The transition to turbulence of plane wakes is characterized by the development of the velocity-fluctuation field from a spectrum of weak random background noise in the initial laminar wake to a nearly featureless broad spectrum of intense fluctuations within the turbulent wake. This transition has also been described as a sequence of instabilities and wave-wave interactions. In the initial small-amplitude stage,. a narrow, but continuous, band of dominant instability modes centered near the most unstable mode, known also as the fundamental mode, grow exponentially at rates that can be calculated from the linearized Navier-Stokes equations. As these modes grow, the nonlinear terms become more important and cannot be neglected anymore. The effect of these terms is to introduce wave-wave interactions that lead to quadratic energy transfer between the different spectral components of the velocity-fluctuation field. While the consequences of these interactions, such as broadening of the power spectra, have been observed in many experiments, the characteristics of these interactions have only been examined in limited cases. Previous measurements of the auto-bispectrum showed that three-wave interaction processes are important in the transitioning wake. However, quantification of these processes can only be obtained from measurement of the nonlinear energy transfer rates resulting from the nonlinear wave-wave interactions. Such quantification is very important for understanding the effects of the different mechanisms involved in the transition and final breakdown to turbulence. An understanding of these mechanisms and their effects can then be used to control the transition by enhancing certain mechanisms and reducing the role of others through external excitation. In this work, quantitative estimates of the auto-bispectrum, linear and quadratic coupling coefficients and the resulting energy transfer rates between the interacting waves at different locations are presented in controlled and natural transitions of the plane wake. The results show that, in both natural and controlled transitions, the underlying nonlinear dynamics are similar. Basically, nonlinear interactions between the instability modes result in energy transfer to harmonic bands as well as low-frequency difference components. These components play an important role in the transfer of energy to the sidebands and the valleys between the peaks. The results also show that, while energy-transfer rates in natural transition are lower than in controlled transition, the random nature of wave excitation in natural transition causes energy transfer to a band of low-frequency components which leads to energy transfer to many sidebands and results in a spectrum that differs dramatically from the one obtained in the controlled case where two instabilities are excited. / Master of Science

A critical evaluation of the Baldwin-lomax (Bl) turbulence model for shock/shear layer interactions, reversed flow, and curved, asymmetric wakes is made. No general definition for reference line is available for wakes, and difficulties exist for length scale prediction in complex flows. An entropy envelope for shear layers, and the locus of maximum entropy to define the wake centerline is proposed. The range of the Bl model is limited to the entropy envelope. This provides all relevant modeling data, and allows general application of existing reversed flow corrections. The total enhancements are flow adaptive and form the Dynamic Bl model. This robust model is more accurate in complex boundary layers and wakes. The Dynamic Bl model is applied to a supersonic fan cascade at the design incidence. Sharp differences in turbulent viscosities were seen between the the original, Baseline Bl, and Dynamic Bl models. Only slight differences exist in the overall cascade solutions. This includes loss factors which were produced by different mechanisms. The Baseline BL model predicted separation on the SS surface and larger standing vorticies off the TE. The Dynamic Bl model predicted attached boundary layers, smaller standing vorticies off the TE, but uniformly higher skin friction. The shock structure in the cascade may reduce the flow field dependence on specific viscosity profile characteristics, so these may be less important than overall turbulence levels. / Master of Science

"This thesis documents the experimental proof of concept study for an ultrasonic method of wake vortex detection. A new acoustic technique is utilized to measure the circulation produced in the wake of lift-generating aircraft. Ultrasonic signals are transmitted in a path around the wake vortex, and are used to determine the average in-line velocity component along the acoustic path. It is shown herein that this velocity component is directly proportional to the net circulation value within the acoustic path. This is the first study to take this methodology and implement it in a realistic airport setting. This project included constructing a prototype and conducting field tests to prove the validity of this technology in a realistic environment setting. During field tests an acoustic path enclosed the vorticity shed behind one wing of a Piper PA-28 aircraft. Fourteen initial test flights were conducted in calm atmospheric conditions, and results show circulation values measured are comparable in magnitude and direction to expected circulations generated by the Piper PA-28 aircraft. Additional testing in various atmospheric conditions revealed the scope of practice for such a measurement technology. This study demonstrates the validity of the acoustic method in detecting aircraft wake vortices. Future investigations and applications utilizing this technique are discussed within."

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.

Thesis(M.S.)--Auburn University, 2007. / Abstract. Vita. Includes bibliographic references.

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.

Vortex identification techniques are used to analyze the flow structure in a 4 x 3 array of scale model wind turbines. Q-criterion, Δ-criterion, and λ2-criterion are applied to Particle Image Velocimetry data gathered fore and aft of the last row centerline turbine. Q-criterion and λ2-criterion provide a clear indication of regions where vortical activity exists while the Δ-criterion does not. Galilean decomposition, Reynolds decomposition, vorticity, and swirling strength are used to further understand the location and behavior of the vortices. The techniques identify and display the high magnitude vortices in high shear zones resulting from the blade tips. Using Galilean and Reynolds decomposition, swirling motions are shown enveloping vortex regions in agreement with the identification criteria. The Galilean decompositions are 20% and 50% of a convective velocity of 7 m/s. As the vortices convect downstream, these vortices weaken in magnitude to approximately 25% of those present in the near wake. A high level of vortex activity is visualized as a result of the top tip of the wind turbine blade; the location where the highest vertical entrainment commences.

Unsteady flow fields over a NACA 0012 at an angle of attack are investigated. The first is the classical pitching motion about the airfoil's quarter chord. The second is the flow over a fixed airfoil immersed in the wake of the pitching airfoil. Large reduced frequencies are considered. Measurements were obtained in a water tunnel by Laser-Doppler velocimetry. Ensemble-averaged velocity measurements were obtained in the vicinity of the trailing edges of both the pitching and the fixed airfoils. The flowfields in the wake and at the trailing edges of both airfoils were studied visually. The validity of the quasi-steady and an extension to an unsteady Kutta condition are examined. A new dynamic similarity parameter is proposed. An analytical method based on the dynamics of discrete vortices is employed. Numerical calculations of the flow over the fixed airfoil are compared with experimental results. / Ph. D.

A Numerical Solution is presented for the problem of flow past a highly swept, slender wing with sharp leading edges. The lifting surface is modelled as a bound vortex sheet, while the wake is modelled as a force-free vortex sheet. The solution is obtained by the use of a unsteady Vortex-Lattice Method which includes the effect of leading edge separation. Numerical predictions for the aerodynamic loads and pressure distributions are compared with experimental data. A 75° Delta wing and a 60° Delta wing with Leading Edge Vortex flaps in uniform, symmetric and steady flow are studied. Uniform and cosine distributions are used to determine the effect of lattice shape on the solution. The results show that good aerodynamic load predictions are obtained by this Vortex-lattice method. The results also indicated that fewer cosine distribution control points predict pressures as well as the use of a larger number of uniform distribution control points. The numerical results for wings with LEVFs show good agreement with experimental data away from the trailing edge. This may be due to the viscous effects in the experiment not modelled in this method. It is also apparent that the size of the wake, trailing and leading edge wakes, is the important factor effecting computation times. / M.S.

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.