Spiral wound heat exchanger (SWHE) (Figure 1) has been widely used as a main cryogenic exchanger in large-scale liquid natural gas (LNG) plants owing to its different advantages, such as multi-stream capability, high compactness, efficient heat transfer, sufficient flexibility, and better robustness among others [1,2]. It also has a great potential in floating liquefied natural gas (FLNG) field. Meanwhile, hydrocarbons are usually used as a working medium in LNG field. Therefore, a better understanding of condensation flow and heat transfer for hydrocarbons in a spiral pipe under static and sloshing conditions can be contributed to the design and optimization of SWHE used in FLNG field.
Some investigations have been carried out on condensation flow and heat transfer characteristics in helically coiled tubes. Wongwises et al.  experimentally studied condensation heat transfer and pressure drop of R134a in a helically tube and found that they were both larger than those in a straight tube, which was also found in Gupta et al.'s study . Mozafari et al.  investigated the effects of different orientations of helical pipe on condensation heat transfer and pressure drop of R600a; the results showed that it had a significant effect on them. Salimpour et al.  suggested that condensation heat transfer coefficients of R404A in helically coiled tubes increased with the decreasing coil diameter and coil pitch. Li et al. [7,8] established a numerical model to study the condensation flow and heat transfer characteristics of propane and ethane/propane mixture in a spiral pipe and compared their simulation results with experimental ones. It could be clearly seen that the deviations between simulation results and experimental ones  were within 15%, which proved the rationality of the model.
At the same time, there have been some studies in literature on flow and heat transfer under sloshing conditions. Tan et al.  investigated single-phase natural circulation flow and heat transfer under rolling conditions. It was shown that the rolling motion could cause heat transfer enhancement, while the effect increased with the increase of rolling amplitude and frequency. Yu et al.  found that the fluctuations of frictional pressure drop and flow rate were synchronous. Jin et al.  investigated the flow resistance of air–water flow under rolling conditions. It stated the fluctuation amplitude of two-phase frictional pressure drop increased with the rise in vapor quality and rolling amplitude and the drop in Reynolds number. Chen et al. [13,14] discussed the effect of rolling motion on frictional pressure drop and heat transfer for boiling flow. It demonstrated that the fluctuation amplitudes both increased as the rolling amplitude, rolling period, and heat flux increased and the system pressure decreased.
The aforementioned surveys indicate that few studies have been devoted to the hydrocarbons condensation in a spiral pipe under sloshing conditions. Therefore, in this article, firstly, a numerical model was proposed and verified by experimental data. Then, the characteristics of hydrocarbons condensation flow and heat transfer in SWHE tube side under static and sloshing conditions were both discussed and some important conclusions were drawn.
A computational model (Figure 2) was established to simulate hydrocarbons condensation upward flow in a spiral pipe. It contains 0.6 m developing section, 0.2 m test section, and 0.2 m regulator section. The hydraulic diameter, curvature diameter, and helix angle are 10 mm, 2 m, and 10º, respectively. The mass flow, static pressure, and constant heat flux were adopted at inlet, outlet, and wall, respectively. The working fluids are methane (C1) and methane/ethane/propane (C1C2C3). All physical properties were gained by REFPROP .
In this article, the inhomogeneous two-fluid model together with standard k- turbulence model and thermal phase change model was adopted. The governing equations are shown as:
(6) where is the interfacial area density between liquid phase and vapor phase
(7) where represents the mean interfacial lengths scale, as shown in :
In this article, the function of the sloshing motion is as follows:
(9) where ( ) denotes sloshing amplitudes, is a sloshing cycle.
The sloshing simulations were achieved by adding an additional force in Eqs. (2, 3), as:
In order to verify the rationality of the model, the comparison between simulated frictional pressure drop and heat transfer coefficient and experimental ones for methane/ propane mixture are shown in Figure 3. It can be found that they both coincide with experimental ones at static and sloshing conditions, which indicates the applicability of the used model.
Condensation pressure drop and heat transfer at static conditions
Figure 4(a) displays the variation of the frictional pressure drop with vapor quality for C1 and C1C2C3 at static conditions. It can be found that for both pure and mixture hydrocarbons, the frictional pressure drop always increases with the increasing vapor quality since as the vapor quality increases, the vapor–liquid velocity ratio increases and shear effect enhances. Meanwhile, at a given vapor quality, the frictional pressure drop of C1C2C3 is always larger than that of C1 due to the larger liquid–vapor density ratio and liquid viscosity for C1C2C3.
Figure 4(b) gives out the heat transfer coefficient varying with vapor quality for C1 and C1C2C3 at static conditions. The results suggest that the heat transfer coefficients of C1 and C1C2C3 both first increase and then decrease as the vapor quality increases, while the maximum value appears, when the vapor quality is 0.75. This is because the larger vapor quality will cause larger void fraction and thinner liquid film, leading to a smaller thermal resistance, but when the vapor quality is large enough, the appearance of partial drying on the wall will cause heat transfer deterioration. Besides, at a given case, the heat transfer of C1C2C3 is worse than that of C1 because of heat and mass transfer thermal resistance for C1C2C3.
Condensation pressure drop and heat transfer at sloshing conditions
The transient relative frictional pressure drop and heat transfer coefficient under different sloshing conditions for C1 are plotted versus time in Figures 5(a) and (b), respectively. The results explain that the relative frictional pressure drop and heat transfer coefficient both change periodically with time under different sloshing conditions. Concurrently, compared to those under static conditions, the frictional pressure drops are almost always smaller, while the heat transfer coefficients are always larger under different sloshing conditions, which indicates that sloshing conditions can not only lead to drag reduction, but also bring about heat transfer enhancement. Moreover, the pitching condition shows the best drag reduction, followed by rolling condition, the worst in heaving condition; while the best heat transfer enhancement is found in heaving condition, followed by rolling condition, the worst in pitching condition.
Figures 6(a) and (b) display the variations of transient relative frictional pressure drop and heat transfer coefficient with time under different vapor qualities at heaving condition for C1C2C3, respectively. The results suggest that at heaving condition, the fluctuations of frictional pressure drop and heat transfer coefficient are both nearly sinusoidal, while the fluctuant magnitudes decrease with the increase of vapor quality. Meanwhile, compared to those at the static state, with the rise in vapor quality, the time-averaged frictional pressure drop decrease about 6.45%, 9.26%, and 0.51%, respectively, while the time-averaged heat transfer coefficient increase about 12.77%, 4.46%, and 4.39%, respectively.
The hydrocarbons condensation flow and heat transfer characteristics in a spiral pipe at static and sloshing conditions were numerically studied. Some key findings are drawn as:
• Compared to methane/ethane/propane (C1C2C3), methane (C1) has better heat transfer, with smaller pressure drop.
• At static conditions, as the vapor quality increases, the heat transfer coefficient first increases and then decreases, while the frictional pressure drop always increases.
• Sloshing motion could cause both heat transfer enhancement and drag reduction.
• With the rise in vapor quality, both pressure drop and heat transfer fluctuations become weakened.