On the behavior of pliable plate dynamics in wind : application to vertical axis wind turbines

Numerous studies have shown that flexible materials improve resilience and durability of a structure. Several studies have investigated the behavior of elastic plates under the influence of a free stream, such as studies of the fluttering flag and others of shape reconfiguration, due to a free stream.

The principle engineering contribution of this thesis is the design and development of a vertical axis wind turbine that features pliable blades which undergo various modes of behavior, ultimately leading to rotational propulsion of the turbine. The wind turbine design was tested in a wind tunnel and at the Caltech Laboratory for Optimized Wind Energy. Ultimately, the flexible blade vertical axis wind turbine proved to be an effective way of harnessing the power of the wind.

In addition, this body of work builds on the current knowledge of elastic cantilever plates in a free stream flow by investigating the inverted flag. While previous studies have focused on the fluid structure interaction of a free stream on elastic cantilever plates, none had studied the plate configuration where the trailing edge was clamped, leaving the leading edge free to move. Furthermore, the studies presented in this thesis establish the geometric boundaries of where the large-amplitude flapping occurs.

Dynamic Stall on Vertical Axis Wind Turbines

In this study the dynamics of flow over the blades of vertical axis wind turbines was investigated using a simplified periodic motion to uncover the fundamental flow physics and provide insight into the design of more efficient turbines. Time-resolved, two-dimensional velocity measurements were made with particle image velocimetry on a wing undergoing pitching and surging motion to mimic the flow on a turbine blade in a non-rotating frame. Dynamic stall prior to maximum angle of attack and a leading edge vortex development were identified in the phase-averaged flow field and captured by a simple model with five modes, including the first two harmonics of the pitch/surge frequency identified using the dynamic mode decomposition. Analysis of these modes identified vortical structures corresponding to both frequencies that led the separation and reattachment processes, while their phase relationship determined the evolution of the flow.

Detailed analysis of the leading edge vortex found multiple regimes of vortex development coupled to the time-varying flow field on the airfoil. The vortex was shown to grow on the airfoil for four convection times, before shedding and causing dynamic stall in agreement with 'optimal' vortex formation theory. Vortex shedding from the trailing edge was identified from instantaneous velocity fields prior to separation. This shedding was found to be in agreement with classical Strouhal frequency scaling and was removed by phase averaging, which indicates that it is not exactly coupled to the phase of the airfoil motion.

The flow field over an airfoil undergoing solely pitch motion was shown to develop similarly to the pitch/surge motion; however, flow separation took place earlier, corresponding to the earlier formation of the leading edge vortex. A similar reduced-order model to the pitch/surge case was developed, with similar vortical structures leading separation and reattachment; however, the relative phase lead of the separation mode, corresponding to earlier separation, necessitated that a third frequency to be incorporated into the reattachment mode to provide a relative lag in reattachment.

Finally, the results are returned to the rotating frame and the effects of each flow phenomena on the turbine are estimated, suggesting kinematic criteria for the design of improved turbines.

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.

Transonic wind tunnel for investigation of turbomachinery blades

The design of a two-stream wind tunnel was undertaken to allow the simulation and study of certain features of the flow field around the blades of high-speed axial-flow turbomachineries. The mixing of the two parallel streams with designed Mach numbers respectively equal to 1.4 and 0.7 will simulate the transonic Mach number distribution generally obtained along the tips of the first stage blades in large bypass-fan engines.

The GALCIT hypersonic compressor plant will be used as an air supply for the wind tunnel, and consequently the calculations contained in the first chapter are derived from the characteristics and the performance of this plant.

The transonic part of the nozzle is computed by using a method developed by K. O. Friedrichs. This method consists essentially of expanding the coordinates and the characteristics of the flow in power series. The development begins with prescribing, more or less arbitrarily, a Mach number distribution along the centerline of the nozzle. This method has been programmed for an IBM 360 computer to define the wall contour of the nozzle.

A further computation is carried out to correct the contour for boundary layer buildup. This boundary layer analysis included geometry, pressure gradient, and Mach number effects. The subsonic nozzle is calculated {including boundary layer buildup) by using the same computer programs. Finally, the mixing zone downstream of the splitter plate was investigated to prescribe the wall contour correction necessary to ensure a constant-pressure test section.