# Numerical and experimental investigations of the propeller characteristics of an electrically powered ultralight aircraft

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## Abstract

The performance and efficiency of a propeller is crucial for electrically powered propulsion systems. Since the energy of the batteries is limited, it is important to develop propellers with high efficiency. Therefore, numerical and experimental investigations of the propeller characteristics are performed. The wind tunnel experiments are performed on a fuselage–propeller configuration. The electrical motor, batteries, and control units are designed to be integrated in the fuselage. Furthermore, force measurements are conducted to provide a data base for the validation of the numerical results. Two different numerical approaches are presented. First, the propeller is fully resolved by applying a rotational domain and a sliding mesh interface. Second, an actuator disk approach including blade element theory with a panel method one-way coupled with a boundary layer integration method is presented. The latter shall be used to reduce computational and mesh generation costs. The thrust, efficiency as well as pressure distribution and the flow field downstream of the propeller are analyzed. The obtained numerical results show a good agreement with the experimental data for the integral values over a wide operating range. Moreover, the results of the inter-method comparison of the two numerical approaches are in a good accordance regarding the local effects for the two highlighted operating points.

## Keywords

Propeller aerodynamics High-fidelity simulations Electric flight Actuator disk modeling## List of symbols

- \(a_{ij}\)
Influence coefficient matrix

- \(B\)
Number of propeller blades

- \(BT\)
Blade tip

- \(c\)
Chord length

- \(c_{D}\)
Drag coefficient

- \(c_{f}\)
Skin friction coefficient

- \(c_{L}\)
Lift coefficient

- \(c_{p}\)
Pressure coefficient

- \(c_{p}\)
Specific heat for constant pressure

- \(c_{Q}\)
Torque coefficient

- \(c_{T}\)
Thrust coefficient

- \(D\)
Drag force

- \(D\)
Diameter

- \(F_{\varphi }\)
Circumferential force

- \(H,H_{1}\)
Shape factor

- \(i,j\)
Indices

- \(J\)
Propeller advance ratio

- \(k\)
Turbulence kinetic energy

- \(L\)
Lift force

- \(l\)
Variable for Thwaites’ model

- \(M_{i}\)
Component of the moment

- \({\text{Ma}}\)
Mach number

- \(n\)
Number of cells

- \(n\)
Rounds per minute

- \(p\)
Pressure

- \(p_{\text{in}} ,p_{\text{out}}\)
Pressure at inlet and outlet

- \(Q\)
Torque

- \(q\)
Heat flux

- \(r\)
Radius

- \(Re\)
Reynolds number

- \(S_{i}\)
Source term component

- \(T\)
Thrust

- \(T\)
Temperature

- \(T_{\text{tot}}\)
Total temperature

- \(U_{e}\)
Effective velocity

- \(U_{\infty }\)
Free-stream velocity

- \(u_{\infty } ,v_{\infty }\)
Free-stream velocity components

- \(u_{d}\)
Velocity far downstream of the propeller plane

- \(u_{\text{ind}} ,v_{\text{ind}}\)
Induced velocity components

- \(u_{i}\)
Component of the velocity

- \({\text{Vol}}\)
Volume

- \(V_{x}\)
Axial velocity

- \(V_{\text{rel}}\)
Relative velocity

- \(V_{r}\)
Radial velocity

- \(V_{\varphi }\)
Circumferential velocity

- \(x,y,z\)
Cartesian coordinates

- \(x,\varphi ,r\)
Cylindrical coordinates

- \(y^{ + }\)
Dimensionless wall distance

- \(\nu\)
Kinematic viscosity

- \(\alpha\)
Angle of attack

- \(\alpha_{\text{dens}}\)
Density relaxation factor

- \(\alpha_{\text{pres}}\)
Pressure relaxation factor

- \(\alpha_{K}\)
Turbulent kinetic energy relaxation factor

- \(\alpha_{\text{mom}}\)
Momentum relaxation factor

- \(\alpha_{\text{temp}}\)
Temperature relaxation factor

- \(\alpha_{\nu t}\)
Turbulence eddy viscosity relaxation factor

- \(\alpha_{\omega }\)
Turbulence eddy frequency relaxation factor

- \(\delta\)
Boundary layer thickness

- \(\delta^{*}\)
Displacement thickness

- \(\gamma\)
Vortex strength

- \(\lambda\)
Thermal conductivity

- \(\lambda\)
Variable for Thwaites’ model

- \(\eta\)
Efficiency

- \(\mu\)
Molecular viscosity

- \(\theta\)
Local angle of incidence

- \(\theta_{75}\)
Angle of incidence at 75 per cent of the blade span

- \(\theta\)
Momentum thickness

- \(\rho\)
Density

- \(\phi\)
Inflow angle

- \(\phi\)
Potential

- \(\omega\)
Turbulence eddy frequency

## Abbreviations

- BET
Blade element theory

- RANS/BET
Combined RANS/blade element theory approach

- RANS/BET-FC
Combined RANS/blade element theory approach including the fuselage configuration in the wind tunnel test section

- RBPA
Reference blade pitch angle

- TUM
Technical University of Munich

- TUM-AER
Chair of Aerodynamics and Fluid Mechanics

- UAV
Unmanned aerial systems

- URANS/RP
URANS results for the calculations of the resolved propeller

## Notes

### Acknowledgements

The authors thank the Bavarian State Ministry of Economic Affairs and Media, Energy and Technology for funding the project EUROPAS under the Grant Agreement Number LABAY76A. Furthermore, the authors want to thank ANSYS for providing the flow simulation software. The authors gratefully acknowledge the Gauss Centre for Supercomputing e.V. (www.gauss-centre.eu) for funding this project by providing computing time on the GCS Supercomputer SuperMUC at Leibniz Supercomputing Centre (LRZ, www.lrz.de).

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