Deep Learning-Based Aerodynamic Analysis for Diverse Aircraft Configurations

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The authors presented the deep learning-based aerodynamic analysis for diverse aircraft configurations.

The prediction method based on the neural networks for the aerodynamic performance of aircraft was provided.

This paper is recommended to be accepted.

Comments:

(1) The authors should add the numerical methods detailed for analysis the aerodynamic performance of aircraft.

(2) The authors should provide the error analysis using neural networks for prediction aerodynamic performance of aircraft.

Author Response

Comments 1: The authors should add the numerical methods detailed for analysis the aerodynamic performance of aircraft.

Response 1: We have added a more detailed description of the numerical mathematical aerodynamic models used in this work:
- the second paragraph in section 2.3, two references [29, 30], and a figure 4: «According to the theoretical foundations of VLM [29, 30] the midsurface of the lifting plane is modeled by a system of vortex frames (Fig. 2), each of which contains a П-shaped vortex consisting of an attached vortex and two free ones. The circulation intensity of each vortex is calculated based on solving systems of linear equations A*Gamma=Vn, where A is the aerodynamic influence matrix (determined by the geometry of the lifting plane), Gamma is the desired column matrix of circulations, Vn is the column matrix of normal velocities obtained from the non-permeability condition of the lifting surface. Based on the calculation of the distribution of circulations Gamma over the lifting surface, the distribution of lifting force over the lifting surface is calculated. The induced drag is calculated based on the distribution of induced velocities and the downwash flow in the Trefftz plane. Figure 4b shows a vortex model of aerodynamics for an arbitrary layout in the OpenVSP software.»

 

Comments 2: The authors should provide the error analysis using neural networks for prediction aerodynamic performance of aircraft.

Response 2: We have added error analysis for the neural network model:
- the last paragraph in section 3.2: «The experiment showed that at angles of attack of more than 10 °, a nonlinear section of the dependence of lift on the angle of attack appears due to the separation of the flow on the wing. Numerical mathematical models used to calculate the database in the linear stationary formulation. Despite taking into account the effect of air viscosity on aerodynamic drag, the models do not take into account the effect of viscosity on the separated flow characteristics of the wing. This is expressed in a linear increase in lifting force at α>10 °, where the experiment shows a decrease in lifting force due to flow separation, and is also expressed in an underestimated resistance at α>10° due to the inability to account for separation flow. The authors of fundamental works [29, 30] note the applicability of these models in a linear formulation in the range of -10°<α<+10°.This circumstance limits the use of the developed surrogate models to a range of angles of attack of -10...+10°, which, however, is quite sufficient for aerodynamic analysis and optimization at the initial stages of designing non-maneuverable aircraft. For these reasons, when comparing, experimental points at angles of attack of 12 and 14 degrees were not considered» 
- the second paragraph from the end in the conclusion: «The accuracy of neural network models depends not only on the quality of training and careful optimization of the hyperparameters of the neural network architecture, but also on the quality of the data in the database, which in turn strongly depends on the ability of numerical mathematical models to simulate physical processes in aerodynamics in detail. This is clearly seen from the results of validation of the neural network model based on experimental data: the neural network predicts aerodynamic characteristics well only in the operating range of the mathematical model used (Table 13, Figure 9). Nevertheless, the mathematical models used made it possible to obtain a database for training a neural network in a fairly short time in order to show new possibilities in accelerating aerodynamic calculations. The achieved accuracy of the neural network model is sufficient for the initial stages of aircraft engineering design. Further refinement of the neural network model is possible by preparing a database based on more detailed mathematical models of aerodynamics, for example, using solutions to the Navier-Stokes equations.»

Reviewer 2 Report

Comments and Suggestions for Authors

In this paper, a neural network is developed to predict the aerodynamic characteristics of fixed-wing aircraft. By the numerical simulations, the neural network models are validated. Overall, the quality of the paper is relatively high. This research work is also meaningful. After minor revisions, it can be accepted for publication. 

In table 1, Geometric design variables are listed. However, we cannot clearly identify these structures and parameters on the figures in the article. I suggest that the author take a typical structure as the object and mark these geometric structure in a figure.

Author Response

Comments 1: In table 1, Geometric design variables are listed. However, we cannot clearly identify these structures and parameters on the figures in the article. I suggest that the author take a typical structure as the object and mark these geometric structure in a figure.

Response 1: We have added Figure 2, which schematically shows the main geometric parameters from Table 1.

Reviewer 3 Report

Comments and Suggestions for Authors

The article is very comprehensive. The preliminary information, such as the consulted bibliography, is consistent with the development of the work. The experimental data are good. Figure 5 is not very clear; I'm not sure how the authors can improve the information presented. Regarding the result in Figure 7, the discrepancy between the experimental and modeled data is related to the fact that the models do not provide information about the viscous phenomena that are important when the angles of attack are high. Therefore, the second-order terms become important, and the curve ceases to exhibit linear behavior in the experimental data, even though the models maintain their linear behavior. This part is not entirely well explained by the authors, and an explanation would be helpful. The conclusions of the work are consistent with the results obtained, and this work can be used by other researchers as a basis for their work.

Author Response

Comments 1: Figure 5 is not very clear

Response 1: We have improved the quality of the figure. 5 (now figure 7)

Comments 2: Regarding the result in Figure 7, the discrepancy between the experimental and modeled data is related to the fact that the models do not provide information about the viscous phenomena that are important when the angles of attack are high. Therefore, the second-order terms become important, and the curve ceases to exhibit linear behavior in the experimental data, even though the models maintain their linear behavior. This part is not entirely well explained by the authors, and an explanation would be helpful. 

Response 2: We have added an analysis of the neural network model validation results based on the experiment: 
- last paragraph in section 3.2: «The experiment showed that at angles of attack of more than 10 °, a nonlinear section of the dependence of lift on the angle of attack appears due to the separation of the flow on the wing. Numerical mathematical models used to calculate the database in the linear stationary formulation. Despite taking into account the effect of air viscosity on aerodynamic drag, the models do not take into account the effect of viscosity on the separated flow characteristics of the wing. This is expressed in a linear increase in lifting force at α>10 °, where the experiment shows a decrease in lifting force due to flow separation, and is also expressed in an underestimated resistance at α>10° due to the inability to account for separation flow. The authors of fundamental works [29, 30] note the applicability of these models in a linear formulation in the range of -10°<α<+10°.This circumstance limits the use of the developed surrogate models to a range of angles of attack of -10...+10°, which, however, is quite sufficient for aerodynamic analysis and optimization at the initial stages of designing non-maneuverable aircraft. For these reasons, when comparing, experimental points at angles of attack of 12 and 14 degrees were not considered» 
- the second paragraph from the end in the conclusion: «The accuracy of neural network models depends not only on the quality of training and careful optimization of the hyperparameters of the neural network architecture, but also on the quality of the data in the database, which in turn strongly depends on the ability of numerical mathematical models to simulate physical processes in aerodynamics in detail. This is clearly seen from the results of validation of the neural network model based on experimental data: the neural network predicts aerodynamic characteristics well only in the operating range of the mathematical model used (Table 13, Figure 9). Nevertheless, the mathematical models used made it possible to obtain a database for training a neural network in a fairly short time in order to show new possibilities in accelerating aerodynamic calculations. The achieved accuracy of the neural network model is sufficient for the initial stages of aircraft engineering design. Further refinement of the neural network model is possible by preparing a database based on more detailed mathematical models of aerodynamics, for example, using solutions to the Navier-Stokes equations.»