David J. Olinger

A low-dimensional model for chaos in open fluid flows

A forced Landau–Stuart equation is studied in order to derive a low‐dimensional model describing the temporal behavior of a paradigm open flow, the two‐dimensional forced cylinder wake. Numerical results from the model exhibit several characteristics of circle maps, and compare qualitatively to previous experimental results for an oscillating cylinder wake. The low‐dimensional model is also shown to reduce to a circle map in the limit of small forcing amplitudes. Observation of circle map dynamics in the forced Landau–Stuart equation strengthens the conjecture that globally unstable fluid flows are amenable to a dynamical systems approach focusing on the study of low‐dimensional iterative maps. The established connection between the Landau–Stuart equation and the circle map unifies certain aspects of spatiotemporal stability and low‐dimensional chaos theory.

A Low-Order Model for Vortex Shedding Patterns Behind Vibrating Flexible Cables

A recent focus in studies of vortex shedding behind circular cylinders has been on the use of low-order dynamical systems such as circle maps to predict wake dynamics. These purely temporal models have been limited by their inability to describe three-dimensional spatial flow variations along the cylinder span, a hallmark of transitional flows such as the cylinder wake. In the present work this limitation is overcome through development of a spatial-temporal map lattice which utilizes a series of coupled circle map oscillators along the cylinder span. This model allows for the study of vortex shedding patterns and wake dynamics behind vibrating flexible cables. Required input for the model includes the forcing frequency, amplitude, mode shape, aspect ratio and wavelength of the cable, Reynolds number, vortex convection velocity, and various phase angles. Model output parameters studied in this work include vortex shedding patterns and wake response frequency. Standing wave mode shapes and traveling waves ...

A Nonlinear Computational Model of Floating Wind Turbines

The dynamic motion of floating wind turbines is studied using numerical simulations. The full three-dimensional Navier–Stokes equations are solved on a regular structured grid using a level set method for the free surface and an immersed boundary method for the turbine platform. The tethers, the tower, the nacelle, and the rotor weight are included using reduced-order dynamic models, resulting in an efficient numerical approach that can handle nearly all the nonlinear hydrodynamic forces on the platform, while imposing no limitation on the platform motion. Wind speed is assumed constant, and rotor gyroscopic effects are accounted for. Other aerodynamic loadings and aeroelastic effects are not considered. Several tests, including comparison with other numerical, experimental, and grid study tests, have been done to validate and verify the numerical approach. The response of a tension leg platform (TLP) to different amplitude waves is examined, and for large waves, a nonlinear trend is seen. The nonlinearity limits the motion and shows that the linear assumption will lead to overprediction of the TLP response. Studying the flow field behind the TLP for moderate amplitude waves shows vortices during the transient response of the platform but not at the steady state, probably due to the small Keulegan–Carpenter number. The effects of changing the platform shape are considered, and finally, the nonlinear response of the platform to a large amplitude wave leading to slacking of the tethers is simulated.

Computational Simulation of the Tethered Undersea Kites for Power Generation

The dynamic motion of tethered undersea kites (TUSK) is studied using numerical simulations. TUSK systems consist of a rigid-winged kite moving in an ocean current. The kite is connected by tethers to a platform on the ocean surface or anchored to the seabed. Hydrodynamic forces generated by the kite are transmitted through the tethers to a generator on the platform to produce electricity. TUSK systems are being considered as an alternative to marine turbines since the kite can move in high speed motions to increase power production compared to conventional marine turbines. The two-dimensional Navier-Stokes equations are solved on a regular structured grid that comprises the ocean current flow, and an immersed boundary method is used for the rigid kite. A two-step projection method along with Open Multi-Processing (OpenMP) is employed to solve the flow equations. The reel-out and reel-in velocities of the two tethers are adjusted to control the kite angle of attack and the resultant hydrodynamic forces. A baseline simulation was studied where a high net power output was achieved during successive kite power and retraction phases. System power output, vorticity flow fields, tether tensions, and hydrodynamic coefficients for the kite are determined. The power output results are in good agreement with established theoretical results for a kite moving in two dimensions.Copyright

Retrospective cost adaptive control for a ground tethered energy system

Ground tethered energy (GTE) systems are a promising technology for addressing the challenge of sustainable electric power production. This paper presents a GTE system that converts wind energy into electric energy by using a kite tethered to a spooling system. More specifically, this system converts the kinetic energy from the kites motion into electric energy. In this paper, we introduce a dynamic model for the ground-tethered kite and present an adaptive controller that is effective for controlling the kites motion. In particular, we present simulation results that demonstrate adaptive command following, where the kite system is able to harvest energy from the wind.

Performance Characteristics of a 1 kW Scale Kite-Powered System

A 1 kW scale kite-powered system that uses kites to convert wind energy into electrical energy has been studied to determine its performance characteristics and establish feasibility of steady-state operation. In this kite-powered system, a kite is connected to a tether that transmits the generated aerodynamic forces on the kite to a power conversion system on the ground. The ground-based power conversion system consists of a rocking arm coupled to a Sprag clutch, flywheel, and electrical generator. Governing equations describing the dynamical motion of the kite, tether, and power conversion mechanism were developed assuming an inflexible, straight-line tether. A steady-state analysis of the kite aerodynamics was incorporated into the dynamical equations of the kite-powered system. The governing equations were solved numerically using a Runge-Kutta scheme to assess how performance parameters of the system such as output power, cycle time, and tether tension varied with wind speed, kite area, and aerodynamic characteristics of the kite. The results showed that a 1 kW scale system is feasible using the proposed design concept with a kite area of 25 m 2 and wind speeds of 6 m/s. Preliminary efforts to build and test a working 1 kW scale kite-powered demonstrator are also reported.

Control of an airborne wind energy system using an aircraft dynamics model

We consider the modeling aspects of an airborne wind energy (AWE) system which consists of a kite (or glider aircraft) with a tether connected between the kite center of mass and a generator (load) on the ground. Kites in AWE systems move in high-speed crosswind motion at several times the wind velocity to efficiently harness wind energy. Central to the controller design for maximum power generation is the accurate modeling of the kite and tether dynamics. In this work we use aircraft dynamics models that incorporate rotational pitch, roll, and yaw dynamics in the equations of motion. Additionally, we assume a variable length, straight-line, inelastic, uniform density tether and model aerodynamic forces on the tether and kite. The resulting dynamical system which includes both translational and rotational motion results in an under-actuated mechanical system for the translational motion. Using Lyapunov-based controller design, the controllers for the translational and rotational motions are designed independently and which take the form of D and PD type controllers. A baseline simulation that achieves successive power-retraction cycles with net power generation is studied.

Control of a tethered undersea kite energy system using a six degree of freedom model

Control aspects of a tethered undersea kite (TUSK) energy system are studied. A TUSK system consists of a rigid undersea wing (or kite) attached by a flexible tether to a support structure on the ocean surface or floor. A turbine is mounted on the undersea kite to harness hydrokinetic energy from an ocean current when the kite moves in high-speed, cross-current motions. In this paper, we adopt a six degree of freedom aircraft model that incorporate the translational motion of the kite center of gravity and rotational dynamics of the Euler angles. To simplify the analysis, we assume a fixed support structure, uniform current conditions and a straight-line, inelastic tether. This results in an under-actuated system whose boundedness is addressed with the Lyapunov method and comparison principle. A passivity based PD controller is proposed to control the kite trajectory and orientation. A baseline simulation for typical design parameter values in a TUSK system is studied.

Nonlinear simulation of a spar buoy floating wind turbine under extreme ocean conditions

A nonlinear computational model, based on solving the Navier-Stokes equation, is used to study the motion of a 5 MW spar buoy floating wind turbine in moderate and extreme sea states with irregular waves. The main advantages of using the current model are that there is no limitation on the platform motion, the hydrodynamic loads do not rely on experimental data, and nonlinear hydrodynamic loads can be predicted. The current work extends a previously developed Navier-Stokes model for regular periodic waves on a tension leg platform floating wind turbine. Free decay tests are performed, and pitch, heave, and surge natural frequencies are determined. The responses of the spar buoy to operating conditions with significant wave height of 8 m and mean period of 10 s, and an extreme sea states including waves over 17 m height are studied. For the extreme sea state, a nonlinear model is required, since the platform response amplitudes are not small with respect to the spar buoy diameter. Effects not included in l...

Stability and Control of Ground Tethered Energy Systems

The combustion of fossil fuels is currently used to meet the majority of global energy needs. Given the anticipated future shortages of fossil fuels, and their contribution to greenhouse gas production and global warming, sustainable methods for energy production