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.
The ability of a Cycloidal Wave Energy Converter (CycWEC) to cancel irregular deep ocean waves is investigated in a 1:300 scale wave tunnel experiment. A CycWEC consists of one or more hydrofoils attached equidistant to a shaft that is aligned parallel to the incoming waves. The entire device is fully submerged in operation. Wave cancellation requires synchronization of the rotation of the CycWEC with the incoming waves, as well as adjustment of the pitch angle of the blades in proportion to the wave height. The performance of a state estimator and controller that achieve this objective were investigated, using the signal from a resistive wave gage located up-wave of the CycWEC as input. The CycWEC model used for the present investigations features two blades that are adjustable in pitch in real time. The performance of the CycWEC for both a superposition of two harmonic waves, as well as irregular waves following a Bretschneider spectrum is shown. Wave cancellation efficiencies as determined by wave measurements of about 80% for the majority of the cases are achieved, with wave periods varying from 0.4s to 0.75s and significant wave heights of Hs ≈ 20mm. This demonstrates that the CycWEC can efficiently interact with irregular waves, which is in good agreement with earlier results obtained from numerical simulations.
The ability of a Cycloidal Wave Energy Converter (CycWEC) to cancel irregular deep ocean waves is investigated in a time integrated, inviscid potential flow simulation. A CycWEC consists of one or more hydrofoils attached eccentrically to a shaft that is aligned parallel to the incoming waves. The entire device is fully submerged in operation. A Bretschneider spectrum with 40 discrete components is used to model an irregular wave environment in the simulations. A sensor placed up-wave of the CycWEC measures the incoming wave height and provides a signal for the wave state estimator, a non-causal Hilbert transformation, to estimate the instantaneous frequency, phase and amplitude of the irregular wave pattern. A linear control scheme which proportionally controls hydrofoil pitch and compensates for phase delays is adopted. Efficiency for the design Bretschneider spectrum shows more than 99% efficiency, while non-optimum, off design operating conditions still maintain more than 85% efficiency. These results are in agreement with concurrent experimental results obtained at a 1:300 scale.
We investigate a lift based wave energy converter (WEC), namely, a cycloidal turbine, as a wave termination device. A cycloidal turbine employs the same geometry as the well established Cycloidal or Voith-Schneider Propeller. The main shaft is aligned parallel to the wave crests and fully submerged at a fixed depth. We show that the geometry of the Cycloidal WEC is suitable for single sided wave generation as well as wave termination of straight crested waves using feedback control.The cycloidal WEC consists of a shaft and one or more hydrofoils that are attached eccentrically to the main shaft. An experimental investigation into the wave generation capabilities of the WEC are presented in this paper, along with initial wave cancellation results for deep water waves. The experiments are conducted in a small 2D wave flume equipped with a flap type wave maker as well as a 1:4 sloped beach. The operation of the Cycloidal WEC both as a wave generator as well as a wave energy converter interacting with a linear Airy wave is demonstrated. The influence that design parameters radius and submergence depth on the performance of the WEC have is shown. For wave cancellation, the incoming wave is reduced in amplitude by ≈ 80% in these experiments. In this case wave termination efficiencies of up to 95% of the incoming wave energy with neglegible harmonic waves generated are achieved by synchronizing the rotational rate and phase of the Cycloidal WEC to the incoming wave.
A lift based cycloidal wave energy converter (CycWEC) is investigated in a 1:300 scale two-dimensional wave flume experiment. This type of wave energy converter consists of a shaft with one or more hydrofoils attached eccentrically at a radius. The main shaft is aligned parallel to the wave crests and submerged at a fixed depth. The operation of the CycWEC both as a wave generator as well as a wave-to-shaft energy converter interacting with straight crested waves is demonstrated. The geometry of the converter is shown to be suitable for wave termination of straight crested harmonic and irregular waves. The impact of design parameters such as device size, submergence depth, and number of hydrofoils on the performance of the converter is shown. For optimal parameter choices, experimental results demonstrate energy extraction efficiencies of more than 95% of the incoming wave energy. This is achieved using feedback control to synchronize the rotation of the CycWEC to the incoming wave, and adjusting the blade pitch angle in proportion to the wave height. Due to the ability of the CycWEC to generate a single sided wave with few harmonic waves, little energy is lost to waves radiating in the up-wave and down-wave directions.
The asymmetric vortex regime of a von Kármán ogive with fineness ratio of 3.5 is computationally studied. Laminar simulations performed at a Re=220,000 at an incidence of 50 • demonstrate significant side force (i.e. vortex asymmetry). Moving wall boundary patches near the tip of the ogive were used to simulate a disturbance to excite the convective instability. The tip disturbance produced a deterministic asymmetric vortex state and corresponding sideforce direction and magnitude. Linear stochastic estimation (a least squares solution) is used to correlate surface pressure information to the time varying flow state. Optimal sensor locations as well as number of sensors are determined from an iterative genetic algorithm. Results show that a physically realizable number and arrangement of surface pressure measurements are achieved for asymmetric vortex estimation.
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