# Numerical Investigation on the Flow and Heat Transfer Characteristics of Supercritical Liquefied Natural Gas in an Airfoil Fin Printed Circuit Heat Exchanger

^{*}

## Abstract

**:**

_{v}= 1.67 mm and the staggered pitch L

_{s}= 0 mm, with the Reynolds number of about 3750. The SST k-ω model was selected and verified by comparing with the experimental data using supercritical liquid nitrogen as cold fluid. The airfoil fin PCHE had better thermal-hydraulic performance than that of the straight channel PCHE. Moreover, the airfoil fins with staggered arrangement displayed better thermal performance than that of the fins with parallel arrangement. The thermal-hydraulic performance of airfoil fin PCHE was improved with increasing L

_{s}and L

_{v}. Moreover, L

_{v}affected the Nusselt number and pressure drop of airfoil fin PCHE more obviously. In conclusion, a sparser staggered arrangement of fins showed a better thermal-hydraulic performance in airfoil fin PCHE.

## 1. Introduction

_{2}as heat source. The new PCHE had about 3.3 times less volume, but it displayed a 37% lower pressure drop on the CO

_{2}side and by ten times on the H

_{2}O side than an existing 1.5 MW/m

^{3}hot water supplier.

_{2}was selected as the working fluid. The heat transfer significantly increased when the pseudocritical temperature and critical pressure were approached.

## 2. Computational Fluid Dynamic Analysis for Thermal-Hydraulic Performance

#### 2.1. Thermal–Physical Properties of Supercritical LNG

#### 2.2. Physical Models and Definition of Airfoil Fin Arrangement Parameters

_{v}and staggered pitch L

_{s}of airfoil fins were 1.67 mm and 0 mm respectively, aiming to compare the heat transfer and flow characteristics of supercritical LNG between airfoil fin and straight channel with the same channel length and hydraulic diameter. The numerical models of straight channel and airfoil fin are shown in Figure 4 and Figure 5, respectively.

_{s}. There is a periodicity between an un-staggered arrangement and a fully staggered arrangement. L

_{h}indicates the separation distance between one airfoil head and adjacent airfoil head in a row. The separation distance between one row and adjacent row in the vertical direction is indicated by L

_{v}. Herein, L

_{h}was 6 mm, L

_{s}varied from 0 to 4 mm and L

_{v}changed from 1.3 mm to 3 mm. According to the configuration, the width (W) of the heat transfer region of the entire domain varied from 3.9 mm to 9 mm. The vertical pitch L

_{v}= 1.67 mm and staggered pitch L

_{s}= 0 mm were selected as the baseline model.

_{v}= 1.67 mm and L

_{s}= 0 mm. The working fluid was supercritical LNG, and the material of substrate plates and fins was steel. The mass flux inlet was applied for the inlet boundary condition of the simulation domain, and the inlet temperature and reference mass flux were set at 121 K and 325 kg/m

^{2}∙s, respectively. The outlet boundary condition was set as pressure outlet. As shown in Figure 7, a periodic boundary condition in the left/right positions, as well as a constant heat flux applied to the top and bottom positions is 58,713.75 W/m

^{2}.

#### 2.3. Numerical Method and Grid Independence

^{−6}. Meanwhile, the second order upwind, which has a smaller truncation error than that of the first order upwind, was used in the momentum equation and energy equation to ensure the accuracy of simulation.

_{s}= 0 mm and vertical number L

_{v}= 1.67 mm was selected as the baseline model. The mesh dependence test dominated the density of meshes (Figure 8). The influence of grid density on the accuracy of calculated results was studied by comparing six sets of grid numbers: 1302567, 1762753, 2415689, 3269854, 3594425 and 4196856 cells. By comparing the outlet temperature and Nusselt number, the optimal grid of 3594422 was selected considering the accuracy and computational efficiency. As shown in Figure 9, the grids are encrypted near the wall surfaces of fins and substrate plates to ensure that y

^{+}is lower than 1. Six boundary layers were established near the top and bottom walls and fin surfaces because of the strict requirements for boundary grid in the supercritical flow and heat transfer, and the thickness of the first boundary layer was 0.01 mm.

#### 2.4. Model Validation

^{2}·s, corresponding to turbulent flow regimes on the cold side of airfoil fin PCHE. In short, this PCHE had a good heat transfer ability at high pressure and low temperature. The overall heat transfer coefficient of this PCHE ranged from 850 to 2600 W/m

^{2}K, and the heat transfer efficiency was up to approximately 98%.

^{2}·s, corresponding to turbulent flow regimes on the cold side of airfoil fin PCHE. The differences in the pressure drop and outlet temperature of the cold side between the numerical solutions and the experimental data were compared using Equation (1):

^{2}·s (Table 2). The numerical results differed from the experimental data by 6.9% on average and by 11.62% at maximum. The deviation may be attributed to the inlet and outlet header pressure drop, as well as the uncertainty of pressure transmitters. Besides, the difference between numerical and experimental outlet temperatures on the cold side had an average error of 0.735% and the maximum difference of 1.127%. Therefore, the numerical data were in fairly good agreement with the experimental data, and the numerical model and method used herein were reliable.

## 3. Objective Function Parameters

_{h}is an important value in dimensionless analysis. It is defined as four times the cross-sectional area over a perimeter in the straight channel. Owing to the continual changes of cross-sectional area and perimeter, the hydraulic diameter cannot be the same as that of straight channel, as shown in Figure 12. Nevertheless, the airfoil fin placement in Figure 3 is periodic. Therefore, the hydraulic diameter can be defined by the equations below [37].

_{a}is the top area of airfoil fin, and P

_{a}is the perimeter of airfoil fin. V and S indicate the volume and side surface area of flow channel, respectively.

_{wall}is the area-average wall temperature, and T

_{in}, T

_{out}and T

_{b}are the inlet, outlet and bulk temperatures of LNG obtained from the Fluent data respectively.

_{h}is the channel hydraulic diameter, and $\lambda $ is the thermal conductivity of LNG.

_{h}is the channel hydraulic diameter, $\rho $ is the density of LNG and $\mu $ is the dynamic viscosity of LNG.

## 4. Results and Discussion

#### 4.1. Comparison of Straight Channel PCHE and Airfoil Fin PCHE

_{h}= 0.917 mm) were numerically investigated. Figure 13 shows the velocity contours of supercritical LNG in airfoil fin and straight channel PCHEs when the mass flux is 325 kg/m

^{2}·s. When supercritical LNG was gradually heated, the bulk velocity significantly increased because of reduced density. However, the velocity increased rapidly in airfoil fin channel owing to continuous expansion and contraction in the sectional area of flow channel. The maximum velocity in the narrowest flow channel was nearly 3 times that in the inlet. Therefore, airfoil fins evidently disturbed supercritical LNG, which increased heat transfer and flow resistance simultaneously.

^{2}∙s and G = 725 kg/m

^{2}∙s, Nu values of airfoil fin PCHE were 1.48 and 1.36 times those of the straight channel PCHE, respectively.

^{2}∙s, the Euler number of the airfoil fin PCHE was 89.7% of that of the straight channel PCHE. Generally, pressure drop increases with rising mass flux. However, Figure 16 shows that the Euler number calculated by Equation (12) decreases as the mass flux increases. According to this equation, the Euler number is proportional to pressure drop $\mathsf{\Delta}P$ but inversely proportional to v

^{2}. Obviously, the velocity of supercritical LNG rose with increasing mass flux, although it also raised the pressure drop. Nevertheless, v

^{2}exerted a stronger effect on Eu than on pressure drop, so the increase of mass flux led to decrease of the Euler number.

#### 4.2. Effect of Fin Arrangement: Staggered Pitch (L_{s})

_{s}= 0 mm) and staggered (L

_{s}= 1~4 mm) in the transverse direction of the PCHE.

_{v}= 1.67 mm. In the start of heating, the velocities of fluid were quite uniform and small in both staggered and parallel arrangements. However, owing to continuous expansion and contraction in the sectional area of flow channel, the non-uniformity of velocity became obvious in parallel arrangement as the velocity increased in the flow direction. Therefore, a staggered arrangement of airfoil fins benefited the formation of smooth flow channel and the improvement of flow field uniformity.

_{v}, the Nusselt numbers of parallel and staggered arrangements were similar. The Nusselt number at L

_{s}= 0 mm differed from that at L

_{s}= 4 mm by 6.9% when the vertical number L

_{v}= 3 mm.

_{s}decreased. Figure 18b,c present the pressure drop and Euler number with the staggered pitch (L

_{s}) at different L

_{v}in an airfoil fin PCHE. In Figure 18c, the Euler number in staggered arrangement (L

_{s}= 1 mm) is smaller (a maximum decrease of 9.86%) than that in parallel arrangement (L

_{s}= 0 mm), with the difference enlarging as the staggered pitch (L

_{s}) increases at the same vertical pitch L

_{v}.

_{s}. Nu/Eu increased with rising staggered number L

_{s}. L

_{s}= 0 mm had a lower Nu/Eu (about 27%) than that at L

_{s}= 4 mm, suggesting that L

_{s}= 4 mm had better heat transfer and pressure drop. Probably, pressure drop was more susceptible to L

_{s}than heat transfer. Collectively, staggered arrangement was superior to parallel arrangement in airfoil fin PCHE, manifested as reduced flow resistance and improved total thermal-hydraulic performance.

#### 4.3. Effect of Fin Arrangement: Vertical Pitch (L_{v})

_{h}(6 mm) is kept constant, L

_{v}directly determines the density of fins and the width of flow channel. Therefore, the effect of vertical separation distance (L

_{v}) on the thermal-hydraulic performance of an airfoil fin PCHE was assessed.

_{v}when the staggered pitch L

_{s}= 1.67 mm are presented in Figure 19. A smaller vertical pitch L

_{v}resulted in a higher velocity, thereby augmenting the flow resistance. In fact, a smaller L

_{v}led to a narrower sectional area of flow channel, so that the flow velocity increased with decreasing L

_{v}at the same mass flux. The maximum velocities of LNG in the narrowest sectional of flow channel were 1.35 m/s and 1.79 m/s in the airfoil fins with L

_{s}= 3 mm and L

_{s}= 1.3 mm, respectively. Therefore, the turbulence intensity of fluid and the flow resistance were both enhanced locally.

_{v}) at different L

_{s}in an airfoil fin PCHE. The convective heat transfer coefficient h decreased with rising L

_{v}at the same L

_{s}, which may attributed to the decreased flow velocity. However, h and Nu changed oppositely with increasing L

_{v}, mainly because the hydraulic diameter increased significantly faster than h decreased with rising L

_{v}. For example, the hydraulic diameter at L

_{v}= 3 mm was nearly 2.7 times that at L

_{v}= 1.3 mm, and h at L

_{v}= 1.3 mm was 1.2 times that at L

_{v}= 1.3 mm when L

_{s}= 4 mm. Thus, the Nusselt number increased with rising L

_{v}of airfoil fins.

_{v}. The total pressure drop decreased as L

_{v}increased, so the Euler number dropped more apparently with increasing L

_{v}at the same L

_{s}. The Euler number at L

_{v}= 3 mm was only 56% of that at L

_{v}= 1.3 mm. Obviously, at the same L

_{s}, reducing L

_{v}slightly facilitated heat transfer, though it also considerably elevated pressure drop.

_{v}increases. Nu/Eu at L

_{v}= 3 mm is nearly 3 times and 1.7 times those at L

_{v}= 1.3 mm and L

_{v}= 2 mm respectively, indicating that a dense fin arrangement was conducive to increasing the heat transfer rate. Meanwhile, it was inevitably more difficult to overcome flow resistance. Accordingly, fins should be sparsely arranged in an airfoil fin PCHE.

## 5. Conclusions

- (1)
- The numerical model and methods were validated with experimental data. Supercritical liquid nitrogen was used as a cold fluid for simulation and experiment. The SST model followed by the enhanced wall treatment method well predicted the outlet temperature and pressure drop of a single airfoil fin in the PCHE. The error between the numerical and experimental data was within 14%, indicating the heat transfer and flow characteristics of supercritical LNG in airfoil fin PCHE could be reliably simulated by the model and method.
- (2)
- As a new type of discontinuous fins, airfoil fins can boost the thermal-hydraulic performance compared with that of a straight channel PCHE using supercritical LNG as the working fluid. The minimum and maximum differences of Nu/Eu between straight channel and airfoil fin PCHEs were 46.2% and 51.07%, respectively. The convective heat transfer coefficient and pressure drop increased in both PCHEs with rising mass flux.
- (3)
- A staggered fin arrangement was more beneficial to the thermal-hydraulic performance of the airfoil fin PCHE than a parallel fin arrangement using supercritical LNG as the working fluid. At the same L
_{v}and L_{h}, airfoil fins arranged at L_{s}= 4 mm displayed better thermal-hydraulic performance than those of the fins at other L_{s}. - (4)
- The velocity of supercritical LNG in the airfoil fin channels increased along the channel length and then plummeted with increasing L
_{v}. The effect of vertical number L_{v}on the thermal-hydraulic performance of airfoil fin PCHE was more evident than that of staggered pitch L_{s}. Based on a comprehensive analysis of heat transfer coefficient and pressure drop, a sparser staggered arrangement of fins can enhance the thermal-hydraulic performance of an airfoil fin PCHE.

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Nomenclature

f | Fanning factor |

v | Velocity (m/s) |

Re | Reynolds number |

h | Convective heat transfer coefficient (W/m^{2}∙K) |

Nu | Nusselt number |

C_{p} | Specific heat (kJ/kg∙K) |

D_{h} | Hydraulic diameter (mm) |

${q}_{m}$ | Mass flow rate (kg/s) |

u | Velocity (m/s) |

q’’ | Heat flux (W/m^{2}) |

G | Mass flux (kg/m^{2}∙s) |

L_{v} | The pitch between one airfoil head and adjacent row in the vertical direction (mm) |

L_{s} | The pitch of the staggered arrangement (mm) |

L_{h} | The pitch between one airfoil head and adjacent airfoil head in a row (mm) |

$\mathsf{\Delta}P$ | Pressure drop (Pa) |

$\mathsf{\Delta}{p}_{fric}$ | Pressure drop due to friction (Pa) |

$\mathsf{\Delta}{p}_{acc}$ | Pressure drop due to acceleration (Pa) |

${\rho}_{in}$ | Density at the inlet of the channel (kg/m^{3}) |

${\rho}_{out}$ | Density at the outlet of the channel (kg/m^{3}) |

${\tau}_{w}$ | Shear stress at the wall (Pa) |

Greek symbols | |

$\mu $ | Viscosity [Pa·s] |

$\rho $ | Density [kg/m^{3}] |

$\lambda $ | Thermal conductivity [W/m^{2}∙K] |

Subscript | |

w | Wall |

b | Bulk mean |

acc | Acceleration |

fric | Friction |

v | Vertical |

s | Staggered |

h | Horizontal |

in | Inlet |

out | Outlet |

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**Figure 3.**Schematic diagram of internal core structure of airfoil fin printed circuit heat exchanger (PCHE).

**Figure 4.**Schematic diagram of (

**a**) Straight channel geometric model and (

**b**) cross-section of straight channel.

**Figure 5.**Schematic diagram of (

**a**) the airfoil fin channel geometric model and (

**b**) cross-section of airfoil fin channel.

**Figure 11.**Experimental system with airfoil fin PCHE of (

**a**) Schematic diagram of experimental set-up and (

**b**) Photo of experimental system.

**Figure 13.**(

**a**) Plots of velocity contours in airfoil fin channel and (

**b**) straight channel when mass flux is 325 kg/m

^{2}·s.

**Figure 18.**Effect of L

_{v}on (

**a**) Nusselt number, (

**b**) pressure drop, (

**c**) Euler number and (

**d**) Nu/Eu.

(1) 121–227 K |

ρ = 8256.5933 − 285.3922 T + 4.3559 T^{2} − 0.035267 T^{3} + 1.5894 × 10^{−4} T^{4} − 3.7784 × 10^{−7} T^{5} + 3.6917 × 10^{−1} T^{6} |

C_{p} = −1.0199 × 10^{6} + 3.8183 × 10^{4} T − 589.1061 T^{2} + 4.8079 T^{3} − 0.02189 T^{4} + 5.28734 × 10^{−5} T^{5} − 5.23296 × 10^{−8} T^{6} |

λ = 1.6663 − 0.051726 T + 7.9379 × 10^{−4} T^{2} − 6.6085 × 10^{−6} T^{3} + 3.0653 × 10^{−8} T^{4} − 7.4993 $\times $ 10^{−11} T^{5} + 7.5617 × 10^{−14} T^{6} |

μ = 4.0977 × 10^{−3} − 1.2117 × 10^{−4} T + 1.5988 × 10^{−6} T^{2} − 1.1623 × 10^{−8} T^{3} + 4.8332 × 10^{−11} T^{4} − 1.0811 × 10^{−13} T^{5} + 1.01103 × 10^{−16} T^{6} |

(2) 227–315 K |

ρ = −3.89476 + 7.7791 × 10^{3} T − 63.6984 T^{2} + 0.273703 T^{3} − 6.4991 × 10^{−4} T^{4} + 8.06233 × 10^{−7} T^{5} − 4.06261 × 10^{−10} T^{6} |

C_{p} = −4.48732 × 10^{7} + 9.7441 × 10^{5} T − 8.78917 × 10^{3} T^{2} + 42.17166 T^{3} − 0.011355 T^{4} + 1.62727 × 10^{−4} T^{5} − 9.6971 × 10^{−8} T^{6} |

λ = −99.92683 + 2.24495 T − 0.0208241 T^{2} + 1.02288 × 10^{−4} T^{3} − 2.8093 × 10^{−7} T^{4} + 4.09353 × 10^{− 10} T^{5} − 2.47389 × 10^{−13} T^{6} |

μ = 1.58763 × 10^{−2} + 3.9445 × 10^{−4} T − 3.96736 × 10^{−6} T^{2} + 2.08564 × 10^{−8} T^{3} − 6.07355 × 10^{−11} T^{4} + 9.3195 × 10^{−14} T^{5} − 5.8999 × 10^{−17} T^{6} |

(3) 315–385 K |

ρ = 9403.1676 − 140.8996 T + 0.90485 T^{2} − 3.14226 × 10^{−3} T^{3} + 6.19397 × 10^{−6} T^{4} − 6.55485 × 10^{−9} T^{5} + 2.905 × 10^{−12} T^{6} |

C_{p} = −4.28439 × 10^{5} − 6.56712 × 10^{3} T + 42.6554 T^{2} − 0.14901 T^{3} + 2.94672 × 10^{−4} T^{4} − 3.12279 × 10^{−7} T^{5} + 1.383995 × 10^{−10} T^{6} |

λ = 2.2909 − 0.03353 T + 2.35313 × 10^{−4} T^{2} − 8.3695 × 10^{−7} T^{3} + 1.68679 × 10^{−9} T^{4} − 1.8217 × 10^{−12} T^{5} + 8.22556 × 10^{−16} T^{6} |

μ = 4.92979 × 10^{−3} − 8.37086 × 10^{−5} T + 5.94466 × 10^{−7} T^{2} − 2.25336 × 10^{−9} T^{3} + 4.8073 × 10^{−12} T^{4} − 5.47099 × 10^{−15} T^{5} + 2.5942 × 10^{−18} T^{6} |

Pressure (MPa) | Experiment Results of ∆P/L (Pa/m) | Simulation Results of ∆P/L (Pa/m) | Error (%) | Experiment Results of T_{out} (K) | Simulation Results of T_{out} (K) | Error (%) |
---|---|---|---|---|---|---|

5.5 | 37,090.61172 | 35,226.12 | 5.03% | 279.45 | 278.13 | 0.472% |

6 | 33,988.7737 | 32,023.7 | 5.78% | 281.15 | 281.96 | 0.288% |

6.5 | 25,650.67624 | 27,635.15 | 7.74% | 282.55 | 283.67 | 1.12% |

7 | 24,175.74669 | 26,985.37 | 11.62% | 284.35 | 285.96 | 0.669% |

7.5 | 23,834.30936 | 24,865.35 | 4.33% | 285.65 | 288.87 | 1.127% |

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## Share and Cite

**MDPI and ACS Style**

Zhao, Z.; Zhao, K.; Jia, D.; Jiang, P.; Shen, R.
Numerical Investigation on the Flow and Heat Transfer Characteristics of Supercritical Liquefied Natural Gas in an Airfoil Fin Printed Circuit Heat Exchanger. *Energies* **2017**, *10*, 1828.
https://doi.org/10.3390/en10111828

**AMA Style**

Zhao Z, Zhao K, Jia D, Jiang P, Shen R.
Numerical Investigation on the Flow and Heat Transfer Characteristics of Supercritical Liquefied Natural Gas in an Airfoil Fin Printed Circuit Heat Exchanger. *Energies*. 2017; 10(11):1828.
https://doi.org/10.3390/en10111828

**Chicago/Turabian Style**

Zhao, Zhongchao, Kai Zhao, Dandan Jia, Pengpeng Jiang, and Rendong Shen.
2017. "Numerical Investigation on the Flow and Heat Transfer Characteristics of Supercritical Liquefied Natural Gas in an Airfoil Fin Printed Circuit Heat Exchanger" *Energies* 10, no. 11: 1828.
https://doi.org/10.3390/en10111828