2.1. Physical Model and Boundary Conditions
In this study, the thermal hydraulic performance of supercritical LNG in zigzag PCHEs is investigated. The cross flow PCHE core model with a full length of 400 mm using supercritical LNG in the cold side and R22 in the hot side is shown in
Figure 1a. The supercritical LNG and R22 flow in the semicircular channel with a diameter of 1.5 mm, the solid is composed of steel with thermal conductive coefficient of 16.27 W/(m·K). In this paper, we only study the performance of supercritical LNG in the cold channel. Considering that the cold side of the PCHE contains hundreds of channels, it is unrealistic to consider all the channels, and it is therefore necessary to simplify the cold channels’ model. Supercritical LNG flows in parallel in each cold channel, so some assumptions on its flow in the cold side are made. The mass flux is the same in every channel, and there is no temperature difference and heat loss between neighboring channels. The flow of supercritical LNG is steady and uniformly distributed. Based on these assumptions, the cold channel can be simplified to a single model with a geometry of 2 mm × 1.75 mm. The cross-section of the fluid channel is semicircular with a diameter of 1.5 mm (
Figure 1b). The bend angles α vary from 0° (which is a straight channel) to 45° (
Figure 1c).
The adjacent cold channels do not exhibit temperature difference and heat transfer loss; only the supercritical LNG in cold channels absorb heat from top and bottom hot channels. Three types of boundary conditions were applied in the model: fluid inlet, fluid outlet, and wall. The mass flow rate boundary condition was set at the inlet of the supercritical LNG channel whereas at the outlet the pressure-outlet boundary condition was applied (
Figure 1b). The left and right walls of the single model are set to adiabatic boundary conditions, and the constant heat flux condition was used at top and bottom walls. The details of the boundary conditions are presented in
Table 1.
2.2. Thermo-Physical Properties of Supercritical LNG
In this paper, the operating pressure of LNG considered varies from 6.5 MPa to 10 MPa, which is supercritical pressure. Supercritical LNG has gas-like properties, such as low viscosity, and liquid-like characteristics, like high density and high thermal conductivity. The thermo-physical properties of supercritical LNG, i.e., density, specific heat, thermal conductivity and viscosity, are affected by temperature and pressure. The properties’ values were obtained from the NIST Standard Reference Database (REFPROP) [
26]. For the numerical simulations, the temperature was changed from 121 K to 385 K. At such a large temperature difference, the properties of supercritical LNG change dramatically, using the average values will cause the inaccurate calculation results in ANSYS Fluent. Therefore, as shown in
Figure 2, the thermal properties of supercritical LNG were approximated as piecewise-polynomial functions of temperature. The piecewise-polynomial functions of temperature at 10 MPa is shown in
Table 2. The error percentages of various properties using the proposed approximation are shown in
Figure 3. The errors were within ±2.5%, which indicates the fitted piecewise-polynomial function approximations are suitable.
2.3. Numerical Method and Grid Independence
The commercial software FLUENT was used to solve the 3D numerical model. Considering the inlet parameters, the flow corresponded to turbulent flow regimes. Some turbulence models have been studied and used in the literature; these include the
κ-
ε standard model, the RNG
κ-
ε model, the shear-stress transport (SST)
κ-
ω model and the low Reynolds number turbulence model [
27,
28]. In this study, the SST
κ-
ω model was used because of its more accurate results on heat transfer of supercritical fluids [
29,
30,
31,
32].
The governing equations for heat transfer were the continuity, momentum, and energy equations, respectively:
Continuity equation:
where
ρ is the density, and
is the velocity vector.
Momentum equation:
where
p is the pressure,
and
are the molecular and turbulent viscosities, respectively.
Energy equation:
where
keff is effective conductivity,
, and
is the turbulent thermal conductivity.
The transport equations are expressed as follows:
where
is the turbulent kinetic energy dissipation rate,
is vorticity, and
is the distance from the wall. The constants and damping functions of the SST
κ-
ω model are shown in
Table 3.
The local convective heat transfer coefficient was calculated using Equation (10):
where
q is the constant heat flux from the top and bottom walls,
Tw is the wall temperature and
Tb is average temperature of the inlet and the outlet.
Nu was defined as:
where
is the hydraulic diameter and
λ is the local thermal conductivity of LNG,
A is the cross-sectional area of the semicircular fluid channel and
is the circumference of the semicircular fluid channel section.
The local Fanning friction coefficient (
) was defined in terms of the pressure drop and is expressed by Equation (12):
where Δ
P is the total pressure and was obtained from Fluent directly, Δ
Pf and Δ
Pa are the frictional and accelerated pressure drops, respectively, L is the channel length,
ρb and
are the bulk density and velocity of LNG, respectively.
The Reynolds number (Re) is given by Equation (14):
The Euler number (Eu) is defined as Equation (15):
For the solution methods, the SIMPLE algorithm was applied to establish the coupling of velocity and pressure. The momentum, turbulent kinetic energy, turbulent dissipation rate and energy were discretized using the second order upwind scheme. The calculation was considered to converge when the residuals were less than 10−6.
The mesh on the computational domain was generated using GAMBIT. The grid independence was verified to confirm numerical result accuracy. The mesh size of solid, fluid and boundary layer’s scale in fluid affect the grid numbers. The influence of the grid numbers on the convective heat transfer coefficient is shown in
Table 4. Case 4 has a larger relative error compared to the other cases. The heat transfer coefficient in Cases 1, 2, and 3 is nearly the same. The relative error of the heat transfer coefficient between Cases 1 and 7 is only 0.08%. Therefore, considering the calculation accuracy and time, the 2,988,329 grid nodes (Case 1), showing in
Figure 4, was selected in the present work.
2.4. Model Validation
To validate the accuracy and reliability of the model, the simulation results of temperature difference and pressure drop were compared to previous experimental results [
30]. The experimental setup is shown in
Figure 5. Since LNG is flammable and explosive, the straight-channel cross flow PCHE used supercritical nitrogen as the cold side fluid and R22 as the hot side fluid. The length of the PCHE cold channel was 520 mm, the inlet temperature was 102 K, and the operating pressure varied from 6.5 MPa to 10 MPa. In the simulation, a straight channel model with a length of 520 mm was selected, which was the same as the experimental case. The boundary conditions are shown in
Figure 1b. Supercritical nitrogen was used as the working fluid to confirm the correctness the experiment. The inlet pressure changed from 6.5 MPa to 10 MPa and the inlet temperature was 102 K. The comparison of temperature difference and pressure drop between simulation and experimental results is listed in
Table 5. The maximum errors of temperature difference and pressure drop are 2.1% and 10.25%, respectively. The simulation pressure drop was less than the experimental, which may be attributed to the following factors: (1) the channel was assumed to be smooth in the numerical study while the PCHE channel of the experiment was rough, (2) the header pressure drop of inlet and the outlet were neglected in the numerical study, but may have been large in the experiment, and (3) the deviation of temperature and pressure transmissions. The simulation results are in accordance with the experiment, illustrating that the simulation model and method were credible.