2.1. Geometric modeling

Three models were created in SolidWorks, each with riser lengths of 4.45 m, 5.45 m, and 6.45 m, respectively. The risers had circular cross-sections with a diameter of 8 mm. In contrast, the headers featured a larger diameter of 35 mm to facilitate proper flow distribution. To simulate realistic inlet and outlet conditions, each model incorporated upper and lower headers. An image of the large-scale FPC is shown in Figure 1, while Figure 2 presents the detailed geometry of the corresponding risers and headers used in the CFD model.

Figure 1. Overview of the large-scale FPC system showing the large-scale unit (A) and a close-up view of the riser tubes and header section (B).

Figure 2. Geometric model of the risers and headers.

2.2. The meshing

The geometries were imported into ANSYS Meshing for grid generation. A tetrahedral mesh was used, with inflation layers added near the wall regions to accurately resolve velocity and temperature gradients. Mesh independence studies were carried out for each configuration, confirming numerical stability with an average element size of 5 mm. The meshing approach and structure for the riser are illustrated in Figure 3.

Figure 3. Meshing structure for the riser.

To verify that the numerical results were not sensitive to mesh resolution, a mesh independence study was carried out for the 5.45 m riser as a representative case. Three meshes were generated by progressively refining the grid while keeping the boundary conditions unchanged. For each mesh, steady-state simulations were performed, and the outlet temperature was monitored as the primary indicator of solution accuracy.

As summarized in Table 1, increasing the mesh from the Mesh 2 to Mesh 3 level altered the riser outlet temperature by less than 0.2%. This confirms that further mesh refinement has a negligible effect on the solution. Consequently, the Mesh 2 was adopted for all subsequent simulations as an appropriate compromise between accuracy and computational cost.

Table 1. Results of the mesh independence study for the 5.45 m riser.

2.3. Domains and boundary conditions of the riser

The simulations were performed under steady-state conditions. A uniform inlet flow velocity of 0.4 m/s was applied, using a 50% glycol–50% water mixture at an inlet temperature of 15 °C as the working fluid. Heat flux boundary conditions were imposed on the outer surfaces of the riser tubes: 750 W/m² on the sun-facing side and 100 W/m² on the shaded side. The tube walls were modeled as thermally conductive copper, and conjugate heat transfer (CHT) was enabled to account for heat conduction within the solid and convective transfer in the fluid. Atmospheric pressure was specified at the outlet, while all wall surfaces were assigned a no-slip boundary condition. The computational domain consisted of three main boundaries: the inlet, the outlet, and the wall surfaces. An illustration of the computational domain for the riser is presented in Figure 4.

Figure 4. Domains and Boundary Conditions of the Riser. A: Inlet, B: Outlet, and C: Riser Wall.

In the real collector, the riser tubes are soldered to a flat absorber plate located beneath a transparent cover, and the entire assembly is subject to optical and thermal losses due to reflection, convection, radiation and conduction [24]. In the present CFD model, these loss mechanisms are not resolved explicitly. Instead, their combined effect is represented through prescribed heat flux boundary conditions of 750 W/m² on the sun-facing side (corresponding to an overall loss of about 21% for an incident irradiation of 950 W/m²) and 100 W/m² on the shaded side of the riser due to radiative exchange. These values are taken to represent the net heat transferred from the absorber plate to the tube wall under typical operating conditions, i.e. after accounting for top, bottom and edge losses at the collector level.

Because the risers are heated along their length, buoyancy is expected to influence the flow to some degree. Therefore, gravitational acceleration was explicitly included in the simulations as g=-9.81 m/s² in the vertical direction, aligned with the riser axis. Buoyancy effects in the fluid were modeled using the Boussinesq approximation.

2.4. Solver configuration

ANSYS Fluent's pressure-based solver was utilized, employing the realizable k–ε turbulence model for solving the momentum equations, along with the energy equation to account for thermal effects. All governing equations were discretized using second-order schemes to ensure higher accuracy. Convergence was considered achieved once the residuals for energy, momentum, and continuity equations fell below their respective thresholds.

The simulations were performed in ANSYS Fluent using a steady-state, pressure-based solver. Pressure–velocity coupling was handled with the SIMPLE algorithm, and pressure was discretized with a second-order scheme [25]. The momentum and energy equations were both solved using second-order upwind discretization to reduce numerical diffusion and improve the accuracy of the predicted velocity and temperature fields. Spatial gradients were evaluated with the Green–Gauss cell-based method.

Convergence was monitored using both residuals and integral quantities. In all cases, the scaled residuals were reduced below 10^-4 for continuity and momentum, and below 10^-6 for the energy equation. In addition, the outlet temperature and pressure drop were tracked to ensure that they had reached steady values before the solution was accepted as converged.

The working fluid, a 50% glycol–50% water mixture, was modeled as a temperature-dependent. Density, dynamic viscosity, thermal conductivity, and specific heat capacity were defined as functions of temperature for glycol–water mixture representative properties at 15 °C are given in Table 2 [26]. These properties were implemented in Fluent as temperature-dependent polynomials, allowing the local Reynolds and Prandtl numbers to be represented more realistically along the riser and leading to more accurate predictions of both heat transfer and pressure losses.

Table 2. Representative thermophysical properties of a 50% glycol–50% water mixture at 15 °C.

Near the walls, inflation layers were used to resolve the boundary layer. The first cell height was selected so that the non-dimensional wall distance y⁺ of the first node typically lay in the range 30–80, with an average value of about 45. This range is suitable for the realizable k–ε turbulence model with standard wall functions and ensures that the near-wall region is treated consistently with the chosen turbulence modeling approach [25].

3.1. Temperature distribution

The temperature distribution within each riser tube exhibited a distinct gradient from inlet to outlet, shaped primarily by the applied surface heat flux and the total riser length. As riser length increased, outlet temperatures rose accordingly, highlighting the combined influence of residence time and available heat transfer surface area on thermal performance.

For the shortest riser (4.45 m), the fluid temperature increased from 15 °C to 89.63 °C (Figure 5). The steep temperature gradient along the tube indicated efficient convective heat transfer and minimal thermal losses. Due to the short residence time, the heat transfer fluid (HTF) experienced limited energy accumulation, resulting in a lower outlet temperature. Such a configuration is well-suited for systems requiring lower outlet temperatures or high-throughput operation, where rapid and stable heat exchange is essential.

Figure 5. Temperature distribution along the 4.45 m riser.

In the intermediate case (5.45 m), the outlet temperature reached 96.8 °C (Figure 6). The gradient was more moderate, suggesting a balanced trade-off between thermal gain and convective efficiency. The increased residence time enabled more effective energy absorption while maintaining stable flow behavior. Although the thermal driving force naturally declined near the outlet, overall convective performance remained sufficient. Stratification risks in this configuration can be effectively mitigated through proper flow control, making this riser length a practical choice for large-scale solar thermal systems seeking a balance between efficiency and operational safety.

Figure 6. Temperature distribution along the 5.45 m riser.

The longest riser (6.45 m) yielded the highest outlet temperature of 103.61 °C, indicating maximum thermal energy gain (Figure 7). However, this also brought the system close to stagnation conditions. Stagnation temperature defined as the maximum temperature the fluid reaches when flow is interrupted, such as during pump failure poses a significant risk to system integrity. According to ISO 9806 and Duffie & Beckman (2013), the critical stagnation range for water-based systems lies between 100 °C and 120 °C [27]. The outlet temperature in the 6.45 m riser falls within this sensitive range, raising concerns over vapor formation, increased material stress, and reduced long-term reliability under off-nominal conditions. Additionally, the temperature gradient flattens near the outlet, signaling a reduction in convective effectiveness due to a weakened thermal driving force. The extended residence time further amplifies the system’s sensitivity to flow disturbances and increases the potential for thermal stratification. ISO 9806 type tests and manufacturer data for the large-scale FPC report stagnation temperatures between 100 °C and 120 °C for water-based operation [27]. Using these measured values as a reference, the 6.45 m riser can be considered to operate within the stagnation band, which raises concerns about vapor formation, increased material stress, and reduced safety margins under off-nominal conditions such as pump failure.

Figure 7. Temperature distribution along the 6.45 m riser.

Overall, the analysis of temperature distribution across the different riser lengths reveals clear trade-offs between thermal efficiency and system stability. Shorter risers enhance convective performance and mitigate thermal risks, while longer risers maximize energy absorption but require more sophisticated control strategies to prevent stagnation and ensure safe operation under varying conditions.

3.2. Velocity distribution

While Section 3.1 examined the thermal response of the different riser lengths, this section turns to the flow behavior, as velocity distribution and viscous resistance are key drivers of pressure drop, pump sizing and overall system stability. The outlet velocity profiles for all three riser configurations are predominantly parabolic, consistent with fully developed laminar flow. Nonetheless, changes in riser length introduce subtle but important differences that influence both thermal performance and hydraulic losses.

For the 4.45 m riser, the peak outlet velocity is approximately 0.53 m/s (Figure 8). The velocity profile retains a classic parabolic shape, indicating well-developed and uniform axial flow. Owing to the shorter flow path, frictional resistance is the lowest among the three cases, giving a frictional pressure drop of about 2.7 kPa per riser and a corresponding pumping power of roughly 0.054 W at the reference operating point. This configuration is therefore attractive in applications where high throughput and low electrical power consumption of the pump are prioritized.

Figure 8. Velocity distribution at the outlet of the 4.45 m riser.

The 5.45 m riser exhibits a slightly higher peak velocity of around 0.605 m/s (Figure 9). Its velocity profile is flatter than that of the 4.45 m case, likely due to the longer residence time and stronger interaction with the heated wall. Despite this, the flow remains stable and fully developed. The increased length raises viscous resistance, resulting in a pressure drop of about 3.3 kPa and a pumping power of approximately 0.066 W per riser. This arrangement preserves good flow uniformity while the longer residence time supports enhanced heat transfer, making it a strong compromise between energy capture and hydraulic penalties.

Figure 9. Velocity distribution at the outlet of the 5.45 m riser.

In the 6.45 m riser, the peak velocity increases only slightly to about 0.61 m/s, but the profile shows more pronounced decay near the tube walls (Figure 10). This additional flattening and peripheral damping indicate higher viscous resistance along the extended wetted surface. As a result, the frictional pressure drop increases to roughly 3.56 kPa, with an associated pumping power of about 0.076 W per riser. These higher losses suggest that, although the 6.45 m riser improves the outlet temperature, it does so at the expense of greater pumping demands and a narrower hydraulic safety margin.

Figure 10. Velocity distribution at the outlet of the 6.45 m riser.

Overall, all three riser lengths maintain essentially parabolic, fully developed laminar profiles. However, the 5.45 m riser offers the most favorable combination of velocity distribution, pressure loss, and pumping power. It provides better thermal performance than the 4.45 m case while avoiding the relatively high pressure drop of the 6.45 m configuration, making it a promising choice for stable and energy-efficient operation in large-scale FPCs. A summary of the pressure losses and pumping powers per riser at the design operating point is given in Table 3.

Table 3. Pressure drop and pumping power per riser for varying riser lengths.

3.3. Model verification

The numerical model was verified to ensure that the results were not influenced by discretization errors. Mesh quality was assessed through the mesh-independence study described in Section 2.2.1, where three different meshes were tested for the 5.45 m riser. As summarized in Table 1, increasing the resolution from Mesh 2 to Mesh 3 changed the riser outlet temperature by less than 0.2%, indicating that further refinement has a negligible impact on the solution. Mesh sensitivity levels of this order typically below about 1% variation in key thermal quantities are generally considered acceptable in CFD studies of internal flows and heat-transfer systems [28,29].

Convergence was also assessed using both residuals and integral quantities. In all simulations, the scaled residuals were reduced below 10^-4 for continuity and momentum and 10^-6 for the energy equation, while the outlet temperature reached a stable value over successive iterations. These convergence criteria are consistent with common practice in CFD analyses of solar collectors [30,31].

Under the considered conditions, the 5.45 m riser yielded a simulated outlet temperature of 96.81 °C, which lies within the measured operating range of 90–100 °C for the collector. Likewise, the 6.45 m riser produced an outlet temperature of 103.61 °C, within the experimentally observed stagnation temperature band of 100–120 °C. This band is consistent with the critical stagnation temperatures reported for water-based FPCs in ISO 9806 and standard solar thermal design literature [27,32]. Overall, this verification and validation process supports the reliability of the present CFD model in representing the thermal performance of the riser tubes under the conditions investigated.

3.4. Energy and exergy efficiency analysis

In this work, three different riser lengths were investigated for the large-scale FPC: 4.45 m, 5.45 m, and 6.45 m. All risers have an inner diameter of 8 mm and are operated with a 50% glycol-50% water mixture entering the collector at 15 °C. The fluid velocity in each riser is 0.4 m/s, which, together with the density (ρ = 1061 k/m³), results in a mass flow rate of approximately 0.0213 kg/s per riser. The specific heat capacity of the fluid is taken as 3348 J/kgK. On the thermal side, the absorber is modelled with a non-uniform heat flux: one half of the riser circumference is irradiated with 750 W/m² and the other half with 100 W/m², representing the non-uniform optical conditions over the absorber plate. For the performance evaluation, the global irradiance G_T is taken 950 W/m² and the ambient temperature is at 15 °C.

On the basis of the overall assessment, a clear pattern emerges. If only energy and exergy indicators are considered, the 6.45 m riser appears to be the most favorable option, as it delivers the highest useful heat together with the highest thermal and exergy efficiencies at the given operating point.

However, this gain in performance is accompanied by a drawback that is critical for practical operation. The outlet temperature of the 6.45 m case (~103.6 °C) lies close to the measured stagnation range (100–120 °C) of the reference collector, which reduces the safety margin under low-flow or no-flow conditions.

The shortest riser (4.45 m) avoids this issue but clearly underperforms in both thermal and exergy terms. The intermediate 5.45 m configuration provides a more balanced compromise: high thermal and exergy efficiencies are still achieved, only slightly lower than those of the 6.45 m case, while outlet temperatures remain at a more acceptable level. Therefore, when energy and exergy performance are evaluated alongside stagnation safety, the 5.45 m riser is identified as the optimal configuration for the large-scale FPC studied here.

Consent for Publication

Not applicable.

Availability of Data and Material

The data presented in this study are available on request from the corresponding author due to project restriction.

Funding

The European Union Project- SolarHub has received funding from the Horizon 2020 Widera research and innovation program under grant agreement No 101086110. The work published in this conference article was supported by the SolarHub project as part of Task 3.1 activities.

Competing Interests

The authors have declared that no competing interests exist.

Author Contributions

Conceptualization: Yusuf Karakaş, Tuba Okutucu-Özyurt; Methodology Yusuf Karakaş, Tuba Okutucu-Özyurt; Software: Yusuf Karakaş, Sevan Karabetoğlu Validation: Yusuf Karakaş, Rosie Christodoulaki, Harry Michalopoulos; Formal Analysis: Yusuf Karakaş; Investigation: Yusuf Karakaş; Resources: Yusuf Karakaş; Data Curation: Yusuf Karakaş.; Writing – Original Draft: Yusuf Karakaş.; Writing – Review & Editing: Tuba Okutucu-Özyurt, Rosie Christodoulaki, Harry Michalopoulos, Sevan Karabetoğlu, Vasiliki Drosou; Visualization: Yusuf Karakaş; Supervision: Tuba Okutucu-Özyurt; Project Administration: Tuba Okutucu-Özyurt, Vasiliki Drosou; Funding Acquisition: Vasiliki Drosou.