Frequency Domain Flutter Boundary Computations Using Navier-Stokes Equations on Superclusters

Abstract

T HEevaluation of flutter characteristics ofwings and rotor blades is critical to avoid structural failures [1]. Wind-tunnel experiments in this area are rare due to the high expenses involved, and flight tests are almost impossible due to high risk [2]. Computational flutter simulations based on linear theory (LT) methods are well established, but they are not adequate to resolve the flow complexities involved in real flights. High-fidelity computational fluid dynamics (CFD) methods based on the Navier–Stokes equations are needed. Aeroelastic computations using the potential flow theory-based CFD were started in conjunction with time-integration (TI) and frequency domain (FD) approaches in the late 1970s [3]. Currently, CFD for aeroelasticity has advanced to use Reynolds averaged Navier–Stokes (RANS) equations [4]. The TI approach [4] needed in the final stages of design is computationally more expensive than the FD [5] approach for computing flutter boundaries, since aeroelastic responses need to be computed for changes in every design parameter. Under certain assumptions, a good prediction of a flutter boundary can be made using the FD approach [5]. The primary assumption in the FD approach is that the aerodynamic loads can be linearly superimposed among modes, since flutter starts as a small perturbation phenomenon. Hence, this approach is computationally less expensive than the TI approach, since only one-time computation of aerodynamic data is required for a selected set of modes and frequencies. Data for arbitrary frequencies are generated by interpolating the precomputed aerodynamic data based on selected frequencies [5]. Similar to the FD, methods based on reduced-order modeling are introduced to reduce the computational cost [6]. However, as stated in [7], studies show that reduced-order models are neither robust with respect to parameter changes nor cheap to generate data when using the Navier–Stokes equations. The FD approach well established in industry [8] for LT-based methods is highly suitable for large-scale computations using CFD. Compared to using LT, the computational time is significantly larger for using the Navier–Stokes-equations-based CFD. Developments in supercomputers have alleviated the computational time issues. This Note describes a procedure using parallel computers for efficiently computing the flutter boundaries by the RANS-based FD approach. The unsteady aerodynamic data are obtained by timeaccurately solving the RANS equations for oscillatory motions. A modal approach is then used to compute the flutter boundary. Contrary to the common practice of generating data by submitting jobs for cases separately (concurrent computing) [9], in the present Note, computations are made efficiently in a single job environment using a parallel protocol [10]. With this protocol, all cases start and end at the same time, eliminating the effort to monitor multiple jobs.