Numerical Simulation of Ice Crystal Accretion and Aerodynamic Impacts on Wind Turbine Blades in Cold Climates
Round 1
Reviewer 1 Report
Comments and Suggestions for AuthorsThis paper relates to Ice Crystal Icing on a wind turbine. However, it is merely a parameter study using the commercial code FENSAP-ICE. The reliability of the numerical results is not guaranteed because of the lack of the grid independence study, the validation study for ice crystal icing (not droplet icing), no descriptions/explanations of the models for stick, rebound, and break-up of an ice crystal on a wall and an ice surface, the secondary droplet generation at the impact of an ice crystal on a water film, and ice erosion.
The authors must revise the paper for these points.
Author Response
Response to the reviewer #1
- The reliability of the numerical results is not guaranteed because of the lack of a grid independence study
- The validation study for ice crystal icing (not droplet icing)
- No descriptions/explanations of the models for stick, rebound, and break-up of an ice crystal on a wall and an ice surface, the secondary droplet generation at the impact of an ice crystal on a water film, and ice erosion.
Response: We greatly appreciate the reviewer for encouraging comments and helpful suggestions. According to the reviewer’s suggestions, we have made a global refinement and verification of the whole manuscript. The detailed modifications are listed as follows:
Comments 1: The reliability of the numerical results is not guaranteed because of the lack of a grid independence study.
Author response 1: We thank the reviewer for highlighting the importance of mesh independence. In response to the reviewer's comment, we have added a detailed explanation of the mesh independence study to the manuscript. The relevant additions to the revised manuscript are as follows:
“The number of elements significantly impacts the calculation results. To accurately simulate the flow process, five different numbers of elements were used to calculate the lift coefficient, and the results are shown in Fig. 3.
Figure. 3 The lift coefficient versus the number of elements.
From Fig. 3, it can be observed that the lift coefficient exhibits a converging trend as the number of elements increases, eventually reaching an asymptotic value of 1.0. When the number of elements was approximately 170,000, the mesh growth ratio was set to 1.1, achieving a mesh quality of 0.95, as shown in Figure 2(b). The accuracy of the grid with approximately 170,000 mesh elements was verified using experimental data from NASA’s turbulence modeling resource[27].”
Comments 2: The validation study for ice crystal icing (not droplet icing).
Author response 2: We appreciate the reviewer's attention to the ice crystal icing validation study. In the icing process of wind turbine blades, unlike aircraft engines, ice crystals do not melt or refreeze. When ice crystals strike the surface of wind turbine blades, solid particles collide with the blade and no ice accretion occurs. We have carried out a detailed study of this process and the results confirm that no ice accretion forms on the blade surface.
Comments 3: No descriptions/explanations of the models for stick, rebound, and break-up of an ice crystal on a wall and an ice surface, the secondary droplet generation at the impact of an ice crystal on a water film, and ice erosion.
Author response 3: Thank you very much for your detailed comments. We have included the relevant models (equations 13 and 14) in the revised manuscript, which provide detailed descriptions of the processes of adhesion, rebound and erosion of ice crystals on surfaces. However, after careful review of the FENSAP help documentation and the FLUENT theoretical manual, we regret that no explicit models for secondary droplet formation were found for the impact of ice crystals on a water film. We have therefore added section 3.1, "The role of ice crystals in the icing process", to the revised manuscript to describe this phenomenon. We hope that this addition clarifies the process. The relevant additions to the manuscript are as follows:
“The droplet impacting a solid surface generally experiences the spreading, retraction, oscillation, splash, rebound or adhesion stages[28][29]. Finally, the droplets adhering to the blade surface are driven by the airflow towards the trailing edge and form a liquid film. The film is affected by heat transfer on the blade surface and convective heat transfer with the surrounding cold air. The freezing process can be divided into five stages based on the temperature transition characteristics[30][31]: liquid cooling, nucleation, recalescence, solidification, and solid cooling. The ice crystals significantly affect the distribution of the accumulated ice on the blade surface. Therefore, ice crystals play a multifaceted role in the icing process, affecting both the droplet impact and freezing stages. Based on previous studies of supercooled droplet icing, new insights have been gained into the combined effects of ice crystals and droplets on the icing process, as shown in Fig 5.
Figure. 5 The blade icing process.
As the ice crystals collide with the water film, droplet splashing occurs, generating secondary droplets. Additionally, the sheet-like structure of the ice crystals adheres more readily to the water film. As the adhered ice crystals accumulate, the fluidity of the water film decreases, leading to a higher concentration of the water film at the blade’s leading edge. The water film releases heat through convective heat transfer and thermal conduction, which wraps around the ice crystals and causes gradual freezing, as illustrated in Figure 5(b). As the operation continues, the accumulated ice on the blade surface tends to form layered structures, increasing the ice thickness and expanding the coverage area. Furthermore, when ice crystals impact the accumulated ice on the blade surface, ice crystals continuously erode the existing ice layer, as shown in Figure 5(c).”
Author Response File: 
Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsPlease see the comments file.
Comments for author File: Comments.pdf
Author Response
Response to the reviewer #2
(1). In Fig. 1, Ice accetion should be Ice accretion.
(2). In Eq. 5, the user-defined source term. Please authors explain more detail in the simulation.
(3). Please authors check the consistency of equation/Equation throughout the manuscript.
(4). In section 2.3, the authors mentioned, "The drag coefficients of ice crystals are derived based on an
aspect ratio of 0.05; the derived drag coefficients of ice crystals are still valid when the aspect ratios are
more than 0.5." Please, authors, explain more about this and prove how. If there is some reference,
please refer.
(5). Please, authors, explain why the NACA0012 airfoil was chosen in this work.
(6). In Table 1, the ambient temperature was set at 15℃. Is this value related to the condition of icing? Also,
is it a coincidence with other simulation models?
(7). In Table 2,l AOA for experimentation to validate was set at 4°. While in the simulation the test cases
were set at 10° and 15°. Please authors explain and verify, also, in Table 3.
(8). Please authors check the consistency of AOA and AoA.
Author response: Thanks very much for the reviewer’s suggestion. According to the reviewer’s
suggestions, we have made a global refinement and verification of the whole manuscript. The detailed
modifications are listed as follows:
Comments 1: In Fig. 1, Ice accetion should be Ice accretion.
Author response 1: Thank you for your careful and thoughtful review. We have corrected "Ice
accetion" to "Ice accretion" in the revised manuscript.
Comments 2: In Eq. 5, the user-defined source term. Please authors explain more detail in the
simulation.
Author response 2: We appreciate the reviewer's attention to this issue. In this study, no specific
settings were applied to the user-defined source term and it was set to zero during the simulations.
The reasons for this are as follows:
In the Spalart-Allmaras turbulence model, the user-defined source can be modified or extended
based on the physical characteristics of specific problems. For example, it can be used to introduce
additional turbulence effects, external forces or specific turbulence dissipation mechanisms to
improve accuracy.
In this study, the user-defined source term was set to zero, but the simulation results still showed
strong agreement with the experimental data, as shown in Figure 4. This demonstrates that the
model can accurately simulate turbulence characteristics without the need for additional
modifications.
Comments 3: Please authors check the consistency of equation/Equation throughout the
manuscript.
Author response 3: Thank you for your suggestion. We have changed "equation" to "equation"
throughout the manuscript to ensure consistency.
Comments 4: In section 2.3, the authors mentioned, "The drag coefficients of ice crystals are
derived based on an aspect ratio of 0.05; the derived drag coefficients of ice crystals are still valid
when the aspect ratios are more than 0.5." Please, authors, explain more about this and prove how.
If there is some reference, please refer.
Author response 4: Thank you for your suggestion. This statement is derived from the FENSAP
help documentation, and we have referred to it in the revised manuscript.
Comments 5: Please, authors, explain why the NACA0012 airfoil was chosen in this work.
Author response 5: The NACA0012 airfoil is widely used and has extensive experimental data.
These data are well-documented, reliable, and helpful for validating the numerical simulations in
this work.
Comments 6: In Table 1, the ambient temperature was set at 15℃. Is this value related to the
condition of icing? Also, is it a coincidence with other simulation models?
Author response 6: This value is not related to the icing condition. It was set to 15℃ to match the
temperature used in the comparison experiment. This setting was done to verify the accuracy of
flow field calculations.
Comments 7: In Table 2,l AOA for experimentation to validate was set at 4°. While in the
simulation the test cases were set at 10° and 15°. Please authors explain and verify, also, in Table 3.
Author response 7: There is no significant correlation between the data presented in Table 1 and
Table 2. Table 1 is employed to validate the accuracy of the flow field simulation, whereas Table 2
is used to verify the accuracy of the icing process simulation. It should be noted that the research
conditions differ because the data were selected from different experiments. Unfortunately, it was
not possible to obtain flow field and icing experimental data under the same conditions.
Comments 8: Please authors check the consistency of AOA and AoA.
Author response 8: Thank you very much for your careful review. We have revised "AOA" to
"AoA" throughout the manuscript to ensure consistency. All typo and grammar errors have been
corrected in the revised manuscript.
Author Response File: Author Response.pdf
Reviewer 3 Report
Comments and Suggestions for AuthorsThe work is interesting.
A review of the literature gives a sufficient view of the physical problem analyzed. The Authors have concentrated their attention on works devoted to wind turbines, although the problem of aircraft icing is both older and more extensive.
In the case of wind turbine blades, there is the additional problem of the presence of large centrifugal forces acting along the leading edge and having a more significant effect than gravitational forces.
The Authors presented a general set of equations describing the build-up of the ice layer. OK. However, it seems that local models for the interaction of water droplets with the surface and the interaction of ice crystals with the dry surface and the water film are missing. Probably these models exist and are used, but they are not presented in the paper.
Nothing is known about the boundary conditions. On the inlet to the computational area and on the surface of the lobe. What is the boundary condition on the airfoil. Constant temperature? A condition of adiabaticity of the wall? Or some other?
The Spalart-Allmaras turbulence model equation is used. However, there is no information about the values of the turbulence level and its spatial magnitude in the inlet section.
The process of growing an ice layer on the leading edge of a wind turbine blade is a process that takes place over time. The thickness of the ice layer changes over time.
Information about the time of obtaining the visually presented icing results can be found only in Tables 2, 3, 4. This information is missing from the drawings presenting the shapes of the ice layer on the leading edge. There is such information only in one figure, figure 8.
Why are the icing times equal 360 sec and 600 sec?
Why is the process of increasing thickness and shape of the growing ice layer not shown?
Is this process regular? Does it propagate in some directions roughly parallel to the surface of the blade? Is the speed constant? How does the surface temperature of the airfoil change?
What I miss in the paper is the presentation of some results that the authors hale, but do not present.
The Authors indicated at least two geometric forms of the emerging ice structure. See Figures 4 a) and 4 b).
These forms are characterized by a different flow structure. Potential areas of detachment and recirculation are important.
It would be interesting to show velocities in these areas, vorticity, pathlines, temperatures, heat fluxes.
The process is undetermined, with the authors indicating some fluid movement and flow across the surface of the adhered ice to the leading edge.
Fig. 4 a) and b) present some instantaneous shapes of the ice growth. From Table 2 it appears that they refer to the state after 360 sec. Why after such? What will happen next?
Table 3 shows that the relative velocity is 50, 100, 150, 200 m/s.
For what relative velocity were the results presented in Figures 5, 6 and 7 obtained ?
In the description of the phenomena occurring in the formation of the ice layer, the authors include a beautiful description:” As shown in Fig. 4(a), when supercooled droplets in the airflow hit the leading edge of the blade, the pressure near the leading edge is reduced due to an increase in flow velocity. Liquid water formed at the stagnation point travels toward surfaces with lower pressure and begins to form ice horns.” The description is a beautiful story, but either based on information not included in the paper or is a thoughtful interpretation by the authors.
Figure 8 shows global changes in flow structure, but they are generated by local changes, deformations, in profile shape caused by the build-up of the ice layer. Shouldn't there be zoom boxes showing the form of deformation of the shape of the leading edge?
Especially when the authors report:” As shown in Fig 8, when the AOA ranged from 5° to 20°, the ice shape caused by the liquid droplets exhibited distinct ice corners.”. This is not shown in Fig. 8.
Further: “At an AOA of 15°, separation vortices formed at the trailing edge of the airfoil under both ice accretion conditions.Compared to the ice shape formed under the combined effect of ice crystals and droplets, the ice shape caused by droplets alone produced a larger separation vortex near the trailing edge.”
This observation is true, but the cause is a local separation near the leading edge, not the trailing edge. Here again, zooming in on the pathlines around the trailing edge would be useful. Because here is the source of the detachment.
Overall, the work is interesting, but the mathematical description of the numerically modeled physical processes is described too briefly.
The main novelty of the work is the addition to the physics of water droplet freezing, the existence of ice crystals in the incoming air and consideration of their influence on the way the ice layer grows.
The results of simulating the influence of a number of inlet parameters, such as the size of the ice crystals, aspect ratio of ice crystals, concentration of ice crystals are presented in a clear way.
The authors' attempts at physical interpretation are noteworthy, but should be supported by the information presented in the work and not just intuitive confabulations.
The work, after minor modifications and additions, is suitable for publication.
Author Response
Response to the reviewer #3
（1）The Authors presented a general set of equations describing the build-up of the ice layer. OK. However, it seems that local models for the interaction of water droplets with the surface and the interaction of ice crystals with the dry surface and the water film are missing. Probably these models exist and are used, but they are not presented in the paper.
（2）Nothing is known about the boundary conditions. On the inlet to the computational area and on the surface of the lobe. What is the boundary condition on the airfoil. Constant temperature? A condition of adiabaticity of the wall? Or some other?
（3）The Spalart-Allmaras turbulence model equation is used. However, there is no information about the values of the turbulence level and its spatial magnitude in the inlet section.
（4）The process of growing an ice layer on the leading edge of a wind turbine blade is a process that takes place over time. The thickness of the ice layer changes over time. Information about the time of obtaining the visually presented icing results can be found only in Tables 2, 3, 4. This information is missing from the drawings presenting the shapes of the ice layer on the leading edge. There is such information only in one figure, figure 8. Why is the process of increasing thickness and shape of the growing ice layer not shown? Is this process regular? Does it propagate in some directions roughly parallel to the surface of the blade? Is the speed constant? How does the surface temperature of the airfoil change?
（5）Why are the icing times equal 360 sec and 600 sec? Fig. 4 a) and b) present some instantaneous shapes of the ice growth. From Table 2 it appears that they refer to the state after 360 sec. Why after such? What will happen next?
（6）These forms are characterized by a different flow structure. Potential areas of detachment and recirculation are important. It would be interesting to show velocities in these areas, vorticity, pathlines, temperatures, heat fluxes.
（7）Table 3 shows that the relative velocity is 50, 100, 150, 200 m/s. For what relative velocity were the results presented in Figures 5, 6 and 7 obtained ?
（8）Figure 8 shows global changes in flow structure, but they are generated by local changes, deformations, in profile shape caused by the build-up of the ice layer. Shouldn't there be zoom boxes showing the form of deformation of the shape of the leading edge?
（9）Especially when the authors report:” As shown in Fig 8, when the AOA ranged from 5° to 20°, the ice shape caused by the liquid droplets exhibited distinct ice corners.”. This is not shown in Fig. 8. Further: “At an AOA of 15°, separation vortices formed at the trailing edge of the airfoil under both ice accretion conditions.Compared to the ice shape formed under the combined effect of ice crystals and droplets, the ice shape caused by droplets alone produced a larger separation vortex near the trailing edge.” This observation is true, but the cause is a local separation near the leading edge, not the trailing edge. Here again, zooming in on the pathlines around the trailing edge would be useful. Because here is the source of the detachment.
Response: We greatly appreciate the reviewer for encouraging comments and helpful suggestions. According to the reviewer’s suggestions, we have made a global refinement and verification of the whole manuscript. The detailed modifications are listed as follows:
Comments 1: The Authors presented a general set of equations describing the build-up of the ice layer. OK. However, it seems that local models for the interaction of water droplets with the surface and the interaction of ice crystals with the dry surface and the water film are missing. Probably these models exist and are used, but they are not presented in the paper.
Response 1: Thank you very much for your detailed comments. We have included the relevant models (equations 13 and 14) in the revised manuscript, which provide detailed descriptions of the processes of adhesion, rebound and erosion of ice crystals on surfaces.
Comments 2: Nothing is known about the boundary conditions. On the inlet to the computational area and on the surface of the lobe. What is the boundary condition on the airfoil. Constant temperature? A condition of adiabaticity of the wall? Or some other?
Response 2: We have added the relevant information to the manuscript in lines 180–181 and Fig. 2.
“The inlet is defined as a velocity inlet, the outlet as a pressure outlet, and the airfoil as a no-slip. ”
Comments 3: The Spalart-Allmaras turbulence model equation is used. However, there is no information about the values of the turbulence level and its spatial magnitude in the inlet section.
Response 3: We have explained the relevant parameter settings for the Spalart-Allmaras turbulence model in the manuscript on lines 181–182. "The turbulent intensity is set to the default value, and the turbulent length scale is set to 0.5334 m."
Comments 4: The process of growing an ice layer on the leading edge of a wind turbine blade is a process that takes place over time. The thickness of the ice layer changes over time. Information about the time of obtaining the visually presented icing results can be found only in Tables 2, 3, 4. This information is missing from the drawings presenting the shapes of the ice layer on the leading edge. There is such information only in one figure, figure 8. Why is the process of increasing thickness and shape of the growing ice layer not shown? Is this process regular? Does it propagate in some directions roughly parallel to the surface of the blade? Is the speed constant? How does the surface temperature of the airfoil change?
Response 4: We have added Figure 8 to the manuscript to illustrate the variation in ice layer thickness and shape over time. Additionally, we have provided a detailed explanation of the propagation pattern of ice thickness in lines 263-274 .
Comments 5: Why are the icing times equal 360 sec and 600 sec? Fig. 4 a) and b) present some instantaneous shapes of the ice growth. From Table 2 it appears that they refer to the state after 360 sec. Why after such? What will happen next?
Response 5: Thank you very much for your detailed comments. The icing time of 360s was chosen because some of the comparative experimental data are only available for this time. Figure 8 shows that ice thickness increases steadily during 120–240–360s. The growth trend is similar in each time period. This suggests that the ice thickness and shape would grow steadily after 360s. However, due to the absence of experimental data beyond 360s, further validation was not possible.
Comments 6: These forms are characterized by a different flow structure. Potential areas of detachment and recirculation are important. It would be interesting to show velocities in these areas, vorticity, pathlines, temperatures, heat fluxes.
Response 6: We have added Figure 7 in the manuscript to show the velocity under different ice shapes in lines 252-262.
Comments 7: Table 3 shows that the relative velocity is 50, 100, 150, 200 m/s. For what relative velocity were the results presented in Figures 5, 6 and 7 obtained ?
Response 7: Thank you for your careful and thoughtful review. We have updated the relative velocity in Table 3 to 67.06 m/s.
Comments 8: Figure 8 shows global changes in flow structure, but they are generated by local changes, deformations, in profile shape caused by the build-up of the ice layer. Shouldn't there be zoom boxes showing the form of deformation of the shape of the leading edge?
Response 8: Thank you for your valuable suggestion. We have enlarged the leading-edge airfoil in Fig.12.
Comments 9: Especially when the authors report:” As shown in Fig 8, when the AOA ranged from 5° to 20°, the ice shape caused by the liquid droplets exhibited distinct ice corners.”. This is not shown in Fig. 8. Further: “At an AOA of 15°, separation vortices formed at the trailing edge of the airfoil under both ice accretion conditions.Compared to the ice shape formed under the combined effect of ice crystals and droplets, the ice shape caused by droplets alone produced a larger separation vortex near the trailing edge.” This observation is true, but the cause is a local separation near the leading edge, not the trailing edge. Here again, zooming in on the pathlines around the trailing edge would be useful. Because here is the source of the detachment.
Response 9: We have appropriately enlarged the streamlines near the trailing edge in Fig.12.
Author Response File: Author Response.pdf
Round 2
Reviewer 1 Report
Comments and Suggestions for AuthorsThe following should be revised.
(1) The paper on the ice erosion model (i.e. Eq. (14)) must be cited in References.
(2) The values used by the parameters in the ice erosion model (B, u_0, ....., A_1 to A_5) must be described.
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Author Response
Comments 1: The paper on the ice erosion model (i.e. Eq. (14)) must be cited in References.
Author response 1: Thank you for your suggestion. We have cited the relevant papers in our manuscript accordingly.
Comments 2: The values used by the parameters in the ice erosion model (B, u_0, ....., A_1 to A_5) must be described.
Author response 2: Thank you very much for your detailed comments. We have added the relevant information to the manuscript in lines 171–174.
Author Response File: Author Response.pdf
Reviewer 2 Report
Comments and Suggestions for AuthorsThe authors responded my comments satisfactorily. Therefore, this manuscript should be accepted for publication.
Author Response
Comments 1: The reliability of the numerical results is not guaranteed because of the lack of a grid independence study.
Author response 1: Thank you for recommending our manuscript for publication. We sincerely appreciate your thoughtful comments and guidance throughout the review process.
