Numerical simulation and wind tunnel experiment on aerodynamic characteristics of an electric aircraft

Taking an electric aircraft with high aspect ratio as the object of research, the CFD numerical simulation based on Navier-Stokes calculation and Spalart-Allmaras onflow pattern is conducted to verify the aerodynamic design and evaluate the flight property and quality of aircraft. With the aim of verifying the reasonability of the CFD calculation, a wind tunnel experiment was conducted for evaluation. The results indicate that the simulation information coincide well with wind tunnel test data, indicating that the simulation method could provide a guidance for the aerodynamic design of electric aircrafts, especially those with high aspect ratio.


Introduction
Aircraft have played a vital role in improving people's lives and promoting economic development, but they have also caused many negative impacts on the ecological environment [1][2].Electric aircraft have zero emissions, low noise and little negative impact on the environment.Therefore, the domestic and overseas relevant institutions invest loads of resources to tackle the technical challenges of electric aircraft [3].Because of the changes in the aircraft power system, the efficiency of the flight becomes more important [4].The most direct way to improve the range and flight time of electric aircraft is to improve aerodynamic efficiency and energy efficiency [5], the most important of which is the improvement of aerodynamic efficiency.Therefore, aerodynamic layout and aerodynamic parameter calculation have become the key technologies in the development of electric aircraft.Selecting a reasonable model has a profound influence on evaluating the rationality of aerodynamic design and flight performance and quality of electric aircraft, which can greatly save the cost of aircraft development.
A lot of researches have been conducted by domestic and foreign scholars on the acquisition of aircraft aerodynamic parameters.For example, Boelens calculated the aerodynamic performance of X-31 fighter jet by CFD numerical simulation method and compared it with wind tunnel experimental data [6].And Bitencourt et al. studied the aerodynamic performance and flight stability of aircraft based on CFD numerical simulation method [7].Moreover, Wei et al. studied the aerodynamic parameters of a light general-purpose aircraft with an external pod by CFD numerical simulation method [8].However, the research objects of the above literatures are all oil-powered aircraft, and there are few articles at home and abroad on aerodynamic performance analysis of high-aspect ratio electric aircraft and wind tunnel experiment of electric aircraft.Therefore, in this study, a high aspect ratio electric aircraft was taken as the research object, and CFD simulation was implemented on account of Reynolds mean Navier-stokes calculation and Spalart-Allmaras turbulence model.With a view to verify the precision of the numerical modeling, wind tunnel experiment of aircraft was carried out.The veracity of the proposed mean is proved from wind tunnel experiment and CFD simulation.

Reseacher Object
The entity of an electric aircraft with high aspect ratio is shown in Figure 1.The aircraft is a single configuration, and the landing gear is not retracted during flight.The particular parameters of electric aircraft are illustrated in Table 1.

Governing Equation
The limited volume method is employed to discretely figure out three dimensional compressible Reynolds mean Navier-stokes calculation [10].And the differential forms of the continuity equation, the shear stress term induced by viscosity and the energy theorem are indicated as below: Where ρ is the air density;  ,  are on behalf of the velocity component along i and j, respectively;  ,  severally represents the displacement in the i and j direction; p delegates fluid pressure;  typifies the shear stress tensor; H is the total enthalpy;  is the heat flux along i.

Turbulence model
Spalart-Allmaras onflow pattern is a single transport formulation model determined by empirical and dimensional analysis, which is effective in solving the problem of flow around complex boundary layer [11].Spalart-Allmaras model uses the equation about the viscosity coefficient of turbulent motion ̅ which can make the equations closed and the transport equation of turbulence model are as follows: Where  is symbolic of the damping coefficient, ̅ symbolizes the viscosity coefficient of turbulent motion and  ,  and  are the generation term, diffusion term and dissipation term of turbulent viscosity respectively.

Calculation method and model
In the simulation calculation, the grid model in the form of Poly-Hexcore is adopted, that is, hexahedral grid is used far away from the aircraft model, and polyhedral grid transition is used near the aircraft model.The grid form is shown in Figure 2. The minimum and maximum size of aircraft surface grid are 0.5 and 50 mm respectively, and the maximum size of flow field grid is 4000 mm.With an eye toward reducing the calculative grid, the cuboid reseau computing domain is established around the aircraft semi-mode.The length, width and height of cuboid computing domain are severally 175, 55 and 100 m.The amount of half mode reseau is 994969.Figure 3 demonstrates that full-mode plane grid and flow field grid.During the time that air speed V reaches 30 m/s and aircraft angles of attack are -4°, -2°, 0°, 2°, 4°, 6°, 8°, 10°, 12°, 14° and 16°, the whole machine is simulated numerically.

Numerical modeling assessment of wing pressure distribution
In an effort to lucubrate aerodynamic peculiarities for high-aspect ratio electric aircraft, the wing with air speed with 30 m/s and attack Angle of 0° was selected as the research object to analyze the wing profile pressure distribution at different positions, as showcased in Figure 4. Depending on cloud images and wing pressure allocation information of electric aircraft flow field, the CFD numerical simulation of electric aircraft flow field accords with the actual situation.

Unpowered wind tunnel test
So as to investigate the basic characteristics of aircraft aerodynamics as well as to determine the design direction of aerodynamic layout and to provide data for the calculation of flight performance and quality, the test was completed by the FL-8 wind channel from AVIC Pneumatic Institution.Figure 5 presents an installation method of the aircraft scaled-down model with compression ratio of one-sixth in the wind tunnel.
The test section is 3.5 m wide, 2.5 m high and 5.5 m long, along with an effective cross-sectional area of 7.685 m 2 , and the wind speed can reach up to 72 m/s.Moreover, the average turbulence is 0.15% and the field coefficient is 1.0032.

Test results and analysis
When the air speed gets up to 30 m/s, numerical calculation assessment for coefficient of lift, coefficient of drag and lift-drag ratio at different attack angles are compared with wind tunnel test data, as shown in Figure 6. Figure 6 demonstrates that lift coefficient, drag coefficient and lift-drag ratio obtained by CFD numerical simulation have a high consistency with that measured by wind tunnel test when the attack Angle makes be small.As the attack angle increases to near aircraft stall attack angle, the experimental value of lift coefficient is relatively smaller than that of CFD numerical simulation.However, the CFD numerical simulation data are moderately smaller than the experimentally measured coefficient of drag and lift-drag ratio.This is due to the fact that the transition belt is placed near the leading edge of the wing in wind tunnel experiment to simulate the transition position in actual flight.As the attack angle changes, the angle between the slope or diamond rough particles on the transition belt and the incoming flow changes, which increases the local flow and brings additional local resistance.
The comparison between numerical simulation and wind tunnel test reveals that the maximum liftdrag ratio is 23 at cruise speed, and the homologous attack angle is about 4°.In general, the resistance coefficient of an aircraft is relatively small when the angle of attack is 0°, so the most reasonable favorable angle of attack should be close to 0°.According to the preliminary analysis, the reason for the favorable angle of attack of 4° may be caused by the small setting of wing mounting angle, which can be properly increased.

Conclusion
In conclusion, the aerodynamic characteristics of an electric aircraft are analyzed and contrasted by wind-tunnel experiment in this article.The conclusions reached can be summed up in a few words.
(1) Compared with traditional structured grids, Poly-Hexcore meshes are equal to effectively economize plenty of grid generation time and one fifth of calculation time, and the results which contrasts with wind tunnel experiment are accurate enough.In the future, Poly-Hexcore mesh is expected to be widely used.
(2) This research adopts the limited volume means to discretely figure out average Reynolds Navierstokes formulas and selects Spalart-Allmaras onflow model to imitate the flow field for an electric aircraft.According to the cloud image and wing pressure distribution information of electric aircraft flow field, the CFD numerical simulation method can reflect the flow condition of electric aircraft flow field more accurately.
(3) The contrast between numerical mimic result and laboratory finding exhibits that CFD numerical simulation has high accuracy.The maximum error of lift coefficient obtained by numerical simulation and wind tunnel experiment is less than 5% but the maximum error of drag coefficient is relatively larger, less than 15%.
(4) The aerodynamic pattern of the high-aspect-ratio electric aircraft is reasonable, with a value of 23 for lift-to-drag ratio and high aerodynamic efficiently.

Figure 4 .
Figure 4. (a) The locations of wing profile.(b) The pressure distribution under each location.

Figure 5 .
Figure 5. Installation diagram of aircraft scale model.

Figure 6 .
Figure 6.Comparison of results about numerical simulation and wind tunnel experiment.(a) Coefficient of lift.(b) Coefficient of drag.(c) Lift-drag ratio.