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One-dimensional design approach to integrated steam generator with helical-coil tube bundles for a sodium-cooled fast reactor
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One-dimensional design approach to integrated steam generator with helical-coil tube bundles for a sodium-cooled fast reactor Namhyeong Kima, Hyungmo Kimc, Jaehyuk Eohc, Moo Hwan Kima,b, HangJin Joa,b,
⁎
a
Division of Advanced Nuclear Engineering, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang 37673, South Korea Department of Mechanical Engineering, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang 37673, South Korea c Korea Atomic Energy Research Institute, Daejeon, South Korea b
A R T I C LE I N FO
A B S T R A C T
Keywords: Sodium-water reaction (SWR) Integrated steam generator (ISG) Helical-coil tube bundles Double tube bundle steam generator (DTBSG)
A potential of a sodium-water reaction in a steam generator (SG) has been known to result in a drastic increase of the capital cost of a sodium-cooled fast reactor (SFR). This is mainly because an essential risk of potential sodium-water reaction (SWR) at the pressure boundary between water/steam and liquid sodium in the SG unit of an SFR. To prevent the SWR event during the whole plant lifetime, the novel design of an integrated steam generator (ISG) concept was proposed and its creative thermal-hydraulic design approach was developed as well. The ISG design for an SFR is based on the concept of combined SG unit with an intermediate heat exchanger (IHX) to make the chance to contact of water vapor with liquid sodium very few. However, it requires far more heat transfer area than that of an existing design with both IHX and SG unit due to the lower thermal conductivity of an alternative intermediate heat transfer medium. In order to minimize the heat transfer area of ISG, its thermal-sizing analyses using three representative design parameters, such as the number of tubes, tube bundle arrangement, and tube inclination angle, were conducted by a one-dimensional analysis code. In this study, the optimal design condition of the integrated steam generator for the reference plant of KALIMER-600 was obtained and the required heat transfer area of the ISG unit was compared to that of the existing SG unit and IHX unit in KALIMER-600. It was found that the proposed ISG design requires 2.25 times of heat transfer area to transport the same amount of heat as the conventional two heat exchanger system.
1. Introduction A sodium-cooled fast reactor (SFR) has an intermediate heat transport system (IHTS) as a safety design feature unlike other types of nuclear power plants (NPPs). The IHTS is a kind of closed loop system containing non-radioactive sodium coolant, which transfers heat from an intermediate heat exchanger (IHX) of a primary heat transport system (PHTS) to a steam generator (SG). Although SG tubes are ruptured and a sodium-water reaction (SWR) occurs subsequently, a pressure boundary of the PHTS can be maintained and an unexpected radioactivity release to the environment can be essentially protected even in that case. However, a potential SWR event in a SG unit in SFRs still worsens plant operability and increases the construction cost of relevant safety design features and special mitigation systems. This feature results in a deterioration of the economics of SFRs when compared to a conventional light water reactor (LWR) type NPPs. Korea Atomic Energy Research Institute (KAERI) proposed an integrated steam generator (ISG) concept, which is an alternative system
⁎
of the IHTS to eliminate a probability of the SWR (Sim et al., 2003; Sim and Kim, 2004). In the proposed ISG unit; separate tube bundles for sodium and water are installed in the same space inside a single-shell, and the gap between the tube bundles is filled with an intermediate heat transfer medium of lead–bismuth eutectic (LBE), which does not chemically react with either sodium or water. This configuration reduces the probability that the sodium can contact the water. Sim and Kim (2004) firstly proposed the ISG concept with helical-coil tube bundles, which was called a double tube bundle steam generator (DTBSG), and analyzed various types of helical-coil tube bundle configuration by using a simplified mathematical model. Kim et al. (2004) developed a one-dimensional analysis code for DTBSG, then Kim et al. (2008) verified the one-dimensional analysis code with experimental data. Choi (2007) conducted multi-dimensional numerical analysis for radially separated DTBSG by using the modified DTBSG COMMIX-AR/P code. Kim and Baek (2011) numerically evaluated the thermo-hydraulic performance of DTBSG in terms of LBE mass flow rate by the one-dimensional analysis code.
Corresponding author at: Division of Advanced Nuclear Engineering, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang 37673, South Korea. E-mail address: [email protected] (H. Jo).
https://doi.org/10.1016/j.nucengdes.2020.110554 Received 11 June 2019; Received in revised form 31 January 2020; Accepted 5 February 2020 0029-5493/ © 2020 Elsevier B.V. All rights reserved.
Please cite this article as: Namhyeong Kim, et al., Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2020.110554
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Fig. 1. Schematics of integrated steam generator.
heat exchangers (Eoh et al., 2011), it was found that the fluid flow across the helical tube bundle implementing the aligned winding model generally swirls over the tube bundle, and there is a rare turbulence effect caused by a cross flow passing the horizontal tube bank. On the other hand, it was also found that the alternate tube row arrangement contributes to mitigating the flow separation around the rear surface of the heat transfer tubes across the flow direction. This feature results in an enhancement of the heat transfer rate of a helically-coiled heat exchanger when compared to the aligned winding model. In addition, the sodium and water tube rows are installed to alternate with each other along the radial direction. This tube bundle arrangement transfers heat locally through the LBE medium in the shellside of ISG unit.
Since the ISG incorporates a single-shell concept eliminating intermediate sodium loop, its structure is relatively simple when compared to the case with the IHTS. However, as LBE coolant is used as a heat transfer medium with poorer heat transfer performance than liquid sodium, more heat transfer area is necessarily required when compared to the conventional SG with IHTS. Therefore, sizing analysis is necessary to minimize the area increase. With regard to the sizing analysis of DTBSG (Kim and Baek, 2011), it was performed with LBE mass flow rate under the fixed geometric condition. Accordingly, in the present study, further analyses on geometric design parameters were conducted using a one-dimensional analysis code for ISG thermal sizing to optimize the design of the ISG. The thermo-hydraulic performance of ISG was evaluated and the optimal design parameters such as the number of tubes, tube bundle arrangement, and tube inclination angle were identified for the reference plant (Kim et al., 2012).
3. Analysis method 2. Conceptual design of integrated steam generator (ISG)
3.1. Analysis code
The main design feature of the ISG concept is the integral-type and the double-region bundle configuration (Sim and Kim, 2004) as shown in Fig. 1. Sodium tube bundles transfer heat from the PHTS to the intermediate medium, and then water tube bundles transfer heat from the intermediate medium to the steam generator system subsequently. The intermediate medium is circulated by a mechanical pump and the flow path is formed by cylindrical baffles (the white lines in Fig. 1) in the shell that envelops all heat transfer tube bundles. Sodium flows downward and water flows upward in consideration of density change. The shell of the ISG unit contains two distinct heat transfer regions, and they have both flow paths for sodium and water. In regard to a helical tubing system, there are generally two kinds of winding methods of helical tubes. One is based on the winding with an aligned direction for all tube rows, and the other is with alternating directions for every other tube row. Based on the previous design experiences on the thermal-sizing of a helically-coiled shell-and-tube type
The one-dimensional analysis code, Sizing and Performance analyzer for INtegrated Steam generator - Helical-coil tube (SPINS-H), was developed to analyze thermo-hydraulic performance of the ISG. The SPINS-H code uses a one-dimensional approximation along the longitudinal direction of heat transfer tubes. The heat transfer calculation in each control volume is described in Fig. 2 using Eqs. (1)–(4). The heat transfer by LBE is assumed to occur simultaneously through both sodium and water tubes because of the local heat transfer. The SPINS-H considered real helical-coil tube configurations. the number of each tubes, tube coiling diameter and flow area of shell were calculated from tube diameter, number of tube coiling rows and tube inclination angle. The correlations, which are used to calculate heat transfer coefficient and pressure drop in the SPINS-H code, are summarized in Table 1. ElGenk and Schriener (2017) showed that the correlation, which matched within 15% with NaK data, also agrees with LBE data to within 20% even though comparing the experimental data for LBE and NaK were 2
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Fig. 2. Heat transfer model in a control volume.
Table 1 Heat transfer and Pressure drop correlations in the SPINS-H code. Heat transfer correlations Sodium Water
Lyon-Martinelli (El-Wakil, 1971) Subcooled/Superheated
Nu = 7.0 + 0.025Pe 0.8
Mori-Nakayama (Mori and Nakayama, 1967)
⎧
4 PrRe 5 2 26.2 ⎛Pr 3 − 0.074⎞
Nu =
Saturated nucleate boiling
Chen (Chen, 1966)
⎜
⎟
⎝
⎠
( )
0.098
⎜
⎟
0.79 0.45 0.49
⎛ kl cp, l ρl ⎞ h = 0.00122 ⎜ 0.5 0.29 0.24 0.24 ⎟ (Tw − Tsat (Pl ))0.24 σ μl ilg ρg ⎝ ⎠
(Psat (Tw ) − Pl )0.75S + 0.023 Departure from nucleate boiling
Duchatelle (Duchatelle et al., 1973)
Film boiling
Bishop (Bishop et al., 1965)
Lead-bismuth eutectic
⎫ ⎪ ⎪ + 1⎬ 2 5 ⎞ ⎛ d ⎪ ⎪ ⎛ i⎞ ⎜Re Dc ⎟ ⎪ ⎪ ⎝ ⎝ ⎠ ⎠ ⎭ ⎩
1 ⎪ di 10 ⎪ 1 Dc ⎨
( ) (Re ) kl di
l
0.8 (Pr )0.4F l
x cr = 1.69 ∗ 10−4q0.719G−0.212exp(2.5 ∗ 10−8P ) ρ
g Nu = 0.0193Re 0.8Pr 1.23 ⎛x + (1 − x ) ⎞ ρl ⎠ ⎝
Kalish-Dwyer (Kalish and Dwyer, 1967)
Nuo =
1 ϕ1 2 do
( )(
1 1 p − do 2 sinβ + sin2 β 2 ⎡ ⎤ 2 p ⎣ 1 + sin β ⎦
)
0.68 ρ 0.068 ⎛ g⎞ ⎝ ρl ⎠
[5.44 + 0.228[Pe]0.614 v, max ]
Pressure drop correlations Sodium Water
Mori-Nakayama (Mori and Nakayama, 1967) Single-phase
Mori-Nakayama (Mori and Nakayama, 1967)
f=
di 0.5 Dc
( )
0.192 1 2.5 ⎛ ⎛ di ⎞ ⎞ 6 ⎟ ⎜Rei Dc ⎝ ⎝ ⎠ ⎠ ⎜
Two-phase
Lead-bismuth eutectic
Homogeneous Equilibrium Model (Carey, 2018)
Gunter-Shaw (Gunter and Shaw, 1945)
3
ΔP =
ΔP =
2fh G2L di
fG2L 2D v ρ
⎟
⎛ ⎜ ⎜1 + ⎜ ⎜ ⎝
⎞ ⎟ ⎟ 1 2.5 ⎛ ⎛ di ⎞ ⎞ 6 ⎟ ⎟ ⎟ ⎜Rei Dc ⎝ ⎝ ⎠ ⎠ ⎠ 0.068
⎜
(vl + xvlg ) + G 2vlg Δx + 0.4 0.6 μw 0.14 D v p ⎛ ⎞ ⎛ L⎞ μ ⎝ pT ⎠ ⎝ pT ⎠
( )
⎟
gLsinθ vl + xvlg
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Table 3 Analysis conditions of ISG compared with KALIMER-600. KALIMER-600
Number of units Heat transfer rate per unit [MWt] PHTS sodium inlet temperature [°C] PHTS sodium inlet pressure [MPa] PHTS sodium mass flow rate per unit [kg/s] Water outlet temperature [°C] Water outlet pressure [MPa] Water mass flow rate per unit [kg/s]
*IHX
*SG
4 387.5 509.8 0.135 2091.5 – – –
2 776.7 – – – 471.2 17.8 344.7
ISG
4 387.05* 510 0.135 2091.5 471.2 17.8 172.3
* Core thermal power: 1548.2 MWt.
3.2. Analysis conditions The thermal sizing analysis was conducted with the system operational conditions of KALIMER-600 (Kim et al., 2012) by using the SPINS-H code. To simulate the same power generation efficiency of KALIMER-600, the temperature and pressure at sodium inlet and at steam outlet were conserved. The number of units of ISG and IHX was set to be identical, and the heat transfer rate was determined quantitatively using the core thermal power of KALIMER-600. The Analysis conditions of ISG are shown in Table 3.
Fig. 3. Validation of the SPINS-H code.
experimental data for parallel flows in bundles, not crossflow in bundles. In addition, we believe that both lead–bismuth eutectic(LBE) and NaK are liquid metals with low Prandtl number so they are expected to be able to apply the same heat transfer correlation. Therefore, the Kalish-Dwyer correlation, which was developed from NaK experimental results, is used for LBE heat transfer correlation. For Kalish-Dwyer correlation, the Peclet number range of design conditions is larger than that of the correlation, however there is little correlations for heat transfer to liquid metal cross-flowing tube bundles. The effect of out range will be evaluated by additional experiments for the integrated steam generator later. The SPINS-H code was verified with the one-dimensional analysis code for DTBSG developed by Kim and Baek (2011) by comparing the results for the same input, and it was found that the SPINS-H code shows good agreement within 3.56% difference as shown in Fig. 3. Additionally, by comparing heat transfer rate and pumping power for same heat transfer area, it is shown that the heat transfer and pressure drop calculation agrees with the previous study as shown in Table 2. The larger pumping power of SPINS-H is considered to be due to minor losses regarding tube chambers. For the sodium tubes, the minor loss constitutes 9.25% of total pressure drop.
3.3. Analysis parameters One of the largest differences between the conventional SGs and the ISG designs is the presence of intermediate heat transfer medium. Since this design feature causes the increase of total thermal resistance, reducing this additional thermal resistance would be one of the key design factors in the ISG thermal-sizing analysis. From the Kalish-Dwyer model (Kalish and Dwyer, 1967) shown in Table 1, the convective heat transfer coefficient of LBE in the shell is affected by pitch-to-diameter ratio, tube inclination angle, and Péclet number. Φ1/do is the theoretical value of the hydrodynamic potential drop as a function of pitch-todiameter ratio (Chia-Jung, 1964). β is the angle between axes of tubes and the direction of flow, and obtained by subtracting the tube inclination angle from 90°. The Péclet number in the Kalish-Dwyer model is defined based on the minimum flow area of shell. The minimum flow area of shell is calculated using Eqs. (5)–(9). The flow area of shell per tube (the yellow region in Fig. 4) is calculated by dividing the occupied area of a tube row (the red region in Fig. 4) by the number of tubes in the row. The width of a tube row is p and the spacing between the tubes in the row is p/sinθ, so the flow area of shell per tube is obtained as Eq. (7). As the flow area of shell per tube has an independent value regardless of position, the total flow area of shell is the product of the flow area of shell per tube and the number of tubes. The minimum flow area of shell is obtained as Eq. (9) from the definition in the KalishDwyer model. Therefore, the heat transfer coefficient of LBE is affected by the pitch-to-diameter ratio, tube inclination angle, tube diameter and the number of tubes. In this study, the diameter of tube and the pitch-to-diameter ratio were fixed at 27.2 mm and 1.5, respectively. In addition, the arrangement method of tube bundles affecting the temperature distribution of the heat transfer fluids was proposed as a parameter. Eventually, the number of tubes, the tube bundle arrangement, and the tube inclination angle were selected as the parameters for the ISG thermal-sizing analysis.
(1)
Q = UAΔT
1
U=
1 hshell
+
1 hF , shell
+
do ln 2k
( )+ do di
do 1 di hF , tube
+
do 1 di htube
(2) (3)
A = Ntube ∗ πdo L
ΔT =
(Ttube, j + 1 − Tshell, j + 1) − (Ttube, j − Tshell, j ) ln
(
Ttube, j + 1 − Tshell, j + 1 Ttube, j − Tshell, j
)
(4)
Table 2 Comparison of between SPINS-H and Kim & Baek at LBE mass flow rate of 400 kg/s.
Heat transfer rate [MWth] LBE mass flow rate [kg/s] Heat transfer area [m2] Sodium pumping power [kW] LBE pumping power [kW] Water pumping power [kW] Heat flux [kW/m2]
SPINS-H
Kim & Baek
192.728 400 2447 1128.269 0.526464 13.09056 78.71332
197.3 400 2447 972 0.4 12.6 80.6
Arow =
Nrow =
4
π [(Di + 2p)2 − Di2] 4
(5)
π (Di + p) p sinθ
(6)
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Fig. 4. Cross-sectional flow area of shell.
Ashell =
p2 Arow = Nrow sinθ
4.2. Tube bundle arrangement (7)
Ashell, tot = Ntube ∗ p2 / sinθ
Ashell, min =
p−d ∗ Ashell, tot = Ntube ∗ d 2 ∗ p
In the ISG design, the temperature distributions in the sodium, water and LBE determines the magnitude of heat transfer rate among them, and even worse, can make the direction of heat transfer opposite to the desired direction; the ‘reversed heat transfer’ (RHT) (Sim and
(8) p d
(
p d
)
−1
sinθ
(9)
4. Results 4.1. The number of heat transfer tubes The number of heat transfer tubes is an important parameter for determining thermo-hydraulic performance of a heat exchanger. As the number of tubes decreases at a given mass flow rate, the heat transfer area decreases, and the pressure drop increases. In order to compare the ISG with the existing SG, the heat transfer areas should be compared under the same conditions of heat transfer rate and pressure drop. Since the heat transfer rates are constant as the analysis conditions, the pressure drops of the two SGs should be identical. The pressure drops of primary sodium were compared as the representative value of pressure drop. The heat transfer area and primary pressure drop of the ISG at LBE mass flow rate of 1000 kg/s are shown in Fig. 5. From the result, the present study set the number of tubes as 6035 to 6041 to make the primary pressure drop of the ISG be similar to that of the IHX of KALIMER-600, 19.6 kPa.
Fig. 5. Heat transfer area and Primary pressure drop according to the number of tubes of the ISG at LBE mass flow rate of 1000 kg/s.
Fig. 6. Temperature distribution of the ISG (a) inner region, (b) outer region (LBE mass flow rate: 3000 kg/s, inclination angle: 15°). 5
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Fig. 7. Schematics of Even arrangement and Odd arrangement.
Kim, 2004). The RHT is a local phenomenon that happens when the LBE is hotter than the sodium or cooler than the water like the green boxs in Fig. 6. The RHT is observed when the LBE has a high mass flow rate, and thereby places a constraint on the heat transfer performance of the ISG unit even if the LBE mass flow rate is increased. To suppress the occurrence of the undesirable RHT and increase the heat transfer performance of the ISG, this study considered two methods to divide whole helical-coil tube bundles into two heat transfer regions, which not significantly impairing the local heat transfer as shown in Fig. 7. The first method is to place the same number of sodium tube rows and water tube rows in each region (the ‘even’ arrangement); the other method is to place one fewer water tube rows than sodium tube rows in the inner region, and one more water tube row in the outer region (the ‘odd’ arrangement). For the odd arrangement compared to the even arrangement, the inner region has one less water row, and the outer region has one more water row. Overall, the number of each tube rows is the same in the both arrangements. The temperature distributions of sodium and water in each heat transfer region are affected by the average heat capacity ratio of sodium to water, R, which is expressed by Eq. (10). The average heat capacity ratio can be calculated by dividing the heat transfer rate by the temperature difference for each fluid. As the average heat capacity ratio increases, the temperature change of sodium becomes small. Conversely, as the average heat capacity ratio decreases, the temperature change of water becomes small.
Table 4 Comparison between the even and odd arrangement at LBE mass flow rate of 2000 kg/s.
*Inner region Number of sodium rows Number of water rows Number of sodium tubes Number of water tubes
28 28 1533 1575
28 27 1533 1475
Heat capacity ratio
1.638
1.762
Temperature change of sodium [°C] Temperature change of water [°C]
169.9 229.6
163.4 232.1
*Outer region Number of sodium rows Number of water rows Number of sodium tubes Number of water tubes
12 12 1454 1473
12 13 1454 1575
Heat capacity ratio
1.885
1.740
Temperature change of sodium [°C] Temperature change of water [°C]
118.7 283.1
125.5 276.7
11,995
10,976
not considered mainly in this paper. As shown in Fig. 9, optimal mass flow rates that minimized the heat transfer area for each tube inclination angles exists due to the RHT, and the mass flow rate of the optimal point increases as the tube inclination angle increases. The heat transfer area of the ISG is smallest at LBE mass flow rate of 1750 kg/s and tube inclination angle of 45°. The number of tubes arranged in a tube row is proportional to the coiling diameter of the tube row, and the sodium tube rows alternate with the water tube rows. So, the ratio between the number of sodium tubes and water tubes is almost the same as the ratio between the number of sodium rows and water rows in each heat transfer region as shown in Table 5. As the tube inclination angle increases, the space between tubes in a tube row, p/sinθ, decreases as shown in Fig. 10, and more tubes are contained in the row. Therefore, the total number of tube rows decreases, and the effect of a tube row due to the odd arrangement becomes larger. The discrepancy of tube number ratio (or tube row ratio) between inner region and outer region increases with increasing the tube inclination angle. It means that the amount of heat capacity ratio change between the two regions becomes larger. Therefore, the suppression effect of the odd arrangement on RHT becomes larger, and it explains why the LBE mass flow rate of the optimal point increases as the tube inclination angle increases. There are different optimal tube inclination angles depending on the
̇ p)sodium (mc −
̇ p) water (mc
Odd arrangement
Heat transfer area [m2]
−
R=
Even arrangement
(10)
The average heat capacity ratio in the inner region is larger in the odd arrangement when compared to the even arrangement, and that in the outer region is smaller because of the difference of the number of water row. This condition reduces the temperature change of sodium in inner region and reduces the temperature change of water in the outer region. Table 4 and Fig. 8 show the comparison result about temperature distributions and heat transfer area between the even arrangement and the odd arrangement when the LBE mass flow rate is 2000 kg/s. The temperature distribution in the odd arrangement is relatively far from the temperature distribution in which RHT can occur, and the heat transfer area is also smaller than that of the even arrangement. 4.3. Tube inclination angle The effect of tube inclination angle was analyzed by comparing the heat transfer area required for the same heat transfer rate at the angles of 5° to 55° and LBE mass flow rates of 250 to 3000 kg/s. To increase the LBE mass flow rate, more pumping power is required. However, the required pumping power to circulate LBE is relatively lower than the existing IHTS of KALIMER-600 because of low velocity of LBE. So it was 6
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Fig. 8. Comparison of temperature distribution between the even and odd arrangement at LBE mass flow rate of 2000 kg/s. Table 5 The number of tubes and the number of tube rows according to tube inclination angles. Inclination angle [°] *Inner region Number of tubes for sodium Number of tubes for water Sodium tubes/water tubes Number of tube coiling rows for sodium Number of tube coiling rows for water Sodium rows/water rows *Outer region Number of tubes for sodium Number of tubes for water Sodium tubes/water tubes Number of tube coiling rows for sodium Number of tube coiling rows for water Sodium rows/water rows
Fig. 9. Heat transfer area along LBE mass flow rate with the inclination angle variation.
value of LBE mass flow rate. The tube inclination angle has an effect on the minimum flow area of the intermediate fluid as described by Eq. (9). As the tube inclination angle increases, the Péclet number term increases, and the Nusselt number of LBE increases. The tube
5
15
25
35
45
55
1529 1501 1.019 50
1533 1475 1.039 28
1572 1500 1.048 22
1521 1436 1.059 18
1547 1449 1.068 16
1635 1526 1.071 15
49
27
21
17
15
14
1.020
1.037
1.048
1.059
1.067
1.071
1469 1538 0.955 21
1454 1575 0.923 12
1404 1560 0.9 9
1450 1631 0.889 8
1419 1621 0.875 7
1329 1551 0.857 6
22
13
10
9
8
7
0.955
0.923
0.9
0.889
0.875
0.857
inclination angle term itself also affects the Nusselt number of LBE in the Kalish-Dwyer model (Kalish and Dwyer, 1967). The individual effects of two terms for LBE mass flow rate of 250 kg/s and 1750 kg/s are 7
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Fig. 10. Tube spacing at tube inclination angles of 15° and 45°. Table 6 Optimal condition of ISG for KALIMER-600. Parameters
ISG
Heat transfer rate [MWth] Number of sodium tubes [ea] Number of water tubes [ea] Outer diameter of tube [mm] Tube thickness for sodium [mm] Tube thickness for water [mm] Length of tubes [m] Height of tube bundles [m] LBE mass flow rate [kg/s] Inclination angle [°] Pitch-to-diameter ratio Heat transfer area [m2] Frictional pressure drop of sodium [kPa] Frictional pressure drop of LBE [kPa] Frictional pressure drop of water [kPa]
387.0 2966 3070 27.2 1.65 2.9 19.18 13.6 1750 45 1.5 9894 22.9 3.51 1.77
Table 7 Design data of IHTS of KALIMER-600. *IHX Number of units Heat transfer area per unit [m2] PHTS pressure drop [kPa]
4 1571 19.6
*SG Number of units Heat transfer area per unit [m2]
2 5638
*Total Total heat transfer area [m2] Total heat transfer area per 4 units [m2]
17,560 4390
shown in Fig. 11. The larger the LBE mass flow rate, the greater the variation of the Péclet number term with the tube inclination angle. But the variation in the tube inclination angle term is constant. Therefore, the optimal tube inclination angle is different in the case of 250 kg/s and 1750 kg/s.
Fig. 11. Effect of tube inclination angle on Nusselt number at LBE mass flow rate of (a) 250 kg/s, (b) 1750 kg/s.
8
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4.4. Optimal condition for KALIMER-600
CRediT authorship contribution statement
The optimal condition for KALIMER-600 was calculated using the results presented here as shown in Table 6, and compared with the IHTS of KALIMER-600 presented in Table 7. Only the heat transfer areas of IHX and SG, except piping system, were used for comparison, and the heat transfer area of IHTS was calculated as the value of total heat transfer areas of IHX and SG divided by the number of ISG unit. The heat transfer area of ISG should be 2.25 times of that of the IHTS to transfer the same amount of heat at the same condition of PHTS pressure drop.
Namhyeong Kim: Data curation, Formal analysis, Methodology, Software, Writing - original draft, Writing - review & editing. Hyungmo Kim: Formal analysis, Methodology, Software, Writing - review & editing. Jaehyuk Eoh: Conceptualization, Funding acquisition, Writing - review & editing. Moo Hwan Kim: Funding acquisition, Supervision, Writing - review & editing. HangJin Jo: Formal analysis, Funding acquisition, Supervision, Writing - review & editing.
5. Conclusion
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Declaration of Competing Interest
Thermal-sizing analysis of the novel ISG unit design was conducted, mainly on geometric design parameters. The goal of analysis was to minimize the additional heat transfer area that is required to compensate for the add-on thermal resistance of the intermediate heat transfer medium. The results of thermal-sizing and resultant heat transfer performance were quantitatively investigated by comparing the required heat transfer area under different conditions, such as the number of tubes, types of tube arrangement, and tube inclination angles.
•
•
•
Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (Ministry of Science and ICT). (NRF-2016M2B2B1944980, 2016M2B2B1944981). References
The changes of heat transfer area and pressure drop of the ISG according to the variation of the number of tubes were observed. In order to compare the ISG with the SG of KALIMER-600 at the identical heat transfer rate and primary pressure drop conditions, the number of tubes was set to have the primary pressure drop close to that of the existing SG. The two methods of tube bundle arrangement, the ‘even’ and ‘odd’ arrangement, were creatively proposed complying with the method of dividing set of tube rows into two distinct heat transfer regions. The ‘odd’ arrangement has a smaller temperature gradient between the two regions, reducing the occurrence of the RHT, and lower required heat transfer area, than does the ‘even’ arrangement. The variation with the tube inclination angle was analyzed by dividing into the change of the optimal LBE mass flow rate and the change of the optimal tube inclination angle. Due to the occurrence of RHT, the optimal point is obtained in which the heat transfer performance no longer increase even when the LBE mass flow rate increases. The odd arrangement has the suppression effect on the RHT, which is increased with the increase of the tube inclination angle. Thus, the optimal LBE mass flow rate increases. The optimal tube inclination angle is determined by the tube inclination angle term and the Péclet number term included in the heat transfer correlation. The tube inclination angle term is constant regardless of the mass flow rate, whereas the Péclet number term increases significantly with larger LBE mass flow rate, so the optimal tube inclination angle has different values depending on the LBE mass flow rate. As a result, the heat transfer area was minimal at an inclination angle of 45° and an LBE mass flow rate of 1750 kg/s.
Bishop, A.A., Sandberg, R., Tong, L., 1965. Forced convection heat transfer at high pressure after critical heat flux. In: Mechanical Engineering. ASME-AMER Soc. Mechanical Eng. 345 E 47th St., New York, NY 10017. Carey, V.P., 2018. Liquid Vapor Phase Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment. CRC Press. Chen, J.C., 1966. Correlation for boiling heat transfer to saturated fluids in convective flow. Ind. Eng. Chem. Process Des. Dev. 5 (3), 322–329. Chia-Jung, H., 1964. Analytical study of heat transfer to liquid metals in cross-flow through rod bundles. Int. J. Heat Mass Transf. 7 (4), 431–446. Choi, B.Y., 2007. Study on Multidimensional Numerical Analysis and Heat Transfer Characteristics of Radially Separated Double Tubed Bundel Steam Generator, in Department of Mechanical Engineering. Chonnam National University. Duchatelle, L., De Nucheze, L., Robin, M., 1973. Departure from nucleate boiling in helical tubes of liquid metal heated steam generators. ASME Paper. (73-HT): p. 57. El-Genk, M.S., Schriener, T.M., 2017. A review of experimental data and heat transfer correlations for parallel flow of alkali liquid metals and lead-bismuth eutectic in bundles. Nucl. Eng. Des. 317, 199–219. El-Wakil, M.M., 1971. Nuclear Heat Transport. Eoh, J.H., et al., 2011. Design and evaluation of the helical-coil sodium-to-air heat exchanger of stella-1. Gunter, A., Shaw, W., 1945. A general correlation of friction factors for various types of surfaces in cross flow. Trans. ASME 67 (8), 643–660. Kalish, S., Dwyer, O.E., 1967. Heat transfer to NaK flowing through unbaffled rod bundles. Int. J. Heat Mass Transf. 10 (11), 1533–1558. Kim, E.K., et al., 2004. Development of a thermal hydraulic analysis code for a combined steam generator-IHX heat exchanger (Integrated Type). Transactions of the Korean Nuclear Society Spring Meeting. Kim, S., et al., 2008. Verification and refinement of the one-dimensional analysis code for the integrated steam generators in an SFR. Int. Commun. Heat Mass Transf. 35 (1), 12–20. Kim, E.-K., Baek, B.-J., 2011. Thermal hydraulic performance analysis of a double tube bundle steam generator for a liquid metal reactor. Ann. Nucl. Energy 38 (12), 2625–2633. Kim, Y., et al., Conceptual design report of SFR Demonstration Reactor of 600MWe capacity, in KAERI/TR-4598. 2012, Korea Atomic Energy Research Institute Daejeon, Republic of Korea. Mori, Y., Nakayama, W., 1967. Study of forced convective heat transfer in curved pipes (2nd report, turbulent region). Int. J. Heat Mass Transf. 10 (1), 37–59. Sim, Y.-S., et al., 2003. A new LMR SG with a double tube bundle free from SWR. Nucl. Eng. Technol. 35 (6), 566–580. Sim, Y.S., Kim, E.K., 2004. Characteristics of the integrated steam generators for a liquid metal reactor. Nucl. Eng. Technol. 36 (2), 127–141.
As the result of the optimal condition of the proposed ISG design for KALIMER-600, the ISG has heat transfer area that is 2.25 times that of IHX-and-SG system at the same heat transfer rate and PHTS pressure drop condition. However, the ISG has great advantages of the safety improvement of SFRs by preventing the occurrence of SWR, and can be expected to make simple the IHTS by substituting the conventional piping system with the single-shell component although only for looptype reactors.
9
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Nuclear Engineering and Design journal homepage: www.elsevier.com/locate/nucengdes
One-dimensional design approach to integrated steam generator with helical-coil tube bundles for a sodium-cooled fast reactor Namhyeong Kima, Hyungmo Kimc, Jaehyuk Eohc, Moo Hwan Kima,b, HangJin Joa,b,
⁎
a
Division of Advanced Nuclear Engineering, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang 37673, South Korea Department of Mechanical Engineering, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang 37673, South Korea c Korea Atomic Energy Research Institute, Daejeon, South Korea b
A R T I C LE I N FO
A B S T R A C T
Keywords: Sodium-water reaction (SWR) Integrated steam generator (ISG) Helical-coil tube bundles Double tube bundle steam generator (DTBSG)
A potential of a sodium-water reaction in a steam generator (SG) has been known to result in a drastic increase of the capital cost of a sodium-cooled fast reactor (SFR). This is mainly because an essential risk of potential sodium-water reaction (SWR) at the pressure boundary between water/steam and liquid sodium in the SG unit of an SFR. To prevent the SWR event during the whole plant lifetime, the novel design of an integrated steam generator (ISG) concept was proposed and its creative thermal-hydraulic design approach was developed as well. The ISG design for an SFR is based on the concept of combined SG unit with an intermediate heat exchanger (IHX) to make the chance to contact of water vapor with liquid sodium very few. However, it requires far more heat transfer area than that of an existing design with both IHX and SG unit due to the lower thermal conductivity of an alternative intermediate heat transfer medium. In order to minimize the heat transfer area of ISG, its thermal-sizing analyses using three representative design parameters, such as the number of tubes, tube bundle arrangement, and tube inclination angle, were conducted by a one-dimensional analysis code. In this study, the optimal design condition of the integrated steam generator for the reference plant of KALIMER-600 was obtained and the required heat transfer area of the ISG unit was compared to that of the existing SG unit and IHX unit in KALIMER-600. It was found that the proposed ISG design requires 2.25 times of heat transfer area to transport the same amount of heat as the conventional two heat exchanger system.
1. Introduction A sodium-cooled fast reactor (SFR) has an intermediate heat transport system (IHTS) as a safety design feature unlike other types of nuclear power plants (NPPs). The IHTS is a kind of closed loop system containing non-radioactive sodium coolant, which transfers heat from an intermediate heat exchanger (IHX) of a primary heat transport system (PHTS) to a steam generator (SG). Although SG tubes are ruptured and a sodium-water reaction (SWR) occurs subsequently, a pressure boundary of the PHTS can be maintained and an unexpected radioactivity release to the environment can be essentially protected even in that case. However, a potential SWR event in a SG unit in SFRs still worsens plant operability and increases the construction cost of relevant safety design features and special mitigation systems. This feature results in a deterioration of the economics of SFRs when compared to a conventional light water reactor (LWR) type NPPs. Korea Atomic Energy Research Institute (KAERI) proposed an integrated steam generator (ISG) concept, which is an alternative system
⁎
of the IHTS to eliminate a probability of the SWR (Sim et al., 2003; Sim and Kim, 2004). In the proposed ISG unit; separate tube bundles for sodium and water are installed in the same space inside a single-shell, and the gap between the tube bundles is filled with an intermediate heat transfer medium of lead–bismuth eutectic (LBE), which does not chemically react with either sodium or water. This configuration reduces the probability that the sodium can contact the water. Sim and Kim (2004) firstly proposed the ISG concept with helical-coil tube bundles, which was called a double tube bundle steam generator (DTBSG), and analyzed various types of helical-coil tube bundle configuration by using a simplified mathematical model. Kim et al. (2004) developed a one-dimensional analysis code for DTBSG, then Kim et al. (2008) verified the one-dimensional analysis code with experimental data. Choi (2007) conducted multi-dimensional numerical analysis for radially separated DTBSG by using the modified DTBSG COMMIX-AR/P code. Kim and Baek (2011) numerically evaluated the thermo-hydraulic performance of DTBSG in terms of LBE mass flow rate by the one-dimensional analysis code.
Corresponding author at: Division of Advanced Nuclear Engineering, POSTECH, 77 Cheongam-ro, Nam-gu, Pohang 37673, South Korea. E-mail address: [email protected] (H. Jo).
https://doi.org/10.1016/j.nucengdes.2020.110554 Received 11 June 2019; Received in revised form 31 January 2020; Accepted 5 February 2020 0029-5493/ © 2020 Elsevier B.V. All rights reserved.
Please cite this article as: Namhyeong Kim, et al., Nuclear Engineering and Design, https://doi.org/10.1016/j.nucengdes.2020.110554
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Fig. 1. Schematics of integrated steam generator.
heat exchangers (Eoh et al., 2011), it was found that the fluid flow across the helical tube bundle implementing the aligned winding model generally swirls over the tube bundle, and there is a rare turbulence effect caused by a cross flow passing the horizontal tube bank. On the other hand, it was also found that the alternate tube row arrangement contributes to mitigating the flow separation around the rear surface of the heat transfer tubes across the flow direction. This feature results in an enhancement of the heat transfer rate of a helically-coiled heat exchanger when compared to the aligned winding model. In addition, the sodium and water tube rows are installed to alternate with each other along the radial direction. This tube bundle arrangement transfers heat locally through the LBE medium in the shellside of ISG unit.
Since the ISG incorporates a single-shell concept eliminating intermediate sodium loop, its structure is relatively simple when compared to the case with the IHTS. However, as LBE coolant is used as a heat transfer medium with poorer heat transfer performance than liquid sodium, more heat transfer area is necessarily required when compared to the conventional SG with IHTS. Therefore, sizing analysis is necessary to minimize the area increase. With regard to the sizing analysis of DTBSG (Kim and Baek, 2011), it was performed with LBE mass flow rate under the fixed geometric condition. Accordingly, in the present study, further analyses on geometric design parameters were conducted using a one-dimensional analysis code for ISG thermal sizing to optimize the design of the ISG. The thermo-hydraulic performance of ISG was evaluated and the optimal design parameters such as the number of tubes, tube bundle arrangement, and tube inclination angle were identified for the reference plant (Kim et al., 2012).
3. Analysis method 2. Conceptual design of integrated steam generator (ISG)
3.1. Analysis code
The main design feature of the ISG concept is the integral-type and the double-region bundle configuration (Sim and Kim, 2004) as shown in Fig. 1. Sodium tube bundles transfer heat from the PHTS to the intermediate medium, and then water tube bundles transfer heat from the intermediate medium to the steam generator system subsequently. The intermediate medium is circulated by a mechanical pump and the flow path is formed by cylindrical baffles (the white lines in Fig. 1) in the shell that envelops all heat transfer tube bundles. Sodium flows downward and water flows upward in consideration of density change. The shell of the ISG unit contains two distinct heat transfer regions, and they have both flow paths for sodium and water. In regard to a helical tubing system, there are generally two kinds of winding methods of helical tubes. One is based on the winding with an aligned direction for all tube rows, and the other is with alternating directions for every other tube row. Based on the previous design experiences on the thermal-sizing of a helically-coiled shell-and-tube type
The one-dimensional analysis code, Sizing and Performance analyzer for INtegrated Steam generator - Helical-coil tube (SPINS-H), was developed to analyze thermo-hydraulic performance of the ISG. The SPINS-H code uses a one-dimensional approximation along the longitudinal direction of heat transfer tubes. The heat transfer calculation in each control volume is described in Fig. 2 using Eqs. (1)–(4). The heat transfer by LBE is assumed to occur simultaneously through both sodium and water tubes because of the local heat transfer. The SPINS-H considered real helical-coil tube configurations. the number of each tubes, tube coiling diameter and flow area of shell were calculated from tube diameter, number of tube coiling rows and tube inclination angle. The correlations, which are used to calculate heat transfer coefficient and pressure drop in the SPINS-H code, are summarized in Table 1. ElGenk and Schriener (2017) showed that the correlation, which matched within 15% with NaK data, also agrees with LBE data to within 20% even though comparing the experimental data for LBE and NaK were 2
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Fig. 2. Heat transfer model in a control volume.
Table 1 Heat transfer and Pressure drop correlations in the SPINS-H code. Heat transfer correlations Sodium Water
Lyon-Martinelli (El-Wakil, 1971) Subcooled/Superheated
Nu = 7.0 + 0.025Pe 0.8
Mori-Nakayama (Mori and Nakayama, 1967)
⎧
4 PrRe 5 2 26.2 ⎛Pr 3 − 0.074⎞
Nu =
Saturated nucleate boiling
Chen (Chen, 1966)
⎜
⎟
⎝
⎠
( )
0.098
⎜
⎟
0.79 0.45 0.49
⎛ kl cp, l ρl ⎞ h = 0.00122 ⎜ 0.5 0.29 0.24 0.24 ⎟ (Tw − Tsat (Pl ))0.24 σ μl ilg ρg ⎝ ⎠
(Psat (Tw ) − Pl )0.75S + 0.023 Departure from nucleate boiling
Duchatelle (Duchatelle et al., 1973)
Film boiling
Bishop (Bishop et al., 1965)
Lead-bismuth eutectic
⎫ ⎪ ⎪ + 1⎬ 2 5 ⎞ ⎛ d ⎪ ⎪ ⎛ i⎞ ⎜Re Dc ⎟ ⎪ ⎪ ⎝ ⎝ ⎠ ⎠ ⎭ ⎩
1 ⎪ di 10 ⎪ 1 Dc ⎨
( ) (Re ) kl di
l
0.8 (Pr )0.4F l
x cr = 1.69 ∗ 10−4q0.719G−0.212exp(2.5 ∗ 10−8P ) ρ
g Nu = 0.0193Re 0.8Pr 1.23 ⎛x + (1 − x ) ⎞ ρl ⎠ ⎝
Kalish-Dwyer (Kalish and Dwyer, 1967)
Nuo =
1 ϕ1 2 do
( )(
1 1 p − do 2 sinβ + sin2 β 2 ⎡ ⎤ 2 p ⎣ 1 + sin β ⎦
)
0.68 ρ 0.068 ⎛ g⎞ ⎝ ρl ⎠
[5.44 + 0.228[Pe]0.614 v, max ]
Pressure drop correlations Sodium Water
Mori-Nakayama (Mori and Nakayama, 1967) Single-phase
Mori-Nakayama (Mori and Nakayama, 1967)
f=
di 0.5 Dc
( )
0.192 1 2.5 ⎛ ⎛ di ⎞ ⎞ 6 ⎟ ⎜Rei Dc ⎝ ⎝ ⎠ ⎠ ⎜
Two-phase
Lead-bismuth eutectic
Homogeneous Equilibrium Model (Carey, 2018)
Gunter-Shaw (Gunter and Shaw, 1945)
3
ΔP =
ΔP =
2fh G2L di
fG2L 2D v ρ
⎟
⎛ ⎜ ⎜1 + ⎜ ⎜ ⎝
⎞ ⎟ ⎟ 1 2.5 ⎛ ⎛ di ⎞ ⎞ 6 ⎟ ⎟ ⎟ ⎜Rei Dc ⎝ ⎝ ⎠ ⎠ ⎠ 0.068
⎜
(vl + xvlg ) + G 2vlg Δx + 0.4 0.6 μw 0.14 D v p ⎛ ⎞ ⎛ L⎞ μ ⎝ pT ⎠ ⎝ pT ⎠
( )
⎟
gLsinθ vl + xvlg
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Table 3 Analysis conditions of ISG compared with KALIMER-600. KALIMER-600
Number of units Heat transfer rate per unit [MWt] PHTS sodium inlet temperature [°C] PHTS sodium inlet pressure [MPa] PHTS sodium mass flow rate per unit [kg/s] Water outlet temperature [°C] Water outlet pressure [MPa] Water mass flow rate per unit [kg/s]
*IHX
*SG
4 387.5 509.8 0.135 2091.5 – – –
2 776.7 – – – 471.2 17.8 344.7
ISG
4 387.05* 510 0.135 2091.5 471.2 17.8 172.3
* Core thermal power: 1548.2 MWt.
3.2. Analysis conditions The thermal sizing analysis was conducted with the system operational conditions of KALIMER-600 (Kim et al., 2012) by using the SPINS-H code. To simulate the same power generation efficiency of KALIMER-600, the temperature and pressure at sodium inlet and at steam outlet were conserved. The number of units of ISG and IHX was set to be identical, and the heat transfer rate was determined quantitatively using the core thermal power of KALIMER-600. The Analysis conditions of ISG are shown in Table 3.
Fig. 3. Validation of the SPINS-H code.
experimental data for parallel flows in bundles, not crossflow in bundles. In addition, we believe that both lead–bismuth eutectic(LBE) and NaK are liquid metals with low Prandtl number so they are expected to be able to apply the same heat transfer correlation. Therefore, the Kalish-Dwyer correlation, which was developed from NaK experimental results, is used for LBE heat transfer correlation. For Kalish-Dwyer correlation, the Peclet number range of design conditions is larger than that of the correlation, however there is little correlations for heat transfer to liquid metal cross-flowing tube bundles. The effect of out range will be evaluated by additional experiments for the integrated steam generator later. The SPINS-H code was verified with the one-dimensional analysis code for DTBSG developed by Kim and Baek (2011) by comparing the results for the same input, and it was found that the SPINS-H code shows good agreement within 3.56% difference as shown in Fig. 3. Additionally, by comparing heat transfer rate and pumping power for same heat transfer area, it is shown that the heat transfer and pressure drop calculation agrees with the previous study as shown in Table 2. The larger pumping power of SPINS-H is considered to be due to minor losses regarding tube chambers. For the sodium tubes, the minor loss constitutes 9.25% of total pressure drop.
3.3. Analysis parameters One of the largest differences between the conventional SGs and the ISG designs is the presence of intermediate heat transfer medium. Since this design feature causes the increase of total thermal resistance, reducing this additional thermal resistance would be one of the key design factors in the ISG thermal-sizing analysis. From the Kalish-Dwyer model (Kalish and Dwyer, 1967) shown in Table 1, the convective heat transfer coefficient of LBE in the shell is affected by pitch-to-diameter ratio, tube inclination angle, and Péclet number. Φ1/do is the theoretical value of the hydrodynamic potential drop as a function of pitch-todiameter ratio (Chia-Jung, 1964). β is the angle between axes of tubes and the direction of flow, and obtained by subtracting the tube inclination angle from 90°. The Péclet number in the Kalish-Dwyer model is defined based on the minimum flow area of shell. The minimum flow area of shell is calculated using Eqs. (5)–(9). The flow area of shell per tube (the yellow region in Fig. 4) is calculated by dividing the occupied area of a tube row (the red region in Fig. 4) by the number of tubes in the row. The width of a tube row is p and the spacing between the tubes in the row is p/sinθ, so the flow area of shell per tube is obtained as Eq. (7). As the flow area of shell per tube has an independent value regardless of position, the total flow area of shell is the product of the flow area of shell per tube and the number of tubes. The minimum flow area of shell is obtained as Eq. (9) from the definition in the KalishDwyer model. Therefore, the heat transfer coefficient of LBE is affected by the pitch-to-diameter ratio, tube inclination angle, tube diameter and the number of tubes. In this study, the diameter of tube and the pitch-to-diameter ratio were fixed at 27.2 mm and 1.5, respectively. In addition, the arrangement method of tube bundles affecting the temperature distribution of the heat transfer fluids was proposed as a parameter. Eventually, the number of tubes, the tube bundle arrangement, and the tube inclination angle were selected as the parameters for the ISG thermal-sizing analysis.
(1)
Q = UAΔT
1
U=
1 hshell
+
1 hF , shell
+
do ln 2k
( )+ do di
do 1 di hF , tube
+
do 1 di htube
(2) (3)
A = Ntube ∗ πdo L
ΔT =
(Ttube, j + 1 − Tshell, j + 1) − (Ttube, j − Tshell, j ) ln
(
Ttube, j + 1 − Tshell, j + 1 Ttube, j − Tshell, j
)
(4)
Table 2 Comparison of between SPINS-H and Kim & Baek at LBE mass flow rate of 400 kg/s.
Heat transfer rate [MWth] LBE mass flow rate [kg/s] Heat transfer area [m2] Sodium pumping power [kW] LBE pumping power [kW] Water pumping power [kW] Heat flux [kW/m2]
SPINS-H
Kim & Baek
192.728 400 2447 1128.269 0.526464 13.09056 78.71332
197.3 400 2447 972 0.4 12.6 80.6
Arow =
Nrow =
4
π [(Di + 2p)2 − Di2] 4
(5)
π (Di + p) p sinθ
(6)
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Fig. 4. Cross-sectional flow area of shell.
Ashell =
p2 Arow = Nrow sinθ
4.2. Tube bundle arrangement (7)
Ashell, tot = Ntube ∗ p2 / sinθ
Ashell, min =
p−d ∗ Ashell, tot = Ntube ∗ d 2 ∗ p
In the ISG design, the temperature distributions in the sodium, water and LBE determines the magnitude of heat transfer rate among them, and even worse, can make the direction of heat transfer opposite to the desired direction; the ‘reversed heat transfer’ (RHT) (Sim and
(8) p d
(
p d
)
−1
sinθ
(9)
4. Results 4.1. The number of heat transfer tubes The number of heat transfer tubes is an important parameter for determining thermo-hydraulic performance of a heat exchanger. As the number of tubes decreases at a given mass flow rate, the heat transfer area decreases, and the pressure drop increases. In order to compare the ISG with the existing SG, the heat transfer areas should be compared under the same conditions of heat transfer rate and pressure drop. Since the heat transfer rates are constant as the analysis conditions, the pressure drops of the two SGs should be identical. The pressure drops of primary sodium were compared as the representative value of pressure drop. The heat transfer area and primary pressure drop of the ISG at LBE mass flow rate of 1000 kg/s are shown in Fig. 5. From the result, the present study set the number of tubes as 6035 to 6041 to make the primary pressure drop of the ISG be similar to that of the IHX of KALIMER-600, 19.6 kPa.
Fig. 5. Heat transfer area and Primary pressure drop according to the number of tubes of the ISG at LBE mass flow rate of 1000 kg/s.
Fig. 6. Temperature distribution of the ISG (a) inner region, (b) outer region (LBE mass flow rate: 3000 kg/s, inclination angle: 15°). 5
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Fig. 7. Schematics of Even arrangement and Odd arrangement.
Kim, 2004). The RHT is a local phenomenon that happens when the LBE is hotter than the sodium or cooler than the water like the green boxs in Fig. 6. The RHT is observed when the LBE has a high mass flow rate, and thereby places a constraint on the heat transfer performance of the ISG unit even if the LBE mass flow rate is increased. To suppress the occurrence of the undesirable RHT and increase the heat transfer performance of the ISG, this study considered two methods to divide whole helical-coil tube bundles into two heat transfer regions, which not significantly impairing the local heat transfer as shown in Fig. 7. The first method is to place the same number of sodium tube rows and water tube rows in each region (the ‘even’ arrangement); the other method is to place one fewer water tube rows than sodium tube rows in the inner region, and one more water tube row in the outer region (the ‘odd’ arrangement). For the odd arrangement compared to the even arrangement, the inner region has one less water row, and the outer region has one more water row. Overall, the number of each tube rows is the same in the both arrangements. The temperature distributions of sodium and water in each heat transfer region are affected by the average heat capacity ratio of sodium to water, R, which is expressed by Eq. (10). The average heat capacity ratio can be calculated by dividing the heat transfer rate by the temperature difference for each fluid. As the average heat capacity ratio increases, the temperature change of sodium becomes small. Conversely, as the average heat capacity ratio decreases, the temperature change of water becomes small.
Table 4 Comparison between the even and odd arrangement at LBE mass flow rate of 2000 kg/s.
*Inner region Number of sodium rows Number of water rows Number of sodium tubes Number of water tubes
28 28 1533 1575
28 27 1533 1475
Heat capacity ratio
1.638
1.762
Temperature change of sodium [°C] Temperature change of water [°C]
169.9 229.6
163.4 232.1
*Outer region Number of sodium rows Number of water rows Number of sodium tubes Number of water tubes
12 12 1454 1473
12 13 1454 1575
Heat capacity ratio
1.885
1.740
Temperature change of sodium [°C] Temperature change of water [°C]
118.7 283.1
125.5 276.7
11,995
10,976
not considered mainly in this paper. As shown in Fig. 9, optimal mass flow rates that minimized the heat transfer area for each tube inclination angles exists due to the RHT, and the mass flow rate of the optimal point increases as the tube inclination angle increases. The heat transfer area of the ISG is smallest at LBE mass flow rate of 1750 kg/s and tube inclination angle of 45°. The number of tubes arranged in a tube row is proportional to the coiling diameter of the tube row, and the sodium tube rows alternate with the water tube rows. So, the ratio between the number of sodium tubes and water tubes is almost the same as the ratio between the number of sodium rows and water rows in each heat transfer region as shown in Table 5. As the tube inclination angle increases, the space between tubes in a tube row, p/sinθ, decreases as shown in Fig. 10, and more tubes are contained in the row. Therefore, the total number of tube rows decreases, and the effect of a tube row due to the odd arrangement becomes larger. The discrepancy of tube number ratio (or tube row ratio) between inner region and outer region increases with increasing the tube inclination angle. It means that the amount of heat capacity ratio change between the two regions becomes larger. Therefore, the suppression effect of the odd arrangement on RHT becomes larger, and it explains why the LBE mass flow rate of the optimal point increases as the tube inclination angle increases. There are different optimal tube inclination angles depending on the
̇ p)sodium (mc −
̇ p) water (mc
Odd arrangement
Heat transfer area [m2]
−
R=
Even arrangement
(10)
The average heat capacity ratio in the inner region is larger in the odd arrangement when compared to the even arrangement, and that in the outer region is smaller because of the difference of the number of water row. This condition reduces the temperature change of sodium in inner region and reduces the temperature change of water in the outer region. Table 4 and Fig. 8 show the comparison result about temperature distributions and heat transfer area between the even arrangement and the odd arrangement when the LBE mass flow rate is 2000 kg/s. The temperature distribution in the odd arrangement is relatively far from the temperature distribution in which RHT can occur, and the heat transfer area is also smaller than that of the even arrangement. 4.3. Tube inclination angle The effect of tube inclination angle was analyzed by comparing the heat transfer area required for the same heat transfer rate at the angles of 5° to 55° and LBE mass flow rates of 250 to 3000 kg/s. To increase the LBE mass flow rate, more pumping power is required. However, the required pumping power to circulate LBE is relatively lower than the existing IHTS of KALIMER-600 because of low velocity of LBE. So it was 6
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Fig. 8. Comparison of temperature distribution between the even and odd arrangement at LBE mass flow rate of 2000 kg/s. Table 5 The number of tubes and the number of tube rows according to tube inclination angles. Inclination angle [°] *Inner region Number of tubes for sodium Number of tubes for water Sodium tubes/water tubes Number of tube coiling rows for sodium Number of tube coiling rows for water Sodium rows/water rows *Outer region Number of tubes for sodium Number of tubes for water Sodium tubes/water tubes Number of tube coiling rows for sodium Number of tube coiling rows for water Sodium rows/water rows
Fig. 9. Heat transfer area along LBE mass flow rate with the inclination angle variation.
value of LBE mass flow rate. The tube inclination angle has an effect on the minimum flow area of the intermediate fluid as described by Eq. (9). As the tube inclination angle increases, the Péclet number term increases, and the Nusselt number of LBE increases. The tube
5
15
25
35
45
55
1529 1501 1.019 50
1533 1475 1.039 28
1572 1500 1.048 22
1521 1436 1.059 18
1547 1449 1.068 16
1635 1526 1.071 15
49
27
21
17
15
14
1.020
1.037
1.048
1.059
1.067
1.071
1469 1538 0.955 21
1454 1575 0.923 12
1404 1560 0.9 9
1450 1631 0.889 8
1419 1621 0.875 7
1329 1551 0.857 6
22
13
10
9
8
7
0.955
0.923
0.9
0.889
0.875
0.857
inclination angle term itself also affects the Nusselt number of LBE in the Kalish-Dwyer model (Kalish and Dwyer, 1967). The individual effects of two terms for LBE mass flow rate of 250 kg/s and 1750 kg/s are 7
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Fig. 10. Tube spacing at tube inclination angles of 15° and 45°. Table 6 Optimal condition of ISG for KALIMER-600. Parameters
ISG
Heat transfer rate [MWth] Number of sodium tubes [ea] Number of water tubes [ea] Outer diameter of tube [mm] Tube thickness for sodium [mm] Tube thickness for water [mm] Length of tubes [m] Height of tube bundles [m] LBE mass flow rate [kg/s] Inclination angle [°] Pitch-to-diameter ratio Heat transfer area [m2] Frictional pressure drop of sodium [kPa] Frictional pressure drop of LBE [kPa] Frictional pressure drop of water [kPa]
387.0 2966 3070 27.2 1.65 2.9 19.18 13.6 1750 45 1.5 9894 22.9 3.51 1.77
Table 7 Design data of IHTS of KALIMER-600. *IHX Number of units Heat transfer area per unit [m2] PHTS pressure drop [kPa]
4 1571 19.6
*SG Number of units Heat transfer area per unit [m2]
2 5638
*Total Total heat transfer area [m2] Total heat transfer area per 4 units [m2]
17,560 4390
shown in Fig. 11. The larger the LBE mass flow rate, the greater the variation of the Péclet number term with the tube inclination angle. But the variation in the tube inclination angle term is constant. Therefore, the optimal tube inclination angle is different in the case of 250 kg/s and 1750 kg/s.
Fig. 11. Effect of tube inclination angle on Nusselt number at LBE mass flow rate of (a) 250 kg/s, (b) 1750 kg/s.
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4.4. Optimal condition for KALIMER-600
CRediT authorship contribution statement
The optimal condition for KALIMER-600 was calculated using the results presented here as shown in Table 6, and compared with the IHTS of KALIMER-600 presented in Table 7. Only the heat transfer areas of IHX and SG, except piping system, were used for comparison, and the heat transfer area of IHTS was calculated as the value of total heat transfer areas of IHX and SG divided by the number of ISG unit. The heat transfer area of ISG should be 2.25 times of that of the IHTS to transfer the same amount of heat at the same condition of PHTS pressure drop.
Namhyeong Kim: Data curation, Formal analysis, Methodology, Software, Writing - original draft, Writing - review & editing. Hyungmo Kim: Formal analysis, Methodology, Software, Writing - review & editing. Jaehyuk Eoh: Conceptualization, Funding acquisition, Writing - review & editing. Moo Hwan Kim: Funding acquisition, Supervision, Writing - review & editing. HangJin Jo: Formal analysis, Funding acquisition, Supervision, Writing - review & editing.
5. Conclusion
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Declaration of Competing Interest
Thermal-sizing analysis of the novel ISG unit design was conducted, mainly on geometric design parameters. The goal of analysis was to minimize the additional heat transfer area that is required to compensate for the add-on thermal resistance of the intermediate heat transfer medium. The results of thermal-sizing and resultant heat transfer performance were quantitatively investigated by comparing the required heat transfer area under different conditions, such as the number of tubes, types of tube arrangement, and tube inclination angles.
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Acknowledgement This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea Government (Ministry of Science and ICT). (NRF-2016M2B2B1944980, 2016M2B2B1944981). References
The changes of heat transfer area and pressure drop of the ISG according to the variation of the number of tubes were observed. In order to compare the ISG with the SG of KALIMER-600 at the identical heat transfer rate and primary pressure drop conditions, the number of tubes was set to have the primary pressure drop close to that of the existing SG. The two methods of tube bundle arrangement, the ‘even’ and ‘odd’ arrangement, were creatively proposed complying with the method of dividing set of tube rows into two distinct heat transfer regions. The ‘odd’ arrangement has a smaller temperature gradient between the two regions, reducing the occurrence of the RHT, and lower required heat transfer area, than does the ‘even’ arrangement. The variation with the tube inclination angle was analyzed by dividing into the change of the optimal LBE mass flow rate and the change of the optimal tube inclination angle. Due to the occurrence of RHT, the optimal point is obtained in which the heat transfer performance no longer increase even when the LBE mass flow rate increases. The odd arrangement has the suppression effect on the RHT, which is increased with the increase of the tube inclination angle. Thus, the optimal LBE mass flow rate increases. The optimal tube inclination angle is determined by the tube inclination angle term and the Péclet number term included in the heat transfer correlation. The tube inclination angle term is constant regardless of the mass flow rate, whereas the Péclet number term increases significantly with larger LBE mass flow rate, so the optimal tube inclination angle has different values depending on the LBE mass flow rate. As a result, the heat transfer area was minimal at an inclination angle of 45° and an LBE mass flow rate of 1750 kg/s.
Bishop, A.A., Sandberg, R., Tong, L., 1965. Forced convection heat transfer at high pressure after critical heat flux. In: Mechanical Engineering. ASME-AMER Soc. Mechanical Eng. 345 E 47th St., New York, NY 10017. Carey, V.P., 2018. Liquid Vapor Phase Change Phenomena: An Introduction to the Thermophysics of Vaporization and Condensation Processes in Heat Transfer Equipment. CRC Press. Chen, J.C., 1966. Correlation for boiling heat transfer to saturated fluids in convective flow. Ind. Eng. Chem. Process Des. Dev. 5 (3), 322–329. Chia-Jung, H., 1964. Analytical study of heat transfer to liquid metals in cross-flow through rod bundles. Int. J. Heat Mass Transf. 7 (4), 431–446. Choi, B.Y., 2007. Study on Multidimensional Numerical Analysis and Heat Transfer Characteristics of Radially Separated Double Tubed Bundel Steam Generator, in Department of Mechanical Engineering. Chonnam National University. Duchatelle, L., De Nucheze, L., Robin, M., 1973. Departure from nucleate boiling in helical tubes of liquid metal heated steam generators. ASME Paper. (73-HT): p. 57. El-Genk, M.S., Schriener, T.M., 2017. A review of experimental data and heat transfer correlations for parallel flow of alkali liquid metals and lead-bismuth eutectic in bundles. Nucl. Eng. Des. 317, 199–219. El-Wakil, M.M., 1971. Nuclear Heat Transport. Eoh, J.H., et al., 2011. Design and evaluation of the helical-coil sodium-to-air heat exchanger of stella-1. Gunter, A., Shaw, W., 1945. A general correlation of friction factors for various types of surfaces in cross flow. Trans. ASME 67 (8), 643–660. Kalish, S., Dwyer, O.E., 1967. Heat transfer to NaK flowing through unbaffled rod bundles. Int. J. Heat Mass Transf. 10 (11), 1533–1558. Kim, E.K., et al., 2004. Development of a thermal hydraulic analysis code for a combined steam generator-IHX heat exchanger (Integrated Type). Transactions of the Korean Nuclear Society Spring Meeting. Kim, S., et al., 2008. Verification and refinement of the one-dimensional analysis code for the integrated steam generators in an SFR. Int. Commun. Heat Mass Transf. 35 (1), 12–20. Kim, E.-K., Baek, B.-J., 2011. Thermal hydraulic performance analysis of a double tube bundle steam generator for a liquid metal reactor. Ann. Nucl. Energy 38 (12), 2625–2633. Kim, Y., et al., Conceptual design report of SFR Demonstration Reactor of 600MWe capacity, in KAERI/TR-4598. 2012, Korea Atomic Energy Research Institute Daejeon, Republic of Korea. Mori, Y., Nakayama, W., 1967. Study of forced convective heat transfer in curved pipes (2nd report, turbulent region). Int. J. Heat Mass Transf. 10 (1), 37–59. Sim, Y.-S., et al., 2003. A new LMR SG with a double tube bundle free from SWR. Nucl. Eng. Technol. 35 (6), 566–580. Sim, Y.S., Kim, E.K., 2004. Characteristics of the integrated steam generators for a liquid metal reactor. Nucl. Eng. Technol. 36 (2), 127–141.
As the result of the optimal condition of the proposed ISG design for KALIMER-600, the ISG has heat transfer area that is 2.25 times that of IHX-and-SG system at the same heat transfer rate and PHTS pressure drop condition. However, the ISG has great advantages of the safety improvement of SFRs by preventing the occurrence of SWR, and can be expected to make simple the IHTS by substituting the conventional piping system with the single-shell component although only for looptype reactors.
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