[11] Zhu, Y. & Breuer, K. (2023). A data-driven approach for modeling large-amplitude aeroelastic oscillations of pitching wings. Under review. [PDF] [arXiv]

We propose and validate a data-driven approach for modeling large-amplitude flow-induced oscillations of elastically mounted pitching wings. We first train a neural networks regression model for the nonlinear aerodynamic moment using data obtained from purely prescribed oscillations and static measurements. We then embed this model into an ordinary differential equation solver to solve for the governing equation of the passive aeroelastic system with desired structural parameters. The system dynamics predicted by the proposed data-driven method are characterized and compared with those obtained from physical experiments. The predicted and experimental pitching amplitude, frequency and aerodynamic moment responses are found to be in excellent agreement. Both the structural mode of high-inertia wings and the hydrodynamic mode of low-inertia wings are successfully predicted. The transient growth and saturation of the oscillation amplitude and the aerodynamic moment are also faithfully captured by the proposed method. Additional test cases demonstrate the broad applicability of this approach.

[10] Zhu, Y. & Breuer, K. (2023). Flow-induced oscillations of pitching swept wings: Stability boundary, vortex dynamics and force partitioning. J. Fluid Mech., 977, A1 [PDF]

Software: Force and moment partitioning influence potential solver 3D

We experimentally study the aeroelastic instability boundaries and three-dimensional vortex dynamics of pitching swept wings, with the sweep angle ranging from 0 to 25 degrees. The structural dynamics of the wings are simulated using a cyber-physical control system. With a constant flow speed, a prescribed high inertia and a small structural damping, we show that the system undergoes a subcritical Hopf bifurcation to large-amplitude limit-cycle oscillations (LCOs) for all the sweep angles. The onset of LCOs depends largely on the static characteristics of the wing. The saddle-node point is found to change non-monotonically with the sweep angle, which we attribute to the non-monotonic power transfer between the ambient fluid and the elastic mount. An optimal sweep angle is observed to enhance the power extraction performance and thus promote LCOs and destabilize the aeroelastic system. The frequency response of the system reveals a structural-hydrodynamic oscillation mode for wings with relatively high sweep angles. Force, moment, and three-dimensional flow structures measured using multi-layer stereoscopic particle image velocimetry are analyzed to explain the differences in power extraction for different swept wings. Finally, we employ a physics-based Force and Moment Partitioning Method (FMPM) to quantitatively correlate the three-dimensional vortex dynamics with the resultant unsteady aerodynamic moment.

[9] Zhu, Y., Lee, H., Kumar, S., Menon, K., Mittal, R. & Breuer, K. (2023). Force moment partitioning and scaling analysis of vortices shed by a 2D pitching wing in quiescent fluid. Exp. Fluids 64, 158 [PDF]

Software: Force and moment partitioning influence potential solver 2D

We experimentally study the dynamics and strength of vortices shed from a NACA 0012 wing undergoing sinusoidal pitching in quiescent water. We characterize the temporal evolution of the vortex trajectory and circulation over a range of pitching frequencies, amplitudes and pivot locations. By employing a physics-based force and moment partitioning method (FMPM), we estimate the vortex-induced aerodynamic moment from the velocity fields measured using particle image velocimetry. The vortex circulation, formation time and vorticity-induced moment are shown to follow scaling laws based on the feeding shear-layer velocity. The vortex dynamics, together with the spatial distribution of the vorticity-induced moment, provide quantitative explanations for the nonlinear behaviors observed in the fluid damping (Zhu et al., J. Fluid Mech., vol. 923, 2021, R2).

[8] Guan, Y., Zhu, Y., Yang, Z., Yin, B., Gupta, V. & Li, L. K. B. (2023). Multifractality and scale-free network topology in a noise-perturbed laminar jet. J. Fluid Mech., 972, A6 [PDF]

We present experimental evidence of multifractality and scale-free network topology in a noise-perturbed laminar jet operated in a globally stable regime, prior to the critical point of a supercritical Hopf bifurcation and prior to the saddle-node point of a subcritical Hopf bifurcation. For both types of bifurcation, we find that (i) the degree of multifractality peaks at intermediate noise intensities, (ii) the conditions for peak multifractality produce a complex network whose node degree distribution obeys an inverse power-law scaling with an exponent of 2<𝛾<3, indicating scale-free topology and (iii) the Hurst exponent and the global clustering coefficient can serve as early warning indicators of global instability under specific operating and forcing conditions. By characterising the noise-induced dynamics of a canonical shear flow, we demonstrate that the multifractal and scale-free network dynamics commonly observed in turbulent flows can also be observed in laminar flows under certain stochastic forcing conditions.

[7] Lee, H., Simone, N., Su, Y., Zhu, Y., Ribeiro, B.L.R., Franck, J.A. and Breuer, K. (2022). Leading edge vortex formation and wake trajectory: Synthesizing measurements, analysis, and machine learning. Phys. Rev. Fluids, 7(7), 074704 [PDF]

The strength and trajectory of a leading edge vortex (LEV) formed by a pitching-heaving hydrofoil is studied. The LEV is identified using the Q-criterion method, which is calculated from the 2D velocity field obtained from particle image velocimetry measurements. The relative angle of attack at midstroke, α_T/4, proves to be an effective method of combining heave amplitude, pitch amplitude, and reduced frequency into a single variable that predicts the maximum value of Q over a wide range of operating conditions. Supervised machine learning algorithms, namely support vector regression and Gaussian process regression, are used to create regression models that predicts the vortex strength, shape, and trajectory during growth and after separation. The regression model successfully captures the features of two vortex regimes observed at different values of α_T/4.

[6] Zhu, Y., Mathai, V. & Breuer, K. (2021), Nonlinear fluid damping of elastically mounted pitching wings in quiescent water. J. Fluid Mech., 923, R2 [PDF]

We experimentally study the nonlinear fluid damping of a rigid but elastically mounted pitching wing in the absence of a free-stream flow. The dynamics of the elastic mount are simulated using a cyber-physical system. We perturb the wing and measure the fluid damping coefficient from damped oscillations over a large range of pitching frequencies, pitching amplitudes, pivot locations and sweep angles. A universal fluid damping scaling is proposed to incorporate all these parameters. Flow fields obtained using particle image velocimetry are analysed to explain the nonlinear behaviours of the fluid damping.

[5] Zhu, Y., Su, Y. & Breuer, K. (2020). Nonlinear flow-induced instability of an elastically mounted pitching wing. J. Fluid Mech., 899, A35 [PDF]

We experimentally study the nonlinear flow-induced instability of a cyber-physically mounted pitching wing in a water tunnel. We vary the wing inertia and stiffness to define stability boundaries for large-amplitude flow-induced oscillations, and report two distinct oscillation modes, namely a structural mode, which occurred via a subcritical bifurcation and was associated with a high inertia, and a hydrodynamic mode, which occurred via a supercritical bifurcation and was associated with a low inertia. We characterize these two oscillation modes by analyzing the corresponding amplitude, frequency, force, and flow response of the wing. Lastly, we use an energy approach to explain the existence of these two modes.

[4] Zhu, Y., Gupta, V. & Li, L. K. B. (2019). Coherence resonance in low-density jets. J. Fluid Mech., 881, R1 [PDF]

We report the first experimental evidence of coherence resonance (CR) in a hydrodynamic system, a low-density jet capable of undergoing both supercritical and subcritical Hopf bifurcations. We then model the CR dynamics with a stochastically forced van der Pol oscillator. The fact that CR occurs in the unconditionally stable regime, prior to both the Hopf and saddle-node points, implies that it can be used to forecast the onset of global instability. Although demonstrated here on a low-density jet, CR is expected to arise in almost all nonlinear dynamical systems near a Hopf bifurcation, opening up new possibilities for the development of global-instability precursors in a variety of hydrodynamic systems.

[3] Lee, M., Zhu, Y., Li, L. K. B. & Gupta, V. (2019). System identification of a low-density jet via its noise-induced dynamics. J. Fluid Mech., 862, 200-215 [PDF]

We perform system identification of a low-density jet using measurements of its noise-induced dynamics in the unconditionally stable regime, prior to both the Hopf and saddle-node points. We show that this approach can enable prediction of (i) the order of nonlinearity, (ii) the locations and types of the bifurcation points (and hence the stability boundaries) and (iii) the resulting limit-cycle oscillations. The only assumption made about the system is that it obeys a Stuart–Landau equation in the vicinity of the Hopf point, thus making the method applicable to a variety of hydrodynamic systems. This study constitutes the first experimental demonstration of system identification using the noise-induced dynamics in only the unconditionally stable regime, which opens up new possibilities for the prediction and analysis of the stability and nonlinear behavior of hydrodynamic systems.

[2] Murugesan, M., Zhu, Y. & Li, L. K. B. (2019). Complex network analysis of forced synchronization in a hydrodynamically self-excited jet. Int. J. Heat Fluid Flow, 76, 14-25 [PDF]

Previous experiments by Li and Juniper (2013) have shown that a hydrodynamically self-excited jet can synchronize with external acoustic forcing via one of two possible routes: a saddle-node (SN) bifurcation or a torus-death (TD) bifurcation. In this study, we use complex networks to analyze and forecast these two routes to synchronization in a prototypical self-excited flow – an axisymmetric low-density jet at an operating condition close to its first Hopf point. This study shows that complex networks can be a useful tool for distinguishing between the SN and TD routes to synchronization, and for forecasting the proximity of a system to its synchronization boundaries. These findings could open up new opportunities for complex networks to be used in the development of open-loop control strategies for hydrodynamically self-excited flows.

[1] Zhu, Y., Gupta, V. & Li, L. K. B. (2017). Onset of global instability in low-density jets. J. Fluid Mech., 828, R1 [PDF]

In low-density axisymmetric jets, the onset of global instability is known to depend on three control parameters, namely the jet-to-ambient density ratio S, the initial momentum thickness θ and the Reynolds number Re. For sufficiently low values of S and θ, these jets bifurcate from a steady state (a fixed point) to a self-excited oscillatory state (a limit cycle) when Re increases above a critical value corresponding to the Hopf point, Re_H. In the literature, this Hopf bifurcation is often regarded as supercritical. In this experimental study, however, we find that under some conditions, there exists a hysteretic bistable region at Re_SN.