## 5 Conclusions  
In this study, an optimization method of a propeller with a Gurney flap for ultra-high-altitude unmanned aerial vehicle was established, and propellers with and without a Gurney flap were optimized under a very low Reynolds number. The aerodynamic characteristics of the optimal propeller with and without a Gurney flap were studied by numerical simulation and a wind tunnel test. Based on the results, the following conclusions are drawn:  
1. Under the same design conditions, the optimal propeller with a Gurney flap and the optimal propeller without a Gurney flap have similar distributions of chord and pitch, but the chords near the blade root of the optimal propeller with a Gurney flap are narrower and its cruising rotational velocity is slightly smaller.
2. The advance ratio corresponding to the design thrust of the optimal propeller with a Gurney flap is smaller than that of the optimal propeller without a Gurney flap, because the angle of attack corresponding to the maximum lift-to-drag ratio of the cross-sectional airfoil with a Gurney flap is smaller than that of the cross-sectional airfoil without a Gurney flap.
3. At the Reynolds number of about \(4\times 10^{4}\) (the design point), the optimal propeller with a Gurney flap can achieve 1.8% higher efficiency than the optimal propeller without a Gurney flap and reach an efficiency of 82.0% near the required thrust. Compared with the optimal propeller without a Gurney flap, adopting the optimal propeller with a Gurney flap can reduce the output power of the ultra-high-altitude unmanned aerial vehicle by 2.2%. This is because under very low Reynolds numbers, the application of a Gurney flap could significantly increase the lift coefficient of the cross-sectional airfoil at a little cost in drag by increasing the camber of the airfoil and suppressing the expansion of the laminar separation bubble. As a result, the lift-to-drag ratio of the cross-sectional airfoil with a Gurney flap increases, and the efficiency of the propeller is improved.
4. As the Reynolds number increases, the improvement in efficiency of the propeller with a Gurney flap compared with the propeller without a Gurney flap will decrease,and even disappear when the Reynolds number is greater than 1.4 \(\times\) 10\({}^{5}\). This is because the laminar separation bubbles on the blade will decrease with the increase in Reynolds number, and its negative effect will diminish. When laminar separation bubbles almost disappear, the Gurney flap is no longer needed to increase the camber of the cross-sectional airfoil and inhibit the separation. Instead, the additional pressure drag caused by the Gurney flap would slightly reduce the lift-to-drag ratio of the airfoil, leading to a decrease in propeller efficiency.
* The results of the wind tunnel test show that the force coefficients and efficiencies of the optimized propellers calculated by the CFD method are in good agreement with the results of the wind tunnel test. Hence, the CFD method has sufficient accuracy, and the optimization has an evident effect.  
Conceptualization, Y.Y. ([PERSON]), D.M. and L.Z.; Data curation, Y.Y. ([PERSON]); Formal analysis, L.Z. and Y.Y. ([PERSON]); Funding acquisition, D.M.; Investigation, Y.Y. ([PERSON]) and Y.Y. ([PERSON]); Methodology, Y.Y. ([PERSON]) and L.Z.; Project administration, D.M. and L.Z.; Resources, D.M.; Software, Y.Y. ([PERSON]) and X.Y.; Supervision, D.M. and L.Z.; Validation, Y.Y. ([PERSON]) and X.Y.; Visualization, Y.Y. ([PERSON]) and X.Y.; Writing--original draft, Y.Y. ([PERSON]); Writing--review and editing, D.M. and L.Z. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Key Project GJXM92579.  
Not applicable.  
The data presented in this study are available on request from the corresponding author.  
The authors declare no conflict of interest.