As compact and efficient heat exchange equipment, helically coiled tube-in-tube heat exchangers (HCTT heat exchangers) are widely used in many industrial processes. However, the thermal-hydraulic research of liquefied natural gas (LNG) as the working fluid in HCTT heat exchangers is rarely reported. In this paper, the characteristics of HCTT heat exchangers, in which LNG flows in the inner tube and ethylene glycol-water solution flows in the outer tube, are studied by numerical simulations. The influences of heat transfer characteristics and pressure drops of the HCTT heat transfers are studied by changing the initial flow velocity, the helical middle diameter, and the helical pitch. The results indicate that different initial flow velocities in the inner tube and the outer tube of the HCTT heat exchanger have little influence on the secondary flow of the fluid in the helical tubes, and the overall flow characteristics tend to be stable. The smaller helical middle diameter of the HCTT heat exchanger leads to the shorter fluid flow length, the smaller resistance along the tubes and the increase of initial pressure under the condition of constant inlet velocity, which promotes the occurrence of secondary flow. The axial flow of fluid promotes the destruction of heat transfer boundary layer and gains strength of the turbulence and heat transfer efficiency. With the increase of the helical pitch of the HCTT heat exchanger, the turbulent intensity and the heat transfer efficiency are also increased. Moreover, the improvement of the flow state of the HCTT exchanger in a longer helical pitch also enhances the heat exchange efficiency.

Helically coiled tube-in-tube heat exchangers are widely applied in engineering fields such as refrigeration, air conditioning systems, chemical engineering, medical equipment and solar concentrators because of their compact structures and excellent heat transfer performances. Tube-in-tube heat exchangers with different structures, working fluids and boundary conditions have different heat exchange efficiencies. In recent years, the research on tube-in-tube heat exchangers has received continuous attention and achieved significant results [_{2}, R-134A, R-600a, etc. The thermal-hydraulic research of LNG as the working fluid in HCTT heat exchangers is rarely reported. In LNG vehicles, the HCTT heat exchangers are important components for LNG gasification and cold energy recovery. To study the thermal and hydrodynamic characteristics of LNG in helically coiled tube-in-tube heat exchangers has great significance.

In general, the tube-in-tube heat exchanger is designed as a spiral structure to generate centrifugal force through the curvature of a coiled tube and make secondary flow in the process of fluid movement under the guidance of centrifugal force so as to raise the heat transfer efficiency. Elattar et al. [

To improve the heat exchange efficiency, HCTT heat exchangers are usually added with spiral grooves or inner corrugated pipes. On the one hand, spiral grooves or inner corrugated pipes can achieve surface roughening of the internal thread of the pipe so that the heat transfer boundary layer is torn or even destroyed during the fluid flow process. On the other hand, fluid resistance near the spiral grooves causes separation vortexes in the heat transfer boundary layer, which strengthens the radial mixing of the fluid and decreases the thermal resistance of the boundary layer. Wang et al. [

Research on HCTT heat exchangers is mostly carried out by numerical simulations. Regarding the model of numerical calculation, Huang et al. [

Working fluids in HCTT heat exchangers are important factors affecting the heat transfer effect. Generally, the working fluids include air, water, R-134A, HFC134-A, R-600a, etc. Fsadni et al. [

Nowadays, HCTT heat exchanger research has gradually expanded to the engineering field. Zhou et al. [

In the presented work, LNG and ethylene glycol-water solution are used as the working fluid. By numerical calculations, the effects of different helical intermediate diameters and helical pitches on the flow and heat transfer characteristics of HCTT heat exchangers under different initial conditions so as to provide a theoretical basis for the optimization of the design of HCTT heat exchangers.

The geometric model of the HCTT heat exchanger is shown in _{t} and helical length of heat exchanger _{t} is:

where _{i} is the diameter of the inner tube, mm.

As shown in

The heat exchange process is carried out in the counter-current operation mode, LNG flows in the inner tube, and the glycol aqueous solution flows in the outer tube. In this study, an eight-turn coil tube (

The outer wall surface of the HCTT heat exchanger is usually assumed to be an adiabatic surface. The heat exchange between the refrigerant and the outer wall surface is ignored. The ethylene glycol-water solution is in a single state. In the calculation process, the following assumptions are made about the ethylene glycol-water solution:

The fluid is Newtonian, incompressible, isotropic and continuous;

The viscous dissipation is ignored;

Gravity is ignored;

No heat leakage around;

The heat transfer only mainly occurs in the tube, and the axial heat exchange inside the HCTT heat exchanger is ignored.

In the HCTT heat exchanger, heat conduction and forced convection begin to occur at the inlet of the tubes, so both the cold fluid and the hot fluid have a certain turbulent intensity, and the fluids flow and heat exchange rapidly develop downstream of the tubes. In fact, in the HCTT heat exchanger, secondary flow is generated by the flowing vortex due to the structure of the helical coil. The three-dimensional governing equations of the turbulent flow and heat transfer of the HCTT heat exchanger are described in the main Cartesian system in the form of tensor, as shown below:

Continuity equation:

Momentum equation:

Energy equation:

In ^{3}; _{p} is the constant pressure specific heat capacity, J (/kg·K);

The inlet and outlet pressure drop

where _{in}, _{out} are the pressure of the inlet and outlet, MPa.

The

where

where _{k} is 1.0, _{ε} is 1.3, _{ε1} is 1.44, _{ε2} is 1.93, _{ε3} is −1.0.

The numerical simulation process of the flow of two non-isothermal fluids is mainly achieved through the heat exchange between the walls of the inner tube, so the calculation settings require that the heat can flow out through the wall so that the calculation of convective heat transfer no longer needs to manually set convection heat transfer coefficient. The interior wall built in Fluent makes the interface of two types of fluids merge. It is believed that there is no thermal resistance between the two fluids because the wall thickness of the inner tube is only 1 mm, and the material is copper. The velocity condition is set to the flow condition of the inlet of the heat exchange tube. The flow condition of the outlet is set to the pressure outlet, and the reflow rate is 0. Ethylene glycol-water solution and LNG are considered incompressible fluids, and wall treatment is achieved through the two-fluid calculation model built into Fluent. The grid division for the HCTT heat exchanger can be seen in

The flow area is divided by the unstructured grids, the boundary layer grid is locally refined, and the low Reynolds number formula is used near the wall surface to completely decompose the velocity distribution into the wall. The boundary layer is set to 8 layers, which can be seen in

To ensure the accuracy of the calculation, the grid independence of the model is verified. The temperature of the cold and hot fluids in the inner and outer tubes is obtained by calculating four different numbers of grids. As shown in

Number of grids | LNG outlet temperature | Ethylene glycol-water solution outlet temperature |
---|---|---|

1979464 | 192.02 K | 281.45 K |

1110675 | 191.63 K | 281.05 K |

1354278 | 189.97 K | 280.74 K |

1586654 | 189.85 K | 280.63 K |

1748761 | 189.91 K | 280.69 K |

The second-order upwind style is adopted for the spatial dispersion to ensure the calculation accuracy, the iterative algorithm adopts the improved SIMPLEC algorithm, and the residual accuracy is controlled to 1e-5. The ethylene glycol-water solution flows in the outer tube of the HCTT heat exchanger, and the LNG flows in the inner tube. This study uses the Mixture mixed-phase model for the numerical calculation of multiphase flow. The mass transfer equation is as follows:

where

This model belongs to the Euler method, but the small slip of the interphase velocity is considered. The reaction between two phases in multiphase flow includes momentum exchange and chemical reaction. The inner tube of the HCTT heat exchanger is only involved in the phase change reaction of LNG. There is no chemical reaction between gaseous and liquid LNG. Therefore, the momentum exchange between the two phases should be mainly considered. The evaporation-condensation model is used to calculate the momentum exchange between the two phases.

The software FLUENT is used for numerical simulation in this paper. The fluid inside the heat exchanger tube is low-temperature LNG, the inlet boundary condition is the velocity inlet, the normal velocity is 1 m/s, and the inlet fluid temperature is 92 K; The outlet is a natural outflow, with a pressure of 0 and a temperature outlet as outflow; The wall of the heat exchanger is made of structural steel with a wall thickness of 1 mm. To calculate the forced convection heat transfer effect between the inner and outer walls of the heat exchanger, it is necessary to consider that it is a heat flow wall.

The main component of LNG is methane, and its physical properties are the parameters of methane during calculation. The physical parameters of methane are:

In order to verify the accuracy of the numerical calculation method, numerical simulation is carried out according to the experimental conditions of the literature [^{2}. The horizontal axis represents the local heat transfer coefficient measured in the experiment, the vertical axis represents the number of experiments, and the four colors represent the measurements made under four sets of mass flow rates. In order to avoid sampling errors, the existing 10 experiments have measured the heat transfer coefficient under four sets of mass flow rates (measured values: 51.6, 104.86, 154.84 and 199.23 kg/(m^{2}

^{2}^{2}^{2}^{2}

Through comparative analysis, it is found that the numerical calculation results of this calculation model are basically in line with the trend of changes in the experimental research mentioned above. Therefore, the subsequent numerical calculations will use the above research methods and models.

The basic conditions of the numerical computation for the flow and heat exchange characteristics of the HCTT heat exchanger have been set. The structural parameters of the flow and heat transfer characteristics can be found by modifying the change of the cavity shape. The results of the study and the discussion will be introduced in the following part.

As shown in

The fluid pressure distribution inside the HCTT heat exchanger can be seen in

As the most important geometric parameter controlling the radial direction of the helical tube, the influence of the pitch diameter

Theoretically, to increase the length of the heat transfer channel will increase the heat exchange area, which will increase the amount of heat transfer between LNG and the ethylene glycol-water solution. The analytical results describing the dynamic characteristics of the flow field must be combined with the pressure loss distribution in the helical flow channel and the flow state. The internal pressure change curve of the helical tube under the two middle diameter sizes is shown in

As shown in

As shown in

The main reason is that the increase in flow process reduces the average velocity of the fluid flow without increasing the inlet flow rate and pressure, and the heat transfer boundary layer near the tube wall is difficult to damage. As a result, the turbulent state is weakened, which reduces the heat transfer effect and slows the temperature change rate. It can be seen from the above that for the HCTT heat exchanger, the effect of increasing the surface heat transfer coefficient caused by changing the middle diameter cannot compensate for the loss of the heat exchange effect caused by the increased power consumption of fluid pumping.

The growth of the heat exchange stroke reduces the average velocity during the fluid flow. The heat transfer boundary layer near the tube wall is difficult to damage, which weakens the turbulent state, reduces the heat exchange efficiency and slows the temperature change rate. The main reason for this phenomenon is that the increase in flow process reduces the average velocity of the fluid flow without increasing the inlet flow rate and pressure, and the heat transfer boundary layer near the tube wall is difficult to damage. As a result, the turbulent state is weakened, which reduces the heat transfer effect and slows the temperature change rate. It can be seen from the above that for the HCTT heat exchanger, the effect of increasing the surface heat transfer coefficient caused by changing the middle diameter cannot compensate for the loss of heat transfer effect caused by the increased power consumption of fluid pumping.

The middle diameter variation is to generate a helical line with a linear change in diameter. The characteristic of this form of helical tube is that the pitch of the helical flow channel changes in the axial direction, which in turn changes the initial state of the flow. The radial dimension gradually increases with increasing axial length. Compared with the HCTT heat exchanger of the same diameter, the flow rate should be the average value of the helical flow channels at both ends. The variable middle diameter of the HCTT heat exchanger is suitable for places where the installation position is limited to maximize the heat exchange capacity of the heat exchanger. The schematic diagram can be seen in

The structure of variable middle diameter is a helical tubes generated by linearly changing the diameter of the first and last ends. This structure has certain advantages in terms of installation requirements and compact structure. Therefore, in the following calculations, numerical simulation calculations will be carried out for this structure.

As shown in

The main flow characteristics of helical tubes with variable diameters are not significantly different from helical tubes of the same diameter. In the area where the helical diameter changes, the flow area of the radial end of the flow gradually increases.

As shown in

From

As shown in

The CFD simulations of the HCTT heat exchanger are carried out by changing the helical diameters and helical pitch parameters under different initial conditions. The main conclusions are summarized as follows:

When the initial velocity of the outer tube fluid increases, the velocity of the inner tube fluid also increases, and the velocity gradient between the two gradually increases. The resistance loss of the helical tube to the fluid is evenly distributed during the flow of fluids with different initial velocities. The distribution of the pressure field inside the helical tube is approximately linearly along the winding direction of the helix.

When the middle diameter of the helical tube becomes larger, the pressure loss along the helix gradually increases, and the trend of pressure change is also more stable. For the helix tube, the change of the middle diameter mainly affects the change of the heat exchange stroke and has an influence on the heat exchange area.

For the HCTT heat exchanger, the effect of increasing the surface heat transfer coefficient caused by changing the middle diameter cannot compensate for the loss of heat exchange efficiency caused by the increased power consumption of the fluid pumping power. The change of the middle diameter causes the overall process to become shorter, the pressure loss along the flow decreases, and the initial pressure rises under the condition of constant inlet flow rate, which is generally beneficial to the flow.

The change in the middle diameter reduces the curvature of the helical tube, which promotes the occurrence of secondary flow. The fluid flow in the axial direction promotes the destruction of the heat transfer boundary layer, to a certain extent, increases the intensity of the turbulent flow to make the fluid velocity distribution and temperature distribution uniform.

The increased pitch reduces the fluid contact area between the inner and outer tubes. However, the increase of the helical pitch reduces the excessive length of each turn of the helical tube, and the curvature of the excessive part increases. The effect of turbulence caused by the increased curvature is enhanced, and the heat transfer effect is improved. The appropriate increase in the pitch improves the heat transfer performance of the helical flow channel.

Area, mm^{2}

_{p}

Constant pressure specific heat capacity, J (/kg·K)

Middle diameter, mm

_{i}

Inner tube diameter, mm

Energy, J

Friction coefficient, N/m^{2}

_{h}

Helix length, mm

Coil pitch, mm

Nusselt number

Pressure, MPa

Prandtl number

Reynolds number

Temperature, K

Velocity, m/s

Vapor volume fraction

Density, kg/m^{3}

Dynamic viscosity, Pa·s

Kinematic viscosity, m/s^{2}

Helically coiled tube-in-tube heat exchanger

We would like to express our heartfelt gratitude to Professor Xu Boyan who point out the research direction of this study.

This work was supported by Innovative Team Introduction Projects for New Universities in Jinan City (No. 2021GXRC075).

Fayi Yan conducted theoretical derivation, numerical simulation and result analysis; Xuejian Pei established the numerical calculation model; He Lu carried out a part of numerical simulation; Shuzhen Zong compiled the calculation results.

Most of the data generated or analysed during this study are included in this published article. Other data is available from corresponding author, please contact

The authors declare that they have no conflicts of interest to report regarding the present study.

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