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

• Haotian Qi
• Guohua Xu
• Congling Lu
• Yongjie Shi
Original Paper

## Keywords

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

## List of Symbols

A

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

c

Chord (m)

CT

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

CQ

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

CL

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

CM

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

cl

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

Cn

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

Cp

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

L1

Blade 1 of the lower rotor

L2

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

Ma

Mach number

R

S1

Blade 1 of the single rotor

S2

Blade 2 of the single rotor

U1

Blade 1 of the upper rotor

U2

Blade 2 of the upper rotor

Vy

Velocity in y direction (m/s)

Vtip

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 (°)

$$\varOmega$$

## Subscripts

L

Lower rotor in coaxial system

U

Upper rotor in coaxial system

## Notes

### Acknowledgements

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

### Conflicts of interest

All authors declare that they have no conflict of interest.

## References

1. 1.
Jeong-In G, Jae-Sang P, Jong-Soo C (2017) Validation on conceptual design and performance analyses for compound rotorcrafts considering lift-offset. Int J Aeronaut Space Sci 18(1):154–164.
2. 2.
Cheney MC Jr (1969) The ABC helicopter. J Am Helicopter Soc 14(4):10–19.
3. 3.
Bagai A (2008) Aerodynamic design of the X2 technology demonstrator main rotor blade. In: 64th American Helicopter Society Forum, Montreal, Canada, April 29–May 1 2008, pp 29–44Google Scholar
4. 4.
Harrington RD (1951) Full-scale-tunnel investigation of the static-thrust performance of a coaxial helicopter rotor. NACA Technical Note, NACA-TN-2318Google Scholar
5. 5.
Dingeldein RC (1954) Wind-tunnel studies of the performance of multirotor configurations. NACA Technical Note, NACA-TN-3236Google Scholar
6. 6.
Ramasamy M (2013) Measurements comparing hover performance of single, Coaxial, Tandem, and tilt-rotor configurations. In: 67th American Helicopter Society Forum, Phoenix, Arizona, USA, May 21, 2013Google Scholar
7. 7.
Cameron CG, Karpatne A, Sirohi J (2016) Performance of a Mach-scale coaxial counter-rotating rotor in hover. J Aircr 53(3):746–755.
8. 8.
Norman TR, Shinoda P, Peterson RL, Datta A (2011) Full-scale wind tunnel test of the UH-60A airloads rotor. In: 67th American Helicopter Society Forum, Virginia Beach, Virginia, USA, May 3–5, 2011Google Scholar
9. 9.
Datta A, Yeo H, Norman TR (2013) Experimental investigation and fundamental understanding of a full-scale slowed rotor at high advance ratios. J Am Helicopter Soc 58(2):1–17
10. 10.
Gessow A (1948) Effect of rotor-blade twist and plan-form taper on helicopter hovering performance. NACA Technical Note, NACA-TN-1542Google Scholar
11. 11.
Leishman JG, Ananthan S (2008) An optimum coaxial rotor system for axial flight. J Am Helicopter Soc 53(4):366–381.
12. 12.
Cardito F, Gori R, Bernardini G, Serafini J, Gennaretti M (2018) State-space coaxial rotors inflow modelling derived from high-fidelity aerodynamic simulations. Ceas Aeronaut J 2:1–20.
13. 13.
Mohammad H-O-R, Jun-Beom S, Young-Seop B, Beom-Soo K (2015) Inflow prediction and first principles modeling of a coaxial rotor unmanned aerial vehicle in forward flight. Int J Aeronaut Space Sci 16(4):614–623.
14. 14.
Kim HW, Brown RE (2006) Coaxial rotor performance and wake dynamics in steady and manoeuvring flight. In: 62nd American Helicopter Society Annual Forum, Phoenix, Arizona, USA, May 9–11, 2006Google Scholar
15. 15.
Kim HW, Duraisamy K, Brown RE (2009) Effect of rotor stiffness and lift offset on the aeroacoustics of a coaxial rotor in level flight. In: 65th American Helicopter Society Annual Forum, Texas, USA, 27–29 May 2009Google Scholar
16. 16.
Tan J, Sun Y, Barakos GN (2018) Unsteady loads for coaxial rotors in forward flight computed using a vortex particle method. Aeronaut J 122(1251):693–714.
17. 17.
Feil R, Rauleder J, Hajek M, Cameron CG, Sirohi J (2016) Computational and experimental aeromechanics analysis of a coaxial rotor system in hover and forward flight. In: European Rotorcraft Forum, 2016Google Scholar
18. 18.
Schmaus J, Chopra I (2015) Aeromechanics for a high advance ratio coaxial helicopter. In: 71st American Helicopter Society Forum, Virginia Beach, Virginia, USA, May 5–7, 2015Google Scholar
19. 19.
Schmaus JH, Chopra I (2017) Aeromechanics of rigid coaxial rotor models for wind-tunnel testing. J Aircr 54(4):1486–1497.
20. 20.
Lakshminarayan VK, Baeder JD (2009) High-resolution computational investigation of trimmed coaxial rotor aerodynamics in hover. J Am Helicopter Soc.
21. 21.
Barbely N, Komerath N (2016) Coaxial rotor flow phenomena in forward flight. In: SAE 2016 aerospace systems and technology conference, 2016. SAE International.
22. 22.
Barbely N, Novak L, Komerath N (2016) A study of coaxial rotor performance and flow field characteristics. In: American Helicopter Society Specialists Meeting on Aeromechanics, Fisherman’s Wharf, San Francisco, USA, Jan 20–22, 2016Google Scholar
23. 23.
Klimchenko V, Sridharan A, Baeder JD (2017) CFD/CSD study of the aerodynamic interactions of a coaxial rotor in high-speed forward flight. In: 35th AIAA Applied Aerodynamics Conference, Denver, Colorado, USA, 5–9 June, 2017. AIAA AVIATION Forum. American Institute of Aeronautics and Astronautics.
24. 24.
Passe BJ, Sridharan A, Baeder JD (2015) Computational investigation of coaxial rotor interactional aerodynamics in steady forward flight. In: 33rd AIAA Applied Aerodynamics Conference, Dallas, TX,U.S.A, June 22–26, 2015. AIAA AVIATION Forum. American Institute of Aeronautics and Astronautics.
25. 25.
Kim JW, Park SH, Yu YH (2009) Euler and Navier-Stokes simulations of helicopter rotor blade in forward flight using an overlapped grid solver. In: 19th AIAA Computational Fluid Dynamics, San Antonio, Texas, 22–25 June 2009. Fluid Dynamics and Co-located Conferences. American Institute of Aeronautics and Astronautics.
26. 26.
Zhao J, He C (2010) A viscous vortex particle model for rotor wake and interference analysis. J Am Helicopter Soc.
27. 27.
Ye Z, Xu G, Shi Y, Xia R (2017) A high-efficiency trim method for CFD numerical calculation of helicopter rotors. Int J Aeronaut Space Sci 18(2):186–196.
28. 28.
Qi H, Xu G, Lu C, Shi Y (2019) A study of coaxial rotor aerodynamic interaction mechanism in hover with high-efficient trim model. Aerosp Sci Technol 84:1116–1130.
29. 29.
Fan F, Huang S, Lin Y (2016) Numerical calculations of aerodynamic and acoustic characteristics for scissor tail-rotor in forward flight. Trans Nanjing Univ Aeronaut Astronaut 33(3):285–293Google Scholar
30. 30.
Ye Z, Xu G, Shi Y (2017) High-resolution simulation and parametric research on helicopter rotor vortex flowfield with TAMI control in hover. Proc IMechE, Part G: J Aerosp Eng.
31. 31.
Roe PL (1981) Approximate Riemann solvers, parameter vectors, and difference schemes. J Comput Phys 43:357–372.
32. 32.
Spalart P, Allmaras S (1992) A one-equation turbulence model for aerodynamic flows. In: 30th Aerospace Sciences Meeting and Exhibit Reno, Reno, NV, USA, 1992. American Institute of Aeronautics and Astronautics.
33. 33.
VaIkov T (1990) Aerodynamic loads computation on coaxial hingeless helicopter rotors. In: 28th Aerospace Sciences Meeting, Reno, NV, USA, 1990. Aerospace Sciences Meetings. American Institute of Aeronautics and Astronautics.

© 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