XFOIL Performance Validation for Medium-Scale Variable Pitch UAV Rotor Systems

XFOIL Performance Validation for MediumScale Variable Pitch UAV Rotor Systems B. V. R. Nielsena, M. Gilpinb Received 11 December 2022, in revised form 14 May 2023 and accepted 5 June 2023 Abstract: This study focuses on experimentally validating the performance of XFOIL, a sophisticated software airfoil analysis tool used for approximating lift and drag coefficients. XFOIL output data was incorporated into a theoretical model simulating a variable pitch rotor system operating in a hovering state. The output of the Blade Element Momentum Theory (BEMT) rotor model is compared to thrust and power output performance data collected from a constructed rotor test bench and analysed in MATLAB. Using XFOIL as input, the BEMT rotor model was observed to yield good robust results when compared to experimental data, but demonstrated sensitivity to airfoil performance characteristics, laying the groundwork for future empirical validation. In comparing BEMT model performance, it was interesting to find that thrust performance remained within tolerance in contrast to an overprediction of rotor power output resulting from XFOIL drag at high blade pitch angles. Upon further interrogation by means of variable isolation, XFOIL demonstrated instability resulting from sensitivity to variability of model constraints. Modification of rotor geometry definitions or environmental constants beyond the test environment framework showed simulated systems may not necessarily behave reliably nor enhance output performance. This highlights the critical importance and utility of experimentation for understanding theoretical model behaviour or validating simulation output performance. Additional keywords: AoA – Angle of Attack, XFOIL – Airfoil Analysis Application, BEMT – Blade Element Momentum Theory, UAV – Unmanned Aerial Vehicle, BEMT – Blade Element Momentum Theory, FSI – Fluid Structure Interaction, BLDC – Brushless Direct Current Motor Nomenclature 𝐴𝐴𝑟𝑟 Annulus Area [𝑚𝑚2 ] Rotor Area [𝑚𝑚2 ] 𝐴𝐴 Blade Mach Number 𝑎𝑎𝐵𝐵 𝐵𝐵 Chord Length [𝑚𝑚] 𝐶𝐶𝐷𝐷 Drag Coefficient Lift Coefficient 𝐶𝐶𝐿𝐿 Power Coefficient 𝐶𝐶𝑃𝑃 Thrust Coefficient 𝐶𝐶𝑇𝑇 𝑐𝑐𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 Speed Of Sound Sea Level [m/s] a. b. Department of Mechanical Engineering, Durban University of Technology, South Africa. E-mail: SAIMechE Member. Department of Mechanical Engineering, Durban University of Technology, South Africa. E-mail: GTW Gross Take-off Weight [𝑘𝑘𝑘𝑘] Mass Inertia [𝑘𝑘𝑘𝑘. 𝑚𝑚2 ] 𝐼𝐼𝑏𝑏 Sample Mean Current [𝐴𝐴] 𝐼𝐼𝑠𝑠𝑠𝑠 Mean Current [𝐴𝐴] 𝐼𝐼𝑚𝑚 Sample Current [𝐴𝐴] 𝐼𝐼𝑠𝑠 Blade Length [𝑚𝑚] 𝑙𝑙𝑏𝑏 𝐿𝐿 Energy [𝐾𝐾𝐾𝐾. 𝑚𝑚2 /𝑠𝑠] Rotor Speed / Head Speed [𝑟𝑟/𝑠𝑠] 𝑁𝑁𝑟𝑟 Blade Section Increment [𝑛𝑛] 𝑛𝑛𝑖𝑖 Pitch Sample Rate / Resolution [𝑛𝑛] 𝑛𝑛𝑝𝑝 𝑛𝑛𝐼𝐼 Current Sample Rate / Resolution [𝑛𝑛] 𝑛𝑛𝑟𝑟𝑟𝑟𝑟𝑟 Raw Sample Rate / Resolution [𝑛𝑛] Number Of Blades 𝑁𝑁𝑏𝑏 Sample Power Output [𝑊𝑊] 𝑃𝑃𝑠𝑠 𝑃𝑃𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 Polynomial Power Output [𝑊𝑊] 𝑅𝑅𝑅𝑅 Reynolds Number 𝑟𝑟𝑖𝑖 Radial Position Increment 𝑇𝑇𝑠𝑠𝑠𝑠 Sample Mean Thrust [𝐾𝐾𝐾𝐾] Mean Thrust [𝑁𝑁] 𝑇𝑇𝑚𝑚 Sample Thrust [𝑁𝑁] 𝑇𝑇𝑠𝑠 𝑇𝑇𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 Thrust Polynomial [𝑁𝑁] 𝑉𝑉𝑎𝑎𝑎𝑎𝑎𝑎 Average Voltage [𝑉𝑉] Mean Voltage [𝑉𝑉] 𝑉𝑉𝑚𝑚 Sample Voltage [𝑉𝑉] 𝑉𝑉𝑠𝑠 𝑣𝑣𝑘𝑘𝑘𝑘𝑘𝑘 Kinematic Viscosity [𝑁𝑁. 𝑠𝑠/𝑚𝑚2 ] 𝛼𝛼 Lift Slope Constant 𝜃𝜃𝑖𝑖𝑖𝑖 Increment Pitch Angle, (AoA) [𝐷𝐷𝐷𝐷𝐷𝐷] 𝜏𝜏𝑛𝑛𝑛𝑛𝑛𝑛 Net Torque [𝑁𝑁. 𝑚𝑚] 𝜔𝜔𝑟𝑟 , 𝜔𝜔𝑏𝑏 Rotational Speed, Tip Speed [𝑟𝑟𝑟𝑟𝑟𝑟/𝑠𝑠] λ Induced Velocity [𝑚𝑚/𝑠𝑠] σ Rotor Solidity [𝑁𝑁/𝑚𝑚2 ] 1 Introduction The UAV market is expected to triple in size by 2027, and the significant investment forces generated by large corporations have accelerated technological development efforts of quad-rotorcraft platforms for light transport, agricultural, and surveillance applications. [1] With advancing electronics, aerodynamics, and materials science, sophisticated rotorcraft technologies will seamlessly integrate into everyday life, becoming nearly imperceptible. [2] Given their success, these platforms continue facing scalability challenges attributed to factors such as energy density constraints and propulsion efficiency. [3] The optimization challenge lies in expanding mission profiles while balancing performance expectations through trade-offs in endurance, payload capacity, cost, and complexity. [4-6] Focusing on propulsion efficiency challenges highlighted earlier – For quadrotors employing fixed-pitch propulsion systems, manoeuvring and stabilization is achieved by altering the thrust balance of opposing rotors through rapid speed modulation, requiring greater effort from motors to R & D Journal of the South African Institution of Mechanical Engineering 2023, 39, 12-22 http://dx.doi.org/10.17159/2309-8988/2023/v39a2 http://www.saimeche.org.za (open access) © SAIMechE All rights reserved. 12 XFOIL Performance Validation for Medium-Scale Variable Pitch UAV Rotor Systems overcome resulting inertial forces produced by rotors. BEMT theory and other works [7-9] show that rotors incur efficiency losses from work required to maintain altitude at low flight speeds. Fixed-pitch propulsion systems used in modern UAV’s [10] are optimized for specific [7-9,11] Combined, the technical challenges presented earlier are especially emphasized in medium scale quad-rotorcraft (GTW>10 kg) considering how payload and endurance are intwined. [1215] If the technical challenges shown in work examining the adaption of variable pitch propulsion technology for quadrotors could be overcome [16-20], the benefits of higher endurance and payload capacities resulting from optimizing rotor efficiency could have significant commercial implications. While software-based modelling and simulation strategies applied to the mentioned problems could provide high-resolution insights, aircraft are sensitive to aerodynamic performance characteristics, often requiring empirical validation to ensure reliable performance. [21] Consequently, this work will focus on empirically evaluating the scalability performance in terms of rotor geometry of a variable pitch rotor system scaled for a medium size quadrotor platform using MATLAB and XFOIL. Developing a MATLAB-based rotary propulsion system is dependent on combining momentum principles with elemental airfoil flow theory [8,22]. Airfoil performance characterized in terms of lift and drag coefficients is traditionally evaluated empirically from measurements obtained in wind tunnel testing [23]. Due to limited cost and access to test equipment, airfoil flow behaviour can also be simulated using software tools such as Ansys Fluent or Ansys CFX which offer sequential (One-Way Coupling) or parallel (Two-Way Coupling) analysis schemes depending on the significance of the FSI (fluid structure interaction) effect [24,25]. In this case, the BEMT model will rely on a wellestablished wind tunnel emulator XFOIL known for its ease of use, robustness, and computational efficiency. In this work, XFOIL is used to simulate the airfoil lift (𝐶𝐶𝐿𝐿 ) and drag (𝐶𝐶𝐷𝐷 ) coefficients using code developed using potential flow panel and integral boundary layer formulati (...truncated)