Numerical study on bionic airfoil fins used in printed circuit plate heat exchanger

2.1 Bionic design of sailfish airfoils

Using a sailfish specimen made by the research team at Seoul National University in South Korea as the bionic object, four novel bionic airfoils are derived through image processing tools. Figure 1(a) illustrates the side view of the sailfish specimen, showcasing a body length (BL) of 1.74 m, a maximum height to BL ratio of 0.161, and a position of maximum thickness situated at 24% of the BL in the flow direction. For additional detailed parameters, please refer to the study by Sagong et al. [22]. The slender bill and expansive dorsal fin are two recognizable morphological features of the sailfish. The protruding upper jaw functions primarily for predation and self-defense [23]. Interestingly, the wind tunnel test conducted on sailfish specimens at an approximate cruising speed of 6.3 km/h demonstrate that the bill does not contribute to drag reduction [22]. The fins serve as the primary organ enhancing body stability and maneuverability during swimming. However, to minimize resistance from an overly expansive wetted area, sailfish retract parts of fins, including the first dorsal fin, the first anal fin, and the abdominal fin, into the fin grooves during coasting.

Figure 1

The construction of a geometric model for bionic sailfish airfoils. (a) Overall morphology of the sailfish specimen; (b) symmetric bionic airfoils based on the initial sailfish airfoil; and (c) design of composite sailfish airfoils.

Based on the above, the side profile curve of the sailfish, with the bill and all fins removed, is selected as the blueprint for bionic airfoil design. The detailed construction process of this geometric model is depicted in Figure 1. Utilizing a third-order spline, the sailfish bone line is extracted, resulting in the initial sailfish airfoil denoted as S _ori, as shown on the left side of Figure 1(b). Gentle transition treatments are implemented at the intersection of the fins and the bone line to ensure a smooth geometric profile. The fish body’s lower jaw tip is designed as the leading-edge point, and the caudal fin is modified into a 0.02 mm diameter arc for modeling and analysis. The midpoint of the tail arc aligns horizontally with the leading-edge point, and the connection between these two points is called chord line. Considering the description and engineering manufacturing issues of the airfoil, a symmetrical structure is typically preferred. Consequently, taking the chord line as the axis of symmetry, the upper (blue line) and lower profile lines (orange line) of S _ori are symmetrized to obtain two symmetrical sailfish airfoils, marked S _up and S _low, as depicted on the right side of Figure 1(b). Both schemes maintain a maximum thickness representing 15% of the chord length, with the largest internal tangent circle positioned at 24% of the mean camber line near the leading edge.

The NACA 0015 represents a non-cambered airfoil, characterized by a 15% ratio of maximum thickness to chord length. In this study, the profile line preceding and following the widest position of the airfoil is divided into two parts, called the head and tail profile lines. Based on the NACA 0015 airfoil, we further adapt the S _up and S _low schemes to obtain two composite sailfish airfoils. As shown in Figure 1(c), the NACA 0015 airfoil is initially modified to shift the maximum inner tangent circle towards the leading edge by 6% of the chord length. Then, with the mean camber lines as a baseline, the modified NACA 0015, S _up, and S _low, possessing the same aspect ratio, are placed at the identical horizontal level. The S _up and S _low schemes are shifted in the direction indicated by the arrows until both the upper and lower surfaces align tangentially with the modified NACA 0015 airfoil. Ultimately, the geometric model undergoes segmentation and reorganizing, linking the tail curve of the NACA 0015 to the head curves of both S _up and S _low. The obtained new airfoils are denoted as S _up-comb and S _low-comb, respectively.

2.2 Simulation domain and boundary conditions

The core, the primary pressure-bearing component and heat transfer unit of a PCHE, consists of a metal block fabricated through the stacking and welding of etched plates. For airfoil PCHEs, the flow channel formed by the periodically arranged fins is the platform for fluid flow and heat transfer. In this study, the NACA 0015 airfoil is selected as a reference to numerically investigate fins with various shapes used in PCHE.

The simplified PCHE model, comprising two airfoil channels depicted in Figure 2, is identified as an ideal model to significantly reduce the computational and time expenses [24]. The single banked computational model is divided into two distinct areas: the heat transfer section with fins, and the plate extension section devoid of fins. The heat exchanger section houses 20 rows of staggered fins on both the hot and cold side. The inlet extension facilitates full development of the boundary layer, whereas the outlet extension inhibits the effect of the return flow on heat transfer. The incoming flow has an attack angle of 0, progressing from the head to the tail of the fins, with the counter-flow pattern causing the fins on the hot and cold side to face in opposite directions. The sizes of the entire simulation domain are 256.6 mm (L) × 2.2 mm (W) × 3 mm (H), of which the length of the extension segment is 18 mm. Figure 2 demonstrates the geometric parameters of the fin layout, and the supplementary geometric details of the simulation domain are listed in Table 1.

Figure 2

Airfoil PCHE simulation domain.

It is noteworthy that, to ensure a meaningful comparison, the dimensional parameters summarized in Table 1 are the same across all types of airfoil fin PCHEs. However, the variations in the shapes among the different types of fins result in discrepancies in the average hydraulic diameter (D _h) of the channel. Considering the geometry and arrangement dimensions of the fins, D _h can be written as [25] follows:

where V _unit, A _s,unit, A _c,unit, and L _unit represent the volume, heat transfer area, average cross-sectional area, and length of the minimum periodic heat transfer unit in the fluid domain, respectively. The calculated values for D _h pertaining to the five types of airfoil channels are given in Table 2. It can be seen that the heat transfer area and D _h of the four sailfish fins exceed those of the NACA 0015 airfoil fin. Interestingly, both S _up and S _low-comb exhibit identical D _h values and possess the largest heat transfer area.

The setting of boundary conditions is shown in Figure 2. Detailed information about the boundary conditions is as follows:

The fluid domain inlet is subjected to a mass flow rate inlet boundary condition, with the cold and hot fluid inlet temperatures fixed at 292 and 333 K, respectively.

The fluid domain outlet is set as a pressure outlet boundary.

There is no slip between the contact wall surfaces of the fluid domain and the solid domain. The contact wall surfaces of the heat exchange section are set to be coupled.

Apply symmetric boundary conditions on the left and right sides of the computational domain.

Apply periodic boundary conditions to the top and bottom surfaces of the computational domain.

There is no heat flux exchange on the remaining surfaces.

The thermophysical properties of N₂, serving as the working fluid in channels, are sourced from the NIST database. Within the investigated range of operating conditions, the density (ρ), thermal conductivity (λ), dynamic viscosity (μ), and specific heat capacity (C _p) exhibit a monotonic temperature dependence.

2.3 Data reduction and model validation

The thermophysical properties of N₂ under an inlet pressure of 3 MPa are presented in Table 3. It can be found that the fluid properties exhibit only minor variations with temperature within the examined operating conditions. Given this, the logarithmic average temperature difference method is employed to calculate the overall heat transfer coefficient (U) of the PCHE, as shown in the following equations:

where Q _ave and A _s,tot are the average heat transfer rate and total heat transfer area, respectively, while ΔT _m refers to the logarithmic average temperature difference. The substitutes h and c represent the fluid in hot and cold sides, respectively; and the substitutes i and o denote the inlet and outlet of the channel on both sides, respectively.

Due to the identical flow channel shape, mass flow rate, and similar working media properties on cold and hot sides, it can be considered that the heat transfer between them has reached a high degree of balance. In other words, the average convection heat transfer coefficients equate for both sides. The total thermal resistance is described as follows:

where h indicates the average convection heat transfer coefficient, and A _s,hot and A _s,cold are the heat transfer areas for the hot and cold sides, respectively. The thermal resistance method described in the above equation neglects the plate thermal resistance, which was verified in the study by Chung et al. [26]. Therefore, the convection heat transfer coefficient on either side can be obtained by the direct method [27] as below:

For the evaluation of flow friction and heat transfer characteristics in PCHE, key dimensionless parameters such as the Reynolds number (Re), average Nusselt number (Nu), Prandtl number (Pr), and Fanning friction coefficient (f) are defined as follows:

where q _m represents the mass flow rate; u indicates the flow velocity; P _in and P _out correspond to the pressures at the inlet and outlet of the heat transfer section, respectively; and μ, ρ, λ, and C _p are the physical parameters at the mean temperature.

A performance evaluation criteria (PEC) for PCHE, which considers both thermal and hydraulic performances, is defined as

With the NACA 0015 airfoil fin as a reference, PEC is used to compare the heat transfer enhancement performance of fins with various configurations at the same pumping power. Consequently, a larger PEC value indicates superior performance. When the value is greater than 1, it indicates that the heat transfer enhancement ratio is greater than the friction enhancement ratio for this fin shape under the same pumping power.

The RNG κ–ε turbulence model is adopted for computational fluid dynamics (CFD) research, combined with enhanced wall functions to reduce the sensitivity of the near-wall grid density. The calculation is performed using the commercial software Fluent, with the target residuals of the continuity equation and the other control equations set to 10⁻³ and 10⁻⁶, respectively. Using the PCHE with S _up fins as an example, Figure 3 gives the independence verification results for five mesh schemes. To ensure the nodes of the first layer grid to fall within the laminar sub-layer, a five-layer boundary grid with a growth ratio of 1.2 is established, with the y+ of the first layer grid always remaining below 5. From the case indicated by the dashed line in the figure, it is observed that numerical results exhibit minimal fluctuations upon grid encryption, with variations in both pressure drop and heat transfer coefficient staying within 1% threshold. Accordingly, the setting method employing a grid count of 9,948,687 is implemented to the mesh system across all examined cases.

Figure 3

Mesh independence test results.

A simulation of the NACA 0020 airfoil fin PCHE used in Chung’s [26] test is conducted to validate the credibility of the numerical results. As shown in Figure 4, the correlation based on CFD data matches well with that obtained from the experiment results. It is concluded that as the Re decreases, the deviation increases, with a maximum value of 18.4%, a level deemed acceptable for engineering studies.

Figure 4

Comparison of simulation results with the experimental correlation.

3.1 Comparison of thermo-hydraulic performance for different fin configurations

In this subsection, we examine the flow and heat transfer performance of PCHEs with five distinct fin shapes. The corresponding Re range for CFD models with inlet mass flows of 0.13, 0.1975, 0.265, 0.3325, and 0.4 g/s are 5,000–15,500. Notably, the mass flow rates for both cold and hot fluids are maintained to be consistent across all operating conditions.

Figure 5 shows the heat transfer performance and flow resistance of hot channels in PCHEs with five fin configurations. It can be seen that the Nusselt number (Nu) and pressure drop per unit length (ΔP/L _h) are proportional to the Reynolds number (Re). This proportionality can be attributed to the fact that an increase in Re enhances the pulsating effect of turbulence, which in turn intensifies heat transfer and the collisions among fluid microclusters. As shown in Figure 5(a), the Nu among the five configurations is quite close to each other, especially at low Re. The greatest discrepancy is a mere 1.74%, occurring between NACA 0015 and S _low. The Nu of NACA 0015 is marginally higher than the other four sailfish fin types, showing the best thermal performance, while the heat transfer performance of S _low-comb is almost the same as that of NACA 0015. Thus, the bionic fins do not necessarily offer superior heat transfer enhancements. This might be attributed to sailfish fins reducing the fluid disturbances, aligning with the findings from a wind-tunnel test on a sailfish specimen [22], which concluded that the unique outline of the sailfish promotes adherent fluid flow over the majority of its body surface. S _low and S _up-comb present the secondary resistance reduction ability compared to that of S _low-comb, but better than that of S_up.

Figure 5

Heat transfer and pressure drop performance of PCHEs with bionic and NACA airfoil fins. (a) Nu vs Re and (b) ΔP/L _h vs Re.

For the pressure drop per unit length (ΔP/L _h), as shown in Figure 5(b), with an increase in Re, the difference in ΔP/L _h among the various fins becomes more pronounced. It can be seen that NACA 0015 possesses the largest resistance loss, whereas S _low-comb shows the best improvement in pressure drop performance, with an average of 4.4% reduction compared to NACA 0015. This means that the streamlined outline of the sailfish airfoil positively impacts flow resistance reduction. Although Figure 5 indicates that NACA 0015 exhibits superior heat transfer performance, the edge in enhancement is marginal, especially in the case of low Re. S _low-comb has the best hydraulic performance, and meanwhile, its heat transfer performance level is the highest among the four sailfish fins. The performance related to heat transfer and pressure drop for S _low and S _up-comb is nearly identical, attributable to their same heat transfer area and hydraulic diameter. Additionally, among the five fins, S _up manifests the worst hydraulic performance.

Figure 6 provides a comparison of the overall performance for five types of fins used in PCHE. The ratio of heat transfer rate per unit area (Q _ave/A _s,hot) to pressure drop per unit length (ΔP/L _h) is often employed as a criterion to assess thermo-hydraulic performance and identify the drag reduction capability of various fins in PCHE [28]. Figure 6(a) plots the variation in heat transfer rate per unit area (Q _ave/A _s,hot) with pressure drop per unit length (ΔP/L _h) in the numerical models for five fin types. At the same ΔP/L _h, S _low-comb show the highest while NACA 0015 has the lowest heat transfer performance. According to ΔP/L _h vs Re plot in Figure 5(b), the difference in thermal-hydraulic performance between them becomes more obvious with the increase in Re. This suggests that S _low-comb possesses the best thermal-hydraulic performance among the five fin types, particularly at high ΔP/L _h resulting from high Re. S _low and S _up-comb showcase similar overall performances, slightly better than that of S _up and NACA 0015. Combined with Figure 5, it can be found that the higher the flow resistance, the worse the overall performance. Hence, in this study, the contribution of the pressure drop performance to the overall assessment exceeds that of heat transfer performance. In other words, intense turbulence at the expense of high pressure drop does not considerably augment heat transfer, while a weakly turbulent degree of fluid can relatively significantly reduce the drag loss. Although this may slightly decrease thermal performance, it improves the overall performance.

Figure 6

Comprehensive performance comparison of PCHEs with bionic and NACA airfoil fins. (a) Q _ave/A _s,hot vs ΔP/L _h and (b) PEC vs q _m.

Figure 6(b) demonstrates the comprehensive enhanced heat transfer performance of the five airfoil fin channels at various inlet mass flow rates (q _m). Obviously, NACA 0015 serves as the reference fin, its PEC value is always 1. However, Figure 6(b) yields different comparative results compared to Figure 6(a). This discrepancy arises since the Q _ave/A _s,hot to ΔP/L _h ratio emphasizes evaluating the effect of flow resistance losses on thermo-hydraulic performance. In Figure 6(b), the PEC values for S _up, S _low, and S _up-comb remain below 1, and they all follow similar variation trends, manifesting the insensitivity to q _m. Hence, at the same pumping power, S _up, S _low, and S _up-comb do not exhibit the heat transfer performance enhancements relative to NACA 0015. The PEC of S _low-comb is only greater than 1 at low mass flow rates, meaning its aptness for applications with either low Re or elevated Re accompanied by low pressure drop requirements.

3.2 Flow field analysis in channels with different fins

Figure 7 shows the velocity and pressure fields near the first four rows of fins in the five types of airfoil channels when the inlet mass flow rate is 0.265 g/s. A similar flow behavior around various fin types can be seen from the figure. Primarily, a region of subdued flow velocity is evident near the leading edge of the airfoil, a consequence of flow stagnation stemming from the collision of the fluid with fins. Subsequently, the fluid around the leading edge of the airfoil surface experiences a gradual acceleration owing to the diminishing flow cross-sectional area, culminating at the position near the maximum thickness of the fins. Behind the fins, the separated fluid streams eventually converge, giving rise to a segment of the velocity boundary layer. The flow velocity within the trailing zone is markedly lower compared to that in the main flow area between two neighboring columns of fins.

Figure 7

Velocity and pressure fields around the first four rows of fins in different types of airfoil channels (q _m = 0.265 g/s). (a) Velocity and (b) pressure.

Variations in fin shapes result in distinct flow fields across different channels. Compared to NACA 0015 configuration, the sailfish airfoils, characterized by their concave leading profiles, expand the fluid domain cross-section along the flow direction. Consequently, these airfoils present a larger low-velocity region near the leading edge, as shown in Figure 7(a), facilitating smaller pressure losses but also simultaneously attenuating heat transfer. Within this context, S _low, S _low-comb, and S _up-comb exhibit analogous extents of low-velocity domain, which are noticeably broader than those seen in S _up and NACA 0015. This phenomenon can be attributed to the wider tail of the S _up compared to the S _up-comb, leading to more contraction of the flow domain along the flow direction from the leading edge under the influence of adjacent columns of fins.

Regions with high flow velocity, located near the widest part of the fins, enhances heat transfer by promoting fluid mixing between the main flow zone and the near-wall surface. However, this also induces an inverse pressure gradient in the flow field. The high flow velocity region compresses the thickness of the velocity boundary layer, causing the dominant flow resistance in this range to switch from viscous friction to differential pressure resistance. As shown in Figure 7(b), the pressure distribution of the sailfish fins is more uniform than that of NACA 0015. Consequently, with the largest area of high-velocity flow region, NACA 0015 presents subpar hydraulic performance, though its heat transfer performance is superior to that of the other four types of fins. Compared to S _low with head profiles featuring shorter concave segments, significant velocity gradients exist in the high-velocity core regions of S _up and S _up-comb, corresponding to the local low pressure at the same location in Figure 7(b), which is believed to impede heat transfer. Therefore, the velocity vectors and profiles of S _up-comb, S _low-comb, and NACA 0015 are further analyzed at the second row of fins, as shown in Figure 8. In Figure 8(aⅠ), (bⅠ), and (cⅠ), it is found that different structural flow passages are streamlined without any transverse vortices generated. Combining Figure 7(b), this indicates that the smaller adverse pressure gradient along the flow direction is not enough to cause flow separation on the wing surface, so the flow resistance is mainly generated by friction. Figure 8(aⅡ), (bⅡ), and (cⅡ) show the velocity distribution of three types of wing channel flow fields. It can be seen that at the leading-edge position, the smaller collision area of the biomimetic wing results in a smoother flow field, which is beneficial for reducing flow resistance. By comparing the cross-sections a2 and a3, it is found that the closer the maximum thickness position is to the front, the larger the velocity peak of the fluid flowing along the wall. In addition, in the wing trailing edge and non-wing area, the velocity distributions of the three types of wings are similar, which may be caused by their identical rear shapes. In order to further analyze the boundary layer flow characteristics on the wing surface, the flow velocity profiles at three positions between cross-sections a1 and a2, a3 and a4 are plotted, respectively, (x/L = 0.067, x/L = 0.333, x/L = 0.6), as shown in Figure 8(d). In Figure 8(dⅠ), the boundary layer of the biomimetic wing is obviously thicker than that of the NACA 0015 wing, especially S _low-comb. This indicates that the concave curve at the front end of the maximum thickness can smooth the velocity gradient of the wall fluid, reduce the momentum exchange normal to the fluid, and reduce the friction resistance. However, at the same time, due to the increase in the thermal resistance boundary layer, the heat transfer between the fluid and the wall is weakened. In Figure 8(dⅡ), compared with the NACA 0015 wing, the turbulence core velocity of the biomimetic wing is higher. The presence of the boundary layer avoids the momentum exchange between the high-speed mainstream and the wing surface, resulting in drag reduction. In Figure 8(dⅢ), the boundary layer flow characteristics of the three types of wings are basically the same, therefore, the contribution of the tail of the biomimetic wing to drag reduction is the smallest.

Figure 8

Velocity vectors and velocity profiles along the flow direction in channels (q _m = 0.265 g/s). (a) NACA, (b) S _up-comb, (c) S _low-comb, and (d) Stream wise velocity profiles along b1, b2, and b3 lines.