the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 14 Aug 2023
The Multi-Scale Coupled Model: a New Framework Capturing Wind Farm-Atmosphere Interaction and Global Blockage Effects
Abstract. The growth in the number and size of wind energy projects in the last decade has revealed structural limitations in the current approach adopted by the wind industry to assess potential wind farm sites. These limitations are the result of neglecting the mutual interaction of large wind farms and the thermally-stratified atmospheric boundary layer. While currently available analytical models are sufficiently accurate to conduct site assessments for isolated rotors or small wind turbine clusters, the wind farm's interaction with the atmosphere cannot be neglected for large-size arrays. Specifically, the wind farm displaces the boundary layer vertically, triggering atmospheric gravity waves that induce large-scale horizontal pressure gradients. These perturbations in pressure alter the velocity field at the turbine locations, ultimately affecting global wind farm power production. The implication of such dynamics can also produce an extended blockage region upstream of the first turbines and a favorable pressure gradient inside the wind farm. In this paper, we present the multi-scale coupled (MSC) model, a novel approach that allows the simultaneous prediction of micro-scale effects occurring at the wind turbine scale, such as individual wake interactions and rotor induction, and meso-scale phenomena occurring at the wind farm scale and larger, such as atmospheric gravity waves. This is achieved by evaluating wake models on a spatially-heterogeneous background velocity field obtained from a reduced-order meso-scale model. The MSC model is validated against two large-eddy simulations (LES) with similar average inflow velocity profiles and a different capping inversion strength, so that two distinct interfacial gravity wave regimes are produced, i.e. subcritical and supercritical. Interfacial waves can produce high blockage in the first case, as they are allowed to propagate upstream. Conversely, in the supercritical regime their propagation speed is less than their advection velocity and upstream blockage is only operated by internal waves. The MSC model not only proves to successfully capture both local induction and global blockage effects in the two regimes, but also captures wind farm gravity-wave interaction, underestimating wind farm power by about only 2 % compared with the LES results. Conversely, wake models alone, even if combined with a local induction model, cannot distinguish between differences in thermal stratification, and are affected by a first-row over-prediction bias that leads to a consistent overestimation of the wind farm power by 13 % to 20 %.
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RC1: 'Comprehensive framework for engineering wind farm models addressing the modular coupling of mesoscale and microscale effects', Javier Sanz Rodrigo, 30 Aug 2023
Excellent work describing the MSC wind farm engineering model framework to simulate array interaction effects through a systematic approach that separates mesoscale and microscale scales. The authors made a great job breaking down the model in its different components and analyzing the differences with respect to simpler (industry standard) wake models and verifying against benchmark results from a high-fidelity LES model. The methodology is sound and the results speak for themselves as to the significant improvements from the earlier 3LM model.
I only have a few editorial suggestions and a couple of discussion points around the tuning and the practical application of the model.
In particular, is the re-tuning of the TI model not a contradiction with the modularity principle discussed in section 2.2 where one can “build upon already-existing sub-models, so that additional tuning parameters or individual sub-model re-tuning are not required”. I wonder if the tuning coefficients for a stand-alone wake model are equivalent to those used in the MSC framework. Is it appropriate to tune the TI model against LES simulations that account for global blockage effects while the wake model doesn’t? Is the separation of scales not happening in TI for now but something worth exploring in the future?
The authors use LES as “ground truth” to tune the TI model and quantify the correctness of the model in very specific neutral conditions. However, from an application point of view, the coefficients of an engineering model are also means to correct the mean bias when the model is integrated over the annual wind climate in a wide range of layout and siting conditions. I wonder if the authors could provide some insights about the foreseen calibration strategy using (observational) validation data, where separation of scales may not be possible. I guess LES offers a high-fidelity benchmark model to tune engineering models but you still need to train the models with measured data to mitigate outstanding biases. Would this training focus on some of the engineering model coefficients or additional ones to preserve the separation-of-scales principle?
Compared to traditional wake models, the MSC model requires significantly more input quantities, some of which are not accesible in wind resource measurement campaigns. While this may fall outside the scope of the paper, I would recommend the authors to discuss how the model could be used in connection to wind farm design. While the model shows significantly higher physical insight compared to traditional wake models it remains to be seen if the additional complexity does not bring additional uncertainties. Further investigation should focus on evaluating the added value of each module in the framework by quantifying accuracy in relevant quantities like AEP and array efficiency over a wide range of layout/siting conditions. These validation datasets would be useful to investigate training methodologies that provide a good trade-off between physical/numerical complexity and accuracy.
Additional comments:
53: duplicated “the”
109: For brevity, I would avoid the outline of the section “The present section is organized…” (likewise in subsequent sections)
185: what about Ct? which wind speed is it based upon?
207: the re-tuning of ds introduces quite a significant change in the turbulence intensity parameterization. This is indicative of the potentially large dependencies on the layout characteristics. Wouldn’t this imply that we need to recalibrate the model with additional LES simulations in new layouts? Otherwise the potential benefits from adding a better description of the mesoscale conditions would be compromised by the underlaying uncertainty of the microscale wake model. The additional cost of this recalibration would also penalize the use of the model as an engineering model.
311: “wake models are usually tuned on velocity for an isolated wind turbine wake”. Is this statement referring to equation (7) on the definition of the wake velocity deficit with respect to U∞ (without blockage)? If so, I would provide the cross-reference. Still, I would say the models are “defined”, not “tuned”, in terms of U∞ to be consistent with the same definition used in theoretical power/Ct curves for an isolated turbine.
316: “turbine thrust distribution” add cross-referenced equation (18).
342: I wouldn’t call (23) an ABL profile. This is rather a generalization of Monin-Obukhov surface-layer model to account for stability. An ABL model would be valid across all three layers. Surface-layer context is reinforced when you assume the the friction velocity only varies horizontally. Since this is only applied to the first layer I think it is appropriate to call it a surface-layer model. However, when extending the model to simulate stable conditions it may be worth exploring the use of a single-column ABL model with mixing-length parameterization.
452: “Reference potential temperature, inversion jump and lapse rate can be prescribed based on observations”. These quantities are not measured in conventional wind resource campaigns. Are you suggesting that the model requires these additional measurements? Wouldn’t it be more practical to rely on mesoscale simulations to characterize these inputs?
473: can you explain what the “fringe region” does?
580 (and elsewhere): Consider using the term “verification” instead of “validation” since you are doing code-to-code comparisons instead of comparing with measurements.
Citation: https://doi.org/10.5194/wes-2023-75-RC1 -
AC2: 'Reply on RC1', Sebastiano Stipa, 15 Nov 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2023-75/wes-2023-75-AC2-supplement.pdf
-
AC2: 'Reply on RC1', Sebastiano Stipa, 15 Nov 2023
-
RC2: 'Comment on wes-2023-75', Anonymous Referee #2, 16 Oct 2023
Summary
This is an excellent, highly relevant contribution to the field of wind farm atmosphere interaction, presenting a multiscale coupled model framework, coupling models that resolve effects from turbine scale to meso-scale. The paper is well written, and the authors provide a very clear description of the models and how they are coupled. The novelty of the contribution is the three-layer model reconstruction (3LMR), the background velocity reconstruction and the new wake superposition.
The MSC model is verified against results from LES simulations for two cases with neutral conditions in the boundary layer and stable conditions above, one supercritical and one subcritical.
The ability of the MSC to better capture the LES results than the earlier 3 layer model is evident. The MSC (and the LES it is verified against) clearly demonstrate the significance of the stability conditions above the boundary layer for the magnitude of the wind farm blockage.
While the verification against a LES simulation is a very valuable exercise, I would recommend as further work (not for the current paper, but as a follow up project to the current submission) some investigations comparing the model against field data (SCADA data as well as dual scanning lidar data measuring blockage upstream of wind farms). Once validating against field data, binning measurements for finite sectors, and averaging the model results over a range of directions, it is possible that some of the conclusions might change slightly, since derived from simulations for a single direction aligned with the wind farm layout.
For the current paper, I would also recommend to clarify that the magnitude of the effects reported, which imply large reduction in wind farm output, are only applicable for the conditions simulated, rather than over the typical overall conditions that will be experienced by a wind farm.
The MSC model can potentially deliver increased fidelity compared to standard engineering models for wakes and blockage, at the fraction of the cost of more expensive high-fidelity simulations such as RANS CFD or LES. How useful the model will end up being for the wind industry will depend on the ability for the users to source the many input parameters that the model requires. Inputs such as the potential temperature profile, the eddy viscosity profiles, the background wind angle profile, etc.. are typically not measured up to the heights of interest (i.e. through the boundary layer height). Have the authors already considered if the outputs from meso-scale models or re-analysis data sets could provide the required information?
More specific comments/questions are raised below for the authors' consideration.
Specific comments
Abstract: it would be a good idea to clarify that the ‘overestimation of the wind farm power by 13% to 20% ‘ is seen for the conditions modelled (~9 m/s at hub height, therefore high Ct, and also for very specific stability conditions) , rather than over the whole range of site conditions.
28: ‘cannot be described by a simple combination of individual wake deficits’ . Should this be softened a bit? Empirical wake models are doing reasonably ok on the wind farm sizes onto which they have been calibrated. May be say that models combining individual wake deficits have their limitations, and explain what these are (e.g. need for a wake superposition model, response to local changes in wind speed/turbulence intensity/shear/veer when these fall outside of the range within which the models have been typically validated).
33: when you write ‘Regarding blockage, or induction (Bleeg et al., 2018)’, this kind of suggests that Bleeg et al imply that blockage is synonym with induction. I don’t think this is the case. Might be better to add the reference to Bleeg et al at the end of the sentence. Because in the Bleeg et al results, the interaction between the wind farm and the thermally stratified atmosphere is very much playing a role in the magnitude of the wind farm blockage.
52: ‘reducing the free stream velocity’. Always reducing? I'd expect mesoscale effects for offshore wind farms operating downstream of a coastal transition to see acceleration of the freestream flow towards the back of the wind farm. Or possibly expect lateral gradients in the background flow if the fetch to the coast varies for different parts of the wind farm. Wouldn't you?
May be this is just because the ‘meso-scale effects’ accounted for by the 3LM are only those representing the feedback from the wind farm onto the background flow. If so , might it be worth clarifying?
54: ‘the coupling between the turbine-scale wake effects and the meso-scale global effects is weak…’: is this documented somewhere? If so, please provide a reference.
74-77: ‘In the subcritical regime … due to internal waves’. Does this belong to the discussion/conclusion section?
118: Questions about the three layers structure: Wind turbines are getting taller... assume a 15MW Vestas turbine, rotor diameter of ~ 240m with a hub height of ~2/3 the RD, has a tip height of 280m. Offshore boundary layer heights can be quite low. How high do you assume the geostrophic height to be above the turbine layer in the model? Could you please comment if this is compatible with realistic offshore conditions?
How are H1 and H2 set/defined?
141: where is the lapse rate defined? Lapse rate above the geostrophic level?
142: ‘dtetha is the potential temperature jump across the inversion layer’: how thick is the inversion layer? Is the thickness affecting the model results?
151: ‘zero vertical pressure gradient inside the ABL’: is this limiting the applicability of the model to neutral conditions in the boundary layer?
152: ‘p can only change in response to a vertical displacement of the ABL’ : Shouldn't p also respond to the presence of the wind farm, in that the horizontal p gradient is usually linked to the Coriolis term. If the wind farm removes momentum it also changes the balance between Coriolis and pressure gradient. If the pressure in the model is not responding to this change, does it mean that the model might produce some flow acceleration/deceleration which are not correct?
Or does this statement only apply to the pressure boundary condition that is the third layer?
175: ‘at wind turbine locations’. Should this be ‘at downstream wind turbine locations’?
312: ‘they do not account for turbine-ABL interaction’. I don't know that this statement is completely true... a lot of wake models, initially tuned on capturing single wakes, were re-tuned based on e.g. capturing PoP at wind farms such as Horns Rev/Nysted/Rodsand... rather than tuned against LES results... so, while they don't explicitly account for the turbine = ABL interaction, they implicitly account for some of it through their calibration.
Equations 21 & 22: how is mass conservation between layer 1 and 2 satisfied in the reconstruction step?
343: given that you include Coriolis in your model equations, how valid is your assumed inflow profile? (thinking about tall turbines that might reach into the Ekman layer)
Table 1 p18:
Is the background shear stress magnitude at the wall related to the friction velocity and the density? (i.e. if you have two of these as inputs, is the third one an input parameter too?)
What height is TI_inf taken (hub height?)
Section 3.1: the description of the LES methodology, with the use of precursor, successor simulations and the role of the fringe region could be more clearly explained.
473: ‘we use both periodic boundary conditions and a fringe region located at the domain inlet’: Do you mean a fringe region at the inflow has periodic BCs, and the resulting profile is applied at an inflow BC to the simulation domain downstream of the fringe region (as opposed to there being periodic BCs at the inflow and outflow downstream of the windfarm?
May be a schematic showing the respective domains would help, illustrating the quantities listed in Table 2 and 3.
493: ‘conducted on a domain smaller than the fringe region’: how large was this domain? Large enough to avoid artificially increasing the correlation between developing turbulence structure (from what I presume are periodic BCs).
495: ‘Inflow slices are then periodized along the spanwise direction and mapped at the concurrent precursor inlet, as it uses inflow-outflow boundary conditions in this initial phase’. Not sure what this means.
Table 4: delta h not defined. I can see it in the text in the next paragraph, but I think it should be defined in the paragraph above, where the other parameters are described.
532: ‘wake models alone’: do you mean ‘engineering wake models alone’?
‘would predict very similar power production for each individual turbine in the two cases’: Should you show the resulting TI values too to be able to state this? I suspect that the resulting TI at HH is similar for both N1 and N2, but may be this should be stated/checked.
Table 5: what is qmin?
Should the Froude numbers be added to this table for quick recollection of which case is which??
594-607: It would be really interesting to develop this section a bit, by adding some plots illustrating what you describe. Since the way engineering models capture (or not) the pattern of production down a line of turbine, and how accounting for blockage might change the redistribution of power between the front and the back of the wind farm are both still hotly debated in the industry.
597: do I understand that you are saying that the gradient in the pattern of production between the front and the back of the array is too steep in the engineering models compared to the LES, when mirroring the turbines? Could this be an issue associated with looking at narrow direction bins, and the fact that you are modelling a layout aligned with the wind direction?
The LES, by resolving the direction fluctuation, will naturally include some effect that would represent wake meandering, while the engineering models, when operating steady state, tend to ignore this. Did you account for direction uncertainty when processing the results from the engineering models? Something like the averaging discussed in Gaumond et al ,Wind Energ. 2014; 17:1169–1178?
Same question about the results from the MSC? Are the results for a single wind direction aligned with the wind farm layout, or are you also averaging results for a finite sector width, accounting for direction uncertainty?
601: ‘in agreement with many previous literature studies’ . Please include references.
609: ‘As the NREL 5-MW thrust curve is not available in official literature..’: this must have been an issue for the LES run too no? How did you deal with this then? Should this be mentioned earlier, when mentioning NREL turbine used in the LES? was the thrust and PC used in the LES consistent with that used in the MSC model?
610: ‘with uniform, non-turbulent inflow’: non-turbulent ? really ? thrust and PC curve typically depend on background conditions, such as TI, shear, ... is this the right approach? Or when saying ‘non-turbulent’, do you mean the turbine is operating in background turbulence only (i.e. no added turbulence from neighbouring turbines)
639: ‘while depth averaged perturbation velocities are overestimated ‘: similar to earlier comment: It would be interesting to find out how your MSC results would change if you
- work out what is the typical wind direction standard deviation at one point in the precursor LES run, use this as a measured of the wind direction (WD) uncertainty and
- carry out additional MSC runs for directions 1-2 stdev away, then average the MSC results over a few directions.
My expectations would be that the pressure signal is not changing much but the velocity might.
Another point to consider is that you appear to be using constant eddy viscosities in the MSC runs, while the LES will have variable turbulence intensity within the wind farm (low in the first 4-5 row, then saturating at a higher value deeper within the array. This will also affect wake recovery, and to some extent the WD uncertainty). OK. I see you mention this lower down.
644: ‘While such limitations…’ : Surely the pressure field is a function of the velocity deficit within the wind farm (which via mass conservation which conditions the vertical displacement at the inversion, which itself will feedback on the pressure). So, is the fact that different velocity distributions between the LES and MSC lead to similar pressure distributions a happy accident? i.e. does it relate to the integrated velocity deficit within the wind farm rather than the shape of the velocity deficit profile?
Figure 11: LES results are time averaged? over what time period? Surprised by the streakiness along the flow direction. What is causing this? not enough distance between the periodic inflow/outflow, leading to turbulence structures which have wrong spatial correlation properties?
720: ‘at least 10%’ . Please clarify that this is for the simulated conditions, at high thrust.
731: again, please clarify that the lapse rate is above the boundary layer
732: mention of inversion strength, but not inversion thickness. Is this because your results are not sensitive to this?
Technical corrections
53: duplicate ‘the’
146: symbol kappa is used here for a wavenumber vector, and later as the von Karman constant. May be use bold k rather than bold kappa.
Table 2 showing after Table 3.
625: ‘This is…’ instead of ‘These is ..’
647: ‘those’ instead of ‘the ones’
689: redundant ‘it’ after the reference to Bleeg et al
Citation: https://doi.org/10.5194/wes-2023-75-RC2 -
AC1: 'Reply on RC2', Sebastiano Stipa, 15 Nov 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2023-75/wes-2023-75-AC1-supplement.pdf
Status: closed
-
RC1: 'Comprehensive framework for engineering wind farm models addressing the modular coupling of mesoscale and microscale effects', Javier Sanz Rodrigo, 30 Aug 2023
Excellent work describing the MSC wind farm engineering model framework to simulate array interaction effects through a systematic approach that separates mesoscale and microscale scales. The authors made a great job breaking down the model in its different components and analyzing the differences with respect to simpler (industry standard) wake models and verifying against benchmark results from a high-fidelity LES model. The methodology is sound and the results speak for themselves as to the significant improvements from the earlier 3LM model.
I only have a few editorial suggestions and a couple of discussion points around the tuning and the practical application of the model.
In particular, is the re-tuning of the TI model not a contradiction with the modularity principle discussed in section 2.2 where one can “build upon already-existing sub-models, so that additional tuning parameters or individual sub-model re-tuning are not required”. I wonder if the tuning coefficients for a stand-alone wake model are equivalent to those used in the MSC framework. Is it appropriate to tune the TI model against LES simulations that account for global blockage effects while the wake model doesn’t? Is the separation of scales not happening in TI for now but something worth exploring in the future?
The authors use LES as “ground truth” to tune the TI model and quantify the correctness of the model in very specific neutral conditions. However, from an application point of view, the coefficients of an engineering model are also means to correct the mean bias when the model is integrated over the annual wind climate in a wide range of layout and siting conditions. I wonder if the authors could provide some insights about the foreseen calibration strategy using (observational) validation data, where separation of scales may not be possible. I guess LES offers a high-fidelity benchmark model to tune engineering models but you still need to train the models with measured data to mitigate outstanding biases. Would this training focus on some of the engineering model coefficients or additional ones to preserve the separation-of-scales principle?
Compared to traditional wake models, the MSC model requires significantly more input quantities, some of which are not accesible in wind resource measurement campaigns. While this may fall outside the scope of the paper, I would recommend the authors to discuss how the model could be used in connection to wind farm design. While the model shows significantly higher physical insight compared to traditional wake models it remains to be seen if the additional complexity does not bring additional uncertainties. Further investigation should focus on evaluating the added value of each module in the framework by quantifying accuracy in relevant quantities like AEP and array efficiency over a wide range of layout/siting conditions. These validation datasets would be useful to investigate training methodologies that provide a good trade-off between physical/numerical complexity and accuracy.
Additional comments:
53: duplicated “the”
109: For brevity, I would avoid the outline of the section “The present section is organized…” (likewise in subsequent sections)
185: what about Ct? which wind speed is it based upon?
207: the re-tuning of ds introduces quite a significant change in the turbulence intensity parameterization. This is indicative of the potentially large dependencies on the layout characteristics. Wouldn’t this imply that we need to recalibrate the model with additional LES simulations in new layouts? Otherwise the potential benefits from adding a better description of the mesoscale conditions would be compromised by the underlaying uncertainty of the microscale wake model. The additional cost of this recalibration would also penalize the use of the model as an engineering model.
311: “wake models are usually tuned on velocity for an isolated wind turbine wake”. Is this statement referring to equation (7) on the definition of the wake velocity deficit with respect to U∞ (without blockage)? If so, I would provide the cross-reference. Still, I would say the models are “defined”, not “tuned”, in terms of U∞ to be consistent with the same definition used in theoretical power/Ct curves for an isolated turbine.
316: “turbine thrust distribution” add cross-referenced equation (18).
342: I wouldn’t call (23) an ABL profile. This is rather a generalization of Monin-Obukhov surface-layer model to account for stability. An ABL model would be valid across all three layers. Surface-layer context is reinforced when you assume the the friction velocity only varies horizontally. Since this is only applied to the first layer I think it is appropriate to call it a surface-layer model. However, when extending the model to simulate stable conditions it may be worth exploring the use of a single-column ABL model with mixing-length parameterization.
452: “Reference potential temperature, inversion jump and lapse rate can be prescribed based on observations”. These quantities are not measured in conventional wind resource campaigns. Are you suggesting that the model requires these additional measurements? Wouldn’t it be more practical to rely on mesoscale simulations to characterize these inputs?
473: can you explain what the “fringe region” does?
580 (and elsewhere): Consider using the term “verification” instead of “validation” since you are doing code-to-code comparisons instead of comparing with measurements.
Citation: https://doi.org/10.5194/wes-2023-75-RC1 -
AC2: 'Reply on RC1', Sebastiano Stipa, 15 Nov 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2023-75/wes-2023-75-AC2-supplement.pdf
-
AC2: 'Reply on RC1', Sebastiano Stipa, 15 Nov 2023
-
RC2: 'Comment on wes-2023-75', Anonymous Referee #2, 16 Oct 2023
Summary
This is an excellent, highly relevant contribution to the field of wind farm atmosphere interaction, presenting a multiscale coupled model framework, coupling models that resolve effects from turbine scale to meso-scale. The paper is well written, and the authors provide a very clear description of the models and how they are coupled. The novelty of the contribution is the three-layer model reconstruction (3LMR), the background velocity reconstruction and the new wake superposition.
The MSC model is verified against results from LES simulations for two cases with neutral conditions in the boundary layer and stable conditions above, one supercritical and one subcritical.
The ability of the MSC to better capture the LES results than the earlier 3 layer model is evident. The MSC (and the LES it is verified against) clearly demonstrate the significance of the stability conditions above the boundary layer for the magnitude of the wind farm blockage.
While the verification against a LES simulation is a very valuable exercise, I would recommend as further work (not for the current paper, but as a follow up project to the current submission) some investigations comparing the model against field data (SCADA data as well as dual scanning lidar data measuring blockage upstream of wind farms). Once validating against field data, binning measurements for finite sectors, and averaging the model results over a range of directions, it is possible that some of the conclusions might change slightly, since derived from simulations for a single direction aligned with the wind farm layout.
For the current paper, I would also recommend to clarify that the magnitude of the effects reported, which imply large reduction in wind farm output, are only applicable for the conditions simulated, rather than over the typical overall conditions that will be experienced by a wind farm.
The MSC model can potentially deliver increased fidelity compared to standard engineering models for wakes and blockage, at the fraction of the cost of more expensive high-fidelity simulations such as RANS CFD or LES. How useful the model will end up being for the wind industry will depend on the ability for the users to source the many input parameters that the model requires. Inputs such as the potential temperature profile, the eddy viscosity profiles, the background wind angle profile, etc.. are typically not measured up to the heights of interest (i.e. through the boundary layer height). Have the authors already considered if the outputs from meso-scale models or re-analysis data sets could provide the required information?
More specific comments/questions are raised below for the authors' consideration.
Specific comments
Abstract: it would be a good idea to clarify that the ‘overestimation of the wind farm power by 13% to 20% ‘ is seen for the conditions modelled (~9 m/s at hub height, therefore high Ct, and also for very specific stability conditions) , rather than over the whole range of site conditions.
28: ‘cannot be described by a simple combination of individual wake deficits’ . Should this be softened a bit? Empirical wake models are doing reasonably ok on the wind farm sizes onto which they have been calibrated. May be say that models combining individual wake deficits have their limitations, and explain what these are (e.g. need for a wake superposition model, response to local changes in wind speed/turbulence intensity/shear/veer when these fall outside of the range within which the models have been typically validated).
33: when you write ‘Regarding blockage, or induction (Bleeg et al., 2018)’, this kind of suggests that Bleeg et al imply that blockage is synonym with induction. I don’t think this is the case. Might be better to add the reference to Bleeg et al at the end of the sentence. Because in the Bleeg et al results, the interaction between the wind farm and the thermally stratified atmosphere is very much playing a role in the magnitude of the wind farm blockage.
52: ‘reducing the free stream velocity’. Always reducing? I'd expect mesoscale effects for offshore wind farms operating downstream of a coastal transition to see acceleration of the freestream flow towards the back of the wind farm. Or possibly expect lateral gradients in the background flow if the fetch to the coast varies for different parts of the wind farm. Wouldn't you?
May be this is just because the ‘meso-scale effects’ accounted for by the 3LM are only those representing the feedback from the wind farm onto the background flow. If so , might it be worth clarifying?
54: ‘the coupling between the turbine-scale wake effects and the meso-scale global effects is weak…’: is this documented somewhere? If so, please provide a reference.
74-77: ‘In the subcritical regime … due to internal waves’. Does this belong to the discussion/conclusion section?
118: Questions about the three layers structure: Wind turbines are getting taller... assume a 15MW Vestas turbine, rotor diameter of ~ 240m with a hub height of ~2/3 the RD, has a tip height of 280m. Offshore boundary layer heights can be quite low. How high do you assume the geostrophic height to be above the turbine layer in the model? Could you please comment if this is compatible with realistic offshore conditions?
How are H1 and H2 set/defined?
141: where is the lapse rate defined? Lapse rate above the geostrophic level?
142: ‘dtetha is the potential temperature jump across the inversion layer’: how thick is the inversion layer? Is the thickness affecting the model results?
151: ‘zero vertical pressure gradient inside the ABL’: is this limiting the applicability of the model to neutral conditions in the boundary layer?
152: ‘p can only change in response to a vertical displacement of the ABL’ : Shouldn't p also respond to the presence of the wind farm, in that the horizontal p gradient is usually linked to the Coriolis term. If the wind farm removes momentum it also changes the balance between Coriolis and pressure gradient. If the pressure in the model is not responding to this change, does it mean that the model might produce some flow acceleration/deceleration which are not correct?
Or does this statement only apply to the pressure boundary condition that is the third layer?
175: ‘at wind turbine locations’. Should this be ‘at downstream wind turbine locations’?
312: ‘they do not account for turbine-ABL interaction’. I don't know that this statement is completely true... a lot of wake models, initially tuned on capturing single wakes, were re-tuned based on e.g. capturing PoP at wind farms such as Horns Rev/Nysted/Rodsand... rather than tuned against LES results... so, while they don't explicitly account for the turbine = ABL interaction, they implicitly account for some of it through their calibration.
Equations 21 & 22: how is mass conservation between layer 1 and 2 satisfied in the reconstruction step?
343: given that you include Coriolis in your model equations, how valid is your assumed inflow profile? (thinking about tall turbines that might reach into the Ekman layer)
Table 1 p18:
Is the background shear stress magnitude at the wall related to the friction velocity and the density? (i.e. if you have two of these as inputs, is the third one an input parameter too?)
What height is TI_inf taken (hub height?)
Section 3.1: the description of the LES methodology, with the use of precursor, successor simulations and the role of the fringe region could be more clearly explained.
473: ‘we use both periodic boundary conditions and a fringe region located at the domain inlet’: Do you mean a fringe region at the inflow has periodic BCs, and the resulting profile is applied at an inflow BC to the simulation domain downstream of the fringe region (as opposed to there being periodic BCs at the inflow and outflow downstream of the windfarm?
May be a schematic showing the respective domains would help, illustrating the quantities listed in Table 2 and 3.
493: ‘conducted on a domain smaller than the fringe region’: how large was this domain? Large enough to avoid artificially increasing the correlation between developing turbulence structure (from what I presume are periodic BCs).
495: ‘Inflow slices are then periodized along the spanwise direction and mapped at the concurrent precursor inlet, as it uses inflow-outflow boundary conditions in this initial phase’. Not sure what this means.
Table 4: delta h not defined. I can see it in the text in the next paragraph, but I think it should be defined in the paragraph above, where the other parameters are described.
532: ‘wake models alone’: do you mean ‘engineering wake models alone’?
‘would predict very similar power production for each individual turbine in the two cases’: Should you show the resulting TI values too to be able to state this? I suspect that the resulting TI at HH is similar for both N1 and N2, but may be this should be stated/checked.
Table 5: what is qmin?
Should the Froude numbers be added to this table for quick recollection of which case is which??
594-607: It would be really interesting to develop this section a bit, by adding some plots illustrating what you describe. Since the way engineering models capture (or not) the pattern of production down a line of turbine, and how accounting for blockage might change the redistribution of power between the front and the back of the wind farm are both still hotly debated in the industry.
597: do I understand that you are saying that the gradient in the pattern of production between the front and the back of the array is too steep in the engineering models compared to the LES, when mirroring the turbines? Could this be an issue associated with looking at narrow direction bins, and the fact that you are modelling a layout aligned with the wind direction?
The LES, by resolving the direction fluctuation, will naturally include some effect that would represent wake meandering, while the engineering models, when operating steady state, tend to ignore this. Did you account for direction uncertainty when processing the results from the engineering models? Something like the averaging discussed in Gaumond et al ,Wind Energ. 2014; 17:1169–1178?
Same question about the results from the MSC? Are the results for a single wind direction aligned with the wind farm layout, or are you also averaging results for a finite sector width, accounting for direction uncertainty?
601: ‘in agreement with many previous literature studies’ . Please include references.
609: ‘As the NREL 5-MW thrust curve is not available in official literature..’: this must have been an issue for the LES run too no? How did you deal with this then? Should this be mentioned earlier, when mentioning NREL turbine used in the LES? was the thrust and PC used in the LES consistent with that used in the MSC model?
610: ‘with uniform, non-turbulent inflow’: non-turbulent ? really ? thrust and PC curve typically depend on background conditions, such as TI, shear, ... is this the right approach? Or when saying ‘non-turbulent’, do you mean the turbine is operating in background turbulence only (i.e. no added turbulence from neighbouring turbines)
639: ‘while depth averaged perturbation velocities are overestimated ‘: similar to earlier comment: It would be interesting to find out how your MSC results would change if you
- work out what is the typical wind direction standard deviation at one point in the precursor LES run, use this as a measured of the wind direction (WD) uncertainty and
- carry out additional MSC runs for directions 1-2 stdev away, then average the MSC results over a few directions.
My expectations would be that the pressure signal is not changing much but the velocity might.
Another point to consider is that you appear to be using constant eddy viscosities in the MSC runs, while the LES will have variable turbulence intensity within the wind farm (low in the first 4-5 row, then saturating at a higher value deeper within the array. This will also affect wake recovery, and to some extent the WD uncertainty). OK. I see you mention this lower down.
644: ‘While such limitations…’ : Surely the pressure field is a function of the velocity deficit within the wind farm (which via mass conservation which conditions the vertical displacement at the inversion, which itself will feedback on the pressure). So, is the fact that different velocity distributions between the LES and MSC lead to similar pressure distributions a happy accident? i.e. does it relate to the integrated velocity deficit within the wind farm rather than the shape of the velocity deficit profile?
Figure 11: LES results are time averaged? over what time period? Surprised by the streakiness along the flow direction. What is causing this? not enough distance between the periodic inflow/outflow, leading to turbulence structures which have wrong spatial correlation properties?
720: ‘at least 10%’ . Please clarify that this is for the simulated conditions, at high thrust.
731: again, please clarify that the lapse rate is above the boundary layer
732: mention of inversion strength, but not inversion thickness. Is this because your results are not sensitive to this?
Technical corrections
53: duplicate ‘the’
146: symbol kappa is used here for a wavenumber vector, and later as the von Karman constant. May be use bold k rather than bold kappa.
Table 2 showing after Table 3.
625: ‘This is…’ instead of ‘These is ..’
647: ‘those’ instead of ‘the ones’
689: redundant ‘it’ after the reference to Bleeg et al
Citation: https://doi.org/10.5194/wes-2023-75-RC2 -
AC1: 'Reply on RC2', Sebastiano Stipa, 15 Nov 2023
The comment was uploaded in the form of a supplement: https://wes.copernicus.org/preprints/wes-2023-75/wes-2023-75-AC1-supplement.pdf
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