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We present an effective reduced-order model (ROM) technique to couple an incompressible flow with a transversely vibrating bluff body in a state-space format. The ROM of the unsteady wake flow is based on the Navier–Stokes equations and is constructed by means of an eigensystem realization algorithm (ERA). We investigate the underlying mechanism of vortex-induced vibration (VIV) of a circular cylinder at low Reynolds number via linear stability analysis. To understand the frequency lock-in mechanism and self-sustained VIV phenomenon, a systematic analysis is performed by examining the eigenvalue trajectories of the ERA-based ROM for a range of reduced oscillation frequency $(F_{s})$, while maintaining fixed values of the Reynolds number ($Re$) and mass ratio ($m^{\ast }$). The effects of the Reynolds number $Re$, the mass ratio $m^{\ast }$ and the rounding of a square cylinder are examined to generalize the proposed ERA-based ROM for the VIV lock-in analysis. The considered cylinder configurations are a basic square with sharp corners, a circle and three intermediate rounded squares, which are created by varying a single rounding parameter. The results show that the two frequency lock-in regimes, the so-called resonance and flutter, only exist when certain conditions are satisfied, and the regimes have a strong dependence on the shape of the bluff body, the Reynolds number and the mass ratio. In addition, the frequency lock-in during VIV of a square cylinder is found to be dominated by the resonance regime, without any coupled-mode flutter at low Reynolds number. To further discern the influence of geometry on the VIV lock-in mechanism, we consider the smooth curve geometry of an ellipse and two sharp corner geometries of forward triangle and diamond-shaped bluff bodies. While the ellipse and diamond geometries exhibit the flutter and mixed resonance–flutter regimes, the forward triangle undergoes only the flutter-induced lock-in for $30\leqslant Re\leqslant 100$ at $m^{\ast }=10$. In the case of the forward triangle configuration, the ERA-based ROM accurately predicts the low-frequency galloping instability. We observe a kink in the amplitude response associated with 1:3 synchronization, whereby the forward triangular body oscillates at a single dominant frequency but the lift force has a frequency component at three times the body oscillation frequency. Finally, we present a stability phase diagram to summarize the VIV lock-in regimes of the five smooth-curve- and sharp-corner-based bluff bodies. These findings attempt to generalize our understanding of the VIV lock-in mechanism for bluff bodies at low Reynolds number. The proposed ERA-based ROM is found to be accurate, efficient and easy to use for the linear stability analysis of VIV, and it can have a profound impact on the development of control strategies for nonlinear vortex shedding and VIV.

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A novel surrogate model is proposed in lieu of Computational Fluid Dynamics (CFD) solvers, for fast nonlinear aerodynamic and aeroelastic modeling. A nonlinear function is identified on selected interpolation points by a discrete empirical interpolation method (DEIM). The flow field is then reconstructed using a least square approximation of the flow modes extracted by proper orthogonal decomposition (POD). The aeroelastic reduce order model (ROM) is completed by introducing a nonlinear mapping function between displacements and the DEIM points. The proposed model is investigated to predict the aerodynamic forces due to forced motions using a N ACA 0012 airfoil undergoing a prescribed pitching oscillation. To investigate aeroelastic problems at transonic conditions, a pitch/plunge airfoil and a cropped delta wing aeroelastic models are built using linear structural models. The presence of shock-waves triggers the appearance of limit cycle oscillations (LCO), which the model is able to predict.For all cases tested, the new ROM shows the ability to replicate the nonlinear aerodynamic forces, structural displacements and reconstruct the complete flow field with sufficient accuracy at a fraction of the cost of full order CFD model.

An Aeroelastic-Harmonic Balance (A-HB) formulation of the Euler flow equations using a high-order spatial discretization scheme coupled with structural dynamic equations is proposed. The main objective of this new approach is to drammatically reduce the computational cost required to predict unsteady, periodic problems such as limit cycle oscillations (LCO). To this end, a new solver based on the Monotonicity Preserving limiter together with the AUSM +-up flux function is developed for the harmonic balance equations. The use of high-order CFD schemes allows the reduction of the number of degrees of freedom required to achieve a given desired accuracy, with respect to lower order schemes. In this paper, the reduction in degrees of freedom of the fluid system is exploited in the context of a CFD based Harmonic-Balance framework using a frequency updating procedure to determine the limit cycle conditions. The standard A-HB methodology has shown over one order of magnitude speed-up over time-marching methods; by employing the proposed high-order scheme in conjunction with coarser grids, the LCO

We present an active feedback blowing and suction (AFBS) procedure via model reduction for unsteady wake flow and the vortex-induced vibration (VIV) of circular cylinders. The reduced-order model (ROM) for the AFBS procedure is developed by the eigensystem realization algorithm (ERA), which provides a low-order representation of the unsteady flow dynamics in the neighbourhood of the equilibrium steady state. The actuation is considered via vertical suction and a blowing jet at the porous surface of a circular cylinder with a body-mounted force sensor. While the optimal gain is obtained using a linear quadratic regulator (LQR), Kalman filtering is employed to estimate the approximate state vector. The feedback control system shifts the unstable eigenvalues of the wake flow and the VIV system to the left half-complex-plane, and subsequently results in suppression of the vortex street and the VIV in elastically mounted structures. The resulting controller designed by a linear low-order approximation is able to suppress the nonlinear saturated state of wake vortex shedding from the circular cylinder. A systematic linear ROM-based stability analysis is performed to understand the eigenvalue distribution for the flow past stationary and elastically mounted circular cylinders. The results from the ROM analysis are consistent with those obtained from full nonlinear fluid–structure interaction simulations, thereby confirming the validity of the proposed ROM-based AFBS procedure. A sensitivity study on the number of suction/blowing actuators, the angular arrangement of actuators and the combined versus independent control architectures has been performed for the flow past a stationary circular cylinder. Overall, the proposed control concept based on the ERA-based ROM and the LQR algorithm is found to be effective in suppressing the vortex street and the VIV for a range of reduced velocities and mass ratios.