ALBERT

Description: Numerical simulations are used to investigate the resonant instabilities in two-dimensional flow past an open cavity. The compressible Navier-Stokes equations are solved directly (no turbulence model) for cavities with laminar boundary layers upstream. The computational domain is large enough to directly resolve a portion of the radiated acoustic field, which is shown to be in good visual agreement with schlieren photographs from experiments at several different Mach numbers. The results show a transition from a shear-layer mode, primarily for shorter cavities and lower Mach numbers, to a wake mode for longer cavities and higher Mach numbers. The shear-layer mode is characterized well by the acoustic feedback process described by Rossiter (1964), and disturbances in the shear layer compare well with predictions based on linear stability analysis of the Kelvin-Helmholtz mode. The wake mode is characterized instead by a large-scale vortex shedding with Strouhal number independent of Mach number. The wake mode oscillation is similar in many ways to that reported by Gharib & Roshko (1987) for incompressible flow with a laminar upstream boundary layer. Transition to wake mode occurs as the length and/or depth of the cavity becomes large compared to the upstream boundary-layer thickness, or as the Mach and/or Reynolds numbers are raised. Under these conditions, it is shown that the Kelvin-Helmholtz instability grows to sufficient strength that a strong recirculating flow is induced in the cavity. The resulting mean flow is similar to wake profiles that are absolutely unstable, and absolute instability may provide an explanation of the hydrodynamic feedback mechanism that leads to wake mode. Predictive criteria for the onset of shear-layer oscillations (from steady flow) and for the transition to wake mode are developed based on linear theory for amplification rates in the shear layer, and a simple model for the acoustic efficiency of edge scattering.

Description: Models for understanding and controlling oscillations in the flow past a rectangular cavity are developed. These models may be used to guide control designs, to understand performance limits of feedback, and to interpret experimental results. Traditionally, cavity oscillations are assumed to be self-sustained: no external disturbances are necessary to maintain the oscillations, and amplitudes are limited by nonlinearities. We present experimental data which suggests that in some regimes, the oscillations may not be self-sustained, but lightly damped: oscillations are sustained by external forcing, such as boundary-layer turbulence. In these regimes, linear models suffice to describe the behaviour, and the final amplitude of oscillations depends on the characteristics of the external disturbances. These linear models are particularly appropriate for describing cavities in which feedback has been used for noise suppression, as the oscillations are small and nonlinearities are less likely to be important. It is shown that increasing the gain too much in such feedback control experiments can lead to a peak-splitting phenomenon, which is explained by the linear models. Fundamental performance limits indicate that peak splitting is likely to occur for narrow-bandwidth actuators and controllers. © 2006 Cambridge University Press.

Description: We present a technique for describing the global behaviour of complex nonlinear flows by decomposing the flow into modes determined from spectral analysis of the Koopman operator, an infinite-dimensional linear operator associated with the full nonlinear system. These modes, referred to as Koopman modes, are associated with a particular observable, and may be determined directly from data (either numerical or experimental) using a variant of a standard Arnoldi method. They have an associated temporal frequency and growth rate and may be viewed as a nonlinear generalization of global eigenmodes of a linearized system. They provide an alternative to proper orthogonal decomposition, and in the case of periodic data the Koopman modes reduce to a discrete temporal Fourier transform. The Arnoldi method used for computations is identical to the dynamic mode decomposition recently proposed by Schmid & Sesterhenn (Sixty-First Annual Meeting of the APS Division of Fluid Dynamics, 2008), so dynamic mode decomposition can be thought of as an algorithm for finding Koopman modes. We illustrate the method on an example of a jet in crossflow, and show that the method captures the dominant frequencies and elucidates the associated spatial structures. © 2009 Cambridge University Press.

Description: In this paper we develop reduced-order models for the unsteady lift on a pitching and plunging aerofoil over a range of angles of attack. In particular, we analyse the pitching and plunging dynamics for two cases: a two-dimensional flat plate at mathit{Re}= 100 using high-fidelity direct numerical simulations and a three-dimensional NACA 0006 aerofoil at mathit{Re}= 65hspace{0.167em} 000 using wind-tunnel measurements. Models are obtained at various angles of attack and they are verified against measurements using frequency response plots and large-amplitude manoeuvres. These models provide a low-dimensional balanced representation of the relevant unsteady fluid dynamics. In simulations, flow structures are visualized using finite-time Lyapunov exponents. A number of phenomenological trends are observed, both in the data and in the models. As the base angle of attack increases, the boundary layer begins to separate, resulting in a decreased quasi-steady lift coefficient slope and a delayed relaxation to steady state at low frequencies. This extends the low-frequency range of motions that excite unsteady effects, meaning that the quasi-steady approximation is not valid until lower frequencies than are predicted by Theodorsen's classical inviscid model. In addition, at small angles of attack, the lift coefficient rises to the steady-state value after a step in angle, while at larger angles of attack, the lift coefficient relaxes down to the steady-state after an initially high lift state. Flow visualization indicates that this coincides with the formation and convection of vortices at the leading edge and trailing edge. As the angle of attack approaches the critical angle for vortex shedding, the poles and zeros of the model approach the imaginary axis in the complex plane, and some zeros cross into the right half plane. This has significant implications for active flow control, which are discussed. These trends are observed in both simulations and wind-tunnel data. © 2013 Cambridge University Press.

Description: Using data from direct numerical simulations, linear models of the compressible flow past a rectangular cavity are found. The emphasis is on forming simple models which capture the input-output behaviour of the system, and which are useful for feedback controller design. Two different approaches for finding a linear model are investigated. The first involves using input-output data of the linearized cavity flow to form a balanced, reduced-order model directly. The second approach is conceptual, and involves modelling each element of the flow physics separately using simple analytical expressions, the parameters of which are chosen based on simulation data at salient points in the cavity's computational domain. Both models are validated: first in the time domain by comparing their impulse responses to that of the full system in direct numerical simulations; and second in the frequency domain by comparing their frequency responses. Finally, the validity of both linear models is shown most clearly by using them for feedback controller design, and then applying each controller in direct numerical simulations. Both controllers completely eliminate oscillations, and demonstrate the advantages of model-based feedback controllers, even when the models upon which they are based are very simple. © 2012 Cambridge University Press.

Description: Particle image velocimetry (PIV) is used to investigate the three-dimensional wakes of rigid pitching panels with a trapezoidal geometry, chosen to model idealized fish caudal fins. Experiments are performed for Strouhal numbers from 0.17 to 0.56 for two different trailing edge pitching amplitudes. A Lagrangian coherent structure (LCS) analysis is employed to investigate the formation and evolution of the panel wake. A classic reverse von Kármán vortex street pattern is observed along the mid-span of the near wake, but the vortices realign and exhibit strong interactions near the spanwise edges of the wake. At higher Strouhal numbers, the complexity of the wake increases downstream of the trailing edge as the spanwise vortices spread transversely and lose coherence as the wake splits. This wake transition is shown to correspond to a qualitative change in the LCS pattern surrounding each vortex core, and can be identified as a quantitative event that is not dependent on arbitrary threshold levels. The location of this transition is observed to depend on both the pitching amplitude and free stream velocity, but is not constant for a fixed Strouhal number. On the panel surface, the trapezoidal planform geometry is observed to create additional vortices along the swept edges that retain coherence for low Strouhal numbers or high sweep angles. These additional swept-edge structures are conjectured to add to the complex three-dimensional flow near the tips of the panel. © 2011 Cambridge University Press.

Description: The linearised complex Ginzburg-Landau equation is a model for the evolution of small fluid perturbations, such as in a bluff body wake. By implementing actuators and sensors and designing an H2 optimal controller, we control a supercritical, infinite-domain formulation of this system. We seek the optimal actuator and sensor placement that minimises the H2 norm of the controlled system, from flow disturbances and sensor noise to a cost on the perturbation and input magnitudes. We formulate the gradient of the H2 squared norm with respect to the actuator and sensor placements and iterate towards the optimal placement. When stochastic flow disturbances are present everywhere in the spatial domain, it is optimal to place the actuator just upstream of the origin and the sensor just downstream. With pairs of actuators and sensors, it is optimal to place each actuator slightly upstream of each corresponding sensor, and scatter the pairs throughout the spatial domain. When disturbances are only introduced upstream, the optimal placement shifts upstream as well. Global mode and Gramian analyses fail to predict the optimal placement; they produce H2 norms about five times higher than at the true optimum. The wavemaker region is a better guess for the optimal placement. © © 2011 Cambridge University Press.

Description: Scaling laws for the propulsive performance of rigid foils undergoing oscillatory heaving and pitching motions are presented. Water tunnel experiments on a nominally two-dimensional flow validate the scaling laws, with the scaled data for thrust, power and efficiency all showing excellent collapse. The analysis indicates that the behaviour of the foils depends on both Strouhal number and reduced frequency, but for motions where the viscous drag is small the thrust closely follows a linear dependence on reduced frequency. The scaling laws are also shown to be consistent with biological data on swimming aquatic animals. © 2017 Cambridge University Press.

Description: Pipe bifurcations are common flow configurations in both natural and man-made systems. This study follows our previous report (Chen et al., Phys. Fluids, vol. 27, 2015, 034107) by describing three aspects of flows through junction angles of 70°, 90° and 110°, with a square cross-section. First, the inflow creates tightly spiralling vortices in four quadrants of the junction. For sufficiently large Reynolds number Re, these vortices undergo behaviour resembling steady near-axisymmetric breakdown. With increasing Re, the flow through the 90° junction remains steady and stable until the first Hopf bifurcation. Beyond the Hopf bifurcation, the vortices undergo a helical instability. The 70° and 110° junctions, however, first exhibit pitchfork bifurcations leading to asymmetric solutions. Second, the direct eigenmodes of the linearised flow are large in vortices in the outlet pipes, whereas the adjoint eigenmodes primarily reside in a small region in the inlet and the junction, near the front and back walls. Third, the sensitivities of the eigenvalues to spatially localised feedback and base flow modifications are greatest in and near the junction vortices. We highlight the regions of high growth rate and frequency sensitivity, as well as regions where the production and transport of perturbations by modifications of the base flow contribute most to the base flow sensitivity. The flow separation at the corners of the junction does not coincide with the eigenmodes or sensitivity regions. © 2017 Cambridge University Press.