## 1 Introduction
Therefore, on the basis of existing propeller design methods, a more in-depth and detailed optimization of the cross-sectional airfoils at low Reynolds number may help to further improve the aerodynamic efficiency of such propellers. A Gurney flap is a flat, vertically mounted plate at the airfoil edge with a height of approximately 0.5% to 5% chord, which can contribute to lift enhancement by increasing the pressure of the lower surface, and can also bring about additional drag [17]. [PERSON] et al. [18] found that a Gurney flap can lead to significant enhancement in the lift and lift-to-drag ratio of airfoil at low speeds. [PERSON] et al. [19] found both the solid and serrated Gurney flaps can increase the maximum lift-to-drag ratio of the wing by wind tunnel investigations. [PERSON] and [PERSON] [20] studied the aerodynamic performance of an S8036 airfoil with a Gurney flap by a wind tunnel test. The results showed that the Gurney flap could significantly increase the maximum lift coefficient and the endurance parameters of the S8036 at Reynolds numbers of \(4\times 10^{4}\)-\(8\times 10^{4}\). [PERSON] et al. [21] studied the aerodynamic characteristics of an NACA0012 with a Gurney flap by wind tunnel test at a Reynolds number of \(2\times 10^{6}\). They found that the Gurney flap of all investigated heights (0.5-3%) could increase the lift-to-drag ratio when the lift coefficient was above 1.2. [PERSON] et al. [22] improved the flapping wing efficiency by the application of an adaptive Gurney flap. [PERSON] et al. [23] demonstrated the implementation and use of Gurney flaps on wings and rotors. [PERSON] et al. [24] applied a Gurney flap to the rotor blade and achieved vibration reduction. Based on the above research, it can be deduced that the application of a Gurney flap to the design of a cross-sectional airfoil has the possibility to help break through the efficiency bottleneck of low Reynolds number propellers. Since the aerodynamic performance of the airfoil is very sensitive to working conditions at low Reynolds numbers, it is better to optimize each cross-sectional airfoil with a Gurney flap under corresponding actual working conditions. However, in the existing methods, the cross-sectional airfoils are not optimized under the actual working Reynolds numbers and lift coefficients determined by the cruise state of the designed propeller. This is because in the traditional non-iterative method, the design parameters and working status of the propeller are temporarily unavailable during the optimization of the cross-sectional airfoil, which can only be obtained after completing the optimization of chord and pitch distributions of the propeller. Therefore, the iterative optimization is necessary in the design of the low Reynolds number propellers. In this study, an optimization method of creating a propeller with a Gurney flap for ultra-high-altitude UAV is established to weaken the adverse influence of low Reynolds numbers, and to research the general law of such a design. The rest of this paper is organized as follows. In Section 2, the aerodynamic analysis methods are introduced and validated. In Section 3, the proposed iterative optimization strategy for a low Reynolds number propeller with a Gurney flap is established. In each iteration of the optimization process, all the cross-sectional airfoils can be optimized under the Reynolds numbers and lift coefficients that are determined by the design state of the propeller obtained from last iteration. The CFD method based on the \(\gamma\)-\(Re_{\theta}\) model, class-shape transformation method, polynomial interpolation method, and genetic algorithm were used to establish an iterative optimization platform. In Section 4, a propeller with a Gurney flap and a propeller without a Gurney flap were optimized by the proposed method for an ultra-high-altitude UAV. After that, a wind tunnel test was carried out to validate the optimization results. Then, a comparative analysis of the two optimized propellers was performed under different Reynolds numbers.