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Aeroelastic Reduced-Order Model Differential Equations in Transonic Buffeting Flow

Michael Candon, Pier Marzocca, Earl H. Dowell

TL;DR

This work tackles the challenge of predicting aeroelastic responses in transonic buffet by introducing a data-driven reduced-order model that fuses a nonlinear fluid oscillator with a memory-bearing Volterra integral term. The IDE-ROM framework identifies both the governing equations and their coefficients from CFD data using Orthogonal Matching Pursuit, enabling accurate capture of self-excited buffet oscillations, lock-in, and memory effects during heave and pitch motions. Applied to the ONERA OAT15A airfoil, the approach yields accurate lift and moment responses and demonstrates substantial computational savings (10^4–10^5× speed-up) over high-fidelity CFD/CSD simulations, while preserving essential nonlinear physics. Limitations include degraded extrapolation at very large amplitudes and challenges extending to fully 3D, broadband buffet; future work includes multi-DOF, multi-input ROMs and integration with PINNs for improved extrapolation and robustness.

Abstract

Numerical simulation of the transonic shock buffet phenomenon remains a formidable challenge due to its inherent nonlinear and unsteady characteristics. These difficulties are further compounded in three-dimensional configurations and when aeroelastic coupling is considered. Consequently, computational studies of aeroelastic shock buffet interactions have largely been confined to two-dimensional systems. This limitation underscores the need for reduced-order models (ROMs) capable of efficiently and accurately capturing the aeroelastic response of structures subjected to shock buffet oscillations. This paper presents a novel nonlinear unsteady aerodynamic ROM that integrates nonlinear oscillator dynamics with Volterra theory to model aeroelastic shock buffet phenomena. The coefficients and terms of the resulting Integro-Differential Equation ROM (IDE-ROM) are identified using the Orthogonal Matching Pursuit (OMP) algorithm. Application of the IDE-ROM to an OAT15A airfoil demonstrates that the compact and computationally efficient formulation can reproduce key nonlinear behaviors, including aeroelastic lock-in, with a high degree of accuracy. The limitations and potential extensions of the proposed approach are also critically examined.

Aeroelastic Reduced-Order Model Differential Equations in Transonic Buffeting Flow

TL;DR

This work tackles the challenge of predicting aeroelastic responses in transonic buffet by introducing a data-driven reduced-order model that fuses a nonlinear fluid oscillator with a memory-bearing Volterra integral term. The IDE-ROM framework identifies both the governing equations and their coefficients from CFD data using Orthogonal Matching Pursuit, enabling accurate capture of self-excited buffet oscillations, lock-in, and memory effects during heave and pitch motions. Applied to the ONERA OAT15A airfoil, the approach yields accurate lift and moment responses and demonstrates substantial computational savings (10^4–10^5× speed-up) over high-fidelity CFD/CSD simulations, while preserving essential nonlinear physics. Limitations include degraded extrapolation at very large amplitudes and challenges extending to fully 3D, broadband buffet; future work includes multi-DOF, multi-input ROMs and integration with PINNs for improved extrapolation and robustness.

Abstract

Numerical simulation of the transonic shock buffet phenomenon remains a formidable challenge due to its inherent nonlinear and unsteady characteristics. These difficulties are further compounded in three-dimensional configurations and when aeroelastic coupling is considered. Consequently, computational studies of aeroelastic shock buffet interactions have largely been confined to two-dimensional systems. This limitation underscores the need for reduced-order models (ROMs) capable of efficiently and accurately capturing the aeroelastic response of structures subjected to shock buffet oscillations. This paper presents a novel nonlinear unsteady aerodynamic ROM that integrates nonlinear oscillator dynamics with Volterra theory to model aeroelastic shock buffet phenomena. The coefficients and terms of the resulting Integro-Differential Equation ROM (IDE-ROM) are identified using the Orthogonal Matching Pursuit (OMP) algorithm. Application of the IDE-ROM to an OAT15A airfoil demonstrates that the compact and computationally efficient formulation can reproduce key nonlinear behaviors, including aeroelastic lock-in, with a high degree of accuracy. The limitations and potential extensions of the proposed approach are also critically examined.
Paper Structure (28 sections, 53 equations, 20 figures, 2 tables, 1 algorithm)

This paper contains 28 sections, 53 equations, 20 figures, 2 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Reduced-Order Model Differential Equations
  3. Known Functions
  4. Function Identification
  5. Generation of Training Data
  6. Orthogonal Matching Pursuit and Constrained Extension
  7. Coefficient Estimation of Known Functions
  8. Coefficient Estimation of Unknown Equations
  9. Computational Framework
  10. Computational Fluid Dynamics Model
  11. Computational Model 1: Aerodynamics Only
  12. Computational Model 2: Aeroelastic
  13. Aeroelastic Equation of Motion
  14. Results
  15. Buffet Only Reduced-Order Model Differential Equations
  16. ...and 13 more sections

Figures (20)

  • Figure 1: Computational grids
  • Figure 2: Mean and RMS pressure coefficient compared to experimental results for CM1 and CM2.
  • Figure 3: Influence low-pass filtering on the moment coefficient at $\alpha_0 = 3.5^\circ$
  • Figure 4: True and identified constants of the Rayleigh oscillator for lift force.
  • Figure 5: True and identified constants of the Rayleigh oscillator for pitching moment.
  • ...and 15 more figures