Computational Investigation on Unsteady Loads of High-Speed Rigid Coaxial Rotor with High-Efficient Trim Model

  • Haotian Qi
  • Guohua XuEmail author
  • Congling Lu
  • Yongjie Shi
Original Paper


A computational fluid dynamics method is built to study the unsteady aerodynamic loads of a high-speed rigid coaxial rotor model, taking account of lift offset (LOS). The flowfield is simulated by solving Reynolds Averaged Navier–Stokes equations, and moving overset mesh is adopted to include blade motions. A high-efficient trim model for coaxial rotor is developed, where the “delta method” is implemented. Performance of Harrington rotor-1 is calculated for validation. Forward flight cases in three advance ratios are conducted. Results indicate that the temporal thrusts of coaxial rotor at low advance ratio share some fluctuations similar to hover state. In forward flight, the impulsive thrust fluctuations caused by blade-meeting are obviously exhibited around 270° for upper blades, and the strengths increase with the increase of LOS and advance ratio. At higher advance ratios, the blade thrusts of the upper and lower rotors tend to be the same. At the advance ratio of 0.6, two new kinds of Blade–vortex interaction (BVI) are captured. One is the parallel BVI caused by the root vortex and the other is the complex interaction among the tip vortex, root vortex and the rear blade.


Rigid coaxial rotor Aerodynamic loads High speed Rotor trim CFD Lift offset 

List of Symbols


\( \pi R^{2} \), rotor disk area (m2)


Chord (m)


\( {T \mathord{\left/ {\vphantom {T {(\rho A\varOmega^{2} R^{2} )}}} \right. \kern-0pt} {(\rho A\varOmega^{2} R^{2} )}} \), rotor thrust coefficient


\( {Q \mathord{\left/ {\vphantom {Q {(\rho A}}} \right. \kern-0pt} {(\rho A}}\varOmega^{2} R^{3} ) \), rotor torque coefficient


\( {L \mathord{\left/ {\vphantom {L {(\rho A}}} \right. \kern-0pt} {(\rho A}}\varOmega^{2} R^{3} ) \), rotor rolling moment coefficient


\( {M \mathord{\left/ {\vphantom {M {(\rho A}}} \right. \kern-0pt} {(\rho A}}\varOmega^{2} R^{3} ) \), rotor pitching moment coefficient


\( {{\text{lift}} \mathord{\left/ {\vphantom {{\text{lift}} {\left( {\frac{1}{2}\rho V^{2} c} \right)}}} \right. \kern-0pt} {\left( {\frac{1}{2}\rho V^{2} c} \right)}} \), blade sectional lift coefficient


\( {{F_{n} } \mathord{\left/ {\vphantom {{F_{n} } {\left( {\frac{1}{2}\rho V^{2} c} \right)}}} \right. \kern-0pt} {\left( {\frac{1}{2}\rho V^{2} c} \right)}} \), blade sectional normal force coefficient


\( {{(p - p_{\infty } )} \mathord{\left/ {\vphantom {{(p - p_{\infty } )} {\left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}\rho V_{\text{tip}}^{2} } \right)}}} \right. \kern-0pt} {\left( {{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0pt} 2}\rho V_{\text{tip}}^{2} } \right)}} \), pressure coefficient


Blade 1 of the lower rotor


Blade 2 of the lower rotor

\( \mu \)

\( {{V_{\infty } } \mathord{\left/ {\vphantom {{V_{\infty } } {\varOmega R}}} \right. \kern-0pt} {\varOmega R}} \), lift offset of coaxial system


Mach number


Rotor radius (m)


Blade 1 of the single rotor


Blade 2 of the single rotor


Blade 1 of the upper rotor


Blade 2 of the upper rotor


Velocity in y direction (m/s)


Rotor tip speed (m/s)

\( V_{\infty } \)

Forward flight speed (m/s)

\( \psi \)

Azimuth angle (°)

\( \theta_{0} \)

Collective pitch angle (°)

\( \theta_{1s} \)

Longitudinal cyclic pitch angle (°)

\( \theta_{1c} \)

Lateral cyclic pitch angle (°)

\( \varOmega \)

Rotor angular velocity (rad/s)



Lower rotor in coaxial system


Upper rotor in coaxial system



This work was supported by the National Natural Science Foundation of China (no. 11302103).

Compliance with ethical standards

Conflicts of interest

All authors declare that they have no conflict of interest.


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Copyright information

© The Korean Society for Aeronautical & Space Sciences 2019

Authors and Affiliations

  • Haotian Qi
    • 1
  • Guohua Xu
    • 1
    Email author
  • Congling Lu
    • 1
  • Yongjie Shi
    • 1
  1. 1.National Key Laboratory of Science and Technology on Rotorcraft AerodynamicsNanjing University of Aeronautics and AstronauticsNanjingChina

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