Figure 1 shows the basic shape of the complex heat exchanger analyzed in this study. The complex heat exchanger, which was initially designed using primary thermal calculations, contains 92 LNG tubes and eight BOG tubes. Table 1 lists the basic specifications of the complex heat exchanger.

Figure 1: 
3D model of the Complex Heat Exchanger

At the inlet of the shell, steam is introduced at 6 barG and 168 ℃, while LNG and BOG are introduced at 16 barG and 4.5 barG, respectively, into the tubes at -163 ℃ and -140 ℃, respectively. The adiabatic condition is applied to the solid walls, except for the inner tubes, where heat exchange occurs. A pressure boundary condition is applied at the outlet.

Figure 2 shows the fluid region of the heat exchanger shown in Figure 1, where the LNG tube bundle (light blue) is located at the center of the heat exchanger, and the BOG tubes (yellow) surround it on both sides. The steam enters from the upper inlet, exchanges heat with the LNG and BOG inside the shell, and is discharged from the lower outlet.

Figure 2: 
Fluid Region of the Complex Heat Exchanger

The fluid flow is considered steady, incompressible, and turbulent. The fluid properties used in the analysis are expressed as functions of temperature, assuming no change in pressure. The continuity equation, momentum equation, and energy equation are provided respectively below [7].

Wherein τij=μ∂Ui∂Xj+∂Uj∂Xi and τijt=-ρuluJ¯.

Here, τ_ij is modeled using the viscous fluid model, whereas τijt should be modeled as the turbulence model.

Furthermore, q_i is modeled based on Fourier postulations, whereas qit and Φ^t should be modeled from the turbulence model. In this study, the standard k-ε turbulent model is used, which exhibits good convergence and stability for calculations compared to other models. For detailed turbulence quantities, please see References [8][9].

To test the grid independence of the analysis model, four mesh systems were generated with nodes ranging from approximately 6.7 million to 24.7 million, the results of the outlet temperatures for the four cases are compared in Figure 3.

Figure 3: 
Grid Independence Test

As shown in Figure 3, the outlet temperatures of the 24.7 million-node analysis grid were within 0.2 °C of those of the 18.8 million-node analysis grid, with an error of less than 1% based on heat transfer rate. Therefore, the analysis in this study is conducted based on a 24.7 million-node grid, which is also used for other analyses under the same conditions.

Table 2 summarizes the cases analyzed in this study. To understand the effect of the steam supply method on the heat exchange, the effects of the presence(O) or absence(X) of a distribution plate for steam dispersion in front of the steam inlet and the number of steam supply inlets to distribute steam more evenly to the tubes were investigated. Cases 1-X in Table 2 indicate that there is only one steam inlet(1) and no distribution plates(X) in front of the steam inlet.

Table 2 presents a summary of the cases examined in this study. To understand the impact of the steam supply method on heat exchange, the effect of the presence (O) or absence (X) of a distribution plate on steam dispersion in front of the steam inlet is investigated. Furthermore, the effect of the number of steam supply inlets used to distribute steam more uniformly across the tubes is investigated. Case 1-X in Table 2 indicates that there is only one steam inlet(1) and no distribution plates(X) in front of the steam inlet.

Figure 4 shows the flow analysis results for steam with and without a distribution plate in front of the inlet, when there is only one steam inlet. The streamlines are represented by lines randomly selected from 128 points on the inlet surface.

Figure 4: 
Streamlines of Steam with Single Steam Inlet

When checking the streamlines in Figure 4, the steam flow toward the tube is relatively evenly distributed when there is a distribution plate in front of the inlet (O) compared to when there is no distribution plate (X). When there is no distribution plate, the steam flow is mainly generated directly below the inlet and toward the right side.

This is due to the fact that there is a flow space between the U-shaped tube and shell on the right side, but the space between the tube bundle and shell on the left side is narrow, resulting in a relatively higher flow resistance. Hence, the streamline develops toward the right side. This flow ultimately affects heat transfer, and it is confirmed that the average outlet temperature of Steam Outlet 1-X is 59.37 ºC, while the average outlet temperature of Steam Outlet 1-O is 55.67 ºC. This shows that more heat is transferred through Steam Outlet 1-O than through 1-X, indicating that 1-O has a better overall heat transfer rate than 1-X.

Figure 5 shows the streamlines of the analysis results used to investigate the effect of the number of steam supply inlets. In this case, the inlet velocity was maintained constant, and the same amount of total heat supply was provided.

Figure 5: 
Effects of Number of Steam Inlets

When checking the streamlines in Figure 5, it can be estimated that as the number of inlets increases, the area where the fluid with a relatively faster velocity passes through the tube and contacts the tube expands uniformly, resulting in more efficient heat transfer. The average outlet temperature of Steam Outlet 1-X in Figure 5 is 59.37 ℃, that of Steam Outlet 3-X is 49.33 ℃, and that of Steam Outlet 5-X is 44.19 ℃, showing that the overall heat transfer rate of steam increases as the number of steam inlets increases. Figure 6 shows the heat transfer rate supplied to the BOG for all the analysis cases, and Figure 7 shows the heat transfer rate supplied to the LNG.

Figure 6: 
Heat Transfer Rate Supplied to BOG

Figure 7: 
Heat Transfer Rate Supplied to LNG

In the case of the LNG, when there was no distribution plate, the amount of heat transferred to the LNG increased linearly as the number of steam inlets increased.

Although there was a significant difference in the heat transferred based on the presence or absence of a distribution plate in front of the steam inlet for BOG, there was almost no difference in the heat transferred based on the number of inlets. The difference in transferred heat, based on the presence or absence of a distribution plate, is shown in Figure 8. When there is a distribution plate in front of the steam inlet, the steam supplied late is deflected toward the BOG tube, whereas without the distribution plate, the steam is deflected toward the LNG tube.

Figure 8: 
Velocity Vectors of Steam Flow with/without Distribution Plate

Figure 9 shows the heat transfer rate released by the steam. When there is a distribution plate, the heat transfer rate decreases as the number of inlets increases, whereas when there is no distribution plate, the heat transfer rate released by steam increases as the number of inlets increases.

Figure 9: 
Heat Transfer Rate Released by Steam

When steam flows inside the heat exchanger, pressure loss occurs because of friction with the tube bundle of the heat exchanger. Figure 10 shows the location of the cross section displaying the pressure distribution shown in Figure 11, which represents the pressure distribution inside the steam shell for each analysis case.

Figure 10: 
Section Locations of Steam Pressure Measurement

Figure 11: 
Steam Pressure at Each Section

Regarding the pressure distribution, even in cases where the pressure change is the highest among all the cases, the difference is only 0.01 barG in absolute value when compared to the absolute pressure (6 barG) supplied to the steam inlet. Therefore, it can be confirmed that the pressure change owing to the change in the supply method to the shell is negligible.

Figure 12 shows the pressure drop between the steam inlet and outlet. The largest pressure difference was 0.07878 barG, which was relatively small compared to the pressure supplied to the steam inlet, which was 6 barG. This indicates that the pressure drop was very small.

Figure 12: 
Steam Pressure Drop from Inlet to Outlet

Figure 13 shows the heat-transfer coefficients of the surfaces of BOG and LNG tubes for each case. Referring to the streamline distributions in Figures 4 and 5, it can be confirmed that in the cases without a distribution plate in front of the steam inlet, steam was directly injected into the LNG tube bundle located at the center of the shell, resulting in a significant amount of heat transfer on the side of the LNG tubes. In the cases with a distribution plate, steam flowed through the distribution plate toward the BOG tube side, where the heat-transfer coefficient increased.

Figure 13: 
Heat Transfer Coefficient on the Surface of BOG and LNG Tubes

Figure 14 and shows the average heat transfer coefficients on the surfaces of BOG tubes, while Figure 15 shows the average heat transfer coefficient on the surface of LNG tubes. Figures 14 and 15 show the same trend as Figures 6 and 8 for the heat transfer amounts of BOG and LNG.

Figure 14: 
Average Heat Transfer Coefficient of BOG Tubes

Figure 15: 
Average Heat Transfer Coefficient of LNG Tubes

The purpose of the complex heat exchanger was to supply heat evenly to LNG and BOG. As shown in Figures 8 and 9, in the cases without a distribution plate, steam is concentrated toward the LNG tube bundle inside the shell, resulting in an increase in the heat transfer amount. In cases with a distribution plate, steam flowed toward the BOG tube side more strongly than toward the LNG tube side, leading to a decrease in heat transfer. Therefore, the selection of an appropriate combination is dependent on the supply rate, supply temperature, and outlet temperature conditions of BOG and LNG. Additionally, the impact of the shape of the distribution plate and selection of the positions of BOG and LNG tubes should be reviewed in the near future.