the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 15 Oct 2024
Spatial development of planar and axisymmetric wakes of porous objects under a pressure gradient: a wind tunnel study
Abstract. We report an experimental study on the effect of a constant adverse pressure gradient on the spatial evolution of turbulent wakes generated by different objects. A porous disk, designed to mimic the wake of a horizontal axis wind turbine, and a porous cylinder, whose wake matches that of a vertical axis wind turbine, were tested in a wind tunnel for Reynolds numbers (based on the generator diameter) in the range of 2.6 × 105 to 3.9 × 105. Experiments were conducted between 1 and 7 diameters downstream of the disk and from 2 to 12 diameters downstream of the cylinder.
We find that the effect of the pressure gradient is significant in all cases, resulting in larger velocity deficits and wider wakes. Moreover, these variations are stronger for the cylinder-generated wake. We also find that current analytical models for wakes evolving in pressure gradients, developed from momentum conservation, satisfactorily fit our data. Our results provide a benchmark case that will contribute to improving energy harvesting in cases where pressure gradients are relevant, such as in wind plants installed over complex topographies and tidal stream generators.
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RC1: 'Comment on wes-2024-116', Anonymous Referee #1, 18 Nov 2024
Review of ‘Spatial development of planar and axisymmetric wakes of porous objects under a pressure gradient: a wind tunnel study’
The article presents an experimental study of porous disk and cylinder wakes under zero and adverse pressure gradients. Moreover, the experimental data is compared with predictions of analytical wake models under pressure gradient for planar and axisymmetric wakes. The findings of the study are not necessarily new; however, they are consistent with and support the findings of several previous experimental and numerical studies on the topic. As argued by the authors, it is the first study that investigates both planar and axisymmetric wakes under comparable flow conditions in the same test facility. The study can be useful for the community and I will recommend its publication once the concerns highlighted in the following sections are addressed.
Specific comments
- The authors claim that the cylinder wake matches the wake of a vertical axis turbine. However, the cylinder used in the study is a two-dimensional cylinder resulting in a planar wake (as suggested by the title of the article). The wake of a vertical axis wind turbine, on the other hand, is not a planar wake. Maybe for very large aspect ratios, it could be similar to a planar wake, but it cannot be true in general. The authors need to clarify this and specify under which conditions the wake of a vertical axis turbine matches with a cylinder (planar) wake.
- How is the theoretical baseline velocity estimated? The authors must provide the equation used for it.
- Page 10 lines 221-223, the authors state that they have verified that the ratio of velocity deficit and wake width is same under zero and adverse pressure gradients, however, they have not included a supporting figure. Is it excluded for brevity? If so, please specify.
- The authors show self-similarity of wake deficit in figure 5c and 5d. According to the data, for porous disks, the wake is self-similar even at x=1D. Why is that? I believe this could be related to the geometry of the disk. In principle, for a turbine wake the self-similarity is valid in the far wake, which scales with turbulence intensity (the lower the turbulence intensity, the further from the turbine is the onset of the far wake). Given the very low turbulence intensity (0.25%), it is surprising to see self-similarity at x=1D. Perhaps, the authors can explain this in more detail.
- In section 5, the authors use power law fit (equations 5 and 6) to model the ZPG wake. These equations have 5 parameters (A, α, B, β, ). It appears to me that for each case (either porous disk or cylinder), the authors have directly fitted the equations to the experimental data resulting in 5 fitted parameters. My first question is how general or universal are these parameters and are they valid only for the cases presented in this study? Secondly, if you need the experimental wake under ZPG to fit these parameters (i.e. the ZPG wake needs to be known a-priori), then why not directly used the experimental wake under ZPG for the input of the pressure gradient models? Why go through an extra step to fit power law equations to the ZPG wake and then use it for the pressure gradient model?
- Page 16 lines 276-277, how do the authors estimate that the far wake starts from x/D ≥ 3? In addition, how practical is it to pick the velocity deficit at the start of the far wake from the experimental data?
- It would be useful if the authors add a comparison of the full velocity deficit profiles between the experiments and the model.
Technical comments
- Page 3 line 65, the averaged streamwise velocity ‘deficit’ is self-similar in the far-wake, please correct.
- Why is the velocity deficit plotted as (1-C(x))? Is there a specific reason for this?
Citation: https://doi.org/10.5194/wes-2024-116-RC1 -
AC1: 'Reply on RC1', Martin Obligado, 27 Dec 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-116/wes-2024-116-AC1-supplement.pdf
-
RC2: 'Comment on wes-2024-116', Anonymous Referee #2, 20 Nov 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-116/wes-2024-116-RC2-supplement.pdf
-
AC2: 'Reply on RC2', Martin Obligado, 27 Dec 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-116/wes-2024-116-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Martin Obligado, 27 Dec 2024
Status: closed
-
RC1: 'Comment on wes-2024-116', Anonymous Referee #1, 18 Nov 2024
Review of ‘Spatial development of planar and axisymmetric wakes of porous objects under a pressure gradient: a wind tunnel study’
The article presents an experimental study of porous disk and cylinder wakes under zero and adverse pressure gradients. Moreover, the experimental data is compared with predictions of analytical wake models under pressure gradient for planar and axisymmetric wakes. The findings of the study are not necessarily new; however, they are consistent with and support the findings of several previous experimental and numerical studies on the topic. As argued by the authors, it is the first study that investigates both planar and axisymmetric wakes under comparable flow conditions in the same test facility. The study can be useful for the community and I will recommend its publication once the concerns highlighted in the following sections are addressed.
Specific comments
- The authors claim that the cylinder wake matches the wake of a vertical axis turbine. However, the cylinder used in the study is a two-dimensional cylinder resulting in a planar wake (as suggested by the title of the article). The wake of a vertical axis wind turbine, on the other hand, is not a planar wake. Maybe for very large aspect ratios, it could be similar to a planar wake, but it cannot be true in general. The authors need to clarify this and specify under which conditions the wake of a vertical axis turbine matches with a cylinder (planar) wake.
- How is the theoretical baseline velocity estimated? The authors must provide the equation used for it.
- Page 10 lines 221-223, the authors state that they have verified that the ratio of velocity deficit and wake width is same under zero and adverse pressure gradients, however, they have not included a supporting figure. Is it excluded for brevity? If so, please specify.
- The authors show self-similarity of wake deficit in figure 5c and 5d. According to the data, for porous disks, the wake is self-similar even at x=1D. Why is that? I believe this could be related to the geometry of the disk. In principle, for a turbine wake the self-similarity is valid in the far wake, which scales with turbulence intensity (the lower the turbulence intensity, the further from the turbine is the onset of the far wake). Given the very low turbulence intensity (0.25%), it is surprising to see self-similarity at x=1D. Perhaps, the authors can explain this in more detail.
- In section 5, the authors use power law fit (equations 5 and 6) to model the ZPG wake. These equations have 5 parameters (A, α, B, β, ). It appears to me that for each case (either porous disk or cylinder), the authors have directly fitted the equations to the experimental data resulting in 5 fitted parameters. My first question is how general or universal are these parameters and are they valid only for the cases presented in this study? Secondly, if you need the experimental wake under ZPG to fit these parameters (i.e. the ZPG wake needs to be known a-priori), then why not directly used the experimental wake under ZPG for the input of the pressure gradient models? Why go through an extra step to fit power law equations to the ZPG wake and then use it for the pressure gradient model?
- Page 16 lines 276-277, how do the authors estimate that the far wake starts from x/D ≥ 3? In addition, how practical is it to pick the velocity deficit at the start of the far wake from the experimental data?
- It would be useful if the authors add a comparison of the full velocity deficit profiles between the experiments and the model.
Technical comments
- Page 3 line 65, the averaged streamwise velocity ‘deficit’ is self-similar in the far-wake, please correct.
- Why is the velocity deficit plotted as (1-C(x))? Is there a specific reason for this?
Citation: https://doi.org/10.5194/wes-2024-116-RC1 -
AC1: 'Reply on RC1', Martin Obligado, 27 Dec 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-116/wes-2024-116-AC1-supplement.pdf
-
RC2: 'Comment on wes-2024-116', Anonymous Referee #2, 20 Nov 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-116/wes-2024-116-RC2-supplement.pdf
-
AC2: 'Reply on RC2', Martin Obligado, 27 Dec 2024
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2024-116/wes-2024-116-AC2-supplement.pdf
-
AC2: 'Reply on RC2', Martin Obligado, 27 Dec 2024
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