# A Mapping Model of Propeller RANS and LES Flow Fields Based on Deep Learning Methods
## 5 Conclusions  
In this work, we proposed a mapping model for the mapping between RANS and LES data based on deep learning methods. The model processes and visualizes both types of flow field data, then utilizes a deep convolutional neural network to extract flow field features and combines them with a nonlinear module for mapping and regression of the two types of flow field features. The experimental results showed that the LES results were accurately predicted by the model based on the RANS simulation data for propeller flow, with an error rate of only 7.92%. By comparing the predicted results produced by the models with actual RANS and LES simulation results, we observed a significant improvement in accuracy and speed with the deep-learning-based mapping model. Furthermore, the model also exhibited good generalization performance across different Reynolds numbers.  
The findings of this research provide a new approach and tool for propeller flow simulations. By incorporating deep learning techniques, we can more accurately predict LES results of propeller flow, thereby saving computational power and time required for generating flow simulation data. This has significant practical implications for propeller design and performance analysis.  
Although the model proposed in this paper offers advantages in terms of accuracy and speed, it also comes with certain limitations. First, the performance of the model is constrained by the availability of limited training data and the coverage of data ranges, so that it is unable to encompass all propeller operating conditions and design scenarios. Second, deep learning models demand substantial computational resources, which may limit their applicability in resource-constrained environments. Additionally, the black-box nature of the model could raise concerns related to interpretability and trustworthiness. The challenges related to generality, uncertainty modeling, and other aspects also require further research and improvement. Therefore, it is essential to consider these limitations comprehensively in real-world engineering applications.  
In summary, this work achieved positive results in mapping RANS and LES flow simulation data for propeller flow using a deep-learning-based approach. This research serves as a valuable example of applying deep learning in the field of fluid mechanics and introduces new ideas and methods for the development of simulation of flow fields.  
Conceptualization, J.J.; Methodology, J.J.; Validation, X.L.; Formal analysis, Y.Y.; Investigation, Y.Y. and J.S.; Resources, L.L.; Data curation, Y.Y.; Writing--original draft, Y.Y.; Writing--review & editing, J.J. and J.S.; Visualization, M.S.; Supervision, J.S.; Project administration, J.J. All authors have read and agreed to the published version of the manuscript.  
The research was funded by National Key R&D Program of China 2022 YFB3306200.  
No applicable.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Error Rate** & _V\_axial_ & _V\_tangential_ & _V\_radial_ \\ \hline mapping between RANS and LES & 6.48\% & 8.84\% & 9.66\% \\ \hline \hline \end{tabular}
\end{table}
Table 6: The error rates of RANS and LES mapping in the dataset with different Reynolds numbers.