Introduction

FHMT

Frontiers in Heat and Mass Transfer

2151-8629

Tech Science Press

USA

76230

10.32604/fhmt.2026.076230

Article

Comparative Study on Flow Heat Transfer Performance of Kelvin Cell and Typical Truss Structures

Liu

Liangliang

lyavicrk@163.com Liu

Haigang

Shenyang Aircraft Design Research Institute, Department of Electromechanical System, Shenyang, China

*Corresponding Author: Liangliang Liu. Email: lyavicrk@163.com

2026

30042026

24 2

17 11 2025 02 02 2026

2026

The Authors

This work is licensed under a Creative Commons Attribution 4.0 International License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

The Kelvin structure is a regular tetrahedral truss structure similar to the pore structure of metal foam, which is often used to simplify the simulation of metal foam. However, its flow heat transfer characteristics have rarely been compared with typical truss structures. To supplement the research work in this aspect and quantify the advantages and disadvantages of these structures compared with typical structures, this paper uses modeling software to create tetrahedrons, BCC truss structures, and Kelvin porous structures with 90% porosity, and uses Fluent to study the distribution rules of temperature, pressure, and velocity of these three structures respectively. The relationship between pressure drop, heat transfer performance, and comprehensive heat transfer performance among different structures and Reynolds number is quantified. The results show that the Kelvin structure has the best heat transfer characteristics, which is 34.6% and 28.9% higher than the tetrahedron and BCC structures, respectively. However, the Kelvin structure has the highest flow resistance, which is 70.7% and 165.3% higher than BCC and tetrahedron structures on average. When the j/f dimensionless calculation criterion is adopted, the comprehensive heat transfer performance of the tetrahedron is 40.5% and 79.8% higher than that of the BCC structure and the Kelvin structure, respectively.

Heat exchanger porous structure flow heat transfer truss structure

1 Introduction

With the advancement of aviation technology, the performance of aero-engines has been improved. However, when an aircraft is at specific altitudes (such as 4000, 6000, and 8000 m), its heat dissipation capacity decreases by 5%, 12%, and 22% respectively compared to that at sea level [1]. This leads to a contradiction between the increased demand for heat dissipation and the decreased heat dissipation capacity, which has become a core issue restricting the improvement of aero-engine performance.

As the core component for heat dissipation, the performance of the heat exchanger directly determines the cooling effect. It operates at high altitudes and under complex working conditions, thus requiring to meet the requirements of light weight, high strength, high temperature and pressure resistance, and compact structure [2]. Truss structures, characterized by large specific surface area, high porosity, and high strength, meet the requirements of aviation heat exchangers and have been applied in fields such as aerospace thermal protection systems [3] and aero-engine heat dissipation [4].

Common truss structures include tetrahedral structures [5], BCC structures [6], etc. The tetrahedral structure is pyramid-shaped, with smooth and convergent sides and a pointed top. It has high stability and is widely used in the aerospace field [7]. Ma et al. [8] inserted a tetrahedral structure into the base material, increasing the overall Nusselt number (Nu) by 11.4%–13.3%. Mahdavi et al. [9] studied two types of tetrahedral structures with aspect ratios of 8.8 and 5 (heat flux: 10–50 W/cm², convective heat transfer coefficient: 2129–6510 W/m²·K) and found that the heat transfer efficiency of the structure with an aspect ratio of 5 was 50%–53% higher than that with an aspect ratio of 8.8. Wang et al. [10] found that the heat transfer coefficient of the BCC arrangement increased significantly with the increase in the number of layers, which was attributed to the rotation of the air flow. Due to its open-cell structure and large specific surface area, metal foam has the characteristics of enhanced heat transfer and low flow resistance, showing broad application prospects [11]. The Kelvin cell has structural characteristics similar to those of metal foam and is regarded as its idealized pore structure [12].

Kong et al. [13] numerically compared the flow and heat transfer characteristics of real foam and Kelvin foam: when the flow was along the elongation direction of the structure, the real foam had higher permeability and lower Nusselt number than the Kelvin structure; the Kelvin foam was more likely to form turbulent flow. The study by Zhang et al. [14] showed that at the same porosity and an inlet velocity of 25 m/s, the Kelvin structure and the metal foam structure exhibited similar overall heat transfer performance, while the Weaire–Phelan structure outperformed the other two by 12.18% in overall heat transfer performance. Further investigation into the performance of the de-strutted structure revealed that, according to the method proposed by Zhang et al. [14], the pressure drop of the de-strutted structure decreased by 20.2%, and its overall heat transfer performance improved by 9.3%. The tetradecahedral structure is a regular structure capable of predicting the performance of metal foams. The prediction error reported by Tang et al. [15] was within 20%, demonstrating that the tetradecahedral structure serves as a suitable for metal foams. In a comparative study of tetradecahedral, octahedral, and rhombic dodecahedral lattices, the tetradecahedral lattice achieved the highest overall heat transfer coefficient, followed by the octahedral and rhombic dodecahedral lattices. The octahedral lattice exhibited the largest pressure drop, followed by the rhombic dodecahedral lattice, while the tetradecahedral lattice showed the smallest pressure drop [16]. Kiyak and Öztop [17] investigated the influence of partially embedding porous copper plates with different configurations into Phase Change Material (PCM) on heat transfer. The study reveals that the orientation, segmentation, and positioning of the porous structure significantly affect heat transfer efficiency and the melting process, offering practical insights for the geometric design and optimization of latent heat thermal energy storage systems.

Studies by Sun et al. [18] showed that the Kelvin structure had a 64.4% higher pressure drop and a 12.3% higher overall heat transfer coefficient than the open-cell metal foam, but its overall heat transfer performance was 26.2% lower at 6 m/s. Although in-depth studies have been conducted on the Kelvin structure, there are relatively few comparative studies between the Kelvin structure and traditional truss structures.

Therefore, it is necessary to quantitatively compare the flow and heat transfer characteristics of the Kelvin structure with other typical truss structures (BCC and tetrahedral structures). In this study, the CFD method was adopted, and software such as ANSYS Fluent was used for numerical simulation of porous structures, aiming to realize the quantitative comparison of the flow and heat transfer characteristics between the Kelvin structure and typical truss structures.

2 Geometric Model

Fig. 1 shows the schematic diagrams of the unit cells of the three structures. All selected structures were designed with a porosity of 90% to ensure consistency in geometric dimensions and porosity, so as to accurately evaluate the impact of the structure itself on the flow and heat transfer performance.

Figure 1 The geometric dimensions of the three structures.

All three structures were constructed within a 2 mm³ cubic lattice: the bottom projection of the tetrahedral structure was an equilateral triangle with a side length of 2 mm, and the distance from the bottom to the vertex was 2 mm; it was composed of three cylinders with a diameter of 0.36 mm intersecting alternately at an angle of 60°. The BCC structure was formed by connecting three cylinders with a length of 23 mm and a diameter of 0.3 mm at their center points. The Kelvin structure was created by positional stretching and was composed of cylinders with a diameter of 0.26 mm connected to each other. The specific surface area andat different structures are shown in Table 1.

Table 1 Characteristic parameters of different structures.

	Tetrahedral Structure	BCC	Kelvin
α_sf	0.586	0.674	0.98

3 Simulation Model 3.1 Governing Equations

The flow and heat transfer process of fluid in porous structures is complex, involving heat conduction, convection, and radiation. This study mainly focuses on the convective heat transfer performance. The fluid medium in the calculation is air, which is regarded as an incompressible gas. The numerical simulation needs to satisfy the continuity equation, momentum equation, and standard k-epsilon turbulence model equation. To further confirm the robustness of our conclusions, we also performed comparative calculations using the SST k–ω turbulence model for the Kelvin, BCC, and tetrahedral structures. The results show that the differences in key parameters, such as pressure drop and convective heat transfer coefficient, are generally within 2%. This confirms that the standard k–ε model provides reliable predictions within the parameter range of this study and supports the credibility of the observed performance trends.

Calculated based on the hydraulic diameter, the Reynolds number ranges from 1350 to 5500, and the flow state is turbulent, so an appropriate turbulence model needs to be selected [19]. The k-epsilon model is a semi-empirical model, which has fast calculation speed and reasonable accuracy in a wide range of turbulent flows [20]. The k-omega model requires boundary layer grids, which will reduce the grid quality. In this study, the Reynolds number is in the medium range and there is no rotating flow. The k-epsilon model balances accuracy and efficiency, so it is selected. (1)∂ui∂xi=0 (2)∂∂xi(ρuiuj)=−∂p∂xi+∂∂xj(µ∂ui∂xj) (3)∂∂xi(ρuicpT)=∂∂xi(λ∂T∂xi) (4)∂∂xj(ρuj∂k∂xj−(μ+μtσk)∂k∂xj)=μt∂ui∂xj(∂ui∂xj+∂uj∂xi)−ρε (5)∂∂xj(ρujε−(μ+μtσε)∂ε∂xj)=cε1εkμt∂ui∂xj(∂ui∂xj+∂uj∂xi)−cε2ρε2k

In the formulas: ρ is the fluid density (kg/m³); u is the velocity (m/s); p is the pressure (Pa); μ is the dynamic viscosity; λ is the thermal conductivity (W/(m·K)); cp is the specific heat capacity (J/(kg·K)); T is the temperature (K); ε is the dissipation rate; μt is the turbulent viscosity; k is the turbulent kinetic energy; cε1=1.45; cε2=1.92; σk=1.0; σε=1.3.

The scheme of the simple algorithm is selected. The second-order upwind advection model is used in the momentum, besides choosing the second-order upwind in turbulent kinetic energy, turbulent dissipation rate, and energy. The boundary conditions near the walls are analyzed using the method of standard wall function. A convergence criterion of 10⁻⁶ is used to ensure the accuracy of the consequences.

3.2 Boundary Conditions

Fig. 2 shows the interconnected form of ten unit cells used in the numerical simulation, with a calculation domain of a cuboid of 20 mm × 2 mm × 2 mm. The inlet of the flow channel is a velocity inlet, and the outlet is a pressure outlet. Seven working conditions with inlet velocities of 10, 15, 20, 25, 30, 35, and 40 m/s were set. The magnitude of heat flux is mostly at the kW/m² level [21]. In this study, a constant heat flux of 40,000 W/m² was applied to the surface of the skeleton, and both the skeleton surface and the fluid wall were set as symmetric boundary conditions.

Figure 2 Schematic diagram of boundary conditions.

In the simulation, the outlet temperature of the flow channel and the inlet pressure were monitored. Since the outlet pressure was set to 0 Pa, the inlet pressure was the pressure drop of the fluid flowing through the porous material. The residuals of all equations and monitored values were set to 1e−6 to ensure the accuracy of the results.

3.3 Grid Independence Verification

When solving with Fluent, the number and quality of grids affect the calculation speed and accuracy. Although hexahedral grids have better quality, the porous structure in this study is complex, and tetrahedral grids have better adaptability and can better capture the structural details, so tetrahedral grids were selected. A dimensionless wall distance y+ < 1 was used to determine the near-wall mesh size. In view of the small size and complex shape of the structure, local grid refinement was carried out in the fluid-solid coupling area to improve the accuracy.

Grid independence verification was performed on the three structures (inlet velocity: 29.5 m/s, heat flux: 40,000 W/m²). Except for the inlet velocity, the boundary conditions were consistent with the simulation settings. As shown in Fig. 3a,b:

Figure 3 Grid independence verification: (<bold>a</bold>) Heat exchange grid independent verification and (<bold>b</bold>) Pressure drop grid independent verification.

When the number of meshes for the BCC structure, tetrahedral structure, and Kelvin structure is 6.23, 6.40, and 7.07 million respectively, the calculation errors are less than 1%, 2%, and 2% respectively. Therefore, the above-mentioned meshes are used for subsequent calculations in this paper to ensure the accuracy of the results and the calculation efficiency.

3.4 Data Processing Method

The pressure drop increases with the increase in the heat transfer coefficient. Low pressure drop and high heat transfer coefficient are ideal targets in practical applications. The comprehensive effect of pressure drop and heat transfer is a key indicator for evaluating the performance of porous materials. In this paper, the dimensionless number j/f [22,23] is used to compare the comprehensive heat transfer characteristics of the three structures, and its formula is as follows: (6)j=NuRePr13 (7)f=ΔPΔL⋅2dhρu2 (8)h=WT1−T2 (9)Nu=hdhλ (10)Re=udhν (11)Pr=μcpλ (12)dh=4Sr(13)αsf=aVtotalwhere: j is the dimensionless surface heat transfer coefficient; f is the friction coefficient; ΔP is the pressure drop; ΔL is the flow direction length of the sample; dh is the hydraulic diameter; ρ is the air density; λ is the thermal conductivity of air; u is the inlet velocity; μ is the dynamic viscosity; ν is the kinematic viscosity of air; cp is the specific heat capacity at constant pressure; h is the heat transfer coefficient; W is the heat flux; T1 is the average temperature of the skeleton; T2 is the volume average temperature of the fluid; S is the cross-sectional area of the flow channel; r is the wetted perimeter. Nu is the Nusselt number; Re is the Reynolds number; Pr is the Prandtl number. a is surface area of the porous structure.

3.5 Simulation Verification

To improve the reliability of the numerical simulation, it is necessary to compare the experimental data with the simulation data to verify the accuracy of the simulation. The experimental system is shown in Fig. 4: the airflow is generated by an ASHIBA^®190 HG-1100L centrifugal blower (with a maximum flow rate of 180 m³/h); the air flow rate is measured by a URE^®LUG-192 2/2/03/Z/D/E/N flowmeter (with a range of 5–50 m³/h and an accuracy of ±1.5%); the air flow rate is accurately controlled by a frequency converter; the real-time monitoring and recording of data are completed by an Agilent^®195 34972A data acquisition unit; the heat source is a heating rod powered by a 60 V DC power supply (with a power of 60 W per rod), and its installation position is shown in Fig. 5 (blue coil); pressure sensors and K-type thermocouples are installed at the inlet and outlet of the system to measure the airflow pressure and temperature. To reduce randomness, multiple repeated experiments are conducted to ensure the stability and reliability of the data.

Figure 4 Overview of the test bench. Figure 5 Comparison between numerical simulation and test of pressure drop of Kelvin structure and BCC structure.

In the experiment, 6 heating rods are used, and the total heating power is controlled at 37.5 W. The fan speed is adjusted by the frequency converter to make the inlet air velocities 5, 7.5, 10, and 12.5 m/s. A comparison between the simulated and experimental results for the Kelvin and BCC structures is presented. Fig. 5 illustrates the pressure drop comparison for both structures, while Fig. 6 shows the heat transfer performance of the Kelvin structure. The results indicate that the simulation predictions follow the same trends as the experimental data.

Figure 6 Comparison between numerical simulation and experiment of heat transfer coefficient of Kelvin structure. 4 Results and Analysis 4.1 Flow Characteristics

The friction factor f is presented as a function of the Reynolds number to characterize the flow resistance behavior of different lattice structures. Here, f is defined based on a characteristic length associated with the lattice unit and the overall flow length. It should be noted that, due to the complex geometry of lattice structures, the characteristic length does not represent a unique physical diameter as in conventional channels. Therefore, the reported friction factor is primarily intended for comparative analysis among structures with identical porosity, geometric scale, and operating conditions. The variation of f with Reynolds number provides insight into the relative flow resistance trends of different lattice configurations rather than serving as a universally applicable friction correlation. Fig. 7 shows the curves of pressure drop vs. Reynolds number for the Kelvin, tetrahedral, and BCC structures with a porosity of 90%.

Figure 7 Liquidity performance comparison chart (<bold>a</bold>) Relation curve between pressure drop and Reynolds number; (<bold>b</bold>) Relation curve between pressure drop and friction factor.

When the inlet velocity is low (e.g., 10 m/s), the pressure drop of each structure is low. When the velocity increases to approximately 15 m/s, the pressure drop rises significantly; as the velocity further increases, the flow resistance increases, leading to a continuous increase in the pressure drop. At a velocity of 10 m/s, the pressure drops of the tetrahedral, BCC, and Kelvin structures are 326.502, 482.472, and 957.992 Pa respectively. When the velocity increases to 40 m/s, the pressure drops increase to 4160.37, 6289.04, and 10,103.3 Pa respectively. The data indicate that with the increase in velocity, the pressure drop of all structures increases significantly; the Kelvin structure has the highest pressure drop (especially at high velocities), and the tetrahedral structure has the lowest pressure drop.

The density of streamlines reflects the flow velocity (the denser the streamlines, the higher the flow velocity). As shown in Fig. 8, when air flows into the porous structure, the flow velocity increases significantly, and the velocity gradient at the narrow throat is relatively large.

Figure 8 Cloud diagram of streamline distribution of porous structure at inlet velocity 30 m/s. (<bold>a</bold>) Kelvin structure streamline distribution; (<bold>b</bold>) BCC structure streamline distribution; (<bold>c</bold>) Streamline distribution of tetrahedral structure. 4.2 Heat Transfer Characteristics

The relationship between the heat transfer coefficient and the Reynolds number is calculated and shown in Fig. 9.

Figure 9 Relation curve between heat transfer coefficient and Reynolds number.

As Reynolds number increases, the convective heat transfer coefficient of all lattice structures increases. However, the relative performance ranking among the Kelvin, BCC, and tetrahedral structures does not change across the investigated Reynolds number range, indicating consistent comparative trends. under the condition of Re = 2738, the Kelvin structure has the best heat transfer performance: it is 28.9% higher than the BCC structure and 34.6% higher than the tetrahedral structure. The heat transfer performance of the BCC structure is slightly better than that of the tetrahedral structure, with a difference of less than 6%.

In this study, the temperature distribution of the three structures at an inlet velocity of 30 m/s is analyzed through temperature contour maps. The results show that the high-temperature regions are concentrated on the leeward side, which is caused by the stagnation of airflow induced by the windward side of the skeleton and the resulting decrease in heat transfer efficiency. As shown in Fig. 10, the high-temperature regions on the leeward side of the middle (red region) and bottom structures are more significant, indicating that their heat transfer efficiency needs to be improved. The temperature distribution of the top (black region) structure is relatively uniform, suggesting that its heat transfer performance may be better. This indicates the importance of structural design for heat transfer efficiency and provides a basis for optimizing the design to reduce airflow stagnation and improve heat transfer efficiency. The Kelvin structure possesses a relatively high specific surface area, which implies that for an identical overall volume, it provides the largest fluid-solid contact area, creating a fundamental advantage for convective heat transfer.

Figure 10 Temperature cloud diagram of porous structure at inlet velocity 30 m/s.

Fig. 11a–c present the velocity contour plots for the tetrahedral, BCC, and Kelvin structures, respectively. The velocity contours indicate that the flow at the inlet and outlet is fully developed. A comparison reveals that in both the tetrahedral and BCC structures, the high-velocity regions are predominantly concentrated along the upper and lower sides of the flow channels, resulting in significantly non-uniform airflow distribution across the cross-section. In contrast, in the Kelvin structure, the flow channel exhibits a pronounced constriction in the throat region, creating a localized high-velocity zone. While this flow acceleration contributes to enhanced local heat transfer, it also inevitably leads to higher flow resistance.

Figure 11 Velocity cloud diagram of porous structure at inlet velocity 30 m/s. (<bold>a</bold>) Tetrahedral velocity contour plot; (<bold>b</bold>) BCC velocity contour plot; (<bold>c</bold>) Kelvin velocity contour plot. 4.3 Comprehensive Heat Transfer Performance

In this paper, the j/f j/f^1/2, and j/f^1/3 area goodness coefficient calculation method is adopted [24]. Fig. 12 shows the comprehensive heat transfer performance of the three structures at different inlet velocities using the j/f method (this method is more suitable for the condition of equal pressure drop). The tetrahedral structure demonstrates the highest overall thermal-hydraulic performance. As shown in Fig. 11a, its performance is 40.5% and 79.8% superior to that of the BCC and Kelvin structures, respectively.

Figure 12 Relationship between comprehensive heat transfer performance and Reynolds number under the <italic>j</italic>/<italic>f j</italic>/<italic>f</italic><italic>1</italic>/<italic>2</italic>, <italic>and j</italic>/<italic>f</italic><italic>1</italic>/<italic>3</italic> methods. (<bold>a</bold>) Relation curve between <italic>j</italic>/<italic>f</italic> and Reynolds number; (<bold>b</bold>) Relation curve between <italic>j</italic>/<italic>f</italic><italic>1</italic>/<italic>2</italic> and Reynolds number; (<bold>c</bold>) Relation curve between <italic>j</italic>/<italic>f</italic><italic>1</italic>/<italic>3</italic> and Reynolds number. 5 Conclusions

In this study, numerical simulations and analyses of the flow and heat transfer characteristics of three porous structures (Kelvin, BCC, and tetrahedral) were conducted using Fluent software. The results indicate that although the Kelvin structure exhibits higher flow resistance due to its larger windward area and geometric complexity, it demonstrates the best heat transfer performance among the three. Through systematic and controlled fair comparisons, evaluations based on comprehensive performance metrics, and in-depth analysis of flow-heat mechanisms, this study clarifies the trade-offs and differences in flow resistance and heat transfer efficiency among the different structures, thereby deriving conclusions with practical significance for engineering applications. Particularly in the selection of lightweight and high-efficiency heat exchange structures, this research provides new data support and theoretical perspectives, offering practical reference value for the design of high-performance compact heat exchangers in fields such as aerospace and energy equipment.

(1) Under the same inlet velocity, the Kelvin structure has the highest heat transfer coefficient, which is significantly better than that of the BCC and tetrahedral structures; its disadvantage in pressure drop does not affect its advantage in heat exchange.

(2) The high resistance of the Kelvin structure is due to its complex geometry and large windward area. Its pressure drop is 165.3% and 70.7% higher than that of the tetrahedral structure and BCC structure respectively; however, its complexity also brings a high heat transfer coefficient, which is 34.6% and 28.9% higher than that of the tetrahedral structure and BCC structure respectively.

(3) In addition to porosity, the shape and specific surface area also significantly affect the performance. In the j/f comparison, under conditions of a single porosity (90%) and a fixed heat flux density, the tetrahedral structure demonstrated the optimal overall performance, exhibiting enhancements of 40.5% and 79.8% relative to the BCC and Kelvin structures, respectively. In conclusion, the geometric characteristics of porous structures significantly affect their flow and heat transfer performance, and the design should be selected according to the application scenario. Although the Kelvin structure has a large pressure drop, its excellent heat transfer capacity makes it have significant advantages in engineering applications that require high heat transfer.

Not applicable.

Funding Statement

The authors received no specific funding for this study.

Author Contributions

The authors confirm contribution to the paper as follows: study conception and design: Yi Lu; data collection: Haigang Liu; analysis and interpretation of results: Yi Lu, Haigang Liu; draft manuscript preparation: Yi Lu; software: Liangliang Liu. All authors reviewed and approved the final version of the manuscript.

Availability of Data and Materials

Not applicable.

Ethics Approval

Not applicable.

Conflicts of Interest

The authors declare no conflicts of interest.

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