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For the systematic development of feedback flow controllers, a numerical model that captures the dynamic behaviour of the flow field to be controlled is required. This poses a particular challenge for flow fields where the dynamic behaviour is nonlinear, and the governing equations cannot easily be solved in closed form. This has led to many versions of low-dimensional modelling techniques, which we extend in this work to represent better the impact of actuation on the flow. For the benchmark problem of a circular cylinder wake in the laminar regime, we introduce a novel extension to the proper orthogonal decomposition (POD) procedure that facilitates mode construction from transient data sets. We demonstrate the performance of this new decomposition by applying it to a data set from the development of the limit cycle oscillation of a circular cylinder wake simulation as well as an ensemble of transient forced simulation results. The modes obtained from this decomposition, which we refer to as the double POD (DPOD) method, correctly track the changes of the spatial modes both during the evolution of the limit cycle and when forcing is applied by transverse translation of the cylinder. The mode amplitudes, which are obtained by projecting the original data sets onto the truncated DPOD modes, can be used to construct a dynamic mathematical model of the wake that accurately predicts the wake flow dynamics within the lock-in region at low forcing amplitudes. This low-dimensional model, derived using nonlinear artificial neural network based system identification methods, is robust and accurate and can be used to simulate the dynamic behaviour of the wake flow. We demonstrate this ability not just for unforced and open-loop forced data, but also for a feedback-controlled simulation that leads to a 90% reduction in lift fluctuations. This indicates the possibility of constructing accurate dynamic low-dimensional models for feedback control by using unforced and transient forced data only.

A low-dimensional Galerkin model is proposed for the flow around a high-lift configuration, describing natural vortex shedding, the high-frequency actuated flow with increased lift and transients between both states. The form of the dynamical system has been derived from a generalized mean-field consideration. Steady state and transient URANS (unsteady Reynolds-averaged Navier–Stokes) simulation data are employed to derive the expansion modes and to calibrate the system parameters. The model identifies the mean field as the mediator between the high-frequency actuation and the low-frequency natural shedding instability.

In this study, a spatiotemporal characterization of forced and unforced flows of a conical swirler is performed based on particle image velocimetry (PIV) and laser Doppler anemometry (LDA). The measurements are performed at a Reynolds number of 33,000 and a swirl number of 0.71. Axisymmetric forcing is applied to approximate the effects of thermoacoustic instabilities on the flow field at the burner inlet and outlet. The actuation frequencies are set at the natural flow frequency (Strouhal number Stf≈0.92) and two higher frequencies (Stf≈1.3 and 1.55) that are not harmonically related to the natural frequency. Phase-averaged measurement are used as a first step to visualize the coherent flow structures. Second, proper orthogonal decomposition (POD) is applied to the PIV data to characterize the effect of the actuation on the fluctuating flow. Measurements indicate a typical natural flow instability of helical nature in the unforced case. The associated induced pressure and flow oscillations travel upstream to the swirler inlet where generally fuel is injected. This observation is of critical importance with respect to the stability of the combustion. Harmonic actuation at different frequencies and amplitudes does not affect the mean velocity profile at the outlet, while the coherent velocity fluctuations are strongly influenced at both the inlet and outlet. On one hand, the dominant helical mode is replaced by an axisymmetric vortex ring if the flow is forced at the natural flow frequency. On the other hand, the natural flow frequency prevails at the outlet under forcing at higher frequencies and POD analysis indicates that the helical structure is still present. The presented results give new insight into the flow dynamics of a swirling flow burner under strong forcing.

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Accurate simulation of flight beyond normal conditions requires models of the aircraft aerodynamics at high angles of attack, for which the flow over the wing and control surfaces may be rapidly changing and massively separated. This study focuses on large-amplitude forced oscillations of a benchmark commercial aircraft configuration. Existing models are modified to describe the unsteady aerodynamic forces on the aircraft up to stall range. Steady-state and periodically forced unsteady Reynolds-averaged Navier-Stokes simulation data are employed to calibrate the model parameters. The results of the reduced-order models are in good overall agreement with those observed in the unsteady Reynolds-averaged Navier-Stokes simulations.

A reduced-order modelling (ROM) strategy is pursued to achieve a mechanistic understanding of jet flow mechanisms targeting jet noise control. Coherent flow structures of the jet are identified by the proper orthogonal decomposition (POD) and wavelet analysis. These techniques are applied to an LES data ensemble with velocity snapshots of a three-dimensional, incompressible jet at a Reynolds number of Re = 3600. A low-dimensional Galerkin model of a three-dimensional jet is extracted and calibrated to the physical dynamics. To obtain the desired mechanistic understanding of jet noise generation, the loudest flow structures are distilled by a goal-oriented generalisation of the POD approach we term 'most observable decomposition' (MOD). Thus, a reduction of the number of dynamically most important degrees of freedom by one order of magnitude is achieved. Capability of the presented ROM strategy for jet noise control is demonstrated by suppression of loud flow structures.

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