Prediction of Transonic LCO using an Harmonic Balance Method

Abstract

This work proposes a novel approach to compute transonic Limit Cycle Oscillations using high fidelity analysis. CFD based Harmonic Balance methods have proven to be efficient tools to predict periodic phenomena. This paper's contribution is to present a new methodology to determine the unknown frequency of oscillations, enabling HB methods to accurately capture Limit Cycle Oscillations (LCOs); this is achieved by defining a frequency updating procedure based on a coupled CFD/CSD Harmonic Balance formulation to find the LCO condition. A pitch/plunge aerofoil and delta wing aerodynamic and respective linear structural models are used to validate the new method against conventional timedomain simulations. Results show consistent agreement between the proposed and timemarching methods for both LCO amplitude and frequency, while producing at least one order of magnitude reduction in computational time. * Research Fellow, MAIAA † Lecturer, MAIAA 1 of 20 Downloaded by UNIVERSITY OF TENNESSEE on August 8, 2015 | http://arc.aiaa.org | Nomenclature A = Harmonic Balance frequency domain matrix b, c = aerofoil semi-chord and chord, respectively D = Harmonic Balance operator matrix E = energy E = Tranformation matrix between frequency and time domains f = fluid force acting on structure F, G, H = convective fluxes for fluid equations h = plunge coordinate I = HB residual K = structure stiffness matrix L = frequency updating figure of merit M = structure mass matrix p = pressure R = vector of fluid and/or structural equation residual t = time step U ∞ = free-stream velocity u, v, w = fluid cartesian velocity components V, V s = reduced velocity and velocity index W = vector of fluid unknowns x, y = vector of structural unknowns α = angle of attack ω, κ = frequency and reduced frequency, κ = 2ω U∞c ρ = density τ = pseudo-time step

Aerodynamic Shape Optimization with Time Spectral Flutter Adjoint

“…Prasad et al [12] propose an alternative energy constraint instead of the small motion constraint proposed in [9] to capture the flutter onset condition. Yao and Marques [13] apply a pseudo-time stepping strategy to solve the harmonic balance flutter equation.…”