A Simplified Numerical Model for the Prediction of Wake Interaction in Multiple Wind Turbines
Round 1
Reviewer 1 Report
The boundary conditions required for the implementation of this actuator disk are not clearly described. The authors do not investigate the effect of grid density on the results. In the case of LES, it has not been investigated after how many time steps the mean flow converges, and also the influence of the time step. The axial velocity is averaged over the actuator disk, which would work well in the case of uniform upstream velocity. However, this uniform distribution can create some problems in the case of complex terrain or when the wake of the upstream wind turbine is not coaxial to the actuator disk. Here, the proposed axial induction factor η1 depends only on the distance from the upstream wind turbine and its tip speed ratio. However the wake behind the wind turbine depends also on the atmospheric turbulence. For example, the wake behind the offshore wind turbine may be significantly longer than the onshore wake. The advantage of the proposed model with a prescribed velocity on the disk surface of is the faster convergence and the better simulation of flow for test cases. However, in practice, it is much more difficult to find data about this velocity field than on the axial force or the power of the real turbines. The originality of the proposed method is that the actuator disk is modeled with prescribed velocity field. If the authors wish to demonstrate its advantages, they must compare with other actuator disk methods as “volume source terms”, “pressure discontinuity” and “porous disk” under the same conditions. The symbols Umin/Umax (Figure 4) are not described.Author Response
The boundary conditions required for the implementation of this actuator disk are not clearly described.
The boundary condition on the actuator disk is explained more in detain in Eq. (12) and Eqs. (14-16), velocity components that are marked in the boundary on the actuator disk in the revised Fig. 3. Also we added some comments on the revised text.
2.The authors do not investigate the effect of grid density on the results.
We added in page 7: “…and to capture the complex flow phenomena at the wake region, the width three times disk diameter is focused to concentrate meshes since the cross-sectional area of stream tube is double of the disk area in the ideal momentum theory.”
The convergence test for the present computation is shown in Fig. 4(a-b).
3. In the case of LES, it has not been investigated after how many time steps the mean flow converges, and also the influence of the time step.
On the LES modeling, ref. [13], we added some comments in page 8.
4. The axial velocity is averaged over the actuator disk, which would work well in the case of uniform upstream velocity. However, this uniform distribution can create some problems in the case of complex terrain or when the wake of the upstream wind turbine is not coaxial to the actuator disk. Here, the proposed axial induction factor η1 depends only on the distance from the upstream wind turbine and its tip speed ratio. However the wake behind the wind turbine depends also on the atmospheric turbulence. For example, the wake behind the offshore wind turbine may be significantly longer than the onshore wake.
The non-uniform atmospheric velocity reflecting turbulent boundary layer is given in Eq. (13), and in page 8, we added on the turbulent intensity:
“Because the wake is obviously affected by the turbulence intensity, it is selected to be 5% for wind tunnel tests and 15% for real wind farm simulations in this research.”
5. The advantage of the proposed model with a prescribed velocity on the disk surface of is the faster convergence and the better simulation of flow for test cases. However, in practice, it is much more difficult to find data about this velocity field than on the axial force or the power of the real turbines. The originality of the proposed method is that the actuator disk is modeled with prescribed velocity field. If the authors wish to demonstrate its advantages, they must compare with other actuator disk methods as “volume source terms”, “pressure discontinuity” and “porous disk” under the same conditions.
In this major revision, we devoted most parts to the comparison with other models such as extended eddy viscous model [15] and porous disk model [16], and compared the present result for a given benchmark experimental validation with them in Fig. 7(b): see also page from 9 to 11.
6. The symbols Umin/Umax (Figure 4) are not described.
Not but , the ratio of minimum to the hub velocity (Because we used a boundary-layer wind speed in Eq. (13), the reference speed is selected that in the hub height.). To avoid this misunderstanding, the symbol is corrected to , and the explanation, “ : centerline velocity ratio at x=1.1D from the disk.” is added at the figure caption in Fig. 5(revised from Fig. 4 in the former version).
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Author Response File: 
Author Response.docx
Reviewer 2 Report
Reference 2 is missing from the Introduction. Please improve the language used in the paper. At the start of section2, its mentioned "In this chapter". Shouldn't it be section? Please provide more details and justification of mesh used. Also comment on mesh quality. What is the significance/meaning of different constants in equations 14 and 15? Please include more recent references. I see only one reference from 2019; none from 2018 or 2017.Author Response
Reference 2 is missing from the Introduction. Please improve the language used in the paper.Checking the reference list, introduction is corrected. We corrected some language error and typos.
2. At the start of section2, its mentioned "In this chapter". Shouldn't it be section?
Yes. In the revised text, “chapter” is substituted to “section”.
3. Please provide more details and justification of mesh used. Also comment on mesh quality.
We added in page 7: “…and to capture the complex flow phenomena at the wake region, the width three times disk diameter is focused to concentrate meshes since the cross-sectional area of stream tube is double of the disk area in the ideal momentum theory.”
The convergence test for the present computation is shown in Fig. 4(a-b) for various mesh scales.
4. What is the significance/meaning of different constants in equations 14 and 15?
Parametric study is expressed with a simplified correlations, and the physical meaning is added in the revised text, page 13, Eqs. (31-34). The sensitivity analysis concludes as:
“From Eqs. (31-34), the sensitivity is independent on the directions of configuration regardless of longitudinal () or lateral () ones. Comparing staggered and inline cases, the slope of staggered is almost three times in order that of inline. Therefore, the power efficiency in the staggered configuration increases far more than in the inline configuration, which will satisfy the general intuition.”
5. Please include more recent references. I see only one reference from 2019; none from 2018 or 2017. Wind Turbine Wake Characterization with Nacelle-Mounted Wind Lidars for Analytical Wake Model Validation,2018
We added a few references according to the reviewer’s suggestion:
[9] Carbajo Fuertes, F., Markfort, C.D., and Porte-Agel, F., 2018, “Wind Turbine Wake Characterization with Nacelle-Mounted Wind Lidars for Analytical Wake Model Validation,” Remote Sensing, 10(5), 668.
[17] Dilip, D., and Porte-Agel, F., 2017, “Wind Turbine Wake Mitigation through Blade Pitch Offset,” Energies, 10(5), 757. .
Author Response File: Author Response.docx
Reviewer 3 Report
The paper deals with a study on wake interaction in multiple wind turbines. The paper is well written and the results clearly presented.
Could the authors better explain how they have determined the turbine induction factor 'a' as a function of the turbine radius?
Could the author better explain the integration method ot their model within the CFD software?
These will make the paper stronger.
Author Response
The paper deals with a study on wake interaction in multiple wind turbines. The paper is well written and the results clearly presented.
Could the authors better explain how they have determined the turbine induction factor 'a' as a function of the turbine radius?Generally, , Eq, (1), and , but we specified it from the wind turbine test data. In the revised text, we added like in page :
“However, can depend on various conditions such as tip speed ratio, turbulence intensity, and other configuration variables, etc.”
2. Could the author better explain the integration method of their model within the CFD software? These will make the paper stronger.
The boundary condition on the actuator disk is explained more in detain in Eq. (12) and Eqs. (14-16), velocity components that are marked in the boundary on the actuator disk in the revised Fig. 3. Also we added some comments on the revised text.
We added in page 7: “…and to capture the complex flow phenomena at the wake region, the width three times disk diameter is focused to concentrate meshes since the cross-sectional area of stream tube is double of the disk area in the ideal momentum theory.”
The convergence test for the present computation is shown in Fig. 4(a-b) for various mesh scales.
Author Response File: Author Response.docx
Round 2
Reviewer 1 Report
Suggestion for future work: The relationship between axial induction and tangential induction factors is true for a perfect wind turbine (zero losses). As consequence, when the difference between actual TSR and the optimal TSR increases and becomes important, the proposed relation is not valid.
