼ e 1 p1 2 p2 _ 2 cp2 _ 1 cp1 m m ð37Þ
ð29Þ
ð31Þ
where l is the hydrodynamic viscosity, kg/(ms). The local resistance coefficient is given as (Hao et al., 2014a):
DT 1 ¼ ð27Þ
ð30Þ
Lxdown
where A1 is the inlet flow area of U-tube, m2; Dp is the inletoutlet pressure drop of U-tube, Pa; f is the friction resistance coefficient; K is the local resistance coefficient; q is the average density, kg/m3. When 4 103 < Re < 105, the friction resistance coefficient can be calculated by the Blasius formula as follows (Chen et al., 2013):
f ¼ ð23Þ
xup
Z xup Z L 2 _ 21 _1 m L @m 1 fL þK qgds qgds ¼ Dp 2 A1 @t 2 d1 2qA1 0 xup Z Lxdown Z L þ qgds þ qgds
n1 ¼ kup
pd1 hsp _ 1 cp1 m
þ
pd1 hsp
ð38Þ
_ 2 cp2 m
pd1 hsp
Combining Eqs. (26)–(29), the temperature loss coefficients of SC due to the transverse heat transfer can be obtained.
n2 ¼
2.4. Pressure drop equations
n3 ¼ kdown
The momentum conservation equation of fluid in the U-tube can be expressed as follows (Jeong et al., 2004):
T 01 ¼
ð39Þ
_ 1 cp1 m
pd1 hsp _ 1 cp1 m
pd1 hsp _ 2 cp2 m
_ 2 cp2 T 2in _ 1 cp1 T 1in þ m m _ 2 cp2 _ 1 cp1 þ m m
ð40Þ
ð41Þ
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
T 02 ¼ T 2out T 03 ¼
ð42Þ
_ 1 cp1 T 1 ðL xdown Þ m _ 2 cp2 T 2out m _ _ m1 cp1 m2 cp2
ð43Þ
From the Eq. (34), it is found that the pressure drop of the fluid in the U-tubes is closely related to the operating conditions of SC in the SG. 3. Example calculation and analysis A type of marine steam generator is selected as the research object, and the operating parameters are shown in Table 2 (Hao et al., 2014a). The fluid temperature distributions in the PC and SC, the curves of gravity pressure drop and the total pressure drop along with the U-tube mass flow rate, and the influences of the reverse flow phenomenon in the U-tube are calculated in this section. 3.1. Fluid temperature distributions in the PC and SC
Table 2 Operating parameters of SG. Secondary circuit (SC)
Operating parameters
Value
Operating parameters
Value
Normal operation pressure, MPa Inlet temperature, °C
14.0
p2
Inlet total mass flow rate, kg/s
25.8
Normal operation pressure, MPa Feed-water temperature, °C Feed-water mass flow rate, kg/s
T1in
Fig. 2. Temperature along the NFDU of SG.
secondary side fluids can be divided into the preheating and boiling section along the U-tube. In the fluid flow and heat transfer process in the SG, the PS fluid temperature decreases exponentially, and the SC fluid temperature increases exponentially in the PS and remains constant in the boiling section. In the PS, because the fluid temperature difference between the PC and SC is large and the heat transfer is vigorous, the PC temperature decreases rapidly in the U-tube AS and slowly in the U-tube DS, and the SC fluid quickly reaches the saturation temperature, When the SC fluid flows in the boiling section, it will reach the saturation temperature, and the fluid temperature difference and heat transfer coefficient between the PC and SC are higher. So the fluid temperature drop rate in the PC is significantly higher than that in the PS. As the fluid temperature of PC gradually approaches the SC saturation temperature, the heat transfer coefficient and temperature difference between the PC and SC decrease gradually along the NFDU. The fluid temperature in the PC with the PS is always higher than that without the PS, and the difference is more obvious in the Utube DS. 3.2. Pressure drop calculation
From the Thermal-hydraulics theoretical, it can be concluded that the fluid temperature distributions in the PC and SC will affect the inlet-outlet total pressure drop of U-tube. Therefore, the temperature distributions have great significance to the research of U-tube reverse flow. Under natural circulation conditions, the fluid temperature distributions in the PC and SC are calculated and compared with the result of existing reverse flow study that doesn’t consider the PS effect, respectively, as shown in Fig. 2. It is found that when the PS of SC is not considered, the SC fluid suffers the surface boiling heat transfer and remains a constant temperature, and the fluid temperature distributions in the PC are exponential along the NFDU. So the heat transfer process between the primary and
Primary circuit (PC)
5
60 3.8
The existing research method for the reverse flow is that the total pressure drop (Dp) and gravity pressure drop (Dpg) with the PC mass flow in the U-tube are calculated respectively under normal natural circulation conditions, which doesn’t consider the PS of SG. As shown in Fig. 3, the gravity pressure drop in the U-tube changes monotonously with the fluid mass flow rate and always maintains the negative slope. However the total pressure drop curves are non-monotonic and have an inflection point (B and B’ points in Fig. 3). The total pressure drop curves have a remarkable negative slope region for the low mass flow rate (AB and A’B’ segments in Fig. 3). In this negative slope region, the gravity pressure drop as the main driving force is difficult to overcome the local resistance and frictional resistance with the continuing decrease of mass flow rate. Once a small flow disturbance is introduced, the reverse flow phenomenon will occur in the U-tubes. Especially after the main pump stops, the fluid in the primary side will flow relatively slowly and keep the natural circulation, and some Utubes will work in the A’B’ segment. So the reverse flow phenomenon will occur. And the reverse flow will make the mass flow in the SG inlet chamber and in the positive flow tubes increase. It can be seen from Fig. 2 that the fluid temperature in the Utube calculated by considering the PS is always higher than that
Fig. 3. Variation of Dp with mass flow rate.
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
temperature difference between the U-tube DS and the SC. So the PS height corresponding to the DS gradually decreases. What’s more, the average heat transfer coefficient and the PS height gradually increase with the mass flow rate in the PS, and their variations are small under low and high flow rate conditions. The variation curves of the U-tube total pressure drop with mass flow rate are calculated and shown in Fig. 4. It can be seen from Fig. 4 that the pressure drop with considering the PS changes with the mass flow rate more slowly than that without considering the PS. The two methods have the same conclusion in the influence of the SC operating pressure on the U-tube flow instability. The steam generation and the temperature difference of PC decrease with the pressure, which leads to the increase of the gravity pressure drop in U-tubes. Therefore, the curves of total pressure drop with mass flow rate move up, and the inflection point appears earlier with the PC flow rate decrease. In other words, the critical mass flow rate will gradually decrease and the critical pressure drop will gradually increase with the SC pressure. So the flow instability range becomes small, and the reverse flow is less likely to appear.
by without considering the PS, but the value of xdown is obviously higher than xup with considering the PS. What’s more, the change of heat transfer coefficient in the PS is not obvious. So the temperature difference between the AS and DS of PC considering the PS is larger than that without considering the PS. This leads to that the absolute value of gravity pressure drop calculated between the inlet and outlet considering the PS is greater than that without considering PS. It can be drawn that when the PS of SG is considered, the total pressure drop and gravity pressure drop are always lower than the calculation results without considering the PS of SG. The higher the critical mass flow rate is, the lower the corresponding critical pressure drop is. In the actual SG operation conditions, considering the PS of SC will affect the fluid reverse flow characteristics in the U-tubes, and the calculation result is more accurate than that by the existing method. 3.3. Effect factors for reverse flow Under natural circulation conditions, the effects of SG operating pressure, U-tubes pitch and circulation ratio on the U-tube reverse flow characteristics are studied in this section.
3.3.2. Effect of U-tubes pitch As we all known, the U-tube pitch will affect the equivalent diameter and flow area of the SC, and it will affect the heat transfer coefficient in the PS from Eq. (2). So the U-tube pitch has an effect
3.3.1. Effect of SC pressure The change of SC pressure will affect the heat transfer between the primary and secondary sides, then the fluid reverse flow characteristics in the U-tubes. In the existed research method, it is assumed that the U-tube outer wall temperature is constant and equal to the SC saturation temperature along the NFDU. What’s more, the SC heat transfer coefficient and the PS height are assumed to be not relevant to the pressure. So the calculation results don’t conform to the actual operating characteristics of SG. To analyze the effect of SC pressure on the U-tube reverse flow, the initial conditions are assumed that the SG water level, the inlet temperature and fluid flow rate in the primary and secondary sides remain unchanged and the outlet temperature of PC is equal to the saturation temperature of SC. The pressures 0.9p2, p2 and 1.1p2 of SC are employed to calculate the average heat transfer coefficient and the PS height in different flow rates, as shown in Tables 3 and 4. It can be seen from Tables 3 and 4 that the average heat transfer coefficient in the U-tube PS gradually decreases within a narrow range with the operating pressure of SC. For we keep the PC inlet temperature constant, the PS height corresponding to the AS increases. However, the outlet temperature of U-tube increases with the pressure, which leads to the increase of
Fig. 4. Variation of Dp with m1 under different SC pressure conditions.
Table 3 Variation of heat transfer coefficient of PS with mass flow and SC pressure. m1 (kg/s)
0.0154
0.0231
0.9p2 2.2p2 1.1p2
0.0308
hsp (W m2 K1)
p2 (MPa) Up
Down
Up
Down
Up
Down
1068.61 1061.07 1053.52
1006.76 1002.34 997.70
1379.73 1369.83 1359.90
1304.35 1298.24 1291.87
1646.97 1635.07 1623.14
1560.91 1553.33 1545.46
Table 4 Variation of PS height with mass flow and SC pressure. m1 (kg/s)
0.0154
0.0231
p2 (MPa)
0.9p2 p2 1.1p2
0.0308
H(m) xup
xdown
xup
xdown
xup
xdown
0.1814 0.1860 0.1906
1.1297 1.1184 1.1076
0.2107 0.2162 0.2215
1.3079 1.2952 1.2830
0.2354 0.2415 0.2475
1.4573 1.4433 1.4300
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx Table 5 Variation of fluid density in PS with mass flow and pitch. m1 (kg/s)
0.077
0.0231
q (kg/m )
P (m)
0.019 0.021 0.023
0.0385
3
qup
qdown
Dq
qup
qdown
Dq
qup
qdown
Dq
800.73 800.69 800.51
845.26 845.59 846.10
44.53 44.90 45.60
788.50 788.31 787.87
842.13 843.07 844.65
53.63 54.77 56.78
781.08 780.94 780.50
840.03 841.59 845.00
58.95 60.65 64.50
on the fluid reverse flow characteristics. Keeping the inlet temperatures of the PC and SC constant, the fluid density, the gravity pressure drop and the total pressure drop with the mass flow in the PC are studied for different pitches 19, 21 and 23 mm, respectively. As shown in Tab.5, it can be found that the fluid average density of U-tube AS (qup ) gradually decreases with the U-tube pitch, while that of U-tube DS (qdown ) is just opposite. So the fluid average density difference between the U-tube AS and DS gradually increases with the U-tube pitch. In addition, for given the mass flow rate, increasing the U-tube pitch will reduce the fluid velocity in the SC and the heat transfer coefficient of the primary and secondary sides in the PS, then the temperature in the U-tube highest point. The variation of fluid average density in the AS is also slower than that in the DS because of the shorter PS corresponding to the AS. The pitch has little effect on the fluid average density in the AS. The fluid density difference (Dq) between the DS and AS changes obviously with the U-tube pitch under the high flow rate conditions (Table 5). The variation curves of the U-tube gravity drop and total pressure drop with mass flow rate are calculated and shown in Figs. 5 and 6, respectively. It can be seen that the variations of gravity drop and total pressure drop with the U-tube pitch are obvious, which is consistent with the variation of PC fluid density with the mass flow rate and U-tube pitch. The fluid gravity drop and total pressure drop gradually decrease with the U-tube pitch, and the corresponding critical mass flow rate and critical pressure drop gradually increases and decreases, respectively. Under low mass flow conditions, the difference between the gravity and total pressure drop calculated for three pitches 19, 21 and 23 mm is small. Based on the flow instability analysis, it is known that with the increase of U-tube pitch the reverse flow becomes easier to occur. Therefore, in order to alleviate the reverse flow phenomenon, the U-tube pitch can be appropriately reduced.
Fig. 6. Variation of Dp with m1 in different U-tube pitches.
Fig. 7. Variation of Dp with m1 at different circulation ratio.
Fig. 5. Variation of Dpg with m1 in different U-tube pitches.
3.3.3. Effect of circulation ratio In order to study the effect of SG circulation ratio on the U-tube reverse flow, the initial conditions are assumed that the inlet temperature of U-tube, the water level of SG and the operating pressure of SC keep constant. When the SG circulation ratio set as 12, 16 and 20 respectively, the variation of U-tube total pressure drop with PS mass flow rate is calculated, and shown in Fig. 7. It is clear that similar to the SC pressure and U-tube pitch under low flow rate conditions, the effect of circulation ratio on the total pressure drop is not obvious, and the smallest critical pressure drop appears at the circulation ratio 20. Because the steam production decreases with the increase of circulation ratio, the heat transfer between the primary and secondary sides decreases, and the temperature
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
difference of the inlet and outlet of the SG decreases. The gravity pressure drop difference between the U-tube’s ascending and descending sections also decreases. According to the flow instability analysis theory, the operating conditions with the high circulation ratio are more likely to generate reverse flow phenomenon. Therefore, in order to alleviate the reverse flow in the U-tube, the circulation ratio of SG can be appropriately reduced.
4. Conclusions In this paper, a single-channel physical model for the marine natural circulation SG is established and compared with the existing research method and model. The fluid temperature distributions in the PC and SC along the NFDU and the U-tube reverse flow characteristics are studied by considering the PS of SC. By this model, the influences of SC pressure, U-tube pitch and circulation ratio on the U-tube reverse flow characteristics are calculated and analyzed. The specific conclusions are summarized as follows: (1) The PC and SC have significant differences in the fluid temperature distributions. The fluid temperature in the PC decreases exponentially along the NFDU. However, the fluid temperature in the SC increases exponentially in the PS and remains unchanged in the boiling section. (2) Compared with the existing reverse flow calculation methods, the critical flow rate is relatively higher, and the critical pressure drop is relatively lower. So the PS will affect the Utube reverse flow. (3) With the increases of SC operating pressure and U-tube pitch as well as circulation ratio, the U-tube flow stability boundary is widened and the reverse flow is not easy to happen.
Acknowledgement This research was financially supported by the National Natural Science Foundation of China (project number 11402300 and 11502298).
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107064.
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Annals of Nuclear Energy journal homepage: www.elsevier.com/locate/anucene
Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides Mingrui Li, Wenzhen Chen ⇑, Jianli Hao, Xi Chu College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China
a r t i c l e
i n f o
Article history: Received 1 April 2019 Received in revised form 19 August 2019 Accepted 15 September 2019 Available online xxxx Keywords: U-tube Reverse flow Preheating section Single channel
a b s t r a c t Under natural circulation conditions, the reverse flow phenomenon may occur within some U-tubes. This will result in the flow resistance coefficient of the steam generator (SG) obviously larger than that under forced circulation conditions, and the decrease of nature circulation capability in the primary circuit (PC). The heat transfer characteristics between the secondary circuit (SC) and PC in the SG are very complicated. Expressly, there is an obvious preheating section due to a certain fluid under-heat degree at the inlet of the ascending passage in the SC. In this paper, a type of marine SG is studied and a theoretical model of the SC single channel is established for the preheating sections (PS) corresponding to the ascending section (AS) and the descending section (DS) of U-tubes. Based on this model, the reverse flow characteristics of U-tubes are researched, and the influence of SC operating pressure, U-tubes pitch and circulation ratio on the U-tube reverse flow characteristics are calculated and analyzed. The results show that compared with the existing reverse flow calculation methods, the temperature distribution in the PS of SC increases exponentially and remains unchanged in the boiling section, and the critical flow rate is relatively higher. The increase of SC operating pressure and U-tubes pitch will decrease the mass flow rate of reverse flow, and the influence of circulation ratio has the opposite conclusion. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction The natural circulation is an important indicator of the inherent safety of the reactor, which can derive the core decay heat without the external driving force and effectively reduce the inhomogeneity of the flow distribution in core. Related natural circulation studies have shown that with the reverse flow phenomenon occurred in the some inverted U-tubes of the steam generator (SG), the lower temperature coolant in the primary circuit (PC) will inversely flow from the outlet cavity to the inlet cavity (Hao et al., 2014a; Loomis and Soda, 1982). Under natural circulation conditions, the emergence of reverse flow can reduce the effective heat transfer area of the SG, and the reverse flow fluid is mixed and dissipated with the thermal fluid in the inlet cavity. Therefore, the flow resistance coefficient in the SG under the natural circulation conditions is greater than that under forced circulation conditions, which results in the decrease of the system natural circulation flow mass. Most of the existing researches on the U-tube reverse flow in the SG aimed to analyze the influence of PC conditions (Kukita ⇑ Corresponding author at: Faculty 304, College of Nuclear Science and Technology, Naval University of Engineering, Wuhan 430033, China. E-mail address: [email protected] (W. Chen).
et al., 1988; Sanders, 1988). Jeong et al. (2004) established a mathematical model to analyze the single phase and two phase natural circulations in the vertical inverted U-tubes. The research showed that there was a negative slope region in the curve of U-tube’s pressure drop with mass flow, and the flow drift may occurred in the U-tube when the low mass flow is inside the region. Yang et al (2010) analyzed the flow and heat transfer characteristics of single-phase water in the parallel U-tubes of SG by establishing mathematical models and corresponding numerical calculation methods, and the calculated results were in good agreement with the experimental results. Based on the one-dimensional heat transfer model established by Sanders (1988), Watanabe et al. (2014) concluded that the reverse flow occurred more easily in the long tube than in the short tube by coupling the CFD software and system program. Hao and Chen (2014a,b) obtained the universal reverse flow judgment criterion and comprehensively analyzed the development mechanism of reverse flow through the combination of theoretical derivation, numerical simulation and proportional modeling experiment for the reverse flow in the SG U-tubes under natural circulation conditions. Hu et al. (2016) proposed to employ the critical curve to judge and evaluate the occurrence of reverse flow phenomenon, and obtained the reverse flow critical curve by the experimental research. Chu et al. (2018) used RELAP5/MOD 3.3 program to study the influence factors of the
https://doi.org/10.1016/j.anucene.2019.107064 0306-4549/Ó 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
two-phase reverse flow in U-tubes under low steam quality conditions. The existing researches on the U-tube reverse flow phenomenon in the SG are under the assumptions that the secondary working conditions remained unchanged. But in the actual operation, the secondary working conditions have an important effect on the development of U-tube reverse flow in the SG. The research showed that the heat transfer characteristics in the U-tubes and the secondary circuit (SC) were very complicated (Ding and Ba, 1982). The fluid in SC had a certain subcooling at the inlet of the ascending passage, which results in an obvious preheating process. The heat transfer characteristics of vapor-liquid two-phase flow in the secondary circuit of SG have been extensively studied. Cong et al. (2014) established the threedimensional physical models for the SG to calculate the two-phase flow and steady thermohydraulics characteristics in the SC based on CFX software. Sun et al. (2015) established a simplified physical model for an actual SG, and simulated the coupled system of fluid and heat transfer characteristics in the PC and SC by CFD software. The calculated results were consistent with that by the measurement and published literature. Razmara et al. (2016) introduced an optimal control method for the transient and steady state operations of internal combustion engines based on exergy, and the calculated results show that the new optimal method can save 6.7% fuel compared with the first law of thermodynamics method. Aiming at the limitations of the existing heat transfer methods, the nanofluid (Hajmohammadi, 2017) and multi-scale annular fins (Hajmohammadi, 2018) were employed to enhance the thermal performance of the assembly. These works were useful in the design of variant cooling devices in the practical engineering applications. Hajmohammadi and Rezaei (2019a) presented a new fast algorithm based on the recursive localization for the optimization to maximize the thermal performance, and it is promising and efficient. Summarizing the literature, it could be found that the characteristics and influence factors of reverse flow in the SG have been well studied. But these researchers simply considered the fluid operating conditions of PC, and assumed that the temperature of U-tube outer wall was always equal to the saturation temperature of SC. Obviously, it was inconsistent with the actual operation conditions of SGs, and the calculation result would not be accurate. In this paper, a single-channel model is established to study the thermo-hydraulic characteristics and the phenomenon of U-tube reverse flow by coupling the PC and SC in the SG. The research conclusion has important guiding significance for the actual SG to slow down the occurrence of the reverse flow under the natural circulation conditions. It also provide a theoretical basis for improving the natural circulation capacity of the marine nuclear power plant system.
2. Theoretical models 2.1. Physical model Fig. 1 shows a simplified single-channel physical model coupling the primary and secondary sides in the natural circulation SG, which consists of four adjacent U-shaped heat transfer tubes, the tube wall and secondary fluid domain. The length of U-tube is 4.0–5.0 m, and the height of straight tube is 2.0 m. The thermal single-phase fluid of PC flows into the inlet of U-tubes, then through the U-tubes by exchanging heat with the cold fluid of SC, finally the cooled PC fluid flows out from the outlet of U-tubes. The cold fluid of SC will be heated to a saturation temperature and changed to the steam. The flow heat transfer process between the PC and SC is divided into the preheating section (PS)
Single-channel Primary flow direction U-tubes
Secondary flow direction
Secondary Wall Secondary inlet Steam Generator Primary inlet Primary outlet
Fig. 1. Single-channel model of PC and SC.
and boiling section along the normal flow direction of U-tube (NFDU). According to the SG-operation conditions, it is assumed that (1) the homogenous flow model is accepted to the SC fluid, so the velocity and temperature of vapor phase are equal to those of liquid phase; (2) the parameter variations of the PC, SC and tube wall are considered only along the axial direction; (3) the inlet mass flow is equivalent to the average mass flow (Hajmohammadi et al., 2019b). 2.2. Heat transfer coefficient equations The convection heat transfer in the U-tube is calculated using the Dittus-Boelter formula as follows (Chen et al., 2013):
h1 ¼ 0:023
k1 0:8 0:3 Re Pr d1
ð1Þ
where k1 is the fluid thermal conductivity in the tube, W/(m.°C); Re is the Reynolds number; Pr is the Prandtl number. Considering the horizontal and longitudinal flow of SC fluid in the PS through the outer wall of U-tubes, the effective surface heat transfer coefficient is given as follows (Chen et al., 2013):
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 ðC H ReAH Pr BH k2 =De Þ þ ðC L ReAL Pr BL k2 =De Þ h2 ¼ 2
ð2Þ
where k2 is the thermal conductivity of the SC fluid, W/(m.°C); De is the equivalent diameter of the SC flow channel, m; P is the U-tubes pitch, m; d2 is the outer diameter of U-tubes, m; A, B, C are the coefficients shown in Table 1. The heat transfer in the SC boiling section is more complicated. For the large-volume nucleate boiling on the clean heat transfer surface, the Rohsenow formula is mostly used for the heat transfer calculation, and the relationship equation is as follows (Rohsenow et al., 1985; Incropera and DeWitt, 2002): 0
h ¼
cpl rPr l C w
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi0:33
ll r g ql qg =r
Q ðsÞ0:67
ð3Þ
The heat flux density in the boiling section can be expressed as: 0
Q ðsÞ ¼ h ðT w T 2out Þ
ð4Þ
Substituting equation (4) into equation (3), the heat transfer coefficient in the boiling section is given by:
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
3
M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx Table 1 The value of coefficients. Direction Arrangement
Horizontal
Triangle
0
h ¼
cpl rPrl C w
Longitudinal
A
B
C
A
B
C
0.563
0.333
0.547
0.8
0.4
0.26P/d2-0.006
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi
3
ll r g ql qg =r ðT w T 2out Þ2
ð5Þ
where Cw is the empirical coefficient of the heating surface, which can be 0.013 for the outer surface of the heat transfer tube; cpl is the specific heat capacity of the saturated liquid, J/(kg ); r is the latent heat of vaporization, J/kg; g is the gravity acceleration, m/ s2;Q2(s) is the heat flux density, W/m2; ll is the dynamic viscosity of the saturated liquid, kg/(ms); ql and qg are the density corresponding to the saturated liquid and vapor, kg/m3; r is the surface tension of liquid-vapor interface, N/m; Tw is the temperature of Utube outer wall, °C; T2out is the fluid saturation temperature in the SC, °C. The experimental study shows that the heat transfer coefficient calculated by Eq. (5) is 30% higher than the experimental value. Therefore, we take a coefficient to corrected the result by Eq. (5), and the value is 0.7 in this paper (Ding and Ba, 1982). 2.3. Heat transfer equations in the PC and SC The energy conservation equation of fluid in the U-tube is:
_ 1 cp1 m
@T 1 ¼ qðsÞ @s
ð6Þ
_ 1 is the mass flow rate in U-tube, kg/s; q is the linear heat where: m flux density, W/m; s is the coordinate in the normal flow direction along the U-tube, m; the subscripts 1 and 2 mean the parameters in the PC and SC, respectively. According to the heat transfer analysis in a single U-tube, we can obtain:
T 1 ðsÞ ¼ T 2 ðsÞ þ
hsp ¼
qðsÞ pd1 hsp
1 1 h1
þ 2kd1w ln dd21 þ hd2 1d2
ð8Þ
T 1 ð0Þ ¼ T 1in T 2 ð0Þ ¼ T 2in ;
ð10Þ
T 2 xup ¼ T 2 ðxdown Þ ¼ T 2out
T 2 ðsÞ ¼ T 2in
ð11Þ
where Tin and Tout are the temperature of inlet and outlet, respectively, °C; the subscripts up and down mean the AS and DS, respectively. Based on the energy conservation equation, we have:
ð12Þ
_ 1 cp1 m ðT ðsÞ T 1in Þ _ 2 cp2 1 m
ð13Þ
According to the countercurrent heat transfer characteristics, when L-xdown s L, the SC fluid temperature in the PS can be obtained from Eq. (9) as follows:
T 2 ðsÞ ¼ T 2out þ
_ 1 cp1 m ðT ðsÞ T 1 ðL xdown ÞÞ _ 2 cp2 1 m
ð14Þ
Combining Eqs. (6), (7) and (13), results in the differential expressions of the fluid temperature in the U-tube as follows:
@T 1 ðsÞ pd1 hsp pd1 hsp pd1 hsp T 1 ð sÞ þ þ T ¼ _ 1 cp1 _ 2 cp2 _ 2 cp2 1in @s m m m pd1 hsp þ T 0 s < xup _ 1 cp1 2in m @T 1 ðsÞ pd1 hsp pd1 hsp ¼ T ðsÞ þ T _ 1 cp1 1 _ 1 cp1 2out @s m m @T 1 ðsÞ ¼ @s
pd1 hsp _ 2 cp2 m
þ
pd1 hsp _ 1 cp1 m
ð15Þ
xup s < L xdown
ð16Þ
pd1 hsp T 1 ðsÞ T ðL xdown Þ _ 1 cp1 _ 2 cp2 1 m m
pd1 hsp
T 2out
ðL xdown s < LÞ
ð17Þ
Integrating Eqs. (15)–(17) along the NFDU, the fluid temperature can be calculated by:
_ 2 cp2 T 2in _ 2 cp2 T 1in m m T 1 ð sÞ ¼ e _ 2 cp2 _ 1 cp1 þ m m _ 2 cp2 T 2in _ 1 cp1 T 1in þ m m þ _ 2 cp2 _ 1 cp1 þ m m
pd1 hsp pd1 hsp _ c þm _ c m 1 p1
_ 2 cp2 T 2in _ 2 cp2 T 1in m m _ 1 cp1 þm _ 2 cp2 m pd1 hsp
e m_ 1 cp1
ðxup sÞ
e
pd1 hsp pd1 hsp _ c þm _ c m 1 p1
þ T 2out
2 p2
s
0 s < xup
T 1 ðsÞ ¼
ð9Þ
It is assumed that xup and xdown denote the PS heights corresponding to the ascending section (AS) and descending section (DS) of the PC, respectively, then there are the boundary conditions as follows:
_ 2 cp2 m ðT T 2in Þ _ 1 cp1 2out m
where L is the total length of the U-tube, m. When 0 s < xup, the SC fluid temperature in the PS can be obtained from Eq. (9) as follows:
ð7Þ
where hsp is the overall heat transfer coefficient between the primary and secondary sides, W/(m2.K); kw is the U-tube wall thermal conductivity, W/(m.K); d1 and d2 are the inner and outer diameter of the U-tube, respectively, m. Based on the thermodynamic equilibrium theory, the heat transfer equation between the primary and secondary sides can be obtained as follows:
_ 2 cp2 DT 2 _ 1 cp1 DT 1 ¼ m m
T 1 ðL xdown Þ ¼ T 1out þ
2 p2
ð18Þ
xup
! þ
_ 2 cp2 T 2in _ 1 cp1 T 1in þm m _ 1 cp1 þm _ 2 cp2 m
T 2out
xup s < L xdown ð19Þ
_ 2 cp2 T 1 ðL xdown Þ pm_d1chsp pm_d1chsp ðLxdown sÞ _ 2 cp2 T 2out m m 1 p1 2 p2 e T 1 ð sÞ ¼ _ 2 cp2 _ 1 cp1 m m þ
_ 2 cp2 T 2out _ 1 cp1 T 1 ðL xdown Þ m m _ 2 cp2 _ 1 cp1 m m
ðL xdown s < LÞ ð20Þ
From Eqs. (18), (19) and (20), the change of fluid temperature in the U-tube can be written as follows:
T 1 ðsÞ ¼ DTens þ T 0
ð21Þ
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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Combining Eqs. (13) and (18), the SC fluid temperature can be evaluated by:
_ 1 cp1 ðT 1in T 2in Þ m T 2 ðsÞ ¼ T 2in þ 1e _ 2 cp2 _ 1 cp1 þ m m
pd1 hsp pd1 hsp _ c þm _ c m 1 p1
2 p2
! s
0 s < xup
L 2
ð22Þ When xup s < L-xdown, the SC fluid reaches the saturation temperature. Combining Eqs. (14) and (20), we can obtain:
_ 1 cp1 T 1 ðL xdown Þ pm_d1chsp pm_d1chsp ðLxdown sÞ _ 1 cp1 T 2out m m 1 p1 2 p2 T 2 ðsÞ ¼ e _ 2 cp2 _ 1 cp1 m m þ
_ 2 cp2 T 2out _ 1 cp1 T 1 ðL xdown Þ m m _ _ m1 cp1 m2 cp2
ðL xdown s LÞ
According to Eqs. (22) and (23), when s = xup and s = L, the heights of the PS corresponding to the AS and DS of U-tube can be obtained as follows, respectively:
_ 2 cp2 ðT 2out T 2in Þ _ 1 cp1 ðT 1in T 2out Þ m m ln ¼ pd1 hsp pd h _ 1 cp1 ðT 1in T 2in Þ m þ 1 sp 1
_ 1 cp1 m
_ 2 cp2 m
ð24Þ xdown
_ 2 cp2 ðT 2in T 2out Þ _ 1 cp1 ðT 2in T 1 ðL xdown ÞÞ m m ln ¼ pd1 hsp pd h _ 1 cp1 ðT 2out T 1 ðL xdown ÞÞ m 1 sp 1
_ 1 cp1 m
_ 2 cp2 m
ð25Þ
The actual operation conditions show that the height ratio of AD to DS in the secondary side PS of SG U-tube is a constant z’, which can be obtained by a large number of modeling calculations and experiments (Cong et al., 2013). It is found that the PS height is related to the increase rate of temperature. Therefore, the reciprocal SC temperature loss coefficients kup and kdown can be expressed as follows:
kup ¼
@T 02up ðsÞ=@s @T 2up ðsÞ=@s
kdown ¼
@T 02down ðsÞ=@s @T 2down ðsÞ=@s
ð26Þ
where the superscript ’ indicates the parameter after the transverse heat transfer. Considering the transverse heat transfer of fluid in PS, we found that the ratio of the temperature increase rate of AD to DS in the secondary side PS of SG U-tube is equal to z’, that is:
z¼
0
z ¼
@T 2down ðsÞ=@s @T 2up ðsÞ=@s @T 02down ðsÞ=@s @T 02up ðsÞ=@s
_ 1 d1 0:25 0:3164 m ¼ 0:3164 Re0:25 A1 l
ð28Þ
3:5 d1 K ¼ 0:262 þ 0:326 ru
ð32Þ
where ru is the bend radius, m; Based on the Boussinesq equation, the fluid density in U-tubes satisfies:
qðT Þ ¼ q0 ½1 bðT T 2out Þ
ð33Þ
where q0 is the reference density, kg/m ; b is the thermal expansion coefficient, K1. Integrating the density along the NFDU, the relationship between the pressure drop of U-tube and the mass flow rate under steady-state conditions can be obtained as follows: 3
_ 21 m fL þ K d1 2A2 q 3 2 L DT 1 n1 xup ð1 e Þ þ DnT22 en2 xup 2en2 2 þ en2 ðLxdown Þ n1 5 q0 gb4 þ DnT33 en3 L ð1 en3 x2 Þ þ T 01 xup xup xdown T 02 T 03 xdown
Dp ¼ pin pout ¼
ð34Þ where:
_ 2 cp2 T 2in _ 2 cp2 T 1in m m _ 2 cp2 _ 1 cp1 þ m m
_ 2 cp2 T 1in m _ 2 cp2 T 2in pm_d1chsp þpm_d1chsp kup xup m 1 p1 2 p2 DT 2 ¼ e _ 1 cp1 þ m _ 2 cp2 m pd1 hsp _ 1 cp1 T 1in þ m _ 2 cp2 T 2in kup xup m T 2out e m_ 1 cp1 þ _ 1 cp1 þ m _ 2 cp2 m
ð35Þ
ð36Þ
_ 2 cp2 T 1 ðL xdown Þ pm_d1chsp pm_d1chsp kdown ðLxdown Þ _ 2 cp2 T 2out m m DT 3 ¼ e 1 p1 2 p2 _ 2 cp2 _ 1 cp1 m m ð37Þ
ð29Þ
ð31Þ
where l is the hydrodynamic viscosity, kg/(ms). The local resistance coefficient is given as (Hao et al., 2014a):
DT 1 ¼ ð27Þ
ð30Þ
Lxdown
where A1 is the inlet flow area of U-tube, m2; Dp is the inletoutlet pressure drop of U-tube, Pa; f is the friction resistance coefficient; K is the local resistance coefficient; q is the average density, kg/m3. When 4 103 < Re < 105, the friction resistance coefficient can be calculated by the Blasius formula as follows (Chen et al., 2013):
f ¼ ð23Þ
xup
Z xup Z L 2 _ 21 _1 m L @m 1 fL þK qgds qgds ¼ Dp 2 A1 @t 2 d1 2qA1 0 xup Z Lxdown Z L þ qgds þ qgds
n1 ¼ kup
pd1 hsp _ 1 cp1 m
þ
pd1 hsp
ð38Þ
_ 2 cp2 m
pd1 hsp
Combining Eqs. (26)–(29), the temperature loss coefficients of SC due to the transverse heat transfer can be obtained.
n2 ¼
2.4. Pressure drop equations
n3 ¼ kdown
The momentum conservation equation of fluid in the U-tube can be expressed as follows (Jeong et al., 2004):
T 01 ¼
ð39Þ
_ 1 cp1 m
pd1 hsp _ 1 cp1 m
pd1 hsp _ 2 cp2 m
_ 2 cp2 T 2in _ 1 cp1 T 1in þ m m _ 2 cp2 _ 1 cp1 þ m m
ð40Þ
ð41Þ
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
T 02 ¼ T 2out T 03 ¼
ð42Þ
_ 1 cp1 T 1 ðL xdown Þ m _ 2 cp2 T 2out m _ _ m1 cp1 m2 cp2
ð43Þ
From the Eq. (34), it is found that the pressure drop of the fluid in the U-tubes is closely related to the operating conditions of SC in the SG. 3. Example calculation and analysis A type of marine steam generator is selected as the research object, and the operating parameters are shown in Table 2 (Hao et al., 2014a). The fluid temperature distributions in the PC and SC, the curves of gravity pressure drop and the total pressure drop along with the U-tube mass flow rate, and the influences of the reverse flow phenomenon in the U-tube are calculated in this section. 3.1. Fluid temperature distributions in the PC and SC
Table 2 Operating parameters of SG. Secondary circuit (SC)
Operating parameters
Value
Operating parameters
Value
Normal operation pressure, MPa Inlet temperature, °C
14.0
p2
Inlet total mass flow rate, kg/s
25.8
Normal operation pressure, MPa Feed-water temperature, °C Feed-water mass flow rate, kg/s
T1in
Fig. 2. Temperature along the NFDU of SG.
secondary side fluids can be divided into the preheating and boiling section along the U-tube. In the fluid flow and heat transfer process in the SG, the PS fluid temperature decreases exponentially, and the SC fluid temperature increases exponentially in the PS and remains constant in the boiling section. In the PS, because the fluid temperature difference between the PC and SC is large and the heat transfer is vigorous, the PC temperature decreases rapidly in the U-tube AS and slowly in the U-tube DS, and the SC fluid quickly reaches the saturation temperature, When the SC fluid flows in the boiling section, it will reach the saturation temperature, and the fluid temperature difference and heat transfer coefficient between the PC and SC are higher. So the fluid temperature drop rate in the PC is significantly higher than that in the PS. As the fluid temperature of PC gradually approaches the SC saturation temperature, the heat transfer coefficient and temperature difference between the PC and SC decrease gradually along the NFDU. The fluid temperature in the PC with the PS is always higher than that without the PS, and the difference is more obvious in the Utube DS. 3.2. Pressure drop calculation
From the Thermal-hydraulics theoretical, it can be concluded that the fluid temperature distributions in the PC and SC will affect the inlet-outlet total pressure drop of U-tube. Therefore, the temperature distributions have great significance to the research of U-tube reverse flow. Under natural circulation conditions, the fluid temperature distributions in the PC and SC are calculated and compared with the result of existing reverse flow study that doesn’t consider the PS effect, respectively, as shown in Fig. 2. It is found that when the PS of SC is not considered, the SC fluid suffers the surface boiling heat transfer and remains a constant temperature, and the fluid temperature distributions in the PC are exponential along the NFDU. So the heat transfer process between the primary and
Primary circuit (PC)
5
60 3.8
The existing research method for the reverse flow is that the total pressure drop (Dp) and gravity pressure drop (Dpg) with the PC mass flow in the U-tube are calculated respectively under normal natural circulation conditions, which doesn’t consider the PS of SG. As shown in Fig. 3, the gravity pressure drop in the U-tube changes monotonously with the fluid mass flow rate and always maintains the negative slope. However the total pressure drop curves are non-monotonic and have an inflection point (B and B’ points in Fig. 3). The total pressure drop curves have a remarkable negative slope region for the low mass flow rate (AB and A’B’ segments in Fig. 3). In this negative slope region, the gravity pressure drop as the main driving force is difficult to overcome the local resistance and frictional resistance with the continuing decrease of mass flow rate. Once a small flow disturbance is introduced, the reverse flow phenomenon will occur in the U-tubes. Especially after the main pump stops, the fluid in the primary side will flow relatively slowly and keep the natural circulation, and some Utubes will work in the A’B’ segment. So the reverse flow phenomenon will occur. And the reverse flow will make the mass flow in the SG inlet chamber and in the positive flow tubes increase. It can be seen from Fig. 2 that the fluid temperature in the Utube calculated by considering the PS is always higher than that
Fig. 3. Variation of Dp with mass flow rate.
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
temperature difference between the U-tube DS and the SC. So the PS height corresponding to the DS gradually decreases. What’s more, the average heat transfer coefficient and the PS height gradually increase with the mass flow rate in the PS, and their variations are small under low and high flow rate conditions. The variation curves of the U-tube total pressure drop with mass flow rate are calculated and shown in Fig. 4. It can be seen from Fig. 4 that the pressure drop with considering the PS changes with the mass flow rate more slowly than that without considering the PS. The two methods have the same conclusion in the influence of the SC operating pressure on the U-tube flow instability. The steam generation and the temperature difference of PC decrease with the pressure, which leads to the increase of the gravity pressure drop in U-tubes. Therefore, the curves of total pressure drop with mass flow rate move up, and the inflection point appears earlier with the PC flow rate decrease. In other words, the critical mass flow rate will gradually decrease and the critical pressure drop will gradually increase with the SC pressure. So the flow instability range becomes small, and the reverse flow is less likely to appear.
by without considering the PS, but the value of xdown is obviously higher than xup with considering the PS. What’s more, the change of heat transfer coefficient in the PS is not obvious. So the temperature difference between the AS and DS of PC considering the PS is larger than that without considering the PS. This leads to that the absolute value of gravity pressure drop calculated between the inlet and outlet considering the PS is greater than that without considering PS. It can be drawn that when the PS of SG is considered, the total pressure drop and gravity pressure drop are always lower than the calculation results without considering the PS of SG. The higher the critical mass flow rate is, the lower the corresponding critical pressure drop is. In the actual SG operation conditions, considering the PS of SC will affect the fluid reverse flow characteristics in the U-tubes, and the calculation result is more accurate than that by the existing method. 3.3. Effect factors for reverse flow Under natural circulation conditions, the effects of SG operating pressure, U-tubes pitch and circulation ratio on the U-tube reverse flow characteristics are studied in this section.
3.3.2. Effect of U-tubes pitch As we all known, the U-tube pitch will affect the equivalent diameter and flow area of the SC, and it will affect the heat transfer coefficient in the PS from Eq. (2). So the U-tube pitch has an effect
3.3.1. Effect of SC pressure The change of SC pressure will affect the heat transfer between the primary and secondary sides, then the fluid reverse flow characteristics in the U-tubes. In the existed research method, it is assumed that the U-tube outer wall temperature is constant and equal to the SC saturation temperature along the NFDU. What’s more, the SC heat transfer coefficient and the PS height are assumed to be not relevant to the pressure. So the calculation results don’t conform to the actual operating characteristics of SG. To analyze the effect of SC pressure on the U-tube reverse flow, the initial conditions are assumed that the SG water level, the inlet temperature and fluid flow rate in the primary and secondary sides remain unchanged and the outlet temperature of PC is equal to the saturation temperature of SC. The pressures 0.9p2, p2 and 1.1p2 of SC are employed to calculate the average heat transfer coefficient and the PS height in different flow rates, as shown in Tables 3 and 4. It can be seen from Tables 3 and 4 that the average heat transfer coefficient in the U-tube PS gradually decreases within a narrow range with the operating pressure of SC. For we keep the PC inlet temperature constant, the PS height corresponding to the AS increases. However, the outlet temperature of U-tube increases with the pressure, which leads to the increase of
Fig. 4. Variation of Dp with m1 under different SC pressure conditions.
Table 3 Variation of heat transfer coefficient of PS with mass flow and SC pressure. m1 (kg/s)
0.0154
0.0231
0.9p2 2.2p2 1.1p2
0.0308
hsp (W m2 K1)
p2 (MPa) Up
Down
Up
Down
Up
Down
1068.61 1061.07 1053.52
1006.76 1002.34 997.70
1379.73 1369.83 1359.90
1304.35 1298.24 1291.87
1646.97 1635.07 1623.14
1560.91 1553.33 1545.46
Table 4 Variation of PS height with mass flow and SC pressure. m1 (kg/s)
0.0154
0.0231
p2 (MPa)
0.9p2 p2 1.1p2
0.0308
H(m) xup
xdown
xup
xdown
xup
xdown
0.1814 0.1860 0.1906
1.1297 1.1184 1.1076
0.2107 0.2162 0.2215
1.3079 1.2952 1.2830
0.2354 0.2415 0.2475
1.4573 1.4433 1.4300
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx Table 5 Variation of fluid density in PS with mass flow and pitch. m1 (kg/s)
0.077
0.0231
q (kg/m )
P (m)
0.019 0.021 0.023
0.0385
3
qup
qdown
Dq
qup
qdown
Dq
qup
qdown
Dq
800.73 800.69 800.51
845.26 845.59 846.10
44.53 44.90 45.60
788.50 788.31 787.87
842.13 843.07 844.65
53.63 54.77 56.78
781.08 780.94 780.50
840.03 841.59 845.00
58.95 60.65 64.50
on the fluid reverse flow characteristics. Keeping the inlet temperatures of the PC and SC constant, the fluid density, the gravity pressure drop and the total pressure drop with the mass flow in the PC are studied for different pitches 19, 21 and 23 mm, respectively. As shown in Tab.5, it can be found that the fluid average density of U-tube AS (qup ) gradually decreases with the U-tube pitch, while that of U-tube DS (qdown ) is just opposite. So the fluid average density difference between the U-tube AS and DS gradually increases with the U-tube pitch. In addition, for given the mass flow rate, increasing the U-tube pitch will reduce the fluid velocity in the SC and the heat transfer coefficient of the primary and secondary sides in the PS, then the temperature in the U-tube highest point. The variation of fluid average density in the AS is also slower than that in the DS because of the shorter PS corresponding to the AS. The pitch has little effect on the fluid average density in the AS. The fluid density difference (Dq) between the DS and AS changes obviously with the U-tube pitch under the high flow rate conditions (Table 5). The variation curves of the U-tube gravity drop and total pressure drop with mass flow rate are calculated and shown in Figs. 5 and 6, respectively. It can be seen that the variations of gravity drop and total pressure drop with the U-tube pitch are obvious, which is consistent with the variation of PC fluid density with the mass flow rate and U-tube pitch. The fluid gravity drop and total pressure drop gradually decrease with the U-tube pitch, and the corresponding critical mass flow rate and critical pressure drop gradually increases and decreases, respectively. Under low mass flow conditions, the difference between the gravity and total pressure drop calculated for three pitches 19, 21 and 23 mm is small. Based on the flow instability analysis, it is known that with the increase of U-tube pitch the reverse flow becomes easier to occur. Therefore, in order to alleviate the reverse flow phenomenon, the U-tube pitch can be appropriately reduced.
Fig. 6. Variation of Dp with m1 in different U-tube pitches.
Fig. 7. Variation of Dp with m1 at different circulation ratio.
Fig. 5. Variation of Dpg with m1 in different U-tube pitches.
3.3.3. Effect of circulation ratio In order to study the effect of SG circulation ratio on the U-tube reverse flow, the initial conditions are assumed that the inlet temperature of U-tube, the water level of SG and the operating pressure of SC keep constant. When the SG circulation ratio set as 12, 16 and 20 respectively, the variation of U-tube total pressure drop with PS mass flow rate is calculated, and shown in Fig. 7. It is clear that similar to the SC pressure and U-tube pitch under low flow rate conditions, the effect of circulation ratio on the total pressure drop is not obvious, and the smallest critical pressure drop appears at the circulation ratio 20. Because the steam production decreases with the increase of circulation ratio, the heat transfer between the primary and secondary sides decreases, and the temperature
Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064
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M. Li et al. / Annals of Nuclear Energy xxx (xxxx) xxx
difference of the inlet and outlet of the SG decreases. The gravity pressure drop difference between the U-tube’s ascending and descending sections also decreases. According to the flow instability analysis theory, the operating conditions with the high circulation ratio are more likely to generate reverse flow phenomenon. Therefore, in order to alleviate the reverse flow in the U-tube, the circulation ratio of SG can be appropriately reduced.
4. Conclusions In this paper, a single-channel physical model for the marine natural circulation SG is established and compared with the existing research method and model. The fluid temperature distributions in the PC and SC along the NFDU and the U-tube reverse flow characteristics are studied by considering the PS of SC. By this model, the influences of SC pressure, U-tube pitch and circulation ratio on the U-tube reverse flow characteristics are calculated and analyzed. The specific conclusions are summarized as follows: (1) The PC and SC have significant differences in the fluid temperature distributions. The fluid temperature in the PC decreases exponentially along the NFDU. However, the fluid temperature in the SC increases exponentially in the PS and remains unchanged in the boiling section. (2) Compared with the existing reverse flow calculation methods, the critical flow rate is relatively higher, and the critical pressure drop is relatively lower. So the PS will affect the Utube reverse flow. (3) With the increases of SC operating pressure and U-tube pitch as well as circulation ratio, the U-tube flow stability boundary is widened and the reverse flow is not easy to happen.
Acknowledgement This research was financially supported by the National Natural Science Foundation of China (project number 11402300 and 11502298).
Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi.org/10.1016/j.anucene.2019.107064.
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Please cite this article as: M. Li, W. Chen, J. Hao et al., Investigation on reverse flow characteristics in UTSGs with coupled heat transfer between primary and secondary sides, Annals of Nuclear Energy, https://doi.org/10.1016/j.anucene.2019.107064