An efficient low-speed airfoil design optimization process using multi-fidelity analysis for UAV flying wing

This paper proposes an efficient lowspeed airfoil selection and design optimization process using multi-fidelity analysis for a long endurance Unmanned Aerial Vehicle (UAV) flying wing. The developed process includes the low speed airfoil database construction, airfoil selection and design optimization steps based on the given design requirements. The multi-fidelity analysis solvers including the panel method and computational fluid dynamics (CFD) are presented to analyze the low speed airfoil aerodynamic characteristics accurately and perform inverse airfoil design optimization effectively without any noticeable turnaround time in the early aircraft design stage. The unconventional flying wing UAV design shows poor reaction in longitudinal stability. However, It has low parasite drag, long endurance, and better performance. The multi-fidelity analysis solvers are validated for the E387 and CAL2463m airfoil compared to the wind tunnel test data. Then, 29 low speed airfoils for flying wing UAV are constructed by using the multifidelity solvers. The weighting score method is used to select the appropriate airfoil for the given design requirements. The selected airfoil is used as a baseline for the inverse airfoil design optimization step to refine and obtain the optimal airfoil configuration. The implementation of proposed method is applied for the real flyingwing UAV airfoil design case to demonstrate the effectiveness and feasibility of the proposed method.


INTRODUCTION
Airfoil plays an extremely important role for the aircraft aerodynamics, performance, and stability.Therefore, the airfoil selection process is very essential and significant at the early aircraft design stage to support designers for selecting an appropriate airfoil with the given Trang 44 requirements.The basic airfoil aerodynamic characteristics include airfoil lift, drag, and pitching moment coefficient that are required to evaluate by performing the test at the specific working condition of the airfoil.For example, many airfoil aerodynamics data were tested at the 2.8×4.0 ft (0.853×1.219 m) low-turbulence wind tunnel in the Subsonic Aerodynamics Research Laboratory at the University of Illinois at Urbana-Champaign (UIUC) [1].However, doing such a test could be time-consuming and costly.
Moreover, errors could be made because the working condition of the selected airfoils is not always the same as the testing data as the result of approximation [1].Hence, many researchers currently implement the reliable and accurate prediction analysis tools such as panel method, Reynolds-averaged Navier-Stokes (RANS), and in-house CFD solvers to analyze and design airfoil.However, these different analysis methods are required for the different flow conditions.In this paper, the flight regime is the low-speed which means the flow through the airfoil includes three regions: laminar, turbulent and transition zone.Besides, the high-fidelity analysis contains fully turbulent problem.Thus, the drag coefficient is higher than experiment results at the low speed regime.The flying wing UAV is well-known for high performance due to the low parasite drag with the same engine power.

EFFICIENT LOW-AIRFOIL DESIGN OPTIMIZATION PROCESS
The overall process of efficient low-speed airfoil design optimization is presented in F. 1.It includes three-steps that are UAV airfoil database construction loop, airfoil section loop, and airfoil design optimization loop.The framework starts with UAV airfoil database construction loop.The fully airfoil database is generated based on requirements and executed by the multi-fidelity analysis.In the airfoil section loop, from the fully airfoil database, Weighted Scoring Method (WSM) is employed for finding maximum weight value by criteria for the UAV flying wing.Then, airfoil selected is sent to airfoil design optimization loop.Then, this airfoil is used for baseline airfoil in order to design optimal airfoil.

UAV airfoil database construction loop
The design of an aircraft or UAV generally begins with identifying requirements, i.e. endurance, stall speed, cruise speed in UAV airfoil database construction loop.Then, finding suitable Airfoils by using requirements.Airfoils in the collection are sent to the multi-fidelity analysis, to analysis aerodynamic characteristics of airfoil.Then, the results are collected in a fully airfoil database.
In this loop, the most important step is Multi-Fidelity Analysis.The multi-fidelity analysis includes the panel method and Reynolds-averaged Navier-Stokes (RANS) solver by XFOIL and ANSYS FLUENT. Creating evaluation table for each airfoil bases on criteria.
 Making sum of all the products and selecting the airfoil with the highest total points from the full airfoil database.

Airfoil design optimization loop
Design formulation: Flying wing configuration operates with speed higher than fixed wing, so it has the low parasite drag, but stability issues inherent in this type of configuration.Thus, the improvement of pitching coefficient in cruise conditions is

Optimizer:
Airfoil geometry representation is sent to multi-fidelity analysis.If the convergence is not satisfied, airfoil geometry representation is updated by changing control point.

MULTI-FIDELITY ANALYSIS SOLVER VALIDATION
The E387 airfoil was designed by Richard

UAV Airfoil Database Construction Loop
From the results of initial sizing, Reynolds number equals 300000 for case study.
Then, 29 airfoils are used for selection, as shown in Table 1.

UAV Airfoil Database Construction Loop
UAV flying wing has low parasite drag and poor stability, so criteria of stability is important, as shown in Table 2.

Airfoil Design Optimization Loop
As discussed above, the 2D airfoil design problem is based on TL54.Thus, the standard optimization problem is written as: subject to: The optimal airfoil is shown in Table 3.The pitching moment coefficient of optimal airfoil increases 42.92% compared with the baseline airfoil TL 54.The maximum lift coefficient, stall angle of attack and minimum drag coefficient constraints are satisfying.3 and F. 8.Because the pitching moment coefficient of optimal airfoil is so good, that increases stability of UAV flying wing.Besides, the pressure distribution of the airfoil for both optimal and baseline shows similar, as shown in F. 9.
XFOIL [7] is probably the best known of the above codes.It dates back to 1986 and was written by Dr. Mark Drela, an aerodynamics professor at Massachusetts Institute of Technology.It is the coupled panel method with an integral boundary layer calculation for analysis [14].

Figure 3 .
Figure 2. Airfoil representation Eppler in the mid-1960s for use in model sailplanes.Because it was designed specifically for the appropriate lift coefficients and Reynolds numbers required by its application, this airfoil became a touchstone for much of the research directed at increasing the understanding of low Reynolds number airfoil aerodynamics.].A C-type grid with 33450 nodes, 33004 cells, 66454 faces and ywall+ = 1.0 is generated for the ANSYS FLUENT using the Pointwise tool [16].In F. 4, these results are compared with those from the UIUC wind-tunnel for Re 300000.As seen from F. 4.a, these analytical tools have high-fidelity, Spalart-Allmaras turbulence models matches with experiment.This case study is the low Mach number, which exists both laminar and turbulent flow.

Figure 6 .
Figure 6.Score of Airfoil database As shown in F. 6, the airfoil TL 54 (No.12) has maximum weight score, so airfoil baseline is TL54.

Figure 7 .
Figure 7. Baseline and optimal airfoil shape

Figure 8 .
Figure 8. Baseline and optimal airfoil polar comparison Small differences in the stall angle of attack, the maximum lift coefficient and the minimum drag coefficient, as shown in Table3

Figure 9 .1
Figure 9. Optimal airfoil pressure distribution at AOA = 0 deg 5. CONCLUSIONS An airfoil design optimization for airfoil TL54 is developed and applied successfully for improving the stability with a trustworthy optimum configuration providing an improvement 42.92% in reliability.By using Multi-fidelity analysis for airfoil selection, designers don't have to spend time, for testing data on airfoils from the wind tunnel, but still getting results close to the experiment.This is a promising approach since its accuracy and feasibility are demonstrated with the help of a case study.

Table 1 .
Collection Low-speed UAV flying wing Airfoil database

Table 2 .
Criteria for case studyUsing WSM and Criteria in Table2for airfoil database to find airfoil has maximum weight value.