Casey Fagley

Low-dimensional modelling of a transient cylinder wake using double proper orthogonal decomposition

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.

Open-Loop Dynamics of the Asymmetric Vortex Wake behind a von Kármán Ogive at High Incidence

The asymmetric vortex regime of a von Karman ogive with fineness ratio of 3.5 is experimentally studied at a Reynolds number of 156,000. Both port and starboard plasma actuators are used to introduce fluidic disturbances at the tip of the ogive which are amplified through the flows convective instability and produce a deterministic port or starboard asymmetric vortex state (i.e. side force). Accurate control or manipulation of this asymmetric vortex state holds the potential for increased maneuverability and stability characteristics of slender flight vehicles at high angle of attack. Open-loop experimental tests are used to understand and quantify the vortex dynamics due to actuation inputs. Linear time invariant models provide a suitable model structure to replicate the vortex dynamics and allow for simulation and closed-loop control design. Standard PID control is designed and implemented. A closed-loop simulation shows arbitrary side force tracking with adequate disturbance rejection.

Predictive Flow Control to Minimize Convective Time Delays

To overcome the convective time delay issue for active closed-loop flow control, a model based predictive control algorithm is analyzed. From a controls perspective, forms of internal model control or model predictive control can be used to accommodate and minimize the effect of systems with pure time delays. Moreover, the Smith predictor is a commonly employed control technique to negate the pure time delay in a closed-loop system. This form of model predictive control is applied to the asymmetric vortex problem of an axisymmetric forebody (specifically a von Karman ogive with fineness ratio of 3.5). The full-order Navier-Stokes equations are numerically solved on the forebody at a high angle of attack and provide the plant process. Small port and starboard blowing patches are used to introduce fluidic disturbances at the nose of the ogive to augment the global flow state and produce a deterministic vortex state. As the active flow control technique exploits a convective instability, a convective time delay exists. Linear-time-invariant and non-linear time-invariant models are developed from the open-loop dynamics. A Smith predictor is employed within the full order CFD simulation. The results of the predictive control are compared to open-loop and model-free closed-loop behavior. It is shown that the predictive control developed in this paper while very suitable for control of this type of flow, is very sensitive to modeling uncertainties.

Experimental Investigation of the Aeroelastic Behavior a NACA0018 Cyber-Physical FlexibleWing

The aeroelastic behavior of a NACA0018, rectangular planform, semi-span aspect ratio (A) of 6, and chord of 0.1 m wing is experimentally explored. Wind tunnel tests were performed over a Mach range from 0 to 0.15 (Re = 220,000) on the test article. The composite wing was designed such that the first torsional mode was isolated and controlled with a motor and feedback control system. This cyberphysical system (CPS) uses dynamic feedback control to make a system behave according to desired equations of motion. The equations of motion can be augmented to replicate any type of dynamics, but for the purposes of this investigation a second-order ordinary differential equation, satisfying Newtonian laws, was used. This research utilized the CPS to investigate the aeroelastic behavior of the wing with varying torsional stiffness, freestream velocity and root angle of attack. Experimental results are qualified by a low-order analytic representation of the aeroelastic phenomenon, aeroelastic data published in the open literature, as well as a high fidelity, fully coupled computational fluidstructural dynamic solver. Two interesting regimes are observed: the case in which the torsional frequency is less than the bending frequency and the inverse relationship. Moreover, a pure stall flutter (excitation of the angular twist) limit cycle oscillation and plunge flutter (excitation of bending mode) are exhibited. Finally, trends between limit cycle oscillations, torsional stiffness, free stream velocity and base angle of attack are observed and discussed. The CPS shows the capability to isolate aero-elastic trends.

EXPERIMENTAL INVESTIGATION OF IRREGULAR WAVE CANCELLATION USING A CYCLOIDAL WAVE ENERGY CONVERTER

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.Copyright

Experimental Wave Generation and Cancellation With a Cycloidal Wave Energy Converter

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.Copyright

Feedback Flow Control of a Shear Layer for Aero-Optic Applications

A Reduced Order Model (ROM) is formulated for the shear layer behind a backward facing step for the purpose of developing feedback control strategies. The ultimate goal of controlling the shear layer is the mitigation of optical aberrations caused by large scale density variations in the flow field. The results of simulations of the unforced and openloop forced shear layer, based on the compressible Navier-Stokes equations, were used to compile a Proper Orthogonal Decomposition (POD) database of the flow states. A Reduced Order Model for the POD time coefficients was then built using Wavenets (WN). This WN model was utilized to simulate closed loop dynamics and ultimately develop feedback control algorithms. Results obtained from applying direct adaptive control to the WN model indicate that a 35% reduction in the optical aberrations is possible.

Reduced Order Model of Cylinder Wake with Direct Adaptive Feedback Control

This paper demonstrates a very systematic approach for feedback flow controller design. Open loop forcing and unforced CFD simulation training data is used to build a reduced order model via the Double Proper Orthogonal Decomposition (DPOD) process. Nonlinear system identification is then used realize a very simple, low dimensional plant. The model has the ability to simulate interior points on the forcing envelope and also predict closed loop dynamics if the model is developed correctly. For simplicity, the model and controller development strategy is shown for a relatively well know flow field, the two dimensional, circular cylinder wake. This paper shows the validity of neural network (ANNARX) models to recreate closed loop simulations while only trained from open loop forcing cases. Direct adaptive feedback control is then applied to the ANN-ARX model. Once satisfying results are seen on the model, the feedback controller is scaled up to a CFD simulation. This control design technique is not limited to laminar two-dimensional flows, but also has capability to model and control more turbulent, non-linear three dimensional flows.

Investigation of Aeroelastic Flow Control of a Fluttering Wing with HPCMP CREATE(trademark)-AV Kestrel

Abstract : The aeroelastic behavior of a finite aspect ratio (AR=6) NACA0018 wing is computationally analyzed. HPCMP CREATE(trademark)-AV Kestrel, a fully coupled computational fluid dynamic (CFD) and computational structural dynamic (CSD) code, is used to compare the effect of blowing on a rigid and an aeroelastically deforming wing. Externally controlled blowing slots distributed along the span of the wing are used to inject mass into the flow field to achieve open-loop flow control. The results indicate that control by blowing has a pronounced effect on the flowfield and therefore on the aerodynamic coefficients. For the rigid wing, the lift is increased, as are the pitching and rolling moments. When aeroelastic deformation is considered, the picture changes significantly. First, the flexible wing showed higher lift and drag compared to the rigid wing due to the increased local angle of attack in the outboard section of the wing. Futhermore, the pitching and rolling moments were significantly reduced.

Closed-Loop Flow Control of a Forebody at a High Incidence Angle

The flowfield around an axisymmetric forebody at a high angle of attack (40<α<60  deg) produces a significant side force. This side force results from an asymmetric pressure distribution around the body due to an asymmetric vortex configuration. Numerical studies of open-loop control using mass blowing slots near the tip of the model have shown a proportional response of the side force over a range of momentum coefficient amplitudes. From the open-loop simulations, a prediction-error minimization method was employed to formulate a linear time-invariant model, which captured the dynamics of the side force response to different mass flow rates applied to either the port or starboard actuator. Based on the linear time-invariant model, a proportional–integral control law was developed for set-point tracking a prescribed side force. The development of the linear time-invariant model, and corresponding linear time-invariant feedback solution are presented to illustrate the model’s capabilities and limitations. ...