## 1 Introduction  
The accurate prediction of flight environments plays a vital role in designing and optimizing aircraft [1, 2]. According to different flight velocities, the vehicle will suffer different external flow environments, including incompressible external flow fields and compressible external flow fields. The properties of a specific external flow field are different from each other, which means the corresponding parameters that need to be confirmed in the simulation prediction are also different and piecewise analysis is required. The compressible external flow field during the ascent of the vehicle is discussed in another paper by [PERSON] and [PERSON] [3]; in this paper, we study the incompressible external flow field. The aircraft is immersed in the external flow field, and the fluid flowing across the airfoil surface will generate pressure in the direction perpendicular to the surface and shear force in the direction parallel to the surface. The resultant force of pressure and shear force in the flow direction is called drag, and the component perpendicular to the flow direction is called lift. The dimensionless drag coefficient (\(C_{d}\)) and lift coefficient (\(C_{l}\)) are the critical coefficients applied to characterize the drag and lift of an aircraft, research on which is of guiding significance [4]. Conventional methods can measure \(C_{d}\) and \(C_{l}\) through wind tunnel experiments [5], but wind tunnel experiments take a long time and are costly. With the development of computer hardware and numerical simulation technology, CFD has been adopted to solve the governing equation of fluid motion to obtain drag and lift [6, 7]. This method has become the primary method to investigate the external flow field of airfoil due to its short period, high efficiency, and low cost. The NACA airfoils developed by the National Advisory Committee for Aeronautics (NACA) are airfoil shapes for aircraft wings. NACA0012 is a typical airfoil for research on the incompressible external flow field. [PERSON]. [8] presents CFD simulations on NACA0012, which adopts Spalart-Allmaras and SST k-omega turbulence models. The conclusion shows that the simulation data of the above turbulence models are in good agreement with published experimental data. [PERSON] and [PERSON] [9] and [PERSON], [PERSON], [PERSON], and [PERSON] [10] investigate the grid strategies for the two-dimensional turbulence flow around the NACA0012 and a flat plate. Spalart-Allmaras is applied and the shape of the trailing edge is found to be a significant factor affecting the accuracy and convergence of discrete solutions. Depending on the applied modeling methods, the NACA0012 model includes the sharp trailing edge and the blunt trailing edge. In terms of the sharp trailing edge, Ref. [11] discusses the effect of the wavy surface on the aerodynamic characteristics of the NACA0012 airfoil at \(R_{e}\) is 0.16 million, which adopts the large eddy model. Similarly, three-dimensional numerical studies on the aerodynamic characteristics with different wavy surfaces are presented in Ref. [12]. The results show that for the wavy airfoil, the \(C_{l}\) data are reduced when the angle of attack (AOA) is less than the baseline stall angle, while when the AOA is larger than the baseline stall angle, the \(C_{l}\) data are increased. Ref. [13] takes airfoils with a step at the upper surface and steps simultaneously at both sides of the upper and lower surfaces to investigate the effects on the aerodynamic performance. \(R_{e}\) is 1.6 million and the turbulence model is SST k-omega. The results indicate significant changes in \(C_{d}\) and \(C_{l}\), and the stall angle is accrued. [PERSON], [PERSON], [PERSON], and [PERSON] [14] and [PERSON], [PERSON], and [PERSON] [15] perform similar researches by applying a square-shaped, dimpled airfoil and a Gurney flaps airfoil under \(R_{e}\) of 2.1 million.