Ground Clearance Effects on the Aerodynamic Loading of Tilted Flat Plates in Tandem

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

Present manuscript presented the aerodynamic drag of tilted flat plates in tandem configuration.

1. In the introduction, on page 2, line 77~84, the illustration of the ground effect of an wing or an aerofoil does not match with the current problem. When the wing is flying near the ground, there will be a ground effect on the wing as illustrated by the Refs. 15~17. However, in this case, the wing is flying over the ground. It means there is a relative motion between the wing and the ground. There should be no boundary layer under the wing for the Wing-In-Ground effect. However, in the present study, there is no relative motion between the ground and the wing, and the boundary layer is considered.
2. In the line 120, if the flow direction is an axial direction, then the chordwise direction represents the length, and the length in the spanwise direction means the width. For 4 plate setup, from line 118~125, what is the Reynolds number based on the chord length(flow direction)?.
3. In the Ref.2, it is said that "the mean surface pressures are not significantly affected by turbulence intensity. Very small-size solar panels may have different mean loads as they are located very close to the ground (‘ground effect’ and uncertainty in wind speed) and hence the uncertainty in the aerodynamic data is relatively high." The conclusion in the Ref.2 looks different from the sentence in line 126~127.
4. Please show how the authors measured the force. Where the sensors are attached to the models, and how the unsteady force are averaged can be of great interesting to the readers.
5. When we show the ground effect on the model, we compare the case of an isolated wing without ground effect with the wing in ground effect. In the present study, the cases for the ground effect are represented. 
6. The flow separation of leading wing and its interaction with the ground will affect significantly the drag of the following wings. The Ref. 15, 16,17 handles the ground effect of an aircraft wing which are completely different from the current wing(panel). Thus, the discussion chapter should be revised.

Author Response

Answers to Reviewer 1

We would like to thank the reviewer for her/his comments. Please see below our answers.

1) Reviewer’s comment:‘In the introduction, on page 2, line 77~84, the illustration of the ground effect of an wing or an aerofoil does not match with the current problem. When the wing is flying near the ground, there will be a ground effect on the wing as illustrated by the Refs. 15~17. However, in this case, the wing is flying over the ground. It means there is a relative motion between the wing and the ground. There should be no boundary layer under the wing for the Wing-In-Ground effect. However, in the present study, there is no relative motion between the ground and the wing, and the boundary layer is considered.’

1 Answer

The statement that ‘, there will be a ground effect on the wing as illustrated by the Refs. 15~17’ is not quite accurate because among the three references 15 to 17, only Ref. 15 which is a numerical work considers the ground as moving, whereas Ref. 16 and 17 which are experimental, the ground is stationary, not moving. More particularly, in Ref. 16, it is mentioned ‘The wing model is mounted horizontally above an elevated flat plate which simulates the flat ground. The aluminum flat plate, 1.4 m long, 1.2 m wide and 2.5 cm thick, is positioned 15 cm above the tunnel floor to eliminate the effects of tunnel boundary layer’. Also, it is mentioned ‘The thickness of the boundary layer develops on the flat plate at the wing’s leading edge is 4 mm or h/c = 1.4% (Fig. 2c)’. So, it is clear that in Ref. 16, both the ground is stationary and there is a boundary layer under the wing (in contrast to the above remark of the reviewer). Regarding Ref. 17, in which the ground effect is examined for the case of a delta wing, there is no moving ground. It is mentioned:’ To analyze the impact of ground effects on the longitudinal characteristics of the delta wing-body-tail model, the model was positioned at various heights above the ground simulator plate. The model was secured on a sting-type support stand in the center of the wind tunnel test section, while the ground plane was adjusted vertically’. This is clearly illustrated in Fig.2 of Ref. 17. Moreover, in Ref. 17, there is a long list of publications about the ground effect, in which the ground is either moving or stationary. 

 

2) Reviewer’s comment: ‘In the line 120, if the flow direction is an axial direction, then the chordwise direction represents the length, and the length in the spanwise direction means the width. For 4 plate setup, from line 118~125, what is the Reynolds number based on the chord length (flow direction)?

2 Answer

In Figure 1, the four plates are presented by four parallel tilted lines, which are essentially the chords of the plates. The spanwise direction is perpendicular to the page, and apparently it is not shown. In the same figure, S1 is the ground clearance and S2 the longitudinal distance between adjacent plates. Therefore, the Reynolds number is based on the chord length which is 30 mm. This is clearly mentioned in lines 153-154.

    

3) Reviewer’s comment: ‘In the Ref.2, it is said that "the mean surface pressures are not significantly affected by turbulence intensity. Very small-size solar panels may have different mean loads as they are located very close to the ground (‘ground effect’ and uncertainty in wind speed) and hence the uncertainty in the aerodynamic data is relatively high." The conclusion in the Ref.2 looks different from the sentence in line 126~127.

3 Answer

In abstract of Ref.2, it is written: ‘While mean loads are not significantly affected by the model size, peak loads are sensitive to both the geometric scale and the spectral content of the test flow.’ Based on the latter conclusion, in lines 126-127 we have written: ‘According to [2], under-scaled models can simulate successfully the mean aerodynamic loading of tilted plates, while failing in reproducing its peak forces.’ Therefore, what we have written is exactly what Ref.2 has concluded. 

 

4) Reviewer’s comment: ‘Please show how the authors measured the force. Where the sensors are attached to the models, and how the unsteady force are averaged can be of great interesting to the readers.’

4 Answer

As it is mentioned in lines 149-150 ‘The experiments were repeated four times for each of the two wind directions, so that each of the four plates was mounted on the force balance.’

The force balance was located outside the wind tunnel, below the test-section. One part of a vertical metallic rod, 150 mm long and 10 mm in diameter, was clamped to the balance while its other edge supported one of the four plates. Since, the force of all four plates had to be measured, the experiment was repeated so that, each time, the plate which was mounted on the balance, was the first, second, third and fourth, in the series, respectively. This detail is included in the new version as follows: ‘The force exerted on each plate was measured using a one-component force balance positioned just below the wind tunnel test section to minimize the influence of vibrations (Fig. 2). A vertical cylindrical metallic rod, 150 mm in length and 10 mm in diameter, was clamped at one end to the balance, while the other end supported one of the four plates (Fig. 2). To measure the force on each individual plate, the experiment was repeated four times, with the balance-mounted plate positioned successively as the first, second, third, and fourth plate in the series.’

The force data were recorded for a period of 20 secs based on which the average value was calculated (lines 254 to 263 of the manuscript).

 

    

Figure 2. (Left) Force balance with the plate- mount attached to it. (Right) Plate- mount

 

5) Reviewer’s comment: ‘When we show the ground effect on the model, we compare the case of an isolated wing without ground effect with the wing in ground effect. In the present study, the cases for the ground effect are represented.’

5 Answer

In the present study, besides the four-panel setup, an isolated panel was examined for two ground clearances, namely for 20% and 60%, respectively, and the drag data were compared with two publications (lines 322 to 337 of the manuscript). Measurements were also performed for larger clearances than 60%, without practical any changes in the measured data. Similar observations regarding the influence of the ground clearance on an isolated plate are reported in Ref. 14, mentioning in its Abstract: ‘Ground proximity-related effects are most notable when the plate was closer than 0.75 chord lengths from the ground, near the stall angle, where pronounced changes in the midspan and wake flow development take place’.   

 

6) Reviewer’s comment: ‘The flow separation of leading wing and its interaction with the ground will affect significantly the drag of the following wings. The Ref. 15, 16,17 handles the ground effect of an aircraft wing which are completely different from the current wing(panel). Thus, the discussion chapter should be revised.’

6 Answer

The tilted flat plates in the present work are essentially rectangular wings of finite aspect ratio and zero camber.  Regarding Ref. 15, the ground effect is numerically examined on a NACA 0015 airfoil, which apparently represents a rectangular wing of infinite aspect ratio at an angle of attack. In the experimental work Ref. 16, a NACA 0012 rectangular wing of finite aspect ratio AR= 101.6/28 = 3.08 is examined. In Ref. 17, a delta wing of an aspect ratio of 2.31 is also examined. Therefore, we believe, there is a clear connection between the examined tilted flat plates with the above examples. In fact, a flat plate at an angle of attack, is a classical case examined in aerodynamics, for which there are analytical solutions in case of an inviscid flow (see for example the Joukowski transformation of the flow about a circular cylinder to that around a flat plate at an angle of attack).

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Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This paper investigates the aerodynamic drag and pressure distribution of four and six tilted flat plates arranged in tandem near the ground, focusing on the effects of ground clearance, tilt angle, and wind direction through wind tunnel measurements. The aerodynamic characteristics in this study were determined experimentally using force measurements with a one-component balance in an open-circuit wind tunnel and surface pressure measurements with pressure taps and scanners in a closed-circuit wind tunnel.

The methodological section lacks sufficient detail and depth to ensure the robustness and reproducibility of the results; in particular, it omits any sensitivity analysis (e.g., to Reynolds number, plate positioning errors, or ground clearance uncertainty), provides limited justification for experimental parameters, and fails to address potential effects of model support structures, measurement noise, or blockage correction beyond surface-level mentions.

The paper lacks a thorough comparison with existing literature, limiting the credibility and contextual relevance of the findings; although minor references are made to previous studies, no rigorous benchmarking is performed—yet even a simplified comparative test case using a standard plate configuration could have validated the experimental approach and enhanced the scientific value of the results.

 

Author Response

Answers to Reviewer 2

We would like to thank the reviewer for her/his comments. Please see below our answers.

1) Reviewer’s comment: ‘it omits any sensitivity analysis (e.g., to Reynolds number, plate positioning errors, or ground clearance uncertainty)

1 Answer:

1a) Regarding the Reynolds number sensitivity study, there is a whole paragraph dedicated on this subject (in page 4 of the original manuscript) explaining that we examined four Reynolds numbers and we proved that our results are Reynolds number independent. Please read the following part from the original manuscript:

’ The experiments were repeated four times for each of the two wind directions, so that each of the four plates was mounted on the force balance, and for four free stream speeds U, namely 12.7 m/s, 18 m/s, 22 m/s and 25.4 m/s. However, it was realized that the drag coefficient was practically invariable for 18 m/s and above. The Reynolds number, Re, for U = 18 m/s, based on the plate chord length, was 3.6 x 10⁴. It is noted that Re was calculated for an air temperature of 19°C which was kept constant by an air-cooling system, with a deviation of no more than 1°C. The small influence of Re on the drag coefficient is attributed to the fixed flow separation lines at the sharp edges of the plates and the fact that the contribution of the shear stresses on the drag is small for this application. It is noted that according to [19] a minimum Re of 5x10⁴ is suggested for the experimental flow studies of sharp-edged models to secure Reynolds independent results. In [20] more details are given about the sensitivity of the mean and unsteady aerodynamic loading of sharp-edged components on Re. Nevertheless, in the current study, the examined free stream speed of 25.4 m/s corresponds to Re = 5 x 10⁴, as suggested above.’

 

Furthermore, in page 6 of the manuscript, the following is mentioned, regarding the free stream speed variations (through the relevant fluctuations of the inlet dynamic pressure), the uncertainty in the measured force as well as in the inclination angle:

 ‘The dynamic pressure  was measured by the Pitot-static tube at the inlet of the test section and a differential pressure manometer, showing fluctuations within ± 1.7% of the mean, based on data collected in 20 s intervals (time duration of each force measurement) and 100 Hz sampling rate. The sampling period of 20 s was decided following a trial and error procedure so that the measured time-averaged force was stable. The maximum uncertainty in the drag coefficient is estimated to be ± 0.05 based on repeated drag force measurements for several indicative cases. It is reminded that the drag applied on the plate support alone was measured for each case and it was subtracted from the total force (of the plate and its support). Regarding the error in the tilt angle, it is estimated to be no more than ± 1.5°.’

1b) Reviewer’s comment: ‘..the plate positioning errors, or ground clearance uncertainty’

1b Answer  

We used the following procedure: the ground clearance was measured with high precision by inserting a flat Plexiglas plate, either 6 mm or 18 mm thick (depending on the ground clearance being tested), between the lower part of the plates and the ground floor. The ground floor was then moved vertically in small increments until the Plexiglas plate made contact with both the lower plate and the ground floor. This contact point allowed for accurate determination of the ground clearance. The above details are mentioned in the new version. Concerning the inclination of the plates, an inclinometer was used and as it is explained in the manuscript, the tilt angle uncertainty was no more than 1.5°.

2) Reviewer’s comment: ‘provides limited justification for experimental parameters, and fails to address potential effects of model support structures, measurement noise, or blockage correction beyond surface-level mentions’

2a Answer

Regarding the blockage correction, there is a whole paragraph devoted to this (pages 6 and 7 of the original manuscript) included in paragraph 2.1.1 entitled ‘Blockage effect’.

2b Answer to the comment ‘potential effects of the model support’.

As it is clearly mentioned in the manuscript (page 3), ‘Each plate was supported by two horizontal bolts at a distance of 180 mm apart, allowing the adjustment of the plate tilt angle’. This decision was made in order to avoid the disturbance that wold be caused to the flow field in case that the supports were positioned under the plates, as it is commonly done in all publications related to the PV panels. However, since our objective was to examine the flow over tilted flat plates, in a way that it could be easier for comparisons with CFD calculations, without any obstacles along the span of the plates, it was decided to have the panels free of any obstructions along their span.  

2c Answer to the comment ‘measurement noise’

As it was pointed out above, relevant details are mentioned about the free stream fluctuations of the open wind tunnel, the uncertainty in the force measurements, in the tilt angle as well as the turbulence level of the closed wind tunnel (please see page 7 of original manuscript).

3) Reviewer’s comment: ‘The paper lacks a thorough comparison with existing literature’,

3 Answer

We do provide comparisons with two works from literature (please see pages 16 and 17 of original manuscript).

4 Reviewer’s comment: ‘although minor references are made to previous studies, no rigorous benchmarking is performed—yet even a simplified comparative test case using a standard plate configuration could have validated the experimental approach and enhanced the scientific value of the results.

4 Answer

In pages 8 and 9, we make comparisons with the comprehensive experimental study of reference [8] which refers to an isolated plate and a number of different aspect ratios, in which we show that the drag coefficient value for a plate of aspect ratio of 6 (as this was our examined case) mentioned in ref. [8] is practically identical with our measured for the 20% ground clearance and 7.9% lower for the 60% clearance. Comparisons are also provided with Ref. 25,  Ref. 7 and Ref. 14 in paragraph 3.1 of isolated plates.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents an experimental investigation into the aerodynamic effects of ground clearance on tilted flat plates arranged in tandem, a configuration inspired by solar panel installations. The authors performed wind tunnel experiments using a movable floor setup to systematically vary the ground clearance. Their results show that increasing ground clearance leads to a notable rise in the drag coefficient of the plates.

The study is clearly written, well-structured, and contributes useful insights relevant to the design and optimization of solar panel arrangements. The experimental findings have strong practical implications in the renewable energy sector, particularly as interest in ground-mounted solar arrays grows. The manuscript aligns well with the scope of Fluids, and I recommend it for publication after addressing the following minor comment.

 

Minor Comment:

The authors mention the use of a one-component force balance to measure drag on the plates, but it remains unclear how and where the load cell was mounted. Further clarification is needed regarding the type of load cell used and its exact placement relative to the plates. Including a schematic or diagram of the force balance setup would greatly enhance reader understanding. Additionally, the authors should provide the measurement uncertainty associated with the force data to contextualize the reported drag coefficients.

Author Response

Answers to Reviewer 3

We would like to thank the reviewer for her/his comments. Please see below our answers.

1) Reviewer comment:’ The authors mention the use of a one-component force balance to measure drag on the plates, but it remains unclear how and where the load cell was mounted. Further clarification is needed regarding the type of load cell used and its exact placement relative to the plates. Including a schematic or diagram of the force balance setup would greatly enhance reader understanding. Additionally, the authors should provide the measurement uncertainty associated with the force data to contextualize the reported drag coefficients.’

 

1 Answer

The force balance was located outside the wind tunnel, below the test-section. One part of a vertical metallic rod, 150 mm long and 10 mm in diameter, was clamped to the balance while its other edge supported one of the four plates (please see below images). Since, the force of all four plates had to be measured, the experiment was repeated so that the plate which was mounted on the balance was the first, second, third and fourth, in the series, respectively. This detail was included in the new version. The force data were recorded for a period of 20 secs based on which the average value was calculated. Regarding the uncertainty in the force measurements, as it is written in lines 258 to 260 of the manuscript ‘The maximum uncertainty in the drag coefficient is estimated to be ± 0.05 based on repeated drag force measurements for several indicative cases.’ Relevant details the are included in paragraph as follows: ‘The force exerted on each plate was measured using a one-component force balance positioned just below the wind tunnel test section to minimize the influence of vibrations (Fig. 2). A vertical cylindrical metallic rod, 150 mm in length and 10 mm in diameter, was clamped at one end to the balance, while the other end supported one of the four plates (Fig. 2). To measure the force on each individual plate, the experiment was repeated four times, with the balance-mounted plate positioned successively as the first, second, third, and fourth plate in the series.’

 

 

Figure 2. (Left) Force balance with the plate- mount attached to it. (Right) Plate- mount

 

 

Author Response File: Author Response.pdf

Reviewer 4 Report

Comments and Suggestions for Authors

This research topic is highly meaningful and valuable. The author's intention to compare results with existing literature represents a commendable analytical approach. However, the overall analysis lacks depth and demonstrates methodological limitations. To strengthen the study, the author should incorporate more comprehensive data and diversified analytical techniques. Below are specific points for revision:

1. Please provide the turbulence intensity of the free stream in the wind tunnel for the four-plate experiments. This parameter significantly influences flow characteristics.
2. The caption of the Figure 2 should contain more information.
3. Since the plates are located within the boundary layer, the aerodynamic forces acting on them are inevitably influenced by the boundary layer flow. In this case, the freestream cannot be considered uniform. For different tilted angles, the incoming flow conditions experienced by the plates will vary accordingly. How do the authors address this issue? This is analogous to the blockage effect discussed later in the manuscript, where the authors applied a velocity correction. A similar consideration or clarification regarding the non-uniformity of the incoming flow due to boundary layer effects would be appreciated.
4. The equation in line 283 is missing a parenthesis.
5. The paragraph in line 318 analyzed the influence of AR in detail. However, AR is not the main focus of the present study. The authors are kindly requested to clarify why such an extensive discussion on AR is included.
6. Figures 6, 7, 8, and 9 present results that appear quite similar, which may give a repetitive impression. The authors may consider alternative ways to present these results, such as using a table, to improve clarity and conciseness.
7. In section 3.2, the authors are encouraged to explain why the drag forces on the third and fourth plates are higher than that on the second plate, preferably from a flow field perspective. A physical explanation based on the flow behavior would enhance the reader’s understanding of the underlying mechanism.
8. What do the horizontal and vertical axes represent in Figure 11? Additionally, in Figure 11(a), why does negative pressure appear on the windward top surface of Plate 1? A clarification based on flow physics would be helpful.

Author Response

Answers to Fourth Reviewer

We would like to thank the reviewer for her/his comments (written in red below). Please see our answers.

This research topic is highly meaningful and valuable. The author's intention to compare results with existing literature represents a commendable analytical approach. However, the overall analysis lacks depth and demonstrates methodological limitations. To strengthen the study, the author should incorporate more comprehensive data and diversified analytical techniques. Below are specific points for revision:

1. Please provide the turbulence intensity of the free stream in the wind tunnel for the four-plate experiments. This parameter significantly influences flow characteristics.

Answer 1

Based on relevant literature, turbulence intensity does not influence significantly the flow field for this particular problem. More particularly, according to the comprehensive experimental and numerical work Ref. 2 (Aly, A.M., Bitsuamlak, G. Aerodynamics of ground-mounted solar panels: test model scale effects. J. Wind Eng. Ind. Aerodyn. 2013, 123, 250–260), it is stated that the mean surface pressures are not significantly affected by turbulence intensity. Also, in Ref.7 (Wittwer, A.R., Podestá, J.M., Castro, H.G., Mroginski, J.L., Marighetti, J.O., De Bortoli, M.E., Paz, R.R., Mateo, F. Wind loading and its effects on photovoltaic modules: An experimental–Computational study to assess the stress on structures. Solar Energy, 2022, 240, 315-328), the results are similar for 1% and 10% free stream turbulence levels (comment at the end of paragraph 4.2 of Ref.7).

Moreover, the fluctuations of the free stream velocity were noted in our original manuscript in terms of the dynamic pressure variations at the inlet of the test section. More specifically, in lines 254-255 it was mentioned: ‘ The dynamic pressure Pd was measured by the Pitot-static tube at the inlet of the test section and a differential pressure manometer, showing fluctuations within ± 1.7% of the mean.’ Since the fluid speed is proportional to the square root of the dynamic pressure, the corresponding speed fluctuations are in the same interval ± 1.7% of the mean. (This is easily proved by employing the binomial expansion , where   Therefore, a good estimate of the turbulence intensity  is  , if the time speed variations are sinusoidal. In order to further clarify this issue, we used a single hot wire (DANTEC 55P11) at the same location where the Pitot-static tube was located and the turbulence level was found to be 1.32%, namely a little higher than the above estimate. Conclusively, in the new version of the manuscript, it was added: ‘The turbulence intensity of the free stream was also recorded by using a single hot wire sensor and it was found to be 1.32%.’

 

2. The caption of the Figure 2 should contain more information.

 

2 Answer

 

The caption of Figure 2 was changed to: ‘Boundary layer velocity profile over the movable ground floor at x = 480 mm. Experimental and 1/7^th power law velocity distributions’

 

3. Since the plates are located within the boundary layer, the aerodynamic forces acting on them are inevitably influenced by the boundary layer flow. In this case, the freestream cannot be considered uniform. For different tilted angles, the incoming flow conditions experienced by the plates will vary accordingly. How do the authors address this issue? This is analogous to the blockage effect discussed later in the manuscript, where the authors applied a velocity correction. A similar consideration or clarification regarding the non-uniformity of the incoming flow due to boundary layer effects would be appreciated.

 

3 Answer

 

The objective of this work is to provide new evidence about the aerodynamic loading of tilted flat plates under well-defined conditions, so that it would be helpful for comparisons with CFD simulations as well as appropriate interpretation of the results. In this respect, the inlet boundary layer velocity distribution for the four-panel set-up is given in Fig. 2. This kind of information is found in all publications related to the aerodynamics of PV panels in which the inlet wind speed distribution u(y) is given normally by a formula like the following:

 where the exponent ‘α’ takes various values (less than 1), simulating the wind boundary layer, taking into account the roughness of the terrain.  For example, in Ref. 7, the exponent ‘α’ was considered to be 0.11, simulating a terrain between rural and suburban and in Ref. 5, the exponent was taken as 0.15, simulating an open terrain. In our case, as it is shown in Fig.2, the measured velocity profile is close to the known turbulent flow velocity profile of the 1/7^th power law, namely the exponent is close to 1/7 = 0.14, whereas in Ref. 8, there is just an inlet velocity profile shown, without mentioning the value of the exponent. Therefore, the inlet boundary layer velocity distribution is used as reference so that the potential users of the data know in detail the boundary conditions. To make this clear, the following sentence was added in paragraph 2.1: ‘This information is crucial for interpreting the results and can be utilized as an appropriate boundary inlet condition in numerical simulations.’

In our opinion this is not analogous to the blockage effect. As it was discussed above, each publication refers to an inlet boundary layer velocity distribution without making any corrections since there is no universal boundary layer, given the fact that the velocity distribution depends on the selected roughness of the terrain.   

 

4. The equation in line 283 is missing a parenthesis.

4 Answer

It was corrected.

5. The paragraph in line 318 analyzed the influence of AR in detail. However, AR is not the main focus of the present study. The authors are kindly requested to clarify why such an extensive discussion on AR is included.

5 Answer

Thank you for highlighting this important point. The aspect ratio (AR) of a flat plate plays a crucial role in determining its aerodynamic loading, a factor that is often overlooked in many studies on the flow dynamics over tilted photovoltaic (PV) panels. As noted in Ref. 8 (Fig. 3), the drag coefficient for plates tilted at 90° varies significantly with aspect ratio: it ranges from 1.15 for an AR of 2 to 1.45 for an AR of 20. Moreover, for an infinite aspect ratio, the drag coefficient approaches a value of 2, as documented in Ref. 22. To further emphasize this point, the following was added in the new version after the sentence ‘It should be noted that Cd values are also dependent on the panel aspect ratio, increasing monotonically with it.’ The added text in paragraph 3.1 is: ‘This parameter, often overlooked in many studies on PV panels, is crucial in determining the aerodynamic loading of tilted plates. The drag coefficient nearly doubles as the aspect ratio increases from 1 to infinity, highlighting its significant impact on aerodynamic behaviour.’

 

6. Figures 6, 7, 8, and 9 present results that appear quite similar, which may give a repetitive impression. The authors may consider alternative ways to present these results, such as using a table, to improve clarity and conciseness.

6 Answer

Figure 7 presents the data from Figure 6 in a clearer format, making it easier for readers to observe the range of Cd​ values for each plate. Figure 8 illustrates the percentage increase in Cd​ values for each plate, resulting from changes in ground clearance. Although Figure 9 compares the drag on the first (windward) plate with that on the remaining plates, we chose to omit it to reduce the number of figures. However, we believe that Figures 7 and 8 are essential for conveying the key trends and should be retained.

7. In section 3.2, the authors are encouraged to explain why the drag forces on the third and fourth plates are higher than that on the second plate, preferably from a flow field perspective. A physical explanation based on the flow behavior would enhance the reader’s understanding of the underlying mechanism.

7 Answer

The following text was added at the end of paragraph 3, providing an explanation of the variation of the forces applied on the panels: ‘An explanation of the force variation based on the pressure distribution, is as follows:  while the suction (negative gauge pressure) at the panels’ rear increases along the series for both the positive and negative tilt angle, the front-side pressure remains relatively unchanged and less negative. This growing pressure differential leads to an increase in drag from the third to the sixth plate. However, the low drag on the second plate can be attributed to the nearly equal pressures on its both sides as shown above.’ Also, in the sentence at line 485: ‘c) the Cp values are negative at both sides of the plates, with the higher absolute values at the suction (back) side’ the following was added: ‘which tend to increase in absolute values, in contrast to the front side that the pressures are practically constant’.

8. What do the horizontal and vertical axes represent in Figure 11? Additionally, in Figure 11(a), why does negative pressure appear on the windward top surface of Plate 1? A clarification based on flow physics would be helpful.

8 Answer

What do the horizontal and vertical axes represent in Figure 11?

In order to clarify this point, the following was written in the beginning of paragraph 3.3: Figure 11 presents the distribution of time-averaged pressure coefficients for the six-plate configuration, displaying both the front side (pressure side) and the back side (suction side) of each plate. Each plate is represented as a rectangle in the figure, with dimensions of 20 cm in width (vertical side) and 110 cm in length (horizontal side). The vertical axis is labelled from 0 at the top edge (farthest from the ground) to 20 at the bottom edge (closest to the ground).

Additionally, in Figure 11(a), why does negative pressure appear on the windward top surface of Plate 1? A clarification based on flow physics would be helpful.

Although positive gauge pressures typically dominate the pressure side of an airfoil, negative pressures can also occur, particularly near the trailing edge, especially at high angles of attack where flow separation occurs. For instance, in the referenced study below, which numerically investigates the stall and post-stall behaviour of three airfoils, it is shown that as the angle of attack increases, negative pressures appear on the pressure side, near the trailing edge. Therefore, the following was added in the new version: Nevertheless, in both angles, the pressure drops from the leading to the trailing edge, on the pressure side, due to the flow speed acceleration. Especially for a = + 30°, negative pressures appear on the pressure side close to the trailing edge. As it is shown in the numerical work [28] which examines the stall and post-stall behaviour of various airfoils, negative pressure coefficients do appear on the pressure side near the trailing edge at high angles of attack, associated with a local recirculation region.

28. Petrilli, J., Paul, R., Gopalarathnam, S. and Frink, N.T. A CFD Database for Airfoils and Wings at Post-Stall Angles of Attack. AIAA 2013-2916, Fluid Dynamics and Co-located Conferences, June 24-27, 2013, San Diego, CA, 31st AIAA Applied Aerodynamics Conference.

Author Response File: Author Response.pdf

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The aim of the present study is clearly described in the introduction. The force measurement are well included. Present manuscript illustrates the effect of the ground proximity and the configurations on the drag forces with the change of the plate's tilt angle. Overall, the reply is well answered and the manuscript is faithfully revised considering the reviewer's opinion. 

Reviewer 2 Report

Comments and Suggestions for Authors

In my opinion, this paper can be published as it is.

Reviewer 4 Report

Comments and Suggestions for Authors

No more comments.