Physically-based reduced order model for unsteady aerodynamic loads of a L-shaped Gurney flap

Abstract

A physically-based linear reduced order model is developed for a NACA 0012 section oscillating in pitch and plunge, equipped with a L-tab Gurney flap in unsteady motion. The model allows for a quick and accurate computation of the first harmonic component of unsteady loads on a three degrees of freedom helicopter blade section model. Moreover, a physically-based identification procedure is carried out for fixed configurations of the airfoil and the L-tab, to complete the reduced order model with the mean steady contribution to aerodynamic loads. Numerical computations carried out with a finite volumes solver for compressible Reynolds Averaged Navier-Stokes equations, are performed and used as reference for the derivation of the reduced order model. Structured multi-block overlapped grids in relative motion are used as computational domain. The reliability of numerical simulations is verified by means of convergence analysis and comparisons with empirical and experimental data. The achieved reduced order model is an equivalent three segments piecewise mean line geometry, which correctly reproduces the effects of the airfoil mean line, including the L-tab, as well as contributions to loads of vortical structures behind the movable device. All these effects are well captured both on the mean value and the first harmonic of aerodynamic loads over the blade section. The strong connection of the parameters of the reduced order model with physical quantities is highlighted, as well as its predictive capability for arbitrary parameters of the imposed motion laws. Nomenclature a n scalar n-th parameter for the analytical load computation b unitary semi-chord for the analytical model c k = 2b airfoil chord for the analytical model, maerodynamic efficiency, C L /C D ELT Equivalent L-Tab ERA Equivalent Rigid airfoil f functional to be minimized for the model order reduction F generic aerodynamic force, N h airfoil plunge position, m k reduced frequency, ωb/2U M Mach number p array of free parameters for the model order reduction P n upwash n-th coefficient for the analytical model Re Reynolds number t time, s * Ph.D. Student, AIAA Aviation U freestream velocity, m/s 2 v vertical component for perturbation velocity VETT counter-rotating Vortices Equivalent Trim Tab x position along the chord of the analytical model, m z vertical position, normal to x, m ℑ imaginary part of a complex parameter ℜ real part of a complex parameter α angle of attack, deg. β L-tab deflection angle, positive upward, deg. ∆C P difference of C P between the lower and the upper side of the body θ x-transformation coordinate χ w wake enlargement with rescaled with respect the numerical chord ω angular velocity, 1/s 2 Subscript K related to the analytical model n index for the series terms in the analytical model N number of terms of the truncated series in the analytical model f related to the equivalent L-tab in the analytical model t related to wake the equivalent trim tab in the analytical model w related to the wake in the analytical model

Active Control on Helicopter Blades with a L-Shaped Gurney Flap

“…The development of a physically consistent ROM for the L-tab equipped NACA 0012 section is discussed in detail in a previous work [37]. Some features of such ROM are briefly reported hereinafter.…”

“…The piece-wise thin-line analytical formulation of the ROM is then briefly reported. To demonstrate the high fidelity of the ROM in reproducing the airloads, as well as in capturing the near body flow field, some results taken from a previous work [37] are reported. Section III presents a comparison between the aerodynamic performance obtained with the L-tab and those achieved with a classical trailing edge flap.…”

“…A different approach was proposed by the authors in a previous work [37], within the aim of developing a physically based linear ROM for the first harmonic component of the unsteady lift and moment. Such approach does not require to run a CFD indicial response simulation, but relies on physical flow features, such as the mean size of the Counter Rotating Vortices structures (CRV) developed past the L-tab discussed in this work.…”

“…The analyses highlighted how the L-tab allowed the enhancement of performance both for small and high angles of attack in steady state conditions. Additionally, simulations carried out for small amplitude pitch oscillations of the section equipped with such L-tab [37] showed the potential suitability of such device, both downward and upward deployed for vibration reduction on helicopter blades.…”

“…Overall the present paper aims to show that the L-shaped movable device under consideration is potentially suitable as a novel solution to reduce vibration on rotor blades, in addition to the performance enhancement [15,37] and dynamic stall alleviation [35,36] taken under consideration in previous works.…”