Prediction of Limit Cycle Oscillations Using an Implicit Aeroelastic-Harmonic Balance Method

This work proposes a extends a novel approach to compute tran sonic 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 methodology to determine the unknown frequency of oscillations using an implicit for- mulation of the HB method 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 respective linear structural models is used to exercise the new method. Results show consistent agreement between the proposed and time-marching methods for both LCO amplitude and frequency.

Investigation of Limit Cycle Oscillations Using Aeroelastic-Harmonic Balance Method

This work investigates limit cycle oscillations in the transonic regime. A novel approach to predict Limit Cycle Oscillations using high fidelity analysis is exploited to accelerate calculations. The method used is an Aeroeasltic Harmonic Balance approach, which has been proven to be efficient and able to predict periodic phenomena. The behaviour of limit cycle oscillations is analysed using uncertainty quantification tools based on polynomial chaos expansions. To improve the efficiency of the sampling process for the polynomial-chaos expansions an adaptive sampling procedure is used. These methods are exercised using two problems: a pitch/plunge aerofoil and a delta-wing. Results indicate that Mach n. variability is determinant to the amplitude of the LCO for the 2D test case, whereas for the wing case analysed here, variability in the Mach n. has an almost negligible influence in amplitude variation and the LCO frequency variability has an almost linear relation with Mach number. Further test cases are required to understand the generality of these results.

Prediction of limit cycle oscillations under uncertainty using a Harmonic Balance method

The Harmonic Balance method is an attractive solution for computing periodic responses and can be an alternative to time domain methods, at a reduced computational cost. The current paper investigates using a Harmonic Balance method for simulating limit cycle oscillations under uncertainty. The Harmonic Balance method is used in conjunction with a non-intrusive polynomial-chaos approach to propagate variability and is validated against Monte Carlo analysis. Results show the potential of the approach for a range of nonlinear dynamical systems, including a full wing configuration exhibiting supercritical and subcritical bifurcations, at a fraction of the cost of performing time domain simulations.