Analysis of the Effect of the Leading-Edge Vortex Structure on Unsteady Secondary Flow at the Endwall of a High-Lift Low-Pressure Turbine
Round 1
Reviewer 1 Report
The manuscript entitled "Analysis of the effect of the leading-edge vortex structure on unsteady secondary flow at the endwall of a high-lift low-pressure turbine " is interesting and the analysis is accurate. The presented work can be accepted for publication if the following comments are addressed adequately:
The numerical method is not complete. The following items should be explained:
* Which fluctuating velocity algorithm was used?
* Pressure-velocity coupling.
* Spatial discretization used for gradients, pressure, and momentum.
Figure 2: The size of this figure should be enlarged in order to better appreciate the details of the mesh.
The mesh independence study is missing.
How was the size of the time step obtained? The choice of the time step is important and should be explained in detail. How sensitive are the results to the time step? How many iterations per time step were used?
How did you ensure that at least 80% of the turbulent kinetic energy of the flow was resolved?
The integral length scale, the chord length and the requirement for the cell size should be commented. Is the time step size sufficient to track the required scales?
How was convergence guaranted?
Eq 1. Why was the total pressure of the incoming flow used instead of the static pressure? And, Why was the outlet velocity used as the reference velocity?
The distributions of the integral length scales should be shown to provide the average size of the largest eddies. In addition, the residual turbulent kinetic energy would be interesting to provide information to check if it is acceptable the spatial resolution to be resolved and not modeled by the LES scheme.
Author Response
Dear Editor and Reviewers,
We thank you for the critical comments and helpful suggestions. We have taken all these comments and suggestions into account, and have made major corrections in this revised manuscript,.Next, I will reply to your review comments.
Q1: Which fluctuating velocity algorithm was used?
Answer1: The fluctuating velocity algorithm at the turbulent inlet is generated by SNGR method. The fluctuating velocity algorithm in the following paper is the difference between the instantaneous velocity value and the mean time value at each point
Q2: Pressure-velocity coupling.
Answer2: It has been added in the article: Pressure-velocity coupling is high resolution
Q3: Spatial discretization used for gradients, pressure, and momentum.
Answer3: It has been added in the article: Spatial discretization used for gradients, pressure, and momentum is central difference.
Q4:Figure 2: The size of this figure should be enlarged in order to better appreciate the details of the mesh.
Answer4: It has been enlarged.
Q5: The mesh independence study is missing.
Answer5: Grid independence verification has been added(Fig.4)
Q6: How was the size of the time step obtained? The choice of the time step is important and should be explained in detail. How sensitive are the results to the time step? How many iterations per time step were used?
Answer6: The time step is obtained according to the criterion that the number of CFLS is less than 1. The reasons for the choice of time step and its influence on the result as well as the number of iterations of each time step are also explained in the revised paper:
Q7: How did you ensure that at least 80% of the turbulent kinetic energy of the flow was resolved?
Answer7: How to ensure that at least 80% of the turbulent kinetic energy of the flow was resolved have been explained in the revised paper.
Q8: The integral length scale, the chord length and the requirement for the cell size should be commented. Is the time step size sufficient to track the required scales?
Answer8: The integral length scale has been described in the paper (FIG. 6), and the chord length is indicated in FIG. 8. This time step ensures that the CFL number is less than 1, that is, the passing distance of the fluid microcluster at each time step is less than one mesh size, and the minimum mesh size is far less than the integral length scale, so the required structure can be fully tracked.
Q9: How was convergence guaranted?
Answer9: The convergence criterion has been given in the paper: Residuals of velocity and pressure in three directions is less than 0.0001.
Q10: Eq 1. Why was the total pressure of the incoming flow used instead of the static pressure? And, Why was the outlet velocity used as the reference velocity?
Answer10: This is because scholars in many related fields have adopted this dimensionless method[1][2][3].
Q11:The distributions of the integral length scales should be shown to provide the average size of the largest eddies. In addition, the residual turbulent kinetic energy would be interesting to provide information to check if it is acceptable the spatial resolution to be resolved and not modeled by the LES scheme.
Answer11: The distributions of the integral length scales and the residual turbulent kinetic energy have been provided in the revised paper.
[1] Satta, F., Simoni, D., Ubaldi, M., Zunino P., Bertini F., Profile and Secondary Flow Losses in a High-Lift LPT Blade Cascade at Different Reynolds Numbers under Steady and Unsteady Inflow Conditions [J]. Journal of Thermal Science, 2012, 21(6): 483-491.
[2] Sun S , Tan T , Wu X , et al. Influence of the Upstream Wakes on the Boundary Layer of a High-Lift Low-Pressure Turbine at Positive Incidence[J]. Journal of Aerospace Engineering, 2020, 33(6).
[3] Zoric, T., Popovic, I., Sjolander S. A., T. Praisner, E. Grover, Comparative Investigation of Three Highly Loaded LP Turbine Airfoils: Part I — Measured Profile and Secondary Losses at Design Incidence [C]. ASME Turbo Expo 2007, GT2007-27537.
Thanks again!
Author Response File: 
Author Response.doc
Reviewer 2 Report
It follows from the article that the numerical code is a method of large vortices, subgrid modeling is carried out on the basis of the Smoroginsky model. This is the simplest scheme, and the disadvantages of the Smoroginsky model are known. The most important disadvantage of this model is the weak ability of this model to account for external turbulence. In particular, the structures in the form of a horseshoe. The paper lacks the results of numerical modeling of horseshoe formation as a function of the magnitude of external turbulence, which is especially important for turbines. It is either necessary to make calculations taking into account external turbulence. Or prove that the solutions obtained do not depend on the level of external turbulence.
Author Response
Please see the attachment
Author Response File: Author Response.doc
Reviewer 3 Report
The authors presented an interesting study of the effect of the leading-edge vortex structure on unsteady secondary flow at the end wall of a high-lift low-pressure turbine.
The paper can be accepted for publication after addressing the following comments:
Some quantitative results are to be added to the abstract.
The novelty of the paper is to be clearly stated.
For the numerical Method:
-The numerical method is to be detailed.
-The solved governing equations are to be presented.
-The boundary conditions are to be expressed mathematically.
-A grid sensitivity test is to be performed.
-What is the convergence criterion?
-Have you considered time dependent or independent governing equation?
-A qualitative (2D or 3D flow structure for example) verification of the numerical model is to be performed.
The expression of Re is to be added.
How the hydraulic dimeter is calculated.
For the experimental study:
- More details on the measurement techniques and data acquisition system are to be provided.
- The mathematical expression used in the experimental uncertainty study are to be presented.
The paper is to be checked against misprints and grammatical mistakes.
Author Response
Please see the attachment.
Author Response File: Author Response.doc
Round 2
Reviewer 1 Report
All comments have been adequately addressed in the revised version of the manuscript.
Author Response
Dear Editor and Reviewers,
Thanks for your critical comments and helpful suggestions, and thank you very much for your recognition of our work.
Best wishes!
Reviewer 2 Report
the author's answer contradicts the results of the practice of numerical codes, which have been known for many decades. The model of large vortices, the Smoroginsky model, does not take into account the effects of diffusion in the sub-grid, and therefore does not take into account the transfer of turbulence energy in the sub-grid model. this is a well-known fact. That is why the les-grands model appeared. it is also known that it is often possible to take into account the diffusion of turbulent transport in the Smoroginsky model, which practically by its nature corresponds to the Boussinesq model, possibly with a mixture of artificial grid (schematic) viscosity. as was obtained in the studies to which the author refers, I include my own results in the tables. it's just a numerical effect of circuit viscosity. such results are universally known. therefore, the authors need to reflect these obvious facts in their article. without this, the results obtained distort the known results in the field of numerical modeling. therefore, the article needs to be finalized by devoting perhaps a small new section that reflects the true content of the results obtained. these results can only be interpreted as possible stable solutions taking into account the grid construction within the framework of the les-Smoroginsky model, with an understanding of its prostate compared to rans-les.
only after that publication is possible, otherwise readers are misled.
Author Response
Dear Editor and Reviewers,
Thanks for the critical comments and helpful suggestions. We have taken all these comments and suggestions into account, and have made major corrections in this revised manuscript.
Q1: The author's answer contradicts the results of the practice of numerical codes, which have been known for many decades. The model of large vortices, the Smoroginsky model, does not take into account the effects of diffusion in the sub-grid, and therefore does not take into account the transfer of turbulence energy in the sub-grid model. this is a well-known fact. That is why the les-grands model appeared. it is also known that it is often possible to take into account the diffusion of turbulent transport in the Smoroginsky model, which practically by its nature corresponds to the Boussinesq model, possibly with a mixture of artificial grid (schematic) viscosity. As was obtained in the studies to which the author refers, I include my own results in the tables. It's just a numerical effect of circuit viscosity. Such results are universally known. Therefore, the authors need to reflect these obvious facts in their article. Without this, the results obtained distort the known results in the field of numerical modeling. Therefore, the article needs to be finalized by devoting perhaps a small new section that reflects the true content of the results obtained. These results can only be interpreted as possible stable solutions taking into account the grid construction within the framework of the les-Smoroginsky model, with an understanding of its prostate compared to rans-les.
Only after that publication is possible, otherwise readers are misled.
Answer1: According to your suggestion, we have added a small new section in the paper (the section is highlighted in blue) : In the present simulation, to avoid the disadvantages of the Smagorinsky model, the Van-Driest wall dumping function was used to according to the studies by Tomi-kawa[1]. We have also adopted this approach in previous papers to avoid the disadvantages of the Smagorinsky model[2]. Application of Smagorinsky model based LES to the analysis of transitional boundary layer may be open to dispute, however, several examples have proved that reasonable results can be obtained for computational grid system with high quality and a large number of grid points[3]. Although this method cannot completely eliminate the disadvantages of Smagorinsky model, it can still capture the configuration changes of leading edge vortex systems. Therefore, these results can be interpreted as possible stable solutions.
Your results have higher accuracy and credibility, which will also make our future research direction.
Best wishes!
[1] Tomikawa, K., H. Horie, and C. Arakawa. 2007. “Parametric surveys of the effects of wake passing on high lift LP turbine flows using LES.” In Proc., ASME/JSME 2007 5th Joint Fluids Engineering Conf. New York: ASME.
[2] Sun S , Tan T , Wu X , et al. Influence of the Upstream Wakes on the Boundary Layer of a High-Lift Low-Pressure Turbine at Positive Incidence[J]. Journal of Aerospace Engineering, 2020, 33(6).
[3] Ooba, Y., Kodama, H., Arakawa, C. and Matsuo, Y., 2002, "Numerical simulation of a Wake-Blade Interaction using LES," 17th Sympojium on Computational Fluid Dynamics. pp.
Author Response File: Author Response.doc
Reviewer 3 Report
Accept in present form
Author Response
Dear Editor and Reviewers,
Thanks for your critical comments and helpful suggestions, and thank you very much for your recognition of our work.
Best wishes!
Round 3
Reviewer 2 Report
Conclusion must includes the note that results may be interpreted as one of possible stable solutions.
Author Response
Dear Editor and Reviewers,
Thanks for the critical comments and helpful suggestions. We have taken all these comments and suggestions into account, and have made minor corrections in this revised manuscript.
Q1: Conclusion must includes the note that results may be interpreted as one of possible stable solutions.
Answer1: We have made relevant additions to the conclusion. Thanks for your critical comments and helpful suggestions, and thank you very much for your recognition of our work.
Best wishes!
