Aerodynamics of vertical-axis wind turbines in full-scale and laboratory-scale experiments

Within a wind farm, multiple turbine wakes can interact and have a substantial effect on the overall power production. This makes an understanding of the wake recovery process critically important to optimizing wind farm efficiency. Vertical-axis wind turbines (VAWTs) exhibit features that are amenable to dramatically improving this efficiency. However, the physics of the flow around VAWTs is not well understood, especially as it pertains to wake interactions, and it is the goal of this thesis to partially fill this void. This objective is approached from two broadly different perspectives: a low-order view of wind farm aerodynamics, and a detailed experimental analysis of the VAWT wake.

One of the contributions of this thesis is the development of a semi-empirical model of wind farm aerodynamics, known as the LRB model, that is able to predict turbine array configurations to leading order accuracy. Another contribution is the characterization of the VAWT wake as a function of turbine solidity. It was found that three distinct regions of flow exist in the VAWT wake: (1) the near wake, where periodic blade shedding of vorticity dominates; (2) a transition region, where growth of a shear-layer instability occurs; (3) the far wake, where bluff-body oscillations dominate. The wake transition can be predicted using a new parameter, the dynamic solidity, which establishes a quantitative connection between the wake of a VAWT and that of a circular cylinder. The results provide insight into the mechanism of the VAWT wake recovery and the potential means to control it.

Advancements in jet turbulence and noise modeling: accurate one-way solutions and empirical evaluation of the nonlinear forcing of wavepackets

Jet noise reduction is an important goal within both commercial and military aviation. Although large-scale numerical simulations are now able to simultaneously compute turbulent jets and their radiated sound, lost-cost, physically-motivated models are needed to guide noise-reduction efforts. A particularly promising modeling approach centers around certain large-scale coherent structures, called wavepackets, that are observed in jets and their radiated sound. The typical approach to modeling wavepackets is to approximate them as linear modal solutions of the Euler or Navier-Stokes equations linearized about the long-time mean of the turbulent flow field. The near-field wavepackets obtained from these models show compelling agreement with those educed from experimental and simulation data for both subsonic and supersonic jets, but the acoustic radiation is severely under-predicted in the subsonic case. This thesis contributes to two aspects of these models. First, two new solution methods are developed that can be used to efficiently compute wavepackets and their acoustic radiation, reducing the computational cost of the model by more than an order of magnitude. The new techniques are spatial integration methods and constitute a well-posed, convergent alternative to the frequently used parabolized stability equations. Using concepts related to well-posed boundary conditions, the methods are formulated for general hyperbolic equations and thus have potential applications in many fields of physics and engineering. Second, the nonlinear and stochastic forcing of wavepackets is investigated with the goal of identifying and characterizing the missing dynamics responsible for the under-prediction of acoustic radiation by linear wavepacket models for subsonic jets. Specifically, we use ensembles of large-eddy-simulation flow and force data along with two data decomposition techniques to educe the actual nonlinear forcing experienced by wavepackets in a Mach 0.9 turbulent jet. Modes with high energy are extracted using proper orthogonal decomposition, while high gain modes are identified using a novel technique called empirical resolvent-mode decomposition. In contrast to the flow and acoustic fields, the forcing field is characterized by a lack of energetic coherent structures. Furthermore, the structures that do exist are largely uncorrelated with the acoustic field. Instead, the forces that most efficiently excite an acoustic response appear to take the form of random turbulent fluctuations, implying that direct feedback from nonlinear interactions amongst wavepackets is not an essential noise source mechanism. This suggests that the essential ingredients of sound generation in high Reynolds number jets are contained within the linearized Navier-Stokes operator rather than in the nonlinear forcing terms, a conclusion that has important implications for jet noise modeling.

Kinematics and Local Motion Planning for Quasi-static Whole-body Mobile Manipulation

This thesis studies mobile robotic manipulators, where one or more robot manipulator arms are integrated with a mobile robotic base. The base could be a wheeled or tracked vehicle, or it might be a multi-limbed locomotor. As robots are increasingly deployed in complex and unstructured environments, the need for mobile manipulation increases. Mobile robotic assistants have the potential to revolutionize human lives in a large variety of settings including home, industrial and outdoor environments.

Mobile Manipulation is the use or study of such mobile robots as they interact with physical objects in their environment. As compared to fixed base manipulators, mobile manipulators can take advantage of the base mechanism’s added degrees of freedom in the task planning and execution process. But their use also poses new problems in the analysis and control of base system stability, and the planning of coordinated base and arm motions. For mobile manipulators to be successfully and efficiently used, a thorough understanding of their kinematics, stability, and capabilities is required. Moreover, because mobile manipulators typically possess a large number of actuators, new and efficient methods to coordinate their large numbers of degrees of freedom are needed to make them practically deployable. This thesis develops new kinematic and stability analyses of mobile manipulation, and new algorithms to efficiently plan their motions.

I first develop detailed and novel descriptions of the kinematics governing the operation of multi- limbed legged robots working in the presence of gravity, and whose limbs may also be simultaneously used for manipulation. The fundamental stance constraint that arises from simple assumptions about friction and the ground contact and feasible motions is derived. Thereafter, a local relationship between joint motions and motions of the robot abdomen and reaching limbs is developed. Baseeon these relationships, one can define and analyze local kinematic qualities including limberness, wrench resistance and local dexterity. While previous researchers have noted the similarity between multi- fingered grasping and quasi-static manipulation, this thesis makes explicit connections between these two problems.

The kinematic expressions form the basis for a local motion planning problem that that determines the joint motions to achieve several simultaneous objectives while maintaining stance stability in the presence of gravity. This problem is translated into a convex quadratic program entitled the balanced priority solution, whose existence and uniqueness properties are developed. This problem is related in spirit to the classical redundancy resoxlution and task-priority approaches. With some simple modifications, this local planning and optimization problem can be extended to handle a large variety of goals and constraints that arise in mobile-manipulation. This local planning problem applies readily to other mobile bases including wheeled and articulated bases. This thesis describes the use of the local planning techniques to generate global plans, as well as for use within a feedback loop. The work in this thesis is motivated in part by many practical tasks involving the Surrogate and RoboSimian robots at NASA/JPL, and a large number of examples involving the two robots, both real and simulated, are provided.

Finally, this thesis provides an analysis of simultaneous force and motion control for multi- limbed legged robots. Starting with a classical linear stiffness relationship, an analysis of this problem for multiple point contacts is described. The local velocity planning problem is extended to include generation of forces, as well as to maintain stability using force-feedback. This thesis also provides a concise, novel definition of static stability, and proves some conditions under which it is satisfied.