A 2-D Unsteady Aerodynamic Application to HHC Test Data Show Performance Improvements

b semi-chord length In 1982, Hughes Helicopter, Inc., in cooperation with the U.S. Army and NASA, conducted flight tests on a modified OH-6A helicopter that incorporated an active higher harmonic control (HHC) system. The results of these tests showed a reduction in vibrations of up to 90% could be achieved. Additionally, the open loop data showed significant reductions in the main rotor shaft torque and engine power indicating that HHC may be providing performance improvements along with the vibration reduction. C(k) Theodorsen’s lift deficiency function C′(k,h,m) C′N(k,h,m) finite wake lift deficiency function, F real part of lift deficiency function G imaginary part of lift deficiency function h non-dimensional distance between layers of shed vorticity (wake spacing), h = 2πv/bQΩ h0 amplitude of deflection in simple harmonic motion In the present study, unsteady, rotary-wing, potential flow theory for a thin, oscillating airfoil is used to explain the mechanism behind the performance improvements seen on the OH-6A. Equations for the two-dimensional, unsteady, rotary-wing aerodynamic forces and moments with a finite number of wakes, or shed layers of vorticity beneath the rotor are developed and applied specifically to the pitch and flap oscillations seen in the hover flight test data. A modified finite-wake lift deficiency function is developed for this finite wake theory that is analogous to the classical Theodorsen and Loewy lift deficiency functions, and is used in used to calculate the horizontal time-averaged propulsive force (negative drag) derived by Garrick to show that unsteady aerodynamics can provide the order of magnitude effects necessary to quantify the performance improvements seen on the OH-6A. Hn Hankel function (complex Bessel function) of second kind of order n, Hn = Jn Yn Jn real part of complex Bessel function of order n k reduced frequency, v k ω = (fixed wing), or b r b k Ω ω = (rotary wing) m ratio of oscillation frequency to rotational frequency, Ω ω = m α M aerodynamic moment about the elastic axis (positive clockwise) n revolution number N number of wakes for a single-blade rotor P aerodynamic force on the airfoil q blade number Q total number of blades r blade section radius from center of rotation t time v freestream velocity Nomenclature V forward airspeed w downwash velocity W Loewy’s wake weighting function a non-dimensional elastic axis location measured from midchord WN finite wake weighting function x non-dimensional distance from mid-chord † Lecturer and Ph.D. Candidate, Department of Aeronautics and Astronautics, Member, AIAA YN imaginary part of complex Bessel function α0 amplitude of rotation in simple harmonic motion ‡ Professor, Department of Aeronautics and Astronautics, Associate Fellow, AIAA γa vorticity generated by reference airfoil γnq vorticity generated by q blade in n revolution This paper is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Γ total circulation around the airfoil μ advance ratio, r V Ω = μ American Institute of Aeronautics and Astronautics 1 ξ non-dimensional distance from mid-chord ρ density of air Φ velocity potential φ1 phase angle between initiation of rotation input and arbitrary reference point φ2 phase angle between initiation of amplitude input and arbitrary reference point ψq phase angle by which motion of q blade leads reference blade ω frequency of oscillation Ω rotational frequency of rotor