Investigation on Thermal-Hydraulic Performance in a Printed Circuit Heat Exchanger with Airfoil and Vortex Generator Fins for Supercritical Liquefied Natural Gas

Figures & data

Table 1. List of references about different PCHE channels.

References	Channels	Working fluid	Working conditions	Main conclusions
Mylavarapu et al. [9]	straight	helium	cold side: 358–663 K and 1–2.7 MPa; hot side: 481–1063 K and 1–2.7 MPa; mass flow rate: 15–49 kg/h	The critical Reynolds number from the laminar to transition flow regime was about 1700, and the experimental correlations were given.
Chu et al. [10]	straight	supercritical CO2, water	hot supercritical CO2: 310–375 K, 8–11 MPa, and 150–650 kg/h	PCHE had better comprehensive performance at higher pressure, and the comprehensive performance was significantly reduced nearly 17.6% at the transcritical state.
Khan et al. [11]	wavy	helium	cold side: 813 K and 3 MPa; hot side: 1173 K and 3 MPa; Re: 350–2100	The wavy channel could provide better thermal-hydraulic performance compared with the straight channel.
Aneesh et al. [12]	wavy	helium	cold side: 813 K, 3 MPa, and Re: 451–2256; hot side: 1173 K, 3 MPa, and Re:348–1741	The highest values of thermal advantages of trapezoidal, sinusoidal and triangular wavy channel, compared with the straight channel, were 41, 33, and 28%, respectively.
Lee and Kim [13]	zigzag	supercritical CO2	cold side: 396 K, 8.3 MPa, and Re: 67000–280000; hot side: 411.2 K, 2.5 MPa, and Re: 71500	The effectiveness of the heat exchanger was maximized when the cold channel angle was similar to the hot channel angle.
Ma et al. [14]	zigzag	helium	cold side: 813 K, 3 MPa; hot side: 1173 K, 3 MPa; mass flow rate: 0.072–0.324 kg/h	With the increase of inclination angle, the heat transfer and pressure drop both increased.
Pan et al. [15]	zigzag	supercritical LNG, propane	cold side: 128.9 K, 7.3 MPa, and 0.0002995 kg/s; hot side: 293.15 K, 0.64 MPa, and 0.00045 kg/s	The larger the bending angle was, the better the heat transfer performance was accompanying larger pressure drop. The channel bending angle 15° offered the best comprehensive performance.
Ngo et al. [16]	S-shape	CO2 , water	water: 280 K, 0.25 MPa, and 48 kg/h; CO2: 391 K, 11.5 MPa, and 57.8 kg/h	The S-shaped PCHE provided about 3.3 times less volume, and lower pressure drop by 37% in the CO2 side and by 10 times in the H2O side, compared with the existing supplier.
Tsuzuki et al. [17]	S-shape, zigzag	supercritical CO2	cold side: 363–381 K and 6.5–10 MPa; hot side: 553–573 K and 2.2–3.2 MPa; mass flow rate: 40–80 kg/h	The S-shaped PCHE, compared with a conventional zigzag configuration, had one-fifth of the pressure drop with equal thermal-hydraulic performance.
Xu et al. [18]	airfoil	supercritical CO2	inlet temperature: 303 K, inlet pressure: 8 MPa, and wall temperature: 333 K	With increase in mass flow rate, the overall thermal and hydraulic performance of airfoil fin PCHE was better than that of other types of fin.
Ma et al. [19]	airfoil	supercritical CO2	cold side: 761.96 K and 7.83 MPa; hot side: 1173.15 K and 7.59 MPa	The maximum difference of Nu between the two models with and without airfoil fin in the PCHE was up to 6.7%, and the maximum difference of f-factor was 6.4%.
Chu et al. [20]	airfoil	supercritical CO2	inlet pressure: 8 MPa, and wall temperature: 393 K	The heat transfer rate decreased because of strong variation of properties of supercritical CO2, but the pressure loss remained almost constant along the main flow direction.
Cui et al. [21]	airfoil	supercritical CO2	cold side: 381.05 K, 8.28 MPa, and 0.4728–1.8912 g/s; hot side: 553.05 K, 2.52 MPa, and 0.4335 g/s	The staggered arrangement and the proper shape of airfoil fin could reduce the effect of boundary layer and improve the heat transfer.
Chu et al. [22]	airfoil	supercritical CO2	inlet temperature: 473.15 K, inlet pressure: 8 MPa, and wall temperature: 313 K	Nu of airfoil fins with different cambers could be improved by 42, 54, 75, and 66%, besides f-factor averagely increased 125, 460, 980. and 890%, respectively.
Zhao et al. [23]	airfoil	supercritical LNG	inlet temperature: 121 K, inlet pressure: 10.5 MPa, and heat flux: 58713.75 W/m^2	A sparser staggered arrangement of fins showed a better thermal and hydraulic performance in airfoil fin PCHE.

Figure 1. Thermal-physical properties of methane at different pressures.

Table 2. Composition of LNG [32].

Composition	Methane	Nitrogen	Ethylene	Propane	Butane
Fraction %	89.62	3.05	5.83	0.14	1.36

Figure 2. Schematic diagram of the physical model.

Figure 3. Schematic diagram of the airfoil.

Table 3. List of different PCHE configurations.

PCHE	Characteristics	Schematic Diagram
Case A	straight channel
Case B	airfoil
Case C	front common-flow-up delta VG and airfoil
Case D	front common-flow-down delta VG and airfoil
Case E	rear common-flow-up delta VG and airfoil
Case F	rear common-flow-down delta VG and airfoil

Table 4. Geometric parameters of different PCHE configurations.

Parameter	Symbol/unit	Case A	Case B	Case C	Case D	Case E	Case F
Channel length	L2/mm	64.0	64.0	64.0	64.0	64.0	64.0
Channel width	W/mm	2.0	2.0	2.0	2.0	2.0	2.0
Channel heigth	H/mm	1.0	1.0	1.0	1.0	1.0	1.0
Transverse pitch	Pt/mm	–	–	1.0	1.0	1.0	1.0
Longitudinal pitch	Pl/mm	–	8.0	8.0	8.0	8.0	8.0
Max airfoil thickness	Wf/mm	–	0.96	0.96	0.96	0.96	0.96
Airfoil chord length	Lf/mm	–	4.0	4.0	4.0	4.0	4.0
Airfoil heigth	Hf/mm	–	1.0	1.0	1.0	1.0	1.0
VG attack angle	α/deg	–	–	45	135	45	135
VG length	LVG/mm	–	–	0.5	0.5	0.5	0.5
VG thickness	WVG/mm	–	–	0.05	0.05	0.05	0.05
VG height	HVG/mm	–	–	0.8	0.8	0.8	0.8
Row	N	–	8	8	8	8	8

Table 5. Expressions for ϕ, Γ_ϕ, and S_ϕ.

ϕ	Γϕ	Sϕ
1	0	0
u	μ + μt	$S_{\mathrm{u}}=-\frac{\partial p}{\partial x}+\frac{\partial }{\partial x}((\mu +{\mu }_{\mathrm{t}})\frac{\partial u}{\partial x})+\frac{\partial }{\partial y}((\mu +{\mu }_{\mathrm{t}})\frac{\partial v}{\partial x})+\frac{\partial }{\partial z}((\mu +{\mu }_{\mathrm{t}})\frac{\partial w}{\partial x})$
v	μ + μt	$S_{\mathrm{v}}=-\frac{\partial p}{\partial y}+\frac{\partial }{\partial x}((\mu +{\mu }_{\mathrm{t}})\frac{\partial u}{\partial y})+\frac{\partial }{\partial y}((\mu +{\mu }_{\mathrm{t}})\frac{\partial v}{\partial y})+\frac{\partial }{\partial z}((\mu +{\mu }_{\mathrm{t}})\frac{\partial w}{\partial y})$
w	μ + μt	$S_{\mathrm{w}}=-\frac{\partial p}{\partial z}+\frac{\partial }{\partial x}((\mu +{\mu }_{\mathrm{t}})\frac{\partial u}{\partial z})+\frac{\partial }{\partial y}((\mu +{\mu }_{\mathrm{t}})\frac{\partial v}{\partial z})+\frac{\partial }{\partial z}((\mu +{\mu }_{\mathrm{t}})\frac{\partial w}{\partial z})$
t	μ/Pr + μt/σt	$S_{\mathrm{t}}$
k	μ + μt/σk	$S_{\mathrm{k}}=\rho G_{\mathrm{k}}-\rho \epsilon$
ε	μ + μt/σε	$S_{\mathrm{\epsilon }}=\frac{\epsilon }{k}(c_1\rho G_{\mathrm{k}}-c_2\rho \epsilon )$

$G_{\mathrm{k}}=\frac{{\mu }_{\mathrm{t}}}{\rho }\left({(\frac{\partial u}{\partial x})}^2+{(\frac{\partial v}{\partial y})}^2+{(\frac{\partial w}{\partial z})}^2+{(\frac{\partial u}{\partial y}+\frac{\partial v}{\partial x})}^2+{(\frac{\partial u}{\partial z}+\frac{\partial w}{\partial x})}^2+{(\frac{\partial v}{\partial z}+\frac{\partial w}{\partial y})}^2\right),$ μ_t=c_μρk²/ε, c_μ=0.09, c₁=1.44, c₂=1.92, σ_t=0.85, σ_ε=1.3, σ_k=1.0.

Figure 4. Boundary conditions for computational model.

Figure 5. Selected grid system.

Table 6. Variation of grid independence (u_in=8.0 m/s).

Configuration	Grid	$\overline{Nu}$	Relative error	f	Relative error
Case A	277300	184.3	5.40%	0.019156	−6.80%
	415950	180.8	3.40%	0.019773	−3.80%
	554610	177.16	1.30%	0.02025	−1.50%
	693250	174.86	–	0.020554	–
Case B	415930	259.19	6.70%	0.018982	−7.60%
	623900	252.63	4.00%	0.01966	−4.30%
	833620	246.61	1.50%	0.02024	−1.50%
	1031870	242.91	–	0.020544	–
Case C	452830	337.98	7.70%	0.037283	−8.60%
	735860	327.62	4.40%	0.038548	−5.50%
	1132170	319.24	1.70%	0.04007	−1.80%
	1471530	313.81	–	0.040791	–

Figure 6. $\overline{Nu}$ and f-factor comparisons between simulated and experimental results.

Table 7. Working conditions for different cases.

Parameter	Symbol/unit	Value
inlet temperature	tin / K	195
temperature difference	Δt / K	>30
inlet pressure	pin / MPa	7–10
pressure drop	Δpf / MPa	<0.1
mass flux	G / kg/m^2⋅s	132.32–2117.12
wall temperature	tw / K	340

Figure 7. Comparisons of c_p for Case B at different pressures.

Figure 8. Comparisons of ρ for Case B at different pressures.

Figure 9. Local Nusselt number Nu_L and c_p along the main flow direction at u_in=2.0 m/s.

Figure 10. $\overline{Nu}$ and f-factor comparisons for Case B at different pressures.

Figure 11. Heat transfer performance comparisons for different PCHEs.

Figure 12. Streamlines at the central cross section in the z-direction of Case B at u_in = 2.0 m/s.

Figure 13. Streamlines in the 7th row of Cases C–F at u_in = 2.0 m/s.

Figure 14. Local Nusselt number Nu_L in the 7th row at u_in=2.0 m/s.

Figure 15. Velocity distributions at the different cross-sections at u_in=2.0 m/s.

Figure 16. Friction factor performance comparisons for different PCHE configurations.

Figure 17. Volume goodness comparisons for different PCHE configurations.

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