# Design and Thermal-Hydraulic Evaluation of Integrated Steam Generator with Serpentine-Tube Configuration for Prevention of Sodium-Water Reaction

Authors: Namhyeong Kim; Jung Yoon; Jaehyuk Eoh; Moo Hwan Kim; HangJin Jo; Hyungmo Kim
Journal: International Journal of Energy Research
 (2023)

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## Abstract

Although sodium-cooled fast reactors (SFRs) can have inherently enhanced safety features, there is a concern regarding unexpected events arising from a sodium-water reaction (SWR) in a Rankine cycle steam generator. Innovative concepts of integrated steam generators (ISGs), including an intermediate heat exchanger, have been suggested for eliminating an SWR by employing an intermediate fluid between liquid sodium and steam/water system. In this study, we propose an ISG designed with a novel tube configuration: a serpentine tube-type integrated steam generator (S-ISG). Furthermore, we developed a dedicated one-dimensional thermal-hydraulic analysis code for the specific design evaluation of the S-ISGs. The evaluation results are reported with reasonable explanations and compared with the results obtained using a conventional CFD tool to analyze local thermal-hydraulic characteristics that cannot be shown in the one-dimensional analyses. The proposed S-ISG has an inherent advantage for modularization as well as prevention of SWR; therefore, it is characterized by its ability to improve operational efficiency even in the case of repair, despite the low space efficiency. The results demonstrate that the component developed in this study can serve as an option to maintain cost efficiency while enhancing the public acceptability of an SFR.


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## Body

## 1. Introduction

The development of Gen-IV nuclear systems has been progressing to realize enhanced safety and effectively utilize uranium resources and minimize waste of spent fuel [1]. A sodium-cooled fast reactor (SFR) is one of the most promising options to pursue the purpose of the Gen-IV systems. In SFRs, the inherent safety of the primary circuit can be significantly improved by using sodium, which has a very high thermal conductivity and exists in a liquid state over a wide temperature range, as a coolant [1]. However, sodium reacts violently with water because of its high chemical reactivity, and it can cause a self-wastage phenomenon, in which a small leak in the steam generator leads to the breakage of multiple tubes owing to sodium-water reaction (SWR). According to the operating experiences of SFRs in France, India, and Russia for several decades, the most frequent and influential accident in SFR systems is the failure of the steam generator caused by the SWR. Although the leakage of sodium in the steam generators in operation has almost disappeared owing to the improvement in manufacturing technology, the risk of major accidents caused by sodium leakage in the steam generator and the SWR is still recognized as a danger to the public. In addition, a decrease in the utilization rate of the plant due to the steam generator failure may be a major cause of the deterioration of the economic efficiency of the SFR system. Therefore, it is important to prevent the SWR in the steam generators of SFRs.Many studies have been conducted on the novel concepts of steam generators to eliminate or mitigate SWRs. A copper-bonded steam generator (CBSG) adds a solid block between sodium and water to prevent SWR [2]. This can be considered as the most reliable way to prevent SWR. However, owing to the concern of high thermal stress at the solid-solid interfaces, it is generally difficult to design and manufacture the steam generators for safe operation during the entire service period. In addition, the application of nanofluids as a coolant can be used as a representative study to suppress SWR [3], but the use of nanoparticles requires further verification to implement it in a real system.Integrated steam generators (ISGs), which include an intermediate heat exchanger (IHX), have been proposed for the inherent elimination of the SWR by employing an intermediate fluid as a physical barrier between the liquid sodium and the steam/water system. That is, the ISG is filled with an intermediate fluid inside the shell, which is unreactive with both water and sodium, such as a lead-bismuth eutectic (LBE). In particular, Sim et al. and Sim and Kim proposed four types of steam generators with a double tube bundle configuration (i.e., double tube bundle steam generators, DTBSGs), which substantially eliminate the possibility of SWR by alternately placing the two types of helical tube bundles for sodium and water row by row in a shell filled with LBE [4, 5]. Although they performed valuable fundamental studies, they only focused on helically coiled tube bundles without considering other configurations. A helical coiled arrangement is a familiar and efficient way to fabricate many practical heat exchangers. However, an ISG with a helical tube arrangement poses some difficult problems to solve the following: (1) the tube chambers must be contained in the intermediate fluid; however, it is difficult to place the chambers appropriately because of the alternately arranged helically coiled tube bundles. (2) The flow path of the intermediate fluid is complicated, and it is difficult to predict the heat transfer performance due to the flow of the intermediate fluid in the vicinity of the tube chambers and connecting tubes, which are not heat exchange parts. (3) It is hard to install a pump for forced circulation of the intermediate fluid; thus, guaranteeing the flow rate of the intermediate fluid is difficult. (4) It is inefficient to replace one large-sized steam generator with several smaller ones for modularity. The design of an ISG with a helical tube arrangement and tube chambers can be found in a previous study [6]. To overcome the problems mentioned above, it is necessary to design a new ISG with new tube configurations and not with a helical tube arrangement.To this end, we propose a novel ISG with a serpentine-tube configuration (i.e., a serpentine tube type ISG, S-ISG) that was designed using a dedicated thermal-hydraulic analysis code developed for the specific design evaluation of the S-ISGs (SPINS-S, sizing and performance analyzer for an integrated steam generator–serpentine tube arrangement). We expect the proposed S-ISG to overcome the heterojunction failure problem of CBSGs owing to high thermal stress and the disadvantages of the DTBSGs with helical tube bundles.


## 2. Concept and Design Approach

### 2.1. Basic Concept of S-ISG

The S-ISG is a novel steam generator concept that can solve the difficulty of pumping an intermediate fluid and is easier to arrange the tube chambers and to modularize than in the helical tube case. Figure1 illustrates the concept of the S-ISG. The serpentine tubes are placed vertically, and the entire tube bundle consists of tube rows placed next to each other (Figure 1(a)). This clear arrangement makes it possible to simply place tube chambers, even if each row of different tubes is placed one by one. In Figure 1(a), the drum-shaped tube chambers for sodium and water/steam can be easily connected with numerous tube rows in the same way. One S-ISG system comprised an “upregion” unit and a “downregion” unit, and two units were connected via pipes (Figure 1(b)). Therefore, a conventional pump could be easily attached to these pipes to achieve certain flow rates of an intermediate fluid. In addition, by placing flow-guide walls that support the serpentine tubes and divide the flow regions, the main flow regions (the yellow-shaded regions) can be defined and the heat transfer by the intermediate flow occurs only in the straight parts of the serpentine tubes, excluding the tube chambers. The size of the S-ISG can be reduced simply by reducing the number of tube rows while maintaining the flow velocities and tube diameters when divided into smaller units for modularization. Therefore, the proposed system is very effective unlike helical tube arrangement.Figure 1
Schematic of the novel S-ISG concept: (a) serpentine tube arrangement in a single unit of S-ISG; (b) entire system of S-ISG.
(a)(b)The steam generator shell is filled with an intermediate fluid, that is, unreactive with water and sodium, such as a lead-bismuth alloy. We chose sodium and water as the working fluids on the tube side, and lead-bismuth eutectic alloy (LBE) as the working fluid on the shell side of the S-ISG. High-temperature sodium branched into the two upper chambers and cooled from top to bottom. Water was divided into the two lower chambers, and superheated steam was ejected through the upper chambers. As the LBE on the shell side flows across the other fluids, the LBE temperature increased from the bottom to the top in the upregion, and the LBE temperature decreased from the top to the bottom to reach the thermal equilibrium state in the downregion.There are two different configurations for transferring heat from sodium to water via the intermediate fluid: separated and integrated. In the separated configuration, the sodium- and water-tube bundles are physically separated. The LBE obtains heat while passing through the high-temperature sodium bundle and then reaches the low-temperature water bundle installed in the other region to transfer the obtained heat by the bulk heat transfer phenomenon. However, in the integrated configuration, the sodium and water tubes are alternately placed row by row to maximize the local heat transfer phenomenon, thereby reducing the thermal load that burdens the solid structures and reducing the required pumping power for intermediate fluid circulation. Because of these advantages, the proposed S-ISG was designed with an integrated configuration.Based on the design concept, a detailed configuration of the single unit of the S-ISG, including the chambers and bending parts, is shown in Figure2. The dimensions of the two units constituting the S-ISG, that is, the “upregion” and “downregion,” were the same; however, the flow directions of the LBE were opposite to each other. To increase the heat transfer tube density and prevent the S-ISG unit from becoming too bulky owing to the large number of tube rows, five tubes were bunched into one tube row, as shown in Figure 2. The heat transfer tubes had a slight slope to allow for drainage. The flow-guide walls, which support the serpentine-tube bundles, divided the internal volume of the S-ISG shell into a main flow region and two stagnant fluid regions. In the main flow region, a forced flow of the LBE existed, and heat transfer between the sodium tubes and the water tubes mainly occurred. The stagnant fluid region was a space for positioning the tube chamber and bending parts, which was filled with LBE; however, the main flow of the LBE did not exist in this region. To accommodate the deformation owing to the thermal expansion of the tubes, the penetration part of the flow-guide wall was designed with a greater margin than the outer diameter of the tube.Figure 2
Detailed configuration of an S-ISG unit.


### 2.2. One-Dimensional Design Approach

The design and analysis code for the S-ISG, sizing and performance analyzer for integrated steam generator-serpentine tube type (SPINS-S), was developed by considering the configurational characteristics of the S-ISG. In the S-ISG, the shell-side fluid flows orthogonally into the serpentine tubes, and the five tubes in a bunch undergo individual heat transfer due to the different conditions of the shell-side fluid resulting from the order of arrangement in the bunch. Considering these heat transfer characteristics of the S-ISG, the SPINS-S code applied a two-dimensional lattice structure, as shown in Figure3. The repeated tube rows in the depth direction were considered identical, and five tubes in a tube rows for sodium or water were individually calculated for their temperature distribution (represented using black lines). The first index of the cells indicates the cell number in the length direction of the tubes, and the second index indicates the position of the tubes in a bunch. The shell-side flow was assumed to move only in the vertical direction (represented using blue lines), and the heat conduction of the shell-side fluid was not considered for the convenience of calculation. Therefore, the heat transfer calculations along each of the black and blue lines were performed with a one-dimensional assumption.Figure 3
Lattice structure of SPINS-S code.


#### 2.2.1. Governing Equations

A control volume was assumed to contain one sodium tube and one water tube of tube bunches, as shown in Figure4. Therefore, the number of control volumes in the height direction was determined by multiplying the number of tube passes by the number of tubes in a bunch. The number of control volume in the width direction was applied to increase the resolution of the properties in that direction. The heat transfer and pressure drop calculations made in each control volume can be expressed using Equations (1)–(9). The heat transfer rate was calculated using the overall heat transfer coefficient and was further utilized for enthalpy calculations (Equations (1)–(5)). The overall heat transfer coefficient was defined as Equation (2) derived using the equivalent thermal circuit from the shell-side fluid to tube-side fluid. The heat transfer area was set based on the outer diameter of tube (Equation (3)), and the log-mean temperature difference was used as the temperature difference between the shell-side and tube-side fluids (Equation (4)). For the shell-side flow, the heat transfer by the LBE was assumed to occur simultaneously through both the sodium and water tubes because of the local heat transfer (Equation (5)). For the pressure drop, frictional, acceleration, and gravitational pressure drops were considered in the calculations. For the pressure drop calculations, the dotted sign in Equation (6) can be positive or negative according to the flow direction and the heating or cooling conditions. When the flow was upward, the sign of the gravitational pressure drop was negative, and for a downward flow, it was positive. The sign of the acceleration pressure drop was positive under the heating condition and negative under the cooling condition.
(1)q=UAΔT,(2)U=11/hconv,LBE+1/hF,LBE+do/2klndo/di+do/di1/hF,tube+do/di1/hconv,tube,(3)A=NtubeπdoL,(4)ΔT=Ttube,i+1−TLBE,j+1−Ttube,i−TLBE,jlnTtube,i+1−TLBE,j+1/Ttube,i−TLBE,j,(5)hLBE,j+1=hLBE,j+qs−qwṁLBE,hs,i+1=hs,i+qsṁs,hw,i+1=hw,i+qwṁw,(6)ΔPtot=ΔPfric±∗ΔPacc±∗ΔPgrav,(7)ΔPfric=fLdi12ρv2,(8)ΔPacc=G21ρi+1−1ρi,(9)ΔPgrav=ρgLsinθ.Figure 4
Heat transfer model in a node of SPINS-S code.


#### 2.2.2. Correlations

The correlations used to calculate the heat transfer coefficient and pressure drop in the SPINS-S code are summarized in Table1. Because the heat transfer parts of the tubes were straight, the correlations for straight tubes, namely, the Lyon-Martinelli, Dittus-Boelter, and Haaland correlations, were used. For boiling heat transfer, the Chen correlation for nucleate boiling and the Bishop correlation for film boiling were used. For shell-side flow, the Kalish-Dwyer and Gunter-Shaw correlations were used for the LBE flow across the tube bundles.Table 1
Heat transfer and pressure drop correlations used in the SPINS-S code.
Heat transfer correlationsSodiumLyon-Martinelli [7]Nu=7.0+0.025Pe0.8WaterSubcooled/superheatedDittus-Boelter [8]Nu=0.023Re0.8Pr0.4Saturated nucleate boilingChen [9]hconv=0.00122kl0.79cp,l0.45ρl0.49/σ0.5μl0.29ilg0.24ρg0.24Tw−TsatPl0.24PsatTw−Pl0.75S+0.023kl/diRel0.8Prl0.4FDeparture from nucleate boilingBiasi [10]qcrit′′=max1883/DmG1/6FBiP/G1/6−x,3780HBiP/DmG0.61−xFilm boilingBishop [11]Nu=0.0193Re0.8Pr1.23x+1−xρgρl0.68ρgρl0.068Lead-bismuth eutecticKalish-Dwyer [12]Nu=ϕ1/do1/2p−do/p1/2sinβ+sin2β/1+sin2β1/25.44+0.228Pev,max0.614Pressure drop correlationsSodiumHaaland [13]f=11.8logRe−1.642WaterSingle-phaseTwo-phaseHomogeneous equilibrium model [14]ΔP=2fhG2Ldivl+xvlg+G2vlgΔx+gLsinθvl+xvlgLead-bismuth eutecticGunter-Shaw [15]ΔP=fG2L2Dvρμwμ0.14DvpT0.4pLpT0.6


#### 2.2.3. Calculation Process

The calculation process for SPINS-S is shown in Figure5. There are four iteration processes for the sizing analysis. The calculation of the heat transfer regions requires an iterative process to converge the inlet temperature, which is the boundary condition here. According to the calculation order of the SPINS-S, the sodium inlet temperature should converge in the upregion, and the water inlet temperature should converge in the downregion. All five tubes in a bunch individually converged. In the calculation of the heat transfer regions, the convergence of heat transfer rate (Q) in every control volume was checked until the change rate of the LBE temperature was less than 10-3. After the convergence of the two heat transfer regions was completed, the thermal equilibrium of the LBE between the up- and downregions was checked. Considering the residual for the LBE thermal equilibrium in the iteration process, 1.8°C was set as an appropriate convergence criterion. If the difference was larger than 1.8°C, the initial LBE temperature was changed, and all of the aforementioned calculations were repeated until it satisfied the criteria. In other words, the converged results can have a temperature difference within 1.8°C between the LBE temperatures at the bottom of the up- and downregions. For the sizing analysis, the heat transfer length was made to converge for the given heat transfer rate by changing the length.Figure 5
Flow diagram of the calculation process of SPINS-S code.


## 2.1. Basic Concept of S-ISG

The S-ISG is a novel steam generator concept that can solve the difficulty of pumping an intermediate fluid and is easier to arrange the tube chambers and to modularize than in the helical tube case. Figure1 illustrates the concept of the S-ISG. The serpentine tubes are placed vertically, and the entire tube bundle consists of tube rows placed next to each other (Figure 1(a)). This clear arrangement makes it possible to simply place tube chambers, even if each row of different tubes is placed one by one. In Figure 1(a), the drum-shaped tube chambers for sodium and water/steam can be easily connected with numerous tube rows in the same way. One S-ISG system comprised an “upregion” unit and a “downregion” unit, and two units were connected via pipes (Figure 1(b)). Therefore, a conventional pump could be easily attached to these pipes to achieve certain flow rates of an intermediate fluid. In addition, by placing flow-guide walls that support the serpentine tubes and divide the flow regions, the main flow regions (the yellow-shaded regions) can be defined and the heat transfer by the intermediate flow occurs only in the straight parts of the serpentine tubes, excluding the tube chambers. The size of the S-ISG can be reduced simply by reducing the number of tube rows while maintaining the flow velocities and tube diameters when divided into smaller units for modularization. Therefore, the proposed system is very effective unlike helical tube arrangement.Figure 1
Schematic of the novel S-ISG concept: (a) serpentine tube arrangement in a single unit of S-ISG; (b) entire system of S-ISG.
(a)(b)The steam generator shell is filled with an intermediate fluid, that is, unreactive with water and sodium, such as a lead-bismuth alloy. We chose sodium and water as the working fluids on the tube side, and lead-bismuth eutectic alloy (LBE) as the working fluid on the shell side of the S-ISG. High-temperature sodium branched into the two upper chambers and cooled from top to bottom. Water was divided into the two lower chambers, and superheated steam was ejected through the upper chambers. As the LBE on the shell side flows across the other fluids, the LBE temperature increased from the bottom to the top in the upregion, and the LBE temperature decreased from the top to the bottom to reach the thermal equilibrium state in the downregion.There are two different configurations for transferring heat from sodium to water via the intermediate fluid: separated and integrated. In the separated configuration, the sodium- and water-tube bundles are physically separated. The LBE obtains heat while passing through the high-temperature sodium bundle and then reaches the low-temperature water bundle installed in the other region to transfer the obtained heat by the bulk heat transfer phenomenon. However, in the integrated configuration, the sodium and water tubes are alternately placed row by row to maximize the local heat transfer phenomenon, thereby reducing the thermal load that burdens the solid structures and reducing the required pumping power for intermediate fluid circulation. Because of these advantages, the proposed S-ISG was designed with an integrated configuration.Based on the design concept, a detailed configuration of the single unit of the S-ISG, including the chambers and bending parts, is shown in Figure2. The dimensions of the two units constituting the S-ISG, that is, the “upregion” and “downregion,” were the same; however, the flow directions of the LBE were opposite to each other. To increase the heat transfer tube density and prevent the S-ISG unit from becoming too bulky owing to the large number of tube rows, five tubes were bunched into one tube row, as shown in Figure 2. The heat transfer tubes had a slight slope to allow for drainage. The flow-guide walls, which support the serpentine-tube bundles, divided the internal volume of the S-ISG shell into a main flow region and two stagnant fluid regions. In the main flow region, a forced flow of the LBE existed, and heat transfer between the sodium tubes and the water tubes mainly occurred. The stagnant fluid region was a space for positioning the tube chamber and bending parts, which was filled with LBE; however, the main flow of the LBE did not exist in this region. To accommodate the deformation owing to the thermal expansion of the tubes, the penetration part of the flow-guide wall was designed with a greater margin than the outer diameter of the tube.Figure 2
Detailed configuration of an S-ISG unit.


## 2.2. One-Dimensional Design Approach

The design and analysis code for the S-ISG, sizing and performance analyzer for integrated steam generator-serpentine tube type (SPINS-S), was developed by considering the configurational characteristics of the S-ISG. In the S-ISG, the shell-side fluid flows orthogonally into the serpentine tubes, and the five tubes in a bunch undergo individual heat transfer due to the different conditions of the shell-side fluid resulting from the order of arrangement in the bunch. Considering these heat transfer characteristics of the S-ISG, the SPINS-S code applied a two-dimensional lattice structure, as shown in Figure3. The repeated tube rows in the depth direction were considered identical, and five tubes in a tube rows for sodium or water were individually calculated for their temperature distribution (represented using black lines). The first index of the cells indicates the cell number in the length direction of the tubes, and the second index indicates the position of the tubes in a bunch. The shell-side flow was assumed to move only in the vertical direction (represented using blue lines), and the heat conduction of the shell-side fluid was not considered for the convenience of calculation. Therefore, the heat transfer calculations along each of the black and blue lines were performed with a one-dimensional assumption.Figure 3
Lattice structure of SPINS-S code.


### 2.2.1. Governing Equations

A control volume was assumed to contain one sodium tube and one water tube of tube bunches, as shown in Figure4. Therefore, the number of control volumes in the height direction was determined by multiplying the number of tube passes by the number of tubes in a bunch. The number of control volume in the width direction was applied to increase the resolution of the properties in that direction. The heat transfer and pressure drop calculations made in each control volume can be expressed using Equations (1)–(9). The heat transfer rate was calculated using the overall heat transfer coefficient and was further utilized for enthalpy calculations (Equations (1)–(5)). The overall heat transfer coefficient was defined as Equation (2) derived using the equivalent thermal circuit from the shell-side fluid to tube-side fluid. The heat transfer area was set based on the outer diameter of tube (Equation (3)), and the log-mean temperature difference was used as the temperature difference between the shell-side and tube-side fluids (Equation (4)). For the shell-side flow, the heat transfer by the LBE was assumed to occur simultaneously through both the sodium and water tubes because of the local heat transfer (Equation (5)). For the pressure drop, frictional, acceleration, and gravitational pressure drops were considered in the calculations. For the pressure drop calculations, the dotted sign in Equation (6) can be positive or negative according to the flow direction and the heating or cooling conditions. When the flow was upward, the sign of the gravitational pressure drop was negative, and for a downward flow, it was positive. The sign of the acceleration pressure drop was positive under the heating condition and negative under the cooling condition.
(1)q=UAΔT,(2)U=11/hconv,LBE+1/hF,LBE+do/2klndo/di+do/di1/hF,tube+do/di1/hconv,tube,(3)A=NtubeπdoL,(4)ΔT=Ttube,i+1−TLBE,j+1−Ttube,i−TLBE,jlnTtube,i+1−TLBE,j+1/Ttube,i−TLBE,j,(5)hLBE,j+1=hLBE,j+qs−qwṁLBE,hs,i+1=hs,i+qsṁs,hw,i+1=hw,i+qwṁw,(6)ΔPtot=ΔPfric±∗ΔPacc±∗ΔPgrav,(7)ΔPfric=fLdi12ρv2,(8)ΔPacc=G21ρi+1−1ρi,(9)ΔPgrav=ρgLsinθ.Figure 4
Heat transfer model in a node of SPINS-S code.


### 2.2.2. Correlations

The correlations used to calculate the heat transfer coefficient and pressure drop in the SPINS-S code are summarized in Table1. Because the heat transfer parts of the tubes were straight, the correlations for straight tubes, namely, the Lyon-Martinelli, Dittus-Boelter, and Haaland correlations, were used. For boiling heat transfer, the Chen correlation for nucleate boiling and the Bishop correlation for film boiling were used. For shell-side flow, the Kalish-Dwyer and Gunter-Shaw correlations were used for the LBE flow across the tube bundles.Table 1
Heat transfer and pressure drop correlations used in the SPINS-S code.
Heat transfer correlationsSodiumLyon-Martinelli [7]Nu=7.0+0.025Pe0.8WaterSubcooled/superheatedDittus-Boelter [8]Nu=0.023Re0.8Pr0.4Saturated nucleate boilingChen [9]hconv=0.00122kl0.79cp,l0.45ρl0.49/σ0.5μl0.29ilg0.24ρg0.24Tw−TsatPl0.24PsatTw−Pl0.75S+0.023kl/diRel0.8Prl0.4FDeparture from nucleate boilingBiasi [10]qcrit′′=max1883/DmG1/6FBiP/G1/6−x,3780HBiP/DmG0.61−xFilm boilingBishop [11]Nu=0.0193Re0.8Pr1.23x+1−xρgρl0.68ρgρl0.068Lead-bismuth eutecticKalish-Dwyer [12]Nu=ϕ1/do1/2p−do/p1/2sinβ+sin2β/1+sin2β1/25.44+0.228Pev,max0.614Pressure drop correlationsSodiumHaaland [13]f=11.8logRe−1.642WaterSingle-phaseTwo-phaseHomogeneous equilibrium model [14]ΔP=2fhG2Ldivl+xvlg+G2vlgΔx+gLsinθvl+xvlgLead-bismuth eutecticGunter-Shaw [15]ΔP=fG2L2Dvρμwμ0.14DvpT0.4pLpT0.6


### 2.2.3. Calculation Process

The calculation process for SPINS-S is shown in Figure5. There are four iteration processes for the sizing analysis. The calculation of the heat transfer regions requires an iterative process to converge the inlet temperature, which is the boundary condition here. According to the calculation order of the SPINS-S, the sodium inlet temperature should converge in the upregion, and the water inlet temperature should converge in the downregion. All five tubes in a bunch individually converged. In the calculation of the heat transfer regions, the convergence of heat transfer rate (Q) in every control volume was checked until the change rate of the LBE temperature was less than 10-3. After the convergence of the two heat transfer regions was completed, the thermal equilibrium of the LBE between the up- and downregions was checked. Considering the residual for the LBE thermal equilibrium in the iteration process, 1.8°C was set as an appropriate convergence criterion. If the difference was larger than 1.8°C, the initial LBE temperature was changed, and all of the aforementioned calculations were repeated until it satisfied the criteria. In other words, the converged results can have a temperature difference within 1.8°C between the LBE temperatures at the bottom of the up- and downregions. For the sizing analysis, the heat transfer length was made to converge for the given heat transfer rate by changing the length.Figure 5
Flow diagram of the calculation process of SPINS-S code.


## 2.2.1. Governing Equations

A control volume was assumed to contain one sodium tube and one water tube of tube bunches, as shown in Figure4. Therefore, the number of control volumes in the height direction was determined by multiplying the number of tube passes by the number of tubes in a bunch. The number of control volume in the width direction was applied to increase the resolution of the properties in that direction. The heat transfer and pressure drop calculations made in each control volume can be expressed using Equations (1)–(9). The heat transfer rate was calculated using the overall heat transfer coefficient and was further utilized for enthalpy calculations (Equations (1)–(5)). The overall heat transfer coefficient was defined as Equation (2) derived using the equivalent thermal circuit from the shell-side fluid to tube-side fluid. The heat transfer area was set based on the outer diameter of tube (Equation (3)), and the log-mean temperature difference was used as the temperature difference between the shell-side and tube-side fluids (Equation (4)). For the shell-side flow, the heat transfer by the LBE was assumed to occur simultaneously through both the sodium and water tubes because of the local heat transfer (Equation (5)). For the pressure drop, frictional, acceleration, and gravitational pressure drops were considered in the calculations. For the pressure drop calculations, the dotted sign in Equation (6) can be positive or negative according to the flow direction and the heating or cooling conditions. When the flow was upward, the sign of the gravitational pressure drop was negative, and for a downward flow, it was positive. The sign of the acceleration pressure drop was positive under the heating condition and negative under the cooling condition.
(1)q=UAΔT,(2)U=11/hconv,LBE+1/hF,LBE+do/2klndo/di+do/di1/hF,tube+do/di1/hconv,tube,(3)A=NtubeπdoL,(4)ΔT=Ttube,i+1−TLBE,j+1−Ttube,i−TLBE,jlnTtube,i+1−TLBE,j+1/Ttube,i−TLBE,j,(5)hLBE,j+1=hLBE,j+qs−qwṁLBE,hs,i+1=hs,i+qsṁs,hw,i+1=hw,i+qwṁw,(6)ΔPtot=ΔPfric±∗ΔPacc±∗ΔPgrav,(7)ΔPfric=fLdi12ρv2,(8)ΔPacc=G21ρi+1−1ρi,(9)ΔPgrav=ρgLsinθ.Figure 4
Heat transfer model in a node of SPINS-S code.


## 2.2.2. Correlations

The correlations used to calculate the heat transfer coefficient and pressure drop in the SPINS-S code are summarized in Table1. Because the heat transfer parts of the tubes were straight, the correlations for straight tubes, namely, the Lyon-Martinelli, Dittus-Boelter, and Haaland correlations, were used. For boiling heat transfer, the Chen correlation for nucleate boiling and the Bishop correlation for film boiling were used. For shell-side flow, the Kalish-Dwyer and Gunter-Shaw correlations were used for the LBE flow across the tube bundles.Table 1
Heat transfer and pressure drop correlations used in the SPINS-S code.
Heat transfer correlationsSodiumLyon-Martinelli [7]Nu=7.0+0.025Pe0.8WaterSubcooled/superheatedDittus-Boelter [8]Nu=0.023Re0.8Pr0.4Saturated nucleate boilingChen [9]hconv=0.00122kl0.79cp,l0.45ρl0.49/σ0.5μl0.29ilg0.24ρg0.24Tw−TsatPl0.24PsatTw−Pl0.75S+0.023kl/diRel0.8Prl0.4FDeparture from nucleate boilingBiasi [10]qcrit′′=max1883/DmG1/6FBiP/G1/6−x,3780HBiP/DmG0.61−xFilm boilingBishop [11]Nu=0.0193Re0.8Pr1.23x+1−xρgρl0.68ρgρl0.068Lead-bismuth eutecticKalish-Dwyer [12]Nu=ϕ1/do1/2p−do/p1/2sinβ+sin2β/1+sin2β1/25.44+0.228Pev,max0.614Pressure drop correlationsSodiumHaaland [13]f=11.8logRe−1.642WaterSingle-phaseTwo-phaseHomogeneous equilibrium model [14]ΔP=2fhG2Ldivl+xvlg+G2vlgΔx+gLsinθvl+xvlgLead-bismuth eutecticGunter-Shaw [15]ΔP=fG2L2Dvρμwμ0.14DvpT0.4pLpT0.6


## 2.2.3. Calculation Process

The calculation process for SPINS-S is shown in Figure5. There are four iteration processes for the sizing analysis. The calculation of the heat transfer regions requires an iterative process to converge the inlet temperature, which is the boundary condition here. According to the calculation order of the SPINS-S, the sodium inlet temperature should converge in the upregion, and the water inlet temperature should converge in the downregion. All five tubes in a bunch individually converged. In the calculation of the heat transfer regions, the convergence of heat transfer rate (Q) in every control volume was checked until the change rate of the LBE temperature was less than 10-3. After the convergence of the two heat transfer regions was completed, the thermal equilibrium of the LBE between the up- and downregions was checked. Considering the residual for the LBE thermal equilibrium in the iteration process, 1.8°C was set as an appropriate convergence criterion. If the difference was larger than 1.8°C, the initial LBE temperature was changed, and all of the aforementioned calculations were repeated until it satisfied the criteria. In other words, the converged results can have a temperature difference within 1.8°C between the LBE temperatures at the bottom of the up- and downregions. For the sizing analysis, the heat transfer length was made to converge for the given heat transfer rate by changing the length.Figure 5
Flow diagram of the calculation process of SPINS-S code.


## 3. Thermal-Hydraulic Characteristics

### 3.1. Thermal-Hydraulic Design of S-ISG

In order to analyze the thermal flow characteristics of the S-ISG, detailed design information including thermally balanced boundary conditions is required. Therefore, in this study, a commercial-scale S-ISG was designed using the developed SPINS-S code. The designed S-ISG has a heat capacity of 96.77 MWth, which is equivalent to 1/8 the scale of one unit of a steam generator for a 600 MWe level reactor with two steam generator units. As the proposed S-ISG required an additional volume for the intermediate fluid, the volumetric efficiency was low, but it had the advantage of modularization. Here, we considered that one steam generator was modularized to 1/8 parts by taking advantage of the modularity feature, as a realistic steam generator for commercial reactor design. As this was a preliminary design to investigate the thermal-hydraulic characteristics of the S-ISG, it was not optimized. It is possible to enhance economic efficiency through further optimization processes.The thermal-fluidic boundary conditions required for the design were derived from the normal operating conditions of the KALIMER-600 designed by KAERI [16]. Table 2 lists the detailed specifications of the designed S-ISG. The material of the structure was assumed to be Mod. 9Cr-1Mo (Gr91), considering the operating temperature. The number of sodium tubes and water/steam tubes in a unit was 190 (i.e., 380 in both units). Each tube had a serpentine configuration with a total length of 40.74 m, a slope of 3°, and 11 bending parts from the upper chamber to the lower chamber. Five tubes were bunched in a row, and 76 rows were provided in total for the two fluids in the depth direction. The outer diameter of the tube was 27.2 mm for both the sodium and water/steam tubes; however, the thickness considering the internal pressure was 1.65 mm and 2.9 mm for the sodium and water/steam tubes, respectively. The sodium and water tubes had an in-line arrangement, and the LBE flowed across the sodium and water tubes. The pitch-to-diameter ratios of the longitudinal and transverse directions were 1.5. Table 2 summarizes and Figure 6 shows the design results of the S-ISG with a thermal capacity of 96.77 MWth obtained using the SPINS-S. As a result of three-dimensional modeling based on the design specification results, the external dimensions of one S-ISG unit were 4.97 m in width, 4.99 m in depth, and 7.265 m in height.Table 2
Design specifications of the S-ISG with a thermal capacity of 96.77 MWth.
Design parameterValueTotal length of a tube (sum of straight parts) (m)40.74Total number of hot tubes (per unit) (ea)190Total number of cold tubes (per unit) (ea)190Number of tubes in a row (ea)5Number of tube rows (ea)76Number of serpentine tube passes (ea)12Spacing between flow-guide walls (m)3.39Height between tube bending parts (m)0.9Height of heat transfer bundle (m)5.297Outer diameter of tube (mm)27.2Thickness of hot tube (mm)1.65Thickness of cold tube (mm)2.90Inclined angle of straight tube (°)3Pitch-to-diameter ratio (P/D) (-)1.5Total heat transfer area (per unit) (m2)1322.8Overall unit size (W×D×H) (m3)4.97×4.99×7.265Figure 6
Detailed configuration and dimension of the designed S-ISG (single unit).


### 3.2. One-Dimensional Performance Evaluation

For the abovementioned S-ISG design specifications, the thermal-hydraulic characteristics were evaluated based on the SPINS-S code results as a one-dimensional approach. Table3 presents the heat transfer and thermal-fluidic information for the designed S-ISG. The sum of the heat transfer rates of the up- and downregions for sodium or water satisfied the target heat transfer rate of the proposed design. There were only small discrepancies between the heat transfer rates of the up- and downregions. The selected mass flow rate of the intermediate fluid was 160 kg/s, which generated only a small velocity of the LBE: 4.5 cm/s based on the minimum flow area. Therefore, flow-induced vibration was not a concern in this design.Table 3
Heat transfer and thermal-fluidic information for S-ISG.
ParameterValue (upregion)Value (downregion)Target heat transfer rate (MWth)96.77Sodium heat transfer rate (MWth)50.6246.23LBE heat transfer rate (MWth)3.653.70Water heat transfer rate (MWth)47.8449.06Sodium mass flow rate (kg/s)522.9Sodium inlet temperature (°C)510.8510.0Sodium outlet temperature (°C)359.2371.5Sodium pressure drop (kPa)124.2124.2Steam/water mass flow rate (kg/s)43.1Water inlet temperature (°C)216.9217.3Steam outlet temperature (°C)463.8481.4Steam/water pressure drop (kPa)17.017.1LBE mass flow rate (kg/s)160.0LBE temperature at top (°C)494.0494.0LBE temperature at bottom (°C)333.2332.8LBE pressure drop (kPa)0.1680.167Figure7 shows the temperatures of the shell-side LBE and the tube-side sodium and water. The temperatures of sodium and water are individually indicated for each tube, and the temperature of the LBE indicates the average temperature passed through the same number of heat transfer tubes. Therefore, the LBE temperatures are indicated in the same way as the average temperature passing through the first tube layer (tube #1) of sodium and water and the average temperature passing through the second tube layer (tube #2). In the case of sodium and water, the normalized elevations were expressed considering the position of each tube, and the elevations based on the center line of the shell were used for the LBE. The temperature distributions in the up- and downregions were different due to the opposite flow directions of the LBE. When the LBE passed through the sodium and water tubes, the heat transfer with the fluid in the countercurrent was greater than that with the fluid in the cocurrent. Therefore, in the upregion, the heat transfer rate with sodium (hot-side fluid) was higher than that with water (cold-side fluid), and vice versa in the downregion, as listed in Table 3. More heat transfer with sodium tube means lower sodium outlet temperature, and more heat transfer with water/steam means higher steam outlet temperature. This feature caused a difference between the temperature distributions in the up- and downregions. Overall, the temperature distribution of each fluid in the upregion showed lower values than that in the downregion. In the S-ISG, each tube meets the shell-side LBE according to the order of the tube layer and transfers heat to and from the LBE. There was a difference in the amount of heat depending on the order in which each tube meets the LBE and the temperatures of the two fluids. However, since the order of the tube layers in the serpentine-tube bundle was reversed, the total amount of heat transferred to each tube did not differ significantly, and the temperatures of the tube-side fluids tended to cross each other. The water tube #5 in the downregion showed a different temperature distribution due to the early phase change from water to steam, but when looking at the temperatures at the inlet and outlet, it was judged that the total amount of heat transferred to the tube #5 was close to that of the other tubes. The temperature of the LBE did not increase or decrease smoothly but tended to be bumpy. It was difficult to recognize this temperature distribution as a realistic temperature distribution in the S-ISG. This can be considered as a limitation of the SPINS-S code, as it does not reflect the heat conduction in the flow. The validity of the SPINS-S code was evaluated by comparing the code results with the CFD simulation results in Section 3.3.Figure 7
Temperature distributions of sodium, LBE, and water in the up- and downregions.


#### 3.2.1. Sensitivity to LBE Mass Flow Rate

Unlike the other fluids constrained by boundary conditions, the LBE mass flow rate, which can be adjusted at the design stage, affects the heat transfer performance of the S-ISG. The sensitivity of the heat transfer performance of the S-ISG with respect to the LBE mass flow rate is evaluated in Figure8. As in the case of general heat exchangers, the heat transfer performance between the three fluids tended to increase as the flow rate of the intermediate fluid (LBE) increased (Figure 8(a)). However, as discussed in Section 3.2, the LBE flow caused a difference in the temperature distributions between the two regions (up- and downregions). This characteristic of the S-ISG became larger as the LBE flow rate increased. At the higher LBE flow rate, in the upregion, the heat transfer rate with sodium became larger, the outlet temperature of sodium became lower (because the sodium is the hot-side fluid), and the temperature distributions in the upregion became lower, whereas in the downregion, the heat transfer rate with water/steam became larger, the outlet temperature of steam became higher (because the water/steam is the cold-side fluid), and the temperature distributions in the downregion became higher. In Figure 8(b), both sodium and steam outlet temperatures showed larger differences between the up- and downregions at the higher LBE mass flow rate. In Figure 9, at the higher LBE flow rate, the heat transfer with sodium increased, but the heat transfer with water/steam slightly decreased in the upregion. On the other hand, the heat transfer with sodium decreased, and the heat transfer with water/steam slightly increased in the downregion. This trend also agreed well with the results in Figure 8. The difference in heat transfer rate between the two tube-side fluids within a single unit is the amount of heat transferred to the LBE, which increased due to the increased flow rate and heat capacity of the LBE. Overall, the heat transfer performance of the S-ISG increased slightly with increasing LBE flow rate; however, the change was negligible. If the heat transfer performance of the S-ISG is sufficient even without the LBE flow, the S-ISG can be further simplified without the pipes connecting the two units and the pump system. The S-ISG design, which can be used in the form of a single unit, utilizes natural convection within a stagnant LBE and can improve economic efficiency and safety in addition to the advantage of modularization. However, to evaluate the single-unit design, the thermal stratification in the stagnant LBE and the natural convection heat transfer performance should be evaluated in advance.Figure 8
Sensitivity analysis results for LBE mass flow rate using SPINS-S code: (a) heat transfer performance of S-ISG; (b) tube-side outlet temperature according to LBE mass flow rates.
(a)(b)Figure 9
Heat transfer rates through each sodium and water tube in the S-ISG.


### 3.3. CFD Analysis-Based Performance Evaluation

#### 3.3.1. Modeling and Method

For the specific design of the S-ISG based on the one-dimensional analysis code, the multidimensional flow and heat transfer characteristics of the S-ISG were analyzed using ANSYS CFX, a commercial CFD software. A steady-state conjugated heat transfer analysis including the solid tube walls was performed, and the phase change of water was reflected using the homogeneous binary mixture and equilibrium phase change model. For all three fluids, the shear stress transport (SST) k-w model was used as the turbulence model.The repeated tube rows were simplified as a domain with one sodium tube row and one water tube row using periodic conditions, as shown in the left figure of Figure10. The inlet and outlet conditions for the tube-side fluids were set in the area where the tubes and the tube chambers were connected, as shown in the right figure of Figure 10. The internal flow of the tube chamber was excluded from the tube-side simulation; however, the tube chamber occupied the space on the shell-side, where the LBE flows. The tube chamber was treated as insulated walls against the LBE flow. For the LBE, both the main flow region and the stagnant fluid region were considered, but the inlet and outlet conditions of the LBE were applied only to the main flow region, as shown in Figure 11. In the stagnant fluid region, there was only flow due to natural convection, and the region was connected to the main flow region via small gaps between the flow-guide walls and the heat transfer tubes. The outermost surfaces of the shell were considered as insulation conditions.Figure 10
Periodic domain of S-ISG for CFD simulation with the realistic mesh generation.Figure 11
Boundary conditions for each fluid in CFD simulation.In the case of inlet flow rate conditions, the total flow rate was divided into two tube rows considering the periodic condition. For the tube-side inlet temperature, the same temperature conditions as those used in the one-dimensional design were applied. The material properties of Mod.9Cr-1Mo were used for the tubes and chambers, and an additional contact thermal resistance was considered at the inner surface of the water tube for the fouling effect. The physical properties of all the fluids used in the simulation were considered for the changes in temperature. The ANSYS CFX IAPWS table was used to determine water properties. Under the LBE temperature condition, the average outlet temperature of the upregion was used as the inlet temperature condition of the downregion, and the average outlet temperature of the downregion was used as the inlet temperature of the upregion. The LBE temperatures of the two S-ISG units converged through an iterative process by separately performing the analysis for the up- and downregions.As shown in Figure12, the mesh used for the simulation consisted of approximately 170 million elements, the shell-side volume was composed of tetrahedral meshes, and the tube walls and internal tube volumes were composed of hexahedral meshes using sweep mesh generation. Prism layers were placed near the solid walls.Figure 12
Mesh structures for S-ISG simulation.


#### 3.3.2. Comparison of CFD Analysis Results with SPINS-S Code Results

The CFD analysis results for the thermal-hydraulic conditions of the S-ISG were compared with the SPINS-S code results, as listed in Table4. In the case of the tube-side fluids, the average values of the five tubes were used, and in the case of the shell-side fluid, the average temperatures at the top and bottom areas of each region (up- and downregions) were used. For the heat transfer rate of the S-ISG, the CFD analysis result fits well within approximately 3% of the SPINS-S results. Figure 13 shows the temperature distributions of sodium, water, and LBE in the S-ISG. The LBE temperature is based on the center plane of the sodium tube row. Like the SPINS-S results (Figure 7), in the CFD results, the temperature distributions of the downregion were found to be higher overall than those of the upregion. Moreover, in Figure 14, the phase change region in the water tubes occurred at lower position in the downregion than the upregion, which was consistent with Figure 7. This means that the heat transfer model in Figure 4, which assumed that heat transfer occurs simultaneously between sodium and water tubes, can be applied sufficiently to predict the heat transfer performance of the three-fluid system, i.e., the S-ISG.Table 4
Comparison of SPINS-S code results with the CFD analysis results for thermal-hydraulic conditions of S-ISG.
FluidVariableSPINS-SCFDUpDownUpDownHot tube (Na)Inlet temp. (°C)510.8510.0510.0510.0Outlet temp. (°C)359.2371.5350.5371.2Pressure drop (kPa)124.2124.2174.7174.6Cold tube (H2O)Inlet temp. (°C)216.9217.3217.0217.0Outlet temp. (°C)463.8481.4484.3499.8Pressure drop (kPa)17.017.114.217.6Shell (LBE)Topside temp. (°C)494.0494.0501.3501.3Bottom temp. (°C)333.2332.8320.6320.6Heat transfer rate (MWth)96.85 (sodium)/96.91 (water)99.69 (sodium)/99.63 (water)Figure 13
Temperature distributions of each fluid in S-ISG: (a) sodium tube side; (b) water tube side; (c) LBE shell side based on center plane of sodium tube row.
(a)(b)(c)Figure 14
Distribution of steam mass quality in water tubes of S-ISG.In addition to the average temperature distributions of the S-ISG, the inlet and outlet temperatures of each tube are compared in Table5. The tubes were numbered from 1 to 5 from top to bottom based on their positions connected to the upper chamber, as shown in Figure 15. In CFD analysis, it is possible to set the inlet condition of each tube to be consistent with the boundary condition. However, while performing the calculations using the SPINS-S code, certain boundary conditions must be predicted through iterative processes. Therefore, the sodium inlet temperature in the upregion and the water inlet temperature in the downregion did not show perfect agreement with the boundary conditions. By comparing the CFD results with the SPINS-S code results, we observed that the CFD results exhibited a uniform temperature increase or decrease in all tubes, whereas the SPINS-S code results exhibited a relatively large deviation for the temperature changes between the tubes. In particular, the temperature changes of tubes 1 and 5 located at both ends of the tube bunch were significantly different from those of tubes 2–4 located in the middle of the bunch. This seems to be because the thermal conduction and mixing effect in the shell-side flow were not reflected in the SPINS-S code.Table 5
Comparison of the SPINS-S code with the CFD analysis results for inlet and outlet temperatures of all tubes in S-ISG.
FluidVariableTube no.Upregion12345Hot tube (Na)Inlet temp. (°C)SPINS-S512.0511.7511.5509.8508.7CFD510.0510.0510.0510.0510.0Outlet temp. (°C)SPINS-S360.1360.5360.5359.4355.4CFD346.1350.8351.7352.3351.5Cold tube (H2O)Inlet temp. (°C)SPINS-S216.9216.9216.9216.9216.9CFD217.0217.0217.0217.0217.0Outlet temp. (°C)SPINS-S457.8465.9468.2467.0460.0CFD485.0485.3485.3484.1481.9Downregion12345Hot tube (Na)Inlet temp. (°C)SPINS-S510.0510.0510.0510.0510.0CFD510.0510.0510.0510.0510.0Outlet temp. (°C)SPINS-S379.7370.6368.0368.1371.1CFD369.0371.0371.4371.6372.9Cold tube (H2O)Inlet temp. (°C)SPINS-S215.0216.8218.1218.5218.2CFD217.0217.0217.0217.0217.0Outlet temp. (°C)SPINS-S479.3478.8479.7482.2487.0CFD500.4499.7499.6499.6499.9Figure 15
Tube-to-chamber connection geometry and tube numbering.


#### 3.3.3. Thermal-Hydraulic Characteristics of S-ISG in CFD Analysis

The distinctive shell-side geometry of the S-ISG created multidimensional characteristics that were difficult to evaluate with the one-dimensional approach. Although the SPINS-S code well-predicted the heat transfer performance of the S-ISG, the multidimensional characteristics should be considered additionally in the design process, especially for the bending part in the stagnant fluid region where natural convection heat transfer occurred and for the space between the tube passes of the serpentine-tube bundle. The thermal-hydraulic characteristics of the S-ISG were evaluated based on the CFD analysis results. First, the average heat flux on the tubes was compared for the main flow and stagnant fluid regions, as listed in Table6. The detailed heat flux values for each tube location are summarized in the appendix (Tables 7 and 8). The straight parts of the serpentine tubes were located in the main flow region, and the LBE flowed by forced convection. The stagnant fluid region featured the bending parts of the serpentine tubes and tube chambers and was separated from the main flow region by the flow-guide walls, so that the region was not affected by the LBE flow. Surprisingly, the average heat flux of the bending parts in the stagnant fluid region was higher than that of the straight parts in the main flow region. The reason for the high heat flux in the bending parts should be analyzed under various conditions; however, it is confirmed that heat transfer using natural convection shows sufficiently comparable performance with forced convection at a very low velocity. This means that a pump system for forced convection is not mandatory in the S-ISG, and as mentioned in Section 3.2.1, the concept of S-ISG using only natural convection can be proposed. Further research on this simplified concept should be conducted in the future.Table 6
Average heat flux on serpentine tubes in main flow region and stagnant fluid region.
Average heat flux (W/m2)Sodium tubesWater tubesUpDownUpDownMain flow region (straight parts)-68,989-59,04462,58764,007Stagnant fluid region (bending parts)-89,738-78,88683,03583,716The flow characteristics of the serpentine-tube bundle are shown in Figures16 and 17. Flow circulations appeared in the entire region, regardless of the main flow and stagnant fluid regions. In particular, there was no clear upward (upregion) or downward (downregion) flow of the LBE even in the main flow region. A flow in the form of circulation flow existed between the tube passes of the serpentine-tube bundle. The flow in the tube bundles at low velocities can be considered a natural convection flow. Therefore, in the multidimensional characteristic evaluation, the natural convection characteristic of the serpentine-tube bundle including the bending parts in the stagnant fluid region needs to be evaluated.Figure 16
Velocity distribution of S-ISG (center plane of sodium tube row).Figure 17
Velocity distribution in the serpentine-tube bundle of S-ISG (center plane of sodium tube row): (a) upregion; (b) downregion.
(a)(b)


## 3.1. Thermal-Hydraulic Design of S-ISG

In order to analyze the thermal flow characteristics of the S-ISG, detailed design information including thermally balanced boundary conditions is required. Therefore, in this study, a commercial-scale S-ISG was designed using the developed SPINS-S code. The designed S-ISG has a heat capacity of 96.77 MWth, which is equivalent to 1/8 the scale of one unit of a steam generator for a 600 MWe level reactor with two steam generator units. As the proposed S-ISG required an additional volume for the intermediate fluid, the volumetric efficiency was low, but it had the advantage of modularization. Here, we considered that one steam generator was modularized to 1/8 parts by taking advantage of the modularity feature, as a realistic steam generator for commercial reactor design. As this was a preliminary design to investigate the thermal-hydraulic characteristics of the S-ISG, it was not optimized. It is possible to enhance economic efficiency through further optimization processes.The thermal-fluidic boundary conditions required for the design were derived from the normal operating conditions of the KALIMER-600 designed by KAERI [16]. Table 2 lists the detailed specifications of the designed S-ISG. The material of the structure was assumed to be Mod. 9Cr-1Mo (Gr91), considering the operating temperature. The number of sodium tubes and water/steam tubes in a unit was 190 (i.e., 380 in both units). Each tube had a serpentine configuration with a total length of 40.74 m, a slope of 3°, and 11 bending parts from the upper chamber to the lower chamber. Five tubes were bunched in a row, and 76 rows were provided in total for the two fluids in the depth direction. The outer diameter of the tube was 27.2 mm for both the sodium and water/steam tubes; however, the thickness considering the internal pressure was 1.65 mm and 2.9 mm for the sodium and water/steam tubes, respectively. The sodium and water tubes had an in-line arrangement, and the LBE flowed across the sodium and water tubes. The pitch-to-diameter ratios of the longitudinal and transverse directions were 1.5. Table 2 summarizes and Figure 6 shows the design results of the S-ISG with a thermal capacity of 96.77 MWth obtained using the SPINS-S. As a result of three-dimensional modeling based on the design specification results, the external dimensions of one S-ISG unit were 4.97 m in width, 4.99 m in depth, and 7.265 m in height.Table 2
Design specifications of the S-ISG with a thermal capacity of 96.77 MWth.
Design parameterValueTotal length of a tube (sum of straight parts) (m)40.74Total number of hot tubes (per unit) (ea)190Total number of cold tubes (per unit) (ea)190Number of tubes in a row (ea)5Number of tube rows (ea)76Number of serpentine tube passes (ea)12Spacing between flow-guide walls (m)3.39Height between tube bending parts (m)0.9Height of heat transfer bundle (m)5.297Outer diameter of tube (mm)27.2Thickness of hot tube (mm)1.65Thickness of cold tube (mm)2.90Inclined angle of straight tube (°)3Pitch-to-diameter ratio (P/D) (-)1.5Total heat transfer area (per unit) (m2)1322.8Overall unit size (W×D×H) (m3)4.97×4.99×7.265Figure 6
Detailed configuration and dimension of the designed S-ISG (single unit).


## 3.2. One-Dimensional Performance Evaluation

For the abovementioned S-ISG design specifications, the thermal-hydraulic characteristics were evaluated based on the SPINS-S code results as a one-dimensional approach. Table3 presents the heat transfer and thermal-fluidic information for the designed S-ISG. The sum of the heat transfer rates of the up- and downregions for sodium or water satisfied the target heat transfer rate of the proposed design. There were only small discrepancies between the heat transfer rates of the up- and downregions. The selected mass flow rate of the intermediate fluid was 160 kg/s, which generated only a small velocity of the LBE: 4.5 cm/s based on the minimum flow area. Therefore, flow-induced vibration was not a concern in this design.Table 3
Heat transfer and thermal-fluidic information for S-ISG.
ParameterValue (upregion)Value (downregion)Target heat transfer rate (MWth)96.77Sodium heat transfer rate (MWth)50.6246.23LBE heat transfer rate (MWth)3.653.70Water heat transfer rate (MWth)47.8449.06Sodium mass flow rate (kg/s)522.9Sodium inlet temperature (°C)510.8510.0Sodium outlet temperature (°C)359.2371.5Sodium pressure drop (kPa)124.2124.2Steam/water mass flow rate (kg/s)43.1Water inlet temperature (°C)216.9217.3Steam outlet temperature (°C)463.8481.4Steam/water pressure drop (kPa)17.017.1LBE mass flow rate (kg/s)160.0LBE temperature at top (°C)494.0494.0LBE temperature at bottom (°C)333.2332.8LBE pressure drop (kPa)0.1680.167Figure7 shows the temperatures of the shell-side LBE and the tube-side sodium and water. The temperatures of sodium and water are individually indicated for each tube, and the temperature of the LBE indicates the average temperature passed through the same number of heat transfer tubes. Therefore, the LBE temperatures are indicated in the same way as the average temperature passing through the first tube layer (tube #1) of sodium and water and the average temperature passing through the second tube layer (tube #2). In the case of sodium and water, the normalized elevations were expressed considering the position of each tube, and the elevations based on the center line of the shell were used for the LBE. The temperature distributions in the up- and downregions were different due to the opposite flow directions of the LBE. When the LBE passed through the sodium and water tubes, the heat transfer with the fluid in the countercurrent was greater than that with the fluid in the cocurrent. Therefore, in the upregion, the heat transfer rate with sodium (hot-side fluid) was higher than that with water (cold-side fluid), and vice versa in the downregion, as listed in Table 3. More heat transfer with sodium tube means lower sodium outlet temperature, and more heat transfer with water/steam means higher steam outlet temperature. This feature caused a difference between the temperature distributions in the up- and downregions. Overall, the temperature distribution of each fluid in the upregion showed lower values than that in the downregion. In the S-ISG, each tube meets the shell-side LBE according to the order of the tube layer and transfers heat to and from the LBE. There was a difference in the amount of heat depending on the order in which each tube meets the LBE and the temperatures of the two fluids. However, since the order of the tube layers in the serpentine-tube bundle was reversed, the total amount of heat transferred to each tube did not differ significantly, and the temperatures of the tube-side fluids tended to cross each other. The water tube #5 in the downregion showed a different temperature distribution due to the early phase change from water to steam, but when looking at the temperatures at the inlet and outlet, it was judged that the total amount of heat transferred to the tube #5 was close to that of the other tubes. The temperature of the LBE did not increase or decrease smoothly but tended to be bumpy. It was difficult to recognize this temperature distribution as a realistic temperature distribution in the S-ISG. This can be considered as a limitation of the SPINS-S code, as it does not reflect the heat conduction in the flow. The validity of the SPINS-S code was evaluated by comparing the code results with the CFD simulation results in Section 3.3.Figure 7
Temperature distributions of sodium, LBE, and water in the up- and downregions.


### 3.2.1. Sensitivity to LBE Mass Flow Rate

Unlike the other fluids constrained by boundary conditions, the LBE mass flow rate, which can be adjusted at the design stage, affects the heat transfer performance of the S-ISG. The sensitivity of the heat transfer performance of the S-ISG with respect to the LBE mass flow rate is evaluated in Figure8. As in the case of general heat exchangers, the heat transfer performance between the three fluids tended to increase as the flow rate of the intermediate fluid (LBE) increased (Figure 8(a)). However, as discussed in Section 3.2, the LBE flow caused a difference in the temperature distributions between the two regions (up- and downregions). This characteristic of the S-ISG became larger as the LBE flow rate increased. At the higher LBE flow rate, in the upregion, the heat transfer rate with sodium became larger, the outlet temperature of sodium became lower (because the sodium is the hot-side fluid), and the temperature distributions in the upregion became lower, whereas in the downregion, the heat transfer rate with water/steam became larger, the outlet temperature of steam became higher (because the water/steam is the cold-side fluid), and the temperature distributions in the downregion became higher. In Figure 8(b), both sodium and steam outlet temperatures showed larger differences between the up- and downregions at the higher LBE mass flow rate. In Figure 9, at the higher LBE flow rate, the heat transfer with sodium increased, but the heat transfer with water/steam slightly decreased in the upregion. On the other hand, the heat transfer with sodium decreased, and the heat transfer with water/steam slightly increased in the downregion. This trend also agreed well with the results in Figure 8. The difference in heat transfer rate between the two tube-side fluids within a single unit is the amount of heat transferred to the LBE, which increased due to the increased flow rate and heat capacity of the LBE. Overall, the heat transfer performance of the S-ISG increased slightly with increasing LBE flow rate; however, the change was negligible. If the heat transfer performance of the S-ISG is sufficient even without the LBE flow, the S-ISG can be further simplified without the pipes connecting the two units and the pump system. The S-ISG design, which can be used in the form of a single unit, utilizes natural convection within a stagnant LBE and can improve economic efficiency and safety in addition to the advantage of modularization. However, to evaluate the single-unit design, the thermal stratification in the stagnant LBE and the natural convection heat transfer performance should be evaluated in advance.Figure 8
Sensitivity analysis results for LBE mass flow rate using SPINS-S code: (a) heat transfer performance of S-ISG; (b) tube-side outlet temperature according to LBE mass flow rates.
(a)(b)Figure 9
Heat transfer rates through each sodium and water tube in the S-ISG.


## 3.2.1. Sensitivity to LBE Mass Flow Rate

Unlike the other fluids constrained by boundary conditions, the LBE mass flow rate, which can be adjusted at the design stage, affects the heat transfer performance of the S-ISG. The sensitivity of the heat transfer performance of the S-ISG with respect to the LBE mass flow rate is evaluated in Figure8. As in the case of general heat exchangers, the heat transfer performance between the three fluids tended to increase as the flow rate of the intermediate fluid (LBE) increased (Figure 8(a)). However, as discussed in Section 3.2, the LBE flow caused a difference in the temperature distributions between the two regions (up- and downregions). This characteristic of the S-ISG became larger as the LBE flow rate increased. At the higher LBE flow rate, in the upregion, the heat transfer rate with sodium became larger, the outlet temperature of sodium became lower (because the sodium is the hot-side fluid), and the temperature distributions in the upregion became lower, whereas in the downregion, the heat transfer rate with water/steam became larger, the outlet temperature of steam became higher (because the water/steam is the cold-side fluid), and the temperature distributions in the downregion became higher. In Figure 8(b), both sodium and steam outlet temperatures showed larger differences between the up- and downregions at the higher LBE mass flow rate. In Figure 9, at the higher LBE flow rate, the heat transfer with sodium increased, but the heat transfer with water/steam slightly decreased in the upregion. On the other hand, the heat transfer with sodium decreased, and the heat transfer with water/steam slightly increased in the downregion. This trend also agreed well with the results in Figure 8. The difference in heat transfer rate between the two tube-side fluids within a single unit is the amount of heat transferred to the LBE, which increased due to the increased flow rate and heat capacity of the LBE. Overall, the heat transfer performance of the S-ISG increased slightly with increasing LBE flow rate; however, the change was negligible. If the heat transfer performance of the S-ISG is sufficient even without the LBE flow, the S-ISG can be further simplified without the pipes connecting the two units and the pump system. The S-ISG design, which can be used in the form of a single unit, utilizes natural convection within a stagnant LBE and can improve economic efficiency and safety in addition to the advantage of modularization. However, to evaluate the single-unit design, the thermal stratification in the stagnant LBE and the natural convection heat transfer performance should be evaluated in advance.Figure 8
Sensitivity analysis results for LBE mass flow rate using SPINS-S code: (a) heat transfer performance of S-ISG; (b) tube-side outlet temperature according to LBE mass flow rates.
(a)(b)Figure 9
Heat transfer rates through each sodium and water tube in the S-ISG.


## 3.3. CFD Analysis-Based Performance Evaluation

### 3.3.1. Modeling and Method

For the specific design of the S-ISG based on the one-dimensional analysis code, the multidimensional flow and heat transfer characteristics of the S-ISG were analyzed using ANSYS CFX, a commercial CFD software. A steady-state conjugated heat transfer analysis including the solid tube walls was performed, and the phase change of water was reflected using the homogeneous binary mixture and equilibrium phase change model. For all three fluids, the shear stress transport (SST) k-w model was used as the turbulence model.The repeated tube rows were simplified as a domain with one sodium tube row and one water tube row using periodic conditions, as shown in the left figure of Figure10. The inlet and outlet conditions for the tube-side fluids were set in the area where the tubes and the tube chambers were connected, as shown in the right figure of Figure 10. The internal flow of the tube chamber was excluded from the tube-side simulation; however, the tube chamber occupied the space on the shell-side, where the LBE flows. The tube chamber was treated as insulated walls against the LBE flow. For the LBE, both the main flow region and the stagnant fluid region were considered, but the inlet and outlet conditions of the LBE were applied only to the main flow region, as shown in Figure 11. In the stagnant fluid region, there was only flow due to natural convection, and the region was connected to the main flow region via small gaps between the flow-guide walls and the heat transfer tubes. The outermost surfaces of the shell were considered as insulation conditions.Figure 10
Periodic domain of S-ISG for CFD simulation with the realistic mesh generation.Figure 11
Boundary conditions for each fluid in CFD simulation.In the case of inlet flow rate conditions, the total flow rate was divided into two tube rows considering the periodic condition. For the tube-side inlet temperature, the same temperature conditions as those used in the one-dimensional design were applied. The material properties of Mod.9Cr-1Mo were used for the tubes and chambers, and an additional contact thermal resistance was considered at the inner surface of the water tube for the fouling effect. The physical properties of all the fluids used in the simulation were considered for the changes in temperature. The ANSYS CFX IAPWS table was used to determine water properties. Under the LBE temperature condition, the average outlet temperature of the upregion was used as the inlet temperature condition of the downregion, and the average outlet temperature of the downregion was used as the inlet temperature of the upregion. The LBE temperatures of the two S-ISG units converged through an iterative process by separately performing the analysis for the up- and downregions.As shown in Figure12, the mesh used for the simulation consisted of approximately 170 million elements, the shell-side volume was composed of tetrahedral meshes, and the tube walls and internal tube volumes were composed of hexahedral meshes using sweep mesh generation. Prism layers were placed near the solid walls.Figure 12
Mesh structures for S-ISG simulation.


### 3.3.2. Comparison of CFD Analysis Results with SPINS-S Code Results

The CFD analysis results for the thermal-hydraulic conditions of the S-ISG were compared with the SPINS-S code results, as listed in Table4. In the case of the tube-side fluids, the average values of the five tubes were used, and in the case of the shell-side fluid, the average temperatures at the top and bottom areas of each region (up- and downregions) were used. For the heat transfer rate of the S-ISG, the CFD analysis result fits well within approximately 3% of the SPINS-S results. Figure 13 shows the temperature distributions of sodium, water, and LBE in the S-ISG. The LBE temperature is based on the center plane of the sodium tube row. Like the SPINS-S results (Figure 7), in the CFD results, the temperature distributions of the downregion were found to be higher overall than those of the upregion. Moreover, in Figure 14, the phase change region in the water tubes occurred at lower position in the downregion than the upregion, which was consistent with Figure 7. This means that the heat transfer model in Figure 4, which assumed that heat transfer occurs simultaneously between sodium and water tubes, can be applied sufficiently to predict the heat transfer performance of the three-fluid system, i.e., the S-ISG.Table 4
Comparison of SPINS-S code results with the CFD analysis results for thermal-hydraulic conditions of S-ISG.
FluidVariableSPINS-SCFDUpDownUpDownHot tube (Na)Inlet temp. (°C)510.8510.0510.0510.0Outlet temp. (°C)359.2371.5350.5371.2Pressure drop (kPa)124.2124.2174.7174.6Cold tube (H2O)Inlet temp. (°C)216.9217.3217.0217.0Outlet temp. (°C)463.8481.4484.3499.8Pressure drop (kPa)17.017.114.217.6Shell (LBE)Topside temp. (°C)494.0494.0501.3501.3Bottom temp. (°C)333.2332.8320.6320.6Heat transfer rate (MWth)96.85 (sodium)/96.91 (water)99.69 (sodium)/99.63 (water)Figure 13
Temperature distributions of each fluid in S-ISG: (a) sodium tube side; (b) water tube side; (c) LBE shell side based on center plane of sodium tube row.
(a)(b)(c)Figure 14
Distribution of steam mass quality in water tubes of S-ISG.In addition to the average temperature distributions of the S-ISG, the inlet and outlet temperatures of each tube are compared in Table5. The tubes were numbered from 1 to 5 from top to bottom based on their positions connected to the upper chamber, as shown in Figure 15. In CFD analysis, it is possible to set the inlet condition of each tube to be consistent with the boundary condition. However, while performing the calculations using the SPINS-S code, certain boundary conditions must be predicted through iterative processes. Therefore, the sodium inlet temperature in the upregion and the water inlet temperature in the downregion did not show perfect agreement with the boundary conditions. By comparing the CFD results with the SPINS-S code results, we observed that the CFD results exhibited a uniform temperature increase or decrease in all tubes, whereas the SPINS-S code results exhibited a relatively large deviation for the temperature changes between the tubes. In particular, the temperature changes of tubes 1 and 5 located at both ends of the tube bunch were significantly different from those of tubes 2–4 located in the middle of the bunch. This seems to be because the thermal conduction and mixing effect in the shell-side flow were not reflected in the SPINS-S code.Table 5
Comparison of the SPINS-S code with the CFD analysis results for inlet and outlet temperatures of all tubes in S-ISG.
FluidVariableTube no.Upregion12345Hot tube (Na)Inlet temp. (°C)SPINS-S512.0511.7511.5509.8508.7CFD510.0510.0510.0510.0510.0Outlet temp. (°C)SPINS-S360.1360.5360.5359.4355.4CFD346.1350.8351.7352.3351.5Cold tube (H2O)Inlet temp. (°C)SPINS-S216.9216.9216.9216.9216.9CFD217.0217.0217.0217.0217.0Outlet temp. (°C)SPINS-S457.8465.9468.2467.0460.0CFD485.0485.3485.3484.1481.9Downregion12345Hot tube (Na)Inlet temp. (°C)SPINS-S510.0510.0510.0510.0510.0CFD510.0510.0510.0510.0510.0Outlet temp. (°C)SPINS-S379.7370.6368.0368.1371.1CFD369.0371.0371.4371.6372.9Cold tube (H2O)Inlet temp. (°C)SPINS-S215.0216.8218.1218.5218.2CFD217.0217.0217.0217.0217.0Outlet temp. (°C)SPINS-S479.3478.8479.7482.2487.0CFD500.4499.7499.6499.6499.9Figure 15
Tube-to-chamber connection geometry and tube numbering.


### 3.3.3. Thermal-Hydraulic Characteristics of S-ISG in CFD Analysis

The distinctive shell-side geometry of the S-ISG created multidimensional characteristics that were difficult to evaluate with the one-dimensional approach. Although the SPINS-S code well-predicted the heat transfer performance of the S-ISG, the multidimensional characteristics should be considered additionally in the design process, especially for the bending part in the stagnant fluid region where natural convection heat transfer occurred and for the space between the tube passes of the serpentine-tube bundle. The thermal-hydraulic characteristics of the S-ISG were evaluated based on the CFD analysis results. First, the average heat flux on the tubes was compared for the main flow and stagnant fluid regions, as listed in Table6. The detailed heat flux values for each tube location are summarized in the appendix (Tables 7 and 8). The straight parts of the serpentine tubes were located in the main flow region, and the LBE flowed by forced convection. The stagnant fluid region featured the bending parts of the serpentine tubes and tube chambers and was separated from the main flow region by the flow-guide walls, so that the region was not affected by the LBE flow. Surprisingly, the average heat flux of the bending parts in the stagnant fluid region was higher than that of the straight parts in the main flow region. The reason for the high heat flux in the bending parts should be analyzed under various conditions; however, it is confirmed that heat transfer using natural convection shows sufficiently comparable performance with forced convection at a very low velocity. This means that a pump system for forced convection is not mandatory in the S-ISG, and as mentioned in Section 3.2.1, the concept of S-ISG using only natural convection can be proposed. Further research on this simplified concept should be conducted in the future.Table 6
Average heat flux on serpentine tubes in main flow region and stagnant fluid region.
Average heat flux (W/m2)Sodium tubesWater tubesUpDownUpDownMain flow region (straight parts)-68,989-59,04462,58764,007Stagnant fluid region (bending parts)-89,738-78,88683,03583,716The flow characteristics of the serpentine-tube bundle are shown in Figures16 and 17. Flow circulations appeared in the entire region, regardless of the main flow and stagnant fluid regions. In particular, there was no clear upward (upregion) or downward (downregion) flow of the LBE even in the main flow region. A flow in the form of circulation flow existed between the tube passes of the serpentine-tube bundle. The flow in the tube bundles at low velocities can be considered a natural convection flow. Therefore, in the multidimensional characteristic evaluation, the natural convection characteristic of the serpentine-tube bundle including the bending parts in the stagnant fluid region needs to be evaluated.Figure 16
Velocity distribution of S-ISG (center plane of sodium tube row).Figure 17
Velocity distribution in the serpentine-tube bundle of S-ISG (center plane of sodium tube row): (a) upregion; (b) downregion.
(a)(b)


## 3.3.1. Modeling and Method

For the specific design of the S-ISG based on the one-dimensional analysis code, the multidimensional flow and heat transfer characteristics of the S-ISG were analyzed using ANSYS CFX, a commercial CFD software. A steady-state conjugated heat transfer analysis including the solid tube walls was performed, and the phase change of water was reflected using the homogeneous binary mixture and equilibrium phase change model. For all three fluids, the shear stress transport (SST) k-w model was used as the turbulence model.The repeated tube rows were simplified as a domain with one sodium tube row and one water tube row using periodic conditions, as shown in the left figure of Figure10. The inlet and outlet conditions for the tube-side fluids were set in the area where the tubes and the tube chambers were connected, as shown in the right figure of Figure 10. The internal flow of the tube chamber was excluded from the tube-side simulation; however, the tube chamber occupied the space on the shell-side, where the LBE flows. The tube chamber was treated as insulated walls against the LBE flow. For the LBE, both the main flow region and the stagnant fluid region were considered, but the inlet and outlet conditions of the LBE were applied only to the main flow region, as shown in Figure 11. In the stagnant fluid region, there was only flow due to natural convection, and the region was connected to the main flow region via small gaps between the flow-guide walls and the heat transfer tubes. The outermost surfaces of the shell were considered as insulation conditions.Figure 10
Periodic domain of S-ISG for CFD simulation with the realistic mesh generation.Figure 11
Boundary conditions for each fluid in CFD simulation.In the case of inlet flow rate conditions, the total flow rate was divided into two tube rows considering the periodic condition. For the tube-side inlet temperature, the same temperature conditions as those used in the one-dimensional design were applied. The material properties of Mod.9Cr-1Mo were used for the tubes and chambers, and an additional contact thermal resistance was considered at the inner surface of the water tube for the fouling effect. The physical properties of all the fluids used in the simulation were considered for the changes in temperature. The ANSYS CFX IAPWS table was used to determine water properties. Under the LBE temperature condition, the average outlet temperature of the upregion was used as the inlet temperature condition of the downregion, and the average outlet temperature of the downregion was used as the inlet temperature of the upregion. The LBE temperatures of the two S-ISG units converged through an iterative process by separately performing the analysis for the up- and downregions.As shown in Figure12, the mesh used for the simulation consisted of approximately 170 million elements, the shell-side volume was composed of tetrahedral meshes, and the tube walls and internal tube volumes were composed of hexahedral meshes using sweep mesh generation. Prism layers were placed near the solid walls.Figure 12
Mesh structures for S-ISG simulation.


## 3.3.2. Comparison of CFD Analysis Results with SPINS-S Code Results

The CFD analysis results for the thermal-hydraulic conditions of the S-ISG were compared with the SPINS-S code results, as listed in Table4. In the case of the tube-side fluids, the average values of the five tubes were used, and in the case of the shell-side fluid, the average temperatures at the top and bottom areas of each region (up- and downregions) were used. For the heat transfer rate of the S-ISG, the CFD analysis result fits well within approximately 3% of the SPINS-S results. Figure 13 shows the temperature distributions of sodium, water, and LBE in the S-ISG. The LBE temperature is based on the center plane of the sodium tube row. Like the SPINS-S results (Figure 7), in the CFD results, the temperature distributions of the downregion were found to be higher overall than those of the upregion. Moreover, in Figure 14, the phase change region in the water tubes occurred at lower position in the downregion than the upregion, which was consistent with Figure 7. This means that the heat transfer model in Figure 4, which assumed that heat transfer occurs simultaneously between sodium and water tubes, can be applied sufficiently to predict the heat transfer performance of the three-fluid system, i.e., the S-ISG.Table 4
Comparison of SPINS-S code results with the CFD analysis results for thermal-hydraulic conditions of S-ISG.
FluidVariableSPINS-SCFDUpDownUpDownHot tube (Na)Inlet temp. (°C)510.8510.0510.0510.0Outlet temp. (°C)359.2371.5350.5371.2Pressure drop (kPa)124.2124.2174.7174.6Cold tube (H2O)Inlet temp. (°C)216.9217.3217.0217.0Outlet temp. (°C)463.8481.4484.3499.8Pressure drop (kPa)17.017.114.217.6Shell (LBE)Topside temp. (°C)494.0494.0501.3501.3Bottom temp. (°C)333.2332.8320.6320.6Heat transfer rate (MWth)96.85 (sodium)/96.91 (water)99.69 (sodium)/99.63 (water)Figure 13
Temperature distributions of each fluid in S-ISG: (a) sodium tube side; (b) water tube side; (c) LBE shell side based on center plane of sodium tube row.
(a)(b)(c)Figure 14
Distribution of steam mass quality in water tubes of S-ISG.In addition to the average temperature distributions of the S-ISG, the inlet and outlet temperatures of each tube are compared in Table5. The tubes were numbered from 1 to 5 from top to bottom based on their positions connected to the upper chamber, as shown in Figure 15. In CFD analysis, it is possible to set the inlet condition of each tube to be consistent with the boundary condition. However, while performing the calculations using the SPINS-S code, certain boundary conditions must be predicted through iterative processes. Therefore, the sodium inlet temperature in the upregion and the water inlet temperature in the downregion did not show perfect agreement with the boundary conditions. By comparing the CFD results with the SPINS-S code results, we observed that the CFD results exhibited a uniform temperature increase or decrease in all tubes, whereas the SPINS-S code results exhibited a relatively large deviation for the temperature changes between the tubes. In particular, the temperature changes of tubes 1 and 5 located at both ends of the tube bunch were significantly different from those of tubes 2–4 located in the middle of the bunch. This seems to be because the thermal conduction and mixing effect in the shell-side flow were not reflected in the SPINS-S code.Table 5
Comparison of the SPINS-S code with the CFD analysis results for inlet and outlet temperatures of all tubes in S-ISG.
FluidVariableTube no.Upregion12345Hot tube (Na)Inlet temp. (°C)SPINS-S512.0511.7511.5509.8508.7CFD510.0510.0510.0510.0510.0Outlet temp. (°C)SPINS-S360.1360.5360.5359.4355.4CFD346.1350.8351.7352.3351.5Cold tube (H2O)Inlet temp. (°C)SPINS-S216.9216.9216.9216.9216.9CFD217.0217.0217.0217.0217.0Outlet temp. (°C)SPINS-S457.8465.9468.2467.0460.0CFD485.0485.3485.3484.1481.9Downregion12345Hot tube (Na)Inlet temp. (°C)SPINS-S510.0510.0510.0510.0510.0CFD510.0510.0510.0510.0510.0Outlet temp. (°C)SPINS-S379.7370.6368.0368.1371.1CFD369.0371.0371.4371.6372.9Cold tube (H2O)Inlet temp. (°C)SPINS-S215.0216.8218.1218.5218.2CFD217.0217.0217.0217.0217.0Outlet temp. (°C)SPINS-S479.3478.8479.7482.2487.0CFD500.4499.7499.6499.6499.9Figure 15
Tube-to-chamber connection geometry and tube numbering.


## 3.3.3. Thermal-Hydraulic Characteristics of S-ISG in CFD Analysis

The distinctive shell-side geometry of the S-ISG created multidimensional characteristics that were difficult to evaluate with the one-dimensional approach. Although the SPINS-S code well-predicted the heat transfer performance of the S-ISG, the multidimensional characteristics should be considered additionally in the design process, especially for the bending part in the stagnant fluid region where natural convection heat transfer occurred and for the space between the tube passes of the serpentine-tube bundle. The thermal-hydraulic characteristics of the S-ISG were evaluated based on the CFD analysis results. First, the average heat flux on the tubes was compared for the main flow and stagnant fluid regions, as listed in Table6. The detailed heat flux values for each tube location are summarized in the appendix (Tables 7 and 8). The straight parts of the serpentine tubes were located in the main flow region, and the LBE flowed by forced convection. The stagnant fluid region featured the bending parts of the serpentine tubes and tube chambers and was separated from the main flow region by the flow-guide walls, so that the region was not affected by the LBE flow. Surprisingly, the average heat flux of the bending parts in the stagnant fluid region was higher than that of the straight parts in the main flow region. The reason for the high heat flux in the bending parts should be analyzed under various conditions; however, it is confirmed that heat transfer using natural convection shows sufficiently comparable performance with forced convection at a very low velocity. This means that a pump system for forced convection is not mandatory in the S-ISG, and as mentioned in Section 3.2.1, the concept of S-ISG using only natural convection can be proposed. Further research on this simplified concept should be conducted in the future.Table 6
Average heat flux on serpentine tubes in main flow region and stagnant fluid region.
Average heat flux (W/m2)Sodium tubesWater tubesUpDownUpDownMain flow region (straight parts)-68,989-59,04462,58764,007Stagnant fluid region (bending parts)-89,738-78,88683,03583,716The flow characteristics of the serpentine-tube bundle are shown in Figures16 and 17. Flow circulations appeared in the entire region, regardless of the main flow and stagnant fluid regions. In particular, there was no clear upward (upregion) or downward (downregion) flow of the LBE even in the main flow region. A flow in the form of circulation flow existed between the tube passes of the serpentine-tube bundle. The flow in the tube bundles at low velocities can be considered a natural convection flow. Therefore, in the multidimensional characteristic evaluation, the natural convection characteristic of the serpentine-tube bundle including the bending parts in the stagnant fluid region needs to be evaluated.Figure 16
Velocity distribution of S-ISG (center plane of sodium tube row).Figure 17
Velocity distribution in the serpentine-tube bundle of S-ISG (center plane of sodium tube row): (a) upregion; (b) downregion.
(a)(b)


## 4. Conclusions

A novel serpentine tube-type steam generator (S-ISG) with an intermediate heat-transfer fluid between sodium and water was proposed. It has the advantage of using the proven power conversion system of the existing Rankine cycle and can prevent SWR by adopting an inactive intermediate fluid with both sodium and water. The S-ISG is advantageous in modularity, and it can effectively maintain the operation rate even in the case of partial failure of SGs, instead of the low volume efficiency compared to the conventional steam generator. To design and analyze the S-ISG, we developed a thermal-hydraulic performance analysis code, and the design results were presented. Using this design data, we conducted a structural layout design comprising chambers, tubes, flow-guide walls, and housing for an intermediate fluid. Through thermal-hydraulic evaluations using the code, we performed preliminary temperature analyses of three working fluids. In addition, we conducted a CFD simulation using a conventional software tool. The CFD analysis results were in good agreements with the SPINS-S code results, and we believe that the calculated results are reasonable. Using the CFD analysis results, the multidimensional thermal-hydraulic characteristics of the S-ISG were evaluated, and it was confirmed that natural convection characteristics appeared throughout the S-ISG even in the main flow region where the forced flow exists. Further studies can achieve the advance in the S-ISG design, including the concept of S-ISG using only natural convection, and provide a technical option for improving the safety and modularization of SFR steam generators.



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*Source: 2825626-2023-03-11.xml*