The Potential of Periodic Cellular Lattice Structures
In the pursuit of more efficient compact heat exchangers (CHXs), researchers have explored diverse thermal-hydraulic performance (THP) enhancement techniques over the past few decades. When seeking approaches to intensify heat transfer rates while minimizing pressure drop penalties, design challenges abound. The main goal in improving the THP of fin-and-tube heat exchangers (FTHXs) or designing innovative ones is to enhance heat transfer between hot/cold fin-tube surfaces and the fluid flow.
Extended surfaces, such as fins, are one of the most significant components of FTHXs and a popular passive heat transfer enhancement method. Optimizing the fin geometry pattern is a beneficial way to enhance air-side heat transfer in FTHXs. Researchers have explored various fin patterns, including wavy, interrupted (slit, offset-strip, louvered, convex-louver, corrugated, and perforated), and enhanced fins with vortex generators, dimples, meshes, and peripheral designs.
However, the engineering and optimization of pumping power (i.e., reducing pressure drop) is also crucial in thermal management applications. Elliptical-tube CHXs, known as fin-and-elliptical tube heat exchangers (FETHXs), have garnered attention due to their ability to reduce pressure loss and pumping costs.
Cellular Materials: A Novel Approach to Thermal-Hydraulic Enhancement
In recent years, researchers have focused on innovative architectures and materials to enhance the efficiency and performance of heat exchange equipment. One such advancement is the use of cellular materials (CMs), which have shown tremendous potential in various thermal engineering applications.
CMs are porous structures with a high surface-area-to-volume ratio (typically 500 to over 10,000 m^2/m^3), highly conductive lattice frameworks, ultra-low weight, and high strength characteristics. These properties make CMs attractive for compact heat exchangers, thermal energy storages, electronics heat sinks, and fuel cells, as they can promote flow mixing and turbulence, leading to improved heat transfer performance.
Among the different types of CMs, periodic cellular lattice (PCL) materials have gained attention for their superior thermal-hydraulic performance compared to stochastic foams. PCL structures comprise a repetitive space meshwork of longitudinal, transverse, and diagonal cylindrical ligaments (or struts) with constant cross-sections and vertices (or nodes). The regular topology of PCL structures allows for better flow mixing and lower pressure drop compared to random foam structures.
Experimental and numerical investigations have shown that the solid ligaments in PCL structures generate spiral and counter-rotating vortices, leading to enhanced flow mixing and heat transfer efficiency. Previous studies have also demonstrated that the effective thermal conductivity of PCL materials is about two to three times higher than that of metal foams with similar porosity.
Leveraging PCL Structures for Air-Cooled Heat Exchanger Enhancement
Building on the potential of PCL materials, the present study introduces a novel trussed fin-and-elliptical tube heat exchanger (FETHX) that integrates high-porosity PCL structures as the core. The key objectives are to:
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Investigate the influence of PCL morphological parameters, such as lattice structure topology (simple cubic, body-centered cubic, reinforced body-centered cubic, face-centered cubic, and reinforced face-centered cubic) and porosity (92% and 98%), on the thermal-hydraulic performance of the trussed FETHX.
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Analyze the complex flow patterns and heat transfer mechanisms within the trussed FETHX with PCL structures using computational fluid dynamics (CFD) simulations.
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Evaluate the thermal-hydraulic performance of the trussed FETHX with PCL structures using advanced techniques, such as the field synergy principle and performance evaluation criteria.
Modeling the PCL Structures
The PCL structures considered in this study can be represented by five types of regular unit cells (UCs): simple cubic (SC), body-centered cubic (BCC), reinforced body-centered cubic with vertical ligaments (BCCZ), face-centered cubic (FCC), and reinforced face-centered cubic with vertical ligaments (FCCZ). Figure 3 illustrates the 3D-CAD models of these PCL structures, highlighting the key geometric parameters:
- Ligament diameter (d_l)
- Ligament length (l)
- Ligament inclination angle (θ)
- Unit cell height (H)
- Unit cell width and length (S)
The porosity (ε) of the PCL structures can be calculated using the following equation:
ε = 1 – (V_lig / V_uc)
Where V_lig is the volume of the ligaments, and V_uc is the overall volume of the unit cell.
Trussed Fin-and-Elliptical Tube Heat Exchanger (FETHX) with PCL Structures
The trussed FETHX with PCL core structures is modeled as a three-dimensional computational domain, as shown in Figure 4. The PCL core is located between adjacent plain fins, with the vertices attached to the lower and upper fin surfaces. For the BCC, BCCZ, FCC, and FCCZ lattice structures, there are also vertices on the middle plane between the two adjacent fin surfaces.
The detailed geometric parameters of the FETHX are provided in Table 2. The computational domain includes the upstream and downstream regions of the FETHX to maintain a uniform inlet velocity and minimize the influence of flow disturbance and recirculation at the outlet.
Numerical Modeling and Validation
The flow governing equations, including the continuity, momentum, and energy equations, are solved using the Menter Shear Stress Transport (SST) κ-ω turbulence model. This hybrid model is recommended for accurately predicting the flow characteristics in FTHXs with flow manipulators or turbulators at Reynolds numbers greater than 500.
To ensure the reliability of the CFD simulations, the numerical model was validated against experimental data from the literature for a conventional FTHX (Figure 6) and against pressure drop correlations for PCL materials (Figure 7). The results demonstrate good agreement, validating the modeling approach.
Insights into the Thermal-Hydraulic Performance of Trussed FETHXs with PCL Structures
Flow Patterns and Heat Transfer Mechanisms
The CFD simulations reveal the complex flow patterns and heat transfer mechanisms within the trussed FETHX with PCL structures. The presence of the PCL ligaments and vertices induces the formation of various secondary flow vortices, including horseshoe and arch-shaped vortices, as well as flow separation on the ligament surfaces (Figures 8-11).
These flow disturbances promote turbulence and mixing, leading to significant enhancements in heat transfer performance. The PCL structures with lower porosity (92%) exhibit stronger vortex intensity and smaller wake regions behind the elliptical tubes, resulting in better thermal-hydraulic performance compared to the higher porosity (98%) cases.
Influence of PCL Morphological Parameters
The numerical results demonstrate that the topology and porosity of the PCL structures significantly impact the thermal-hydraulic performance of the trussed FETHX.
Average Nusselt Number (Nu):
– Decreasing the porosity from 98% to 92% leads to an increase in the average Nusselt number for all PCL structures (Figure 16).
– The BCCZ and FCCZ lattice structures exhibit the highest average Nusselt numbers among the investigated cases, attributed to their better flow disturbance and mixing capabilities.
Friction Factor (f):
– As the porosity increases to 98%, the friction factor decreases significantly, indicating a reduction in the pressure drop penalty (Figure 17).
– The SC and BCC lattice structures have the lowest friction factors due to their lower channel blockage and surface drag.
Field Synergy Principle (FSP):
– The trussed FETHX with PCL structures shows a higher average field synergy number (F_c) compared to the baseline case without PCL, indicating better synergy between the velocity and temperature gradient fields (Figure 18).
– The BCCZ lattice structure with 92% porosity exhibits the highest F_c, demonstrating superior heat transfer enhancement.
Performance Evaluation Criteria (PEC)
To holistically assess the thermal-hydraulic performance of the trussed FETHX with PCL structures, two PEC indices were evaluated:
- Modified Flow Area GF (j/f^(1/3) vs. Re_Dh): This criterion indicates the direct analogy of the j/f^(1/3) ratio as a function of Reynolds number, which is crucial for identifying the extended surface that requires the minimal frontal area for a constant pressure loss penalty.
- Core Volume GF (Z vs. E): This criterion compares the isothermal heat transport per unit core volume (Z) to the pumping power required per unit core volume (E), providing insights into the overall thermal-hydraulic efficiency.
The results show that the BCCZ lattice structure with 92% porosity and the FCCZ lattice structure with 98% porosity exhibit the best performance in terms of the flow area GF and core volume GF, respectively (Figures 19-20).
When comparing the trussed FETHX with PCL structures to other enhanced FTHX designs, the BCCZ lattice structure with 92% porosity demonstrates the highest overall thermal-hydraulic performance (Figure 21).
Conclusion
The present study highlights the significant potential of integrating high-porosity periodic cellular lattice (PCL) structures into air-cooled heat exchangers to enhance thermal-hydraulic performance. The key findings are:
- The complex flow patterns induced by the PCL ligaments and vertices, including horseshoe and arch-shaped vortices, promote turbulence and mixing, leading to substantial heat transfer improvements.
- Decreasing the porosity of the PCL structures from 98% to 92% results in an increase in the average Nusselt number, while the friction factor decreases, indicating a better balance between heat transfer and pressure drop.
- The BCCZ and FCCZ lattice structures exhibit the best thermal-hydraulic performance among the investigated PCL topologies, with the BCCZ at 92% porosity providing the overall optimal performance.
- The trussed FETHX with PCL structures outperforms other enhanced FTHX designs, demonstrating the effectiveness of this novel approach in improving air-cooled heat exchanger efficiency.
These findings highlight the tremendous potential of PCL structures in advancing the design and performance of air-cooled heat exchangers, paving the way for more efficient thermal management solutions across various industries. By leveraging the unique properties and flow characteristics of these periodic cellular materials, engineers can unlock new levels of thermal-hydraulic enhancement for critical heat transfer applications.
