Finite element method-based investigation of heat exchanger hydrodynamics: Effects of triangular vortex generator shape and size on flow characteristics

The integration of thermal solar energy (TSE) into Renewable Energy Systems (RESs) has become a key focus in contemporary research, where TSE, involving the conversion of solar radiation into usable thermal energy via solar heat exchangers (SHEs), is complemented by the use of vortex generators (VGs) to enhance heat transfer in solar thermal systems (STSs) through controlled vortices, as highlighted in Table I by recent studies (e.g., Saravanakumar et al.,¹ Sharma et al.,² Khanlari et al.,³ Al-Aloosi et al.,⁴ Daliran and Ajabshirchi,⁵ Alshibil et al.,⁶ Zhu et al.,⁷ Rajaseenivasan et al.,⁸ Mohammadi and Sabzpooshani,⁹ and Romdhane¹⁰), offering a promising pathway to enhance the efficiency and sustainability of renewable energy applications in response to the global demand for clean energy sources.

The integration of VGs as both baffles and fins presents a promising method to enhance the performance of heat exchanger channels (HECs), as demonstrated by findings from various numerical and experimental studies summarized in Table II (e.g., Boonloi et al.,¹¹ Phila et al.,¹² Jayranaiwachira et al.,¹³ Alam et al.,¹⁴ Thianpong et al.,¹⁵ Eiamsa-ard et al.,¹⁶ Yang et al.,¹⁷ Promvonge and Skullong,¹⁸ and Muñoz-Cámara et al.¹⁹). Strategically, incorporating VGs into HECs optimizes fluid dynamics and heat transfer by exploiting controlled vortical structures. As baffles, VGs induce turbulence that disrupts the thermal boundary layer, enhancing heat exchange. When used as fins, VGs enhance convective heat transfer rates by improving airflow patterns and thermal mixing. This dual functionality makes VGs versatile components for improving both laminar and turbulent heat transfer regimes, thus significantly advancing the performance of HECs under various operational conditions.

Among the various parameters affecting VG performance, the inclination angle of these devices has received considerable attention in the literature. Studies by Arslan et al.,²⁰ Salhi et al.,²¹ Menni et al.,²² Xiao et al.,²³ Datta et al.,²⁴ Abidi and Sajadi,²⁵ Luan and Phu,²⁶ Eiamsa-ard and Chuwattanakul,²⁷ and Alqahtani et al.²⁸ consistently highlighted the importance of the inclination angle of VGs. This angle affects the size, strength, and stability of the vortices, which in turn impacts convective heat transfer in HECs.

Using VGs with various shapes, as shown by Eiamsa-ard and Promvonge,²⁹ Mohammadzadeh et al.,³⁰ Eiamsa-ard et al.,³¹ Kumar et al.,³² Kaewkohkiat et al.,³³ Chompookham et al.,³⁴ Mahdi et al.,³⁵ Zhang et al.,³⁶ Chamkha and Menni,³⁷ Chamkha et al.,³⁸ Salmi et al.,³⁹ Ameur et al.,⁴⁰ Medjahed et al.,⁴¹ and Menni et al.,^42–44 is a major step forward in improving VG performance and durability. This approach uses different VG shapes and configurations to optimize performance and create a more efficient design.

This study is focused on assessing how two distinct VGs affect the dynamics of turbulent airflow within a channel under steady-state conditions. The first VG is set in a staggered arrangement, featuring a rectangular shape placed in the upper section of the channel. The second VG, which is triangular, is positioned on the opposite wall at different heights from 40 to 80 mm. In addition, the triangular VG is analyzed in two configurations: one with an inclined front-face and another with an inclined rear-face. In particular, the study focuses on the following objectives:

• To analyze the performance of the rectangular VG positioned in the upper section of the channel.

• To examine the differences in flow dynamics caused by positioning the triangular VG in the lower section of the channel with either an inclined front-face or an inclined rear-face.

• To evaluate the impact of triangular VGs at various heights in 10 mm increments.

The computational domain simulated is illustrated in Fig. 1. It consists of a channel measuring 554 mm in length (L), featuring two distinct VGs with differing shapes and sizes. The first VG, rectangular in shape, is positioned in the upper section of the channel, 218 mm from the inlet (L₁). The second VG, which is triangular, is positioned on the opposite wall at distances of 355 mm from the channel inlet (L₂) and 159 mm from the channel outlet.

Two distinct cases are investigated to analyze the impact of the triangular VG structure. The first case entails a triangular VG with a front-face inclined toward the mainstream flow, as depicted in Fig. 1(a). Meanwhile, the second case features another triangular VG with a rear-face opposing the flow direction, as illustrated in Fig. 1(b). These cases are designed to analyze and compare the induced vortex structures and subsequent flow dynamics, providing insight into the role of the triangular VGs in shaping the flow within the HE channel.

During the simulation, the height of the rectangular VG remains fixed at h = 80 mm, while the height of the triangular VG (h_t) varies between 40 mm, half the height of the rectangular VG, and 80 mm, which is equal to the height of the rectangular VG.

The dimensions of the channel, including L, L₁, H, h, and e, were selected based on the experimental study carried out by Demartini et al.⁴⁵ 

The HE, characterized by turbulent airflow, operates under steady-state conditions with air as the working fluid, modeled as a Newtonian fluid. The standard K-epsilon turbulence model is applied.⁴⁶ The physical properties of the fluid, along with the characteristic parameters of the flow and the HE channel, essential for the mathematical formulation, are comprehensively outlined in Table III.

The HE channel is subjected to specific boundary conditions to simulate all scenarios being investigated. At the inlet, a uniform velocity profile (U_in) is imposed to represent the incoming airflow. At the outlet, the pressure is set to atmospheric conditions (P_atm). In addition, the non-slip and impermeable condition is imposed on the walls.

The numerical solution of the governing equations is obtained using the Finite Element Method (FEM), a well-established technique for discretizing and solving partial differential equations. COMSOL Multiphysics is used as the main tool for this numerical analysis. The mesh employed in the simulations adopts a non-uniform structure composed of triangular and square elements, ensuring accurate and systematic discretization. It is refined near the walls to better capture flow details and boundary layer effects, as illustrated in Fig. 2, enhancing the accuracy of the results and allowing for a more detailed examination of complex flow areas.

In both cases, the meshes exhibit similar compositions, with 20 225 triangles, 5808 quads, 849 edge elements, and 11 vertex elements in the first instance, and 20 129 triangles, 5808 quads, 849 edge elements, and 11 vertex elements in the second. The domain element statistics for the first case encompass a total of 26 033 elements, featuring a minimum element quality of 0.1678, an average element quality of 0.8192, an element area ratio of 0.002 141, and a mesh area of 79 280 mm². Similarly, the second case involves 25 937 elements, with a minimum element quality of 0.1714, an average element quality of 0.8183, an element area ratio of 0.002 17, and the same mesh area of 79 280 mm². These numerical representations provide detailed views of the mesh structures, helping compare element types and domain statistics between the two cases.

In this assessment, we examine flow characteristics by measuring the maximum axial velocity values (u_max) at the channel outlet, as shown in our initial case. To systematically evaluate how grid resolution affects accuracy, grids of different sizes are used. A grid with 26 033 elements performs well, with less than 0.5% error compared to a finer grid with 54 000 elements, making it a good balance between accuracy and efficiency. Thus, it is used throughout the study for the first case. A similar analysis for the second case leads to the use of a 25 937-element grid, which shows errors of less than 0.35% compared to the reference grid used for the first case.

Verification of numerical results is essential to ensure the reliability and accuracy of simulation processes. In this section, a numerical simulation was conducted on the same HE channel exchanger but with simplified VGs [see Fig. 3(a)] to assess axial velocity [see Fig. 3(b)] and compare it with the experimental results of Demartini et al.,⁴⁵ who conducted a study involving simple baffles as well. The inlet velocity is consistently and uniformly set to 7.8 m/s to maintain a consistent comparison. The comparison revealed quantitative and qualitative agreement along the cross-sectional station, x = 525 mm, examined near the channel outlet, as depicted in Fig. 3(c). After confirming the accuracy of the numerical model used, the same model is introduced for the present simulation.

Initially, the flow characteristics are evaluated for both cases of triangular VGs at a constant height (h_t) of 40 mm. The results revealed that as the airflow passed through a narrow gap from the upper edges of the first VG to the opposing lower wall, the P_d increased, reaching its maximum value near the edge of the triangular VG in both cases. The P_d values were optimized up to the outlet, indicating effective P_d maintenance along the flow path. In the initial scenario, the pressure values peaked at 502 Pa; see Fig. 4(a).

A significant improvement occurs in the next case, with the pressure levels rising to 624 Pa, as shown in Fig. 4(b). This substantial increase highlights the effectiveness of tilting the VG’s back-face, showing its crucial role in augmenting P_d. The rise from 502 to 624 Pa clearly demonstrates the significant improvement from this strategic adjustment in the VG’s design. However, a decrease in P_d was observed behind both VGs due to flow separation and vortex formation.

The analysis of velocity magnitude (V_m) in both cases, as shown in Fig. 5, displayed a similar behavior to the distribution of P_d. As the airflow moved through the narrow gap from the edges of the upper VG to the opposite bottom wall, V_m gradually increased, reaching its peak near the edge of the second VG in both cases. The V_m fields were consistently optimized throughout the flow path, continuing up to the exit, as illustrated by the velocity vectors in Fig. 6. This consistent enhancement along the flow path highlights the effectiveness of the studied configuration in maintaining and boosting flow velocities.

The alignment between the optimized V_m fields and the velocity vectors provides a clear visualization of the favorable changes induced by the studied parameters. However, a decrease in V_m was observed downstream of the VGs in both cases, due to vortex regions and flow separation. In assessing the speed, the first model with an inclined front-face showed an increase in V_m to 28.6 m/s, as shown in Fig. 5(a). In the presence of the second model with the inclined rear-face, this value increases by 11.53%, significantly improving the flow structure, as shown in Fig. 5(b).

The analysis of axial-velocity (u) distribution was conducted with the inlet velocity (U_in) set at 7.8 m/s, as shown in Fig. 7. An increase in u was observed below the initial set of VGs and above the second set. The maximum u is achieved near the upper wall of the channel, especially in the second case, near the outlet.

In contrast, negative axial velocities were noted behind the VGs due to pressure drops and the formation of recirculation cells from flow separation at the edges, as shown by streamlines in Fig. 8. The orientation of the second obstacle’s faces is crucial in shaping the flow characteristics of the entire channel. The inclination of the back-face of the second VG toward the entrance significantly enhances axial velocity, reaching about 31.9 m/s. However, this value decreases by about 11.91% when using the first model.

The distribution of vertical velocity (v) is investigated with an inlet velocity of 7.8 m/s, as shown in Fig. 9. Extreme v values were observed in both positive and negative directions. In the negative direction, the highest v values were seen around the leading edge of the first VG, as it directed airflow downward. In the positive vertical direction, the highest v values consistently appeared near the edge of the triangular VG in both cases. The second configuration of triangular VGs showed a significant increase in v, due to its vertical front area. In contrast, the first case showed a smaller increase in v because of its inclined front-face. These results highlight the significant impact of the triangular VG’s geometry, especially the inclined back-face, on the distribution of vertical velocity and the resulting flow characteristics.

The distribution of turbulence kinetic energy (k) is analyzed at an inlet speed of 7.8 m/s, as shown in Fig. 10. The analysis revealed distinct patterns in the distribution of k throughout the flow field. High k values were mainly observed in areas with flow separation and vortex formation, which are characterized by flow disturbances. These areas, especially around the edges and corners of the VGs, showed increased k energy, indicating enhanced turbulence generation and dissipation. Conversely, regions with smoother flow and fewer disturbances showed lower k energy values in both cases studied.

The inclination of the VG’s rear-face resulted in higher k energy due to the more turbulent flow created by this configuration. The inclined rear-face introduces additional flow disturbances and induces a higher level of turbulence compared to the other case. This increased turbulence leads to higher levels of k energy in the flow. This comparison highlights the substantial impact of the triangular VGs, especially those configured with a right-side inclination opposing the flow direction. This design significantly amplifies flow turbulence, intensifies recirculation zones, and disrupts flow dynamics more noticeably.

The analysis of turbulence intensity (TI) distribution is conducted at a constant inlet velocity of 7.8 m/s for both studied scenarios, as illustrated in Fig. 11. The results revealed variations in TI across different regions of the flow field. A high TI was observed behind the VGs, where the recirculation zones are situated. Moreover, an extensive region of higher intensities was observed, centered next to the upper wall, above the triangular VGs. Its TI reached about 67.1% in the first case, while it increased by about 1.49% in the second case.

To evaluate the effect of the triangular VG configurations, we analyzed axial velocity curves (u/U_in) at locations corresponding to the recirculation zones behind both the upper and lower VGs. Figure 12 shows how these configurations affect the size of the recirculation area behind the upper VG. We examined two transverse locations in the upper section of the channel, at x = 0.25 m [Figure 12(a)] and x = 0.28 m [Fig. 12(b)]. The figure reveals negative velocity values, indicating the presence of recirculation cells in these areas. In addition, the triangular VG in the second case, with a vertical front-face and tilted rear face, significantly enhances flow strength and disturbances.

This improvement helps create recirculation cells with a longer recirculation length compared to the first triangular VG case, showing better performance. The same effect is seen on the rear-side of the lower VG. Here, the recirculation region with negative velocity values becomes more intense and longer when using the triangular VG in the second configuration (at x = 0.42 m in Fig. 13(a) and x = 0.52 m in Fig. 13(b).

The vertical leading face of the second triangular VG increases the vertical component of the velocity (y-speed) and extends the length of the recirculation region behind the VG. In the lower gap, at the axial location x = 0.223 m, velocity values rise significantly in both cases, reaching 2.5 times the inlet velocity (see Fig. 14). In this area, the effect of the second VG’s geometry on the velocity profiles is less pronounced.

On the other hand, the u/U_in profiles are measured in the second gap at x = 0.375 m. As expected, these values have increased significantly due to the higher flow pressure caused by the second VG (see Fig. 15). In the first case, the velocity increased to about 2.43 times the inlet velocity, while in the second case, it increased to around 2.66 times the inlet velocity.

The effect of the second VG on flow velocity at the channel outlet is also shown. In both cases, the velocity increased, reaching 26.17 m/s in the first case and 27.93 m/s in the second case, which are 3.35 and 3.85 times the inlet velocity, respectively (see Fig. 16). The 6.72% increase compared to the initial case highlights the importance of the triangular VG with a slanted back-face in improving flow in the simulated HE channel.

This section of the simulation examines how changing the inlet velocity from 7.8 to 9.8 m/s affects flow characteristics at h_t = 40 mm.

It first analyzes the evolution of axial velocity by studying the recirculation cells behind the triangular VG on the lower side of the channel at two positions, x = 0.42 m and x = 0.52 m [see Figs. 17(a) and 17(b)]. Next, the axial velocity in the positive direction is examined at two locations. The first location, x = 0.223 m, runs from the end of the first VG to the bottom wall [see Fig. 18(a)]. The second location, x = 0.375 m, extends from the end of the second VG to the upper wall [also in Fig. 18(a)]. By varying the inlet flow velocity as 7.8, 8.8, and 9.8 m/s, it is clear that increasing the velocity enhances the flow structure by expanding the recirculation cells and augmenting their velocity in the negative direction. In addition, the flow becomes stronger from left to right through the gaps. This analysis confirms that the second type of triangular VGs improves flow characteristics across all tested inlet velocities.

To better understand how triangular VGs perform, simulations were conducted at various heights, as illustrated in Fig. 19. Heights (h_t) ranged from 40 to 80 mm, with specific tests conducted at 40, 50, 60, 70, and 80 mm.

Initially, with the triangular VG having an inclined front-surface, and at the lowest inlet velocity of 7.8 m/s, the axial velocity was 28.1 m/s at the lowest studied height of 40 mm. Increasing the height to 50 mm enhanced the flow velocity to ∼29.9 m/s, representing an increase of about 6.4%. This improvement in velocity continued with the triangular VG’s height increase, reaching around 32 and 34.5 m/s at heights of 60 and 70 mm, corresponding to increases of ∼13.9% and 22.8%. The maximum velocity was observed at the highest height of 80 mm, where it reached 37.6 m/s, improving by 33.8% compared to the lowest height and by 382.1% compared to the inlet velocity. This progressive enhancement in velocity is attributed to the gradual increase in the triangular VG height, which reduces the flow area above the same VG.

The same phenomenon was observed with the second model of the triangular VG with an inclined back-surface, but with greater improvements. At the smallest height, the axial velocity was about 31.9 m/s, improving by 13.5% compared to the first model and by 308.7% compared to the inlet velocity. At the medium height of 60 mm, the axial velocity reached 37.3 m/s, which is an increase of 16.6% compared to the first model at the same height. Moreover, the highest axial velocity recorded was 44 m/s at the maximum simulated height, an improvement of 17.0% compared to the first model at the same height.

Increasing the inlet velocity further amplifies the effect of triangular VG size on axial velocity values in both cases. When the inlet velocity is increased to 8.8 m/s, the flow velocity reaches its peak at the maximum height, and in the second model, it reached 49.7 m/s, representing an improvement of 17.2% compared to the first model. Furthermore, with a continuous increase in the inlet velocity to 9.8 m/s, the axial velocity increased to 47.3 m/s in the first model and 55.3 m/s in the second model.

The analysis of axial velocity values shows that increasing the height of the triangular VG greatly augments flow turbulence. This occurs because the flow area decreases and the velocity, especially in the vertical direction, increases. As a result, the size of the recirculation cells around the VGs grows. In the second model, these recirculation cells have higher axial velocity values in the opposite direction, which further increases the direct flow velocity.

This study provides comprehensive insights into the dynamic responses within a channel equipped with VGs, highlighting the significant effects on flow distortions and recirculation zones. The effectiveness of both rectangular and triangular VGs in enhancing flow dynamics within HE channels has been demonstrated:

• Both rectangular and triangular VGs significantly enhance flow patterns and recirculation zones within the channel.

• Tilting the back-face of triangular VGs improves the airflow structure of the HE channel.

• Increasing the height of triangular VGs enhances flow velocity significantly:

  • A 33.8% increase when VG height is raised from 40 to 80 mm in one case.

  • About a 37.9% increase in another case at the lowest inlet velocity of 7.8 m/s.

• Triangular VGs with an inclined back-surface achieve higher axial velocities compared to those with an inclined front-surface:

  • A 13.5% increase at the smallest height.

  • A 17.0% increase at the maximum height.

• Raising the inlet velocity to 9.8 m/s resulted in a 17.1% higher axial velocity in the second model, reaching 55.4 m/s compared to 47.3 m/s in the first model.

The authors extend their appreciation to the Deanship of Research and Graduate Studies at King Khalid University for funding this work through Large Research Project under Grant No. RGP2/352/45.

The authors have no conflicts to disclose.

Sultan Alqahtani: Investigation (equal); Software (equal); Writing – review & editing (equal). Noureddine Kaid: Methodology (equal); Validation (equal); Writing – original draft (equal). Mohammad Salman Haque: Formal analysis (equal); Supervision (equal); Writing – review & editing (equal). Younes Menni: Methodology (equal); Supervision (equal); Writing – original draft (equal).

The data that support the findings of this study are available within the article.