# A Mapping Model of Propeller RANS and LES Flow Fields Based on Deep Learning Methods
## 1 Introduction  
The turbulence problem encompasses various engineering fields, so that finding a solution for this problem is of great significance in these fields. During the past decades, researchers have continuously conducted exploration and research of turbulence. The concept of rapid distortion of a fluid [1; 2] and the proposition of different scaling rates and the demonstration of turbulent boundary layers [3] have given us a better understanding of turbulent flow. With the advancement of computer technologies and the implementation of particle image velocimetry (PIV), research on turbulence has become increasingly profound and detailed. While previous efforts have deepened our comprehension of turbulent flow, the fundamental issues related to turbulent flow [4], and its effective application in engineering remain unaddressed. Turbulent flow is still a significant hurdle for success in the engineering of aviation, aerospace and navigation. The essence of turbulent flow, the physical laws governing its evolution, and optimal utilization in engineering have always been important research topics attracting the attention of researchers. Numerical computation methods for turbulence flow can be categorized into direct numerical simulation (DNS), large eddy simulation (LES), and Reynolds-averaged Navier-Stokes (RANS) based on grid resolution scales. With improvement in computer performance and the development of parallel computing, DNS and LES have been increasingly utilized both in research and engineering. However, for complex geometries andflows with a high Reynolds number, the substantial increase in grid size severely limits the applicability of these methods. In contrast, although the accuracy of the RANS model is inferior to the former two methods, its user-friendly nature and high efficiency have made it widely adopted in engineering practice [5]. Particularly in the aerospace domain, where the Reynolds numbers of flows are generally high, turbulence computation mainly depends on existing RANS models. Reynolds-averaged numerical simulation (RANS) is the most extensively employed turbulence numerical simulation method in engineering. Most of the RANS models are based on the assumption of eddy viscosity, which yields satisfactory results for attached flows. However, in the case of complex flows such as separated flow, the relationship between Reynolds stress and strain is no longer that of a simple linear correlation. The anisotropy of turbulent flow makes turbulence modeling significantly challenging [6], and consequently, the calculation results of the RANS model often exhibit significant deviations from the actual flows. In addition, empirical parameters in the model are often determined based on some specific flows, which increases the model's uncertainty and subsequently affects its applicability. Large eddy simulation (LES) is a turbulence numerical simulation method that lies between direct numerical simulation (DNS) and Reynolds-averaged numerical simulation (RANS). It filters the Navier-Stokes equations, dividing the flow field into large-scale and small-scale components. LES directly simulates the large-scale eddies, while a sub-grid-scale model is used to model and solve the small-scale components. However, on the near-wall surface, since there is no inertial sub-region, the number of grids for LES near the wall surface is always required to reach the fineness of DNS. This also leads to a large consumption of computing resources for LES simulation, which limits its application in engineering applications, especially engineering computation for flows with complex shapes. Therefore, many researchers have attempted to integrate RANS and LES models to establish complex system models to reduce computational costs while achieving accurate simulation results. In fact, there are two main types of approaches to establishing complex system models.