Data-driven reduced order modelling for the analysis and prediction of transonic buffet and flutter
Creators: name: Das, Arpan
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 400106
subject: Hypersonic propulsion and hypersonic aerothermodynamics
classificationCode: 401204
subject: Computational methods in fluid flow, heat and mass transfer (incl. computational fluid dynamics)
classificationCode: 401706
subject: Numerical modelling and mechanical characterisation

description: Within the very narrow regime of transonic flow, complex interactions between shock waves and boundary layer cause some airfoil/wing configurations to experience self-sustained shock oscillations that induce large aerodynamic load variations. Such oscillations, referred to as transonic shock buffet, can cause a reduction in stability, control, handling qualities, and structural integrity, thereby limiting the aircraft buffet envelope. Due to the complexity and the severity of this phenomenon, it has been an active topic of research for the last few decades which requires either expensive experimental investigations in the wind tunnel or high-fidelity computations which, due to the inherent large-scale nature of the models, demands extensive computational resources. In this work, numerical investigation for analyzing transonic buffet has been conducted on OAT15A supercritical airfoil. A thorough validation study is carried out to compare the numerical results with its experimental counterparts conducted by ONERA. At first, the CFD results were studied and the shock buffet behavior was examined by analyzing the flow fields and characterized based on the shock dynamical behavior. Three different types of shock oscillatory behavior were identified for OAT15A supercritical airfoil: Type A, Combined Type, and High AOA shock buffet with massive separation.

Several data-driven modal decomposition techniques were applied to the CFD-generated flow field data to construct a Reduced Order Model (ROM) to diagnose and predict future states of different shock buffet phenomena observed for the OAT15A profile. At first, for Type A, a snapshot-POD has been applied, and the modal contribution of the first three dominant modes was discussed. The effect of the shock position during its oscillatory motion, the shear layer, and boundary layer thickness variation were discussed in detail pertaining to each mode’s contribution to the flow field. Thereafter, several DMD techniques were applied to construct a ROM based on spatiotemporal decomposition of data. It was found that the first dominant dynamic mode has the exact same frequency as the shock’s oscillatory motion and represents the main features of shock buffet. Moreover, the next few dominant modes were identified to be superharmonics of the buffet mode. Furthermore, a machine learning based sparsity-promoting DMD was applied to select sparsely optimal modes for a parsimonious and stable ROM creation, and it was found that only a handful of modes are needed for ROM construction with sufficient accuracy. After that, compressed DMD was utilized to construct a ROM with a significantly low number of spatial measurements, and to reduce computational time and memory usage while also retaining relatively high accuracy. In addition to that, two very common sources of noise: white noise and salt and pepper type spurious noise were added to shock buffet flow field data. Various DMD techniques were applied to the noise corrupted data and their abilities were tested regarding sufficiently accurate ROM construction from the noise corrupted data.

Due to the high nonlinearities present in the High AOA shock buffet with massive separation, and combined Type buffet, an augmented DMD with Taken’s time-delay embedding theorem was implemented to analyze the intricate buffet behavior. In the case of the former, although the shock motion is periodic, the presence of multiple harmonics is easily identified from load oscillation, and the shock movement stays very close to the leading edge. The dominant dynamic mode identifies the massive separation that has a significant contribution towards the shock oscillatory behavior. In case of Combined Type buffet, two different characteristics are observed: 1. In some cases of Combine Type, the second most dominant dynamic mode (the first superharmonic of the buffet mode) has a significantly strong amplitude compared to Type A case, thereby has a strong influence in association with the nonlinearities present in shock dynamical behavior 2. A few cases of Combined Type have the second most dominant dynamic mode as the subharmonic of the buffet mode, these cases have significantly stronger nonlinearities present that are also reflected in load oscillations and shock dynamical behavior.

Data-driven methods were applied to analyze flight test data obtained during a flutter flight test campaign by Gulfstream Aerospace Company. Three sets of flight test data for three flight tests conducted at three test points in a flutter flight test operation were obtained. The extremely noisy dataset was stacked in a data matrix consisting of five maneuvers and filtered through the RPCA algorithm, and conjunction of several methods was implemented to identify flutter modes, their frequencies, and damping characteristics with minimal human intervention. The potential of the developed method for flutter mode detection can be extended in a way so that it can handle streaming datasets (online calculation) with absolute zero human intervention.