5.1. Flow Dynamics Analysis
The geometry in this section was designed using an open-source program without any simplifications or symmetry planes. Using the SALOME platform (v. 9.8.0), the discretization’s element density was significantly higher than the grid utilized with proprietary software. Substantial benefits were observed using the open-source platform; for example, it is possible to study the three-dimensional flow behavior and the wake development that occurs between the channels of fins using non-steady numerical simulations. The results of the numerical simulations that were calculated using OpenFOAM are presented. (The section on
Supplementary Materials has a download link for an animation of the three-dimensional flow behavior at three different angles. This animation uses an open-source platform to make it simpler to visualize and understand the results of non-steady state numerical simulations.)
The calculation process completed 20 s. The figures depict the flow behavior at different process times, as well as the development of the flow along the duct. A quasi-stationary flow behavior was established after the initialization of the simulation. Approximately 10 s of process were necessary to observe stable flow conditions in the simulation analysis.
Figure 5 uses an isometric back perspective of the numerical simulation results to depict the fourth and fifth channel of fins attached to a cylinder. The flow hits the angled fins and flows horizontally close to the fin’s edge, as shown by 3D vectors colored by flow velocity magnitude; meanwhile, below the fin, at the internal wall, the flow interacts and generates a high turbulent flow stream. At
φ = 0°, the flow passes through the fin, and at approximately
φ = 110°, one horseshoe vortex system (HVS) forms at each fin’s channel. The flow interacts with the finned cylinder walls and high velocity streams just after the cylinder achieves a low-velocity area.
Between the lateral walls of the control volume and the fin edges, 0.5 equivalent diameters were defined on each lateral side. There were no significant changes in the flow behavior due to the wall’s influence in this study.
The flow velocity magnitude colors the fin surfaces. The flow separation sites can be identified by the color variations on the cylinder and fin. Because of the turbulence, the flow stream direction changes, and oscillations are detected throughout the simulations.
A second smaller HVS was discovered and grown around the cylinder between the fifth and sixth channel fin. The fourth channel flow interacts with the fifth channel flow, but the flow structure in each channel appears to be autonomous and is not totally absorbed by the generated turbulence behind the cylinder.
In
Figure 6, which depicts the top view of the control volume, the flow passes along the fourth channel of the cylinder fins. Although a large amount of data was collected, the third and fourth fin channel streamlines are shown in this figure to make visualization easier.
Because the angle of the fins and the vertical cylinder walls vary the flow direction, the flow enters the control volume at the inlet wall, interacts with the finned cylinder, and generates turbulence along the duct. The velocity magnitude of the flow colors the cylinder fin surfaces, resulting in a non-uniformity distribution along the surface. From φ = 0°, the flow decelerates along the fin surface, splitting into two lateral streams, and then accelerates and separates from the fin’s surface between φ = 95° and φ = −95°.
The finned cylinder is followed by a turbulent wake. A symmetric flow pattern was identified in this perspective, although the produced turbulence surrounding the fins constantly changes the wake.
The separation point is where the flow separates from the cylinder or the surface of the fins. In this situation, there are two pairs of separation points. The first pair occurs between φ = 40 and φ = 50 degrees, as well as φ = −40° and φ = −50°. Between φ = 100° and φ = 115° and φ = −100° and φ = −115°, the second pair appears.
The flow passes around the finned cylinder, forming the wake with two lateral flow streams at
φ = 45° and
φ = −45°, with an approximately larger flow velocity magnitude, as shown in
Figure 6. The horseshoe vortex system is the flow behavior that swirls and continues forward in the wake. At varying channels of fins, the low velocity center flow streams interact.
Figure 7 depicts the bottom viewpoint of the simulation at the same time. Because of the finned cylinder’s vertical location, the flow stream passes between the third and fourth channel of fins and splits into two lateral streams. The flow swirls and produces the HVS, and high-velocity flows move from the region near the cylinder to the immediate region at the base, causing a localized area of increased turbulence.
The HVS is continuously developed because of the formation of unsteady vortices at the front side of the cylinder. Streamwise streaks and turbulent structures are also developed at the end of the control volume. The streams between channel interacts behind the cylinder and develops highly turbulent structures. At two equivalent distance diameters in the wake, a high turbulence zone can be observed because of the flow interaction with the cylinder.
Figure 8 shows the simulations result of the wake; in this viewpoint, it is possible to observe that the flow in the wake moves downwards, and the interaction of this turbulent flow will interact with the lower channel fin flow. The HVS leads the flow downwards. Behind the cylinder, an upward flow stream in the wake is also observed that interacts with the next HVS channel. The downward flow hits the bottom wall of the volume and then moves forwards close to the wall.
The information obtained from
Figure 6,
Figure 7 and
Figure 8 shows that there is no interaction of the flow with the control volume’s lateral walls. On each side, the cylinder and the volume walls are separated by 0.5 of the cylinder’s equivalent diameter. The velocity magnitude inlet condition prevents the flow from moving to the volume’s walls. Additionally,
Figure 8 illustrates that the wake does not extend beyond the diameter of the finned cylinder.
Figure 9 depicts two distinct wake patterns of two fin channels. The flow passes through the fins on the second and fifth channels and around the cylinder. The wake from the second channel flows downward and upward; meanwhile, the wake from the fifth channel tends to move upward. The interaction of the two wakes increases the turbulence, and this structure occupies the remaining volume after one equivalent diameter distance. This figure shows that the horseshoe vortex separates from the fin surface edge and also demonstrates how its structure is maintained along the wake. Although the velocity distribution on each fin differs, the hydrodynamics in each channel are comparable.
It is worth noting that the finned cylinder ends in the experimental setup were built to eliminate junctions between the fin and wind tunnel surfaces. In the numerical model, the surfaces of the fin and cylinder were combined to prevent the turbulence at the edges of the first and the last fin channels.
5.2. Comparison between Experimental and Numerical Techniques
The results of the numerical simulation were compared with the results of the prior experiment. For the internal and external surfaces of the fin, three distinct rotation angles were used, 0, 90, and 180 degrees, which corresponded to the frontal, lateral, and back regions, respectively, of the inclined fin. The following equation was used to calculate the pressure coefficient in numeric computations.
Figure 10 shows the length of the fin on the
x axis and the
value at
φ = 0°,
φ = 90°, and
φ = 180° on the
y axis. It is feasible to see that the length of the curves in numeric results is longer than that of the experimental results. It was possible to insert a 3D line in numeric results and retrieve results all along the fin. On the contrary, it was difficult to install the pressure taps and their tubes inside the limited space of the inclined fin, particularly at the root and edge zones of the fins, as mentioned in
Section 2.
Figure 10a shows the
distribution on the internal surface of the inclined fin. The numeric and experimental results have similar trends in the frontal region of the inclined fin. The numeric results underestimate the experimental data, from 0.0075 to 0.014 m of the fin’s length, with a difference of 35%, bringing the OpenFOAM results closer. On the other hand, after 0.014 m, the FLUENT results have a negligible difference with respect to the experimental results, while the OpenFOAM results underestimate them with a maximum difference of 48%.
The values for lateral and back regions range from 0 to −1.5, but there are differences in the fluctuations between the two regions. The curves depict a normal distribution behavior at the lateral region. The defines a concave downwards behavior at the back region. The numerical results have a similar pattern to the experimental findings in both regions; however, the differences are distinct for each software. In the lateral region, the FLUENT results show a minimum difference of 5% and a maximum of 34%, while the OpenFOAM results show 12% and 40%, respectively. In the back region, the FLUENT results show a minimum difference of 5% and a maximum of 25%, while OpenFOAM results show 25% and 40%, respectively. The flow behavior condition and the non-steady condition utilized in the numerical simulations could be used to explain the disparities between the experimental and numerical methodologies.
in the lateral region has the lowest value out of the three studied regions. The values are closed to 0 at the back region; moreover, the value at this region yields the greatest difference between the two approaches, numerical and experimental, because turbulence is larger in this zone. It is reasonable to suppose that the numerical simulations’ deviations are greater because of these flow circumstances.
Figure 10b shows the pressure coefficient values at the external surface of the fourth channel fin calculated from experimental data and numerical calculations for the frontal region, colored in blue; the lateral region, colored in green; and the back region, colored in orange. On the external surface, at lateral and back regions, there were variations between the experiment and the computations. Because of the interaction with the cylinder walls, there are significant flow changes at this zone due to turbulence.
The trend of the experiment curve is comparable to the numerical techniques at the frontal region, as shown in 10b, and the differences between the results are less than 5%. The curve shape is comparable in both ways at the lateral region. The OpenFOAM results show a minimum difference of 3% and a maximum of 20%, while the FLUENT results show 13% and 24%, respectively. In the back region, the curves resembled each other in shape. The OpenFOAM results show a minimum difference of 18% and a maximum of 34%, while the FLUENT results show 12% and 18%, respectively. The magnitude difference between the two procedures is larger than in the previous two regions.
The numerical simulations using proprietary software were performed using the Reynold’s stress model (RSM) turbulence model. Based on Garcia-Figueroa’s work, the RSM obtained the best results of seven different turbulence models using the same proprietary software [
16]. The RSM considers the turbulence anisotropy to model the vortexes and the hydrodynamic flow behavior. This feature offers several advantages in comparison to other turbulence models.
Proprietary software has multiple benefits. For example, it is possible to use different types of turbulence models in one study case. However, it also has some limitations. One of these limitations is the total number of elements used in one case. For academic licensing, the grid limitation could be greater than the student license. The discretization limitation in proprietary software should be considered when deciding between open-source and proprietary software. Because of the turbulent nature of the hydrodynamics in the case presented in this work, the grid resolution allows the regions over the fin surface to be located where the wake is developed. The flow behavior in the wake is important when an array of tubes is configured.
Although proprietary software provides several advantages, it also several limitations, including the total amount of elements that can be used in a single case. The grid restriction could be changed because of the licensing type. When choosing between proprietary and open-source software in CFD numerical simulations, the discretization restriction in proprietary software may be a crucial factor. The grid resolution in this study’s case, using the open-source platform, allows researchers to identify the areas over the fin surface where the wake develops due to the turbulent character of the hydrodynamics. This result could not be obtained in the proprietary platform because of the lower number of elements. Is also important to mention that the turbulence model applied in every case could be essential to approach the numerical results in the experimental data.
In this study, different turbulence models were used in the open-source and the proprietary platform. In OpenFOAM, the turbulence model used was Spalart–Allmaras DDES, while in Fluent, the RSM was the turbulence model. Based on the findings in
Figure 10, it is feasible to compare the two numerical approaches and indicate that the open-source platform was able to replicate the time variations seen during the experiment. These changes have a significant impact on the results and possibly make it challenging to simultaneously compare the fluctuations in the pressure coefficient distribution over time from three distinct rotation angles. An averaged result might replicate the overall flow behavior across the cylinder, just as the proprietary program did.
Important information regarding the flow behavior was shared by the results from this work using both proprietary and open-source software. As a final remark, it was shown that the open-source platform allows a large element count to be reached, as well as the grid’s topological properties. Moreover, the chosen turbulence model could obtain crucial flow behavior data, which was not possible with commercial software.