Tilting the nacelle of a wind turbine modifies entrainment into the wind plant and impacts total efficiency. Extreme angles can produce flying and crashing wakes where the wake either disrupts entertainment from the undisturbed flow above or is decimated on the ground. The effect of tilt angle on downstream wake behavior was investigated in a series of wind tunnel experiments. Scale model turbines with a hub height and diameter of 12 cm were arranged in a Cartesian array comprised of four rows of three turbines each. Nacelle tilt was varied in the third row from -15° to 15° in chosen 5° increments. Stereo PIV measurements of the instantaneous velocity field were recorded at four locations for each angle. Tilted wakes are described in terms of the average streamwise velocity field, wall-normal velocity field, Reynolds stresses, and mean vertical transport of kinetic energy. Conditional sampling is used to quantify the importance of sweep vs. ejection events and thus downwards vs. upwards momentum transfer. Additionally, wake center displacement and changes in net power are presented and compared to existing models. The results demonstrate large variations in wake velocity and vertical displacement with enhanced vertical energy and momentum transfer for negative tilt angles. Simulation models accurately predict wake deflection while analytic models deviate considerably highlighting the difficulties in describing tilt phenomena. Negative angles successfully produce crashing wakes and improve the availability of kinetic energy thereby improving the power output of the wind plant.

To maximize the effectiveness of the rapidly increasing capacity of installed wind energy resources, new models must be developed that are capable of more nuanced control of each wind turbine so that each device is more responsive to inflow events. Models used to plan wind turbine arrays and control behavior of devices within the farm currently make questionable estimates of the incoming atmospheric flow and update turbine configurations infrequently. As a result, wind turbines often operate at diminished capacities, especially in arrays where wind turbine wakes interact and inflow conditions are far from ideal. New turbine control and wake prediction models must be developed to tune individual devices and make accurate power predictions. To that end, wind tunnel experiments are conducted detailing the turbulent flow in the wake of a wind turbine in a model-scale array. The proper orthogonal decomposition (POD) is applied to characterize the spatial evolution of structures in the wake. Mode bases from distinct downstream locations are reconciled through a secondary decomposition, called double proper orthogonal decomposition (DPOD), indicating that modes of common rank in the wake share an ordered set of sub-modal projections whose organization delineates underlying wake structures and spatial evolution. The doubly truncated basis of sub-modal structures represents a reduction to 0.015% of the total degrees of freedom of the wind turbine wake. Low-order representations of the Reynolds stress tensor are made using only the most dominant DPOD modes, corrected to account for energy excluded from the truncated basis with a tensor of constant coefficients defined to rescale the low-order representation of the stresses to match the original statistics. Data from the wind turbine wake are contrasted against simulation data from a fully-developed channel flow, illuminating a range of anisotropic states of turbulence. Complexity of flow descriptions resulting from truncated POD bases is suppressed in severe basis truncations, exaggerating anisotropy of the modeled flow and, in extreme cases, can lead to the loss of three dimensionality. Constant corrections to the low-order descriptions of the Reynolds stress tensor reduce the root-mean-square error between low-order descriptions of the flow and the full statistics as much as 40% and, in some cases, reintroduce three-dimensionality to severe truncations of POD bases. Low-dimensional models are constructed by coupling the evolution of the dynamic mode coefficients through their respective time derivatives and successfully account for non-linear mode interaction. Deviation between time derivatives of mode coefficients and their least-squares fit is amplified in numerical integration of the system, leading to unstable long-time solutions. Periodic recalibration of the dynamical system is undertaken by limiting the integration time and using a virtual sensor upstream of the wind turbine actuator disk in to read the effective inflow velocity. A series of open-loop transfer functions are designed to inform the low-order dynamical system of the flow incident to the wind turbine rotor. Validation data shows that the model tuned to the inflow reproduces dynamic mode coefficients with little to no error given a sufficiently small interval between instances of recalibration. The reduced-order model makes accurate predictions of the wake when informed of turbulent inflow events. The modeling scheme represents a viable path for continuous time feedback and control that may be used to selectively tune a wind turbine in the effort to maximize power output of large wind farms.

A new rotor dynamic wake distortion model, which can be used to account for the rotor transient wake distortion effect on inflow across the rotor disk during helicopter maneuvering and transitional flight in both hover and forward flight conditions, is developed. The dynamic growths of the induced inflow perturbation across the rotor disk during different transient maneuvers, such as a step pitch or roll rate, a step climb rate and a step change of advance ratio are investigated by using a dynamic vortex tube analysis. Based on the vortex tube results, a rotor dynamic wake distortion model, which is expressed in terms of a set of ordinary differential equations, with rotor longitudinal and lateral wake curvatures, wake skew and wake spacing as states, is developed. Also, both the Pitt-Peters dynamic inflow model and the Peters-He finite state inflow model for axial or forward flight are augmented to account for rotor dynamic wake distortion effect during helicopter maneuvering flight. To model the aerodynamic interaction among main rotor, tail rotor and empennage caused by rotor wake curvature effect during helicopter maneuvering flight, a reduced order model based on a vortex tube analysis is developed. Both the augmented Pitt-Peters dynamic inflow model and the augmented Peters-He finite state inflow model, combined with the developed dynamic wake distortion model, together with the interaction model are implemented in a generic helicopter simulation program of UH-60 Black Hawk helicopter and the simulated vehicle control responses in both time domain and frequency domain are compared with flight test data of a UH-60 Black Hawk helicopter in both hover and low speed forward flight conditions.