The presence of roughness on a surface subject to high Reynolds number flows promotes the formation of a turbulent boundary layer and the generation of a fluctuating pressure field imposed on the surface. While numerous studies have investigated the wall pressure fluctuations over zero-pressure gradient smooth walls, few studies have examined the effects of surface roughness on the wall pressure field. Additionally, due to the difficulties in obtaining high Reynolds number flows over fully rough surfaces in laboratory settings, an even fewer number of studies have investigated this phenomenon under flow conditions predicted to be fully free of transitional effects that would ensure similarity laws could be observed. This study presents the efforts to scale and describe the wall pressure spectrum of a rough wall, high Reynolds number turbulent boundary layer free of transitional effects. Measurements were taken in the Virginia Tech Stability Wind Tunnel for both smooth and rough walls. A deterministic roughness fetch composed of 3-mm hemispheres arranged in a 16.5-mm square array was used for the rough surface. Smooth and rough wall flows were examined achieving Reynolds numbers up to Re_θ = 68700 and Re_θ = 80200 respectively, with the rough wall flows reaching roughness based Reynolds numbers up to k_g⁺ = 507 with a simultaneous blockage ratio of δ/k_g = 76. A new roughness based inner variable scaling is proposed that provides a much more complete collapse of the rough wall pressure spectra than previous scales had provided over a large range of Reynolds numbers and roughness configurations. This scaling implies the presence of two separate time scales associated with the near wall turbulence structure generation. A clearly defined overlap region was observed for the rough wall surface pressure spectra displaying a frequency dependence of Ï ^-1.33, believed to be a function of the surface roughness configuration and its associated transport of turbulent energy. The rough wall pressure spectra were shown to decay more rapidly, but based on the same function as what defined the smooth wall decay. / Master of Science

An oscillating-hot-wire system is developed to allow mean-flow velocity measurements in separated flows. Disturbance velocities can also be measured in regions of interest. An oscillating-arm assembly provides a directional bias to the hot-wire probe, and a linear-step assembly steps the probe through the boundary layer. These assemblies are mounted to a positioning plate which allows profiles to be taken at a discrete number of chord locations. Data sampling is computer regulated using a trigger pulse from an exterior source. A distance proximity probe gives the distance of the hot-wire probe from the model. Series of mean-velocity profiles over an airfoil are measured for R_C 150,000, 200,000, 250,000, and 300,000 with a= 14° and for R_C = 200,000 and 250,000 with α= 12°. / M.S.

This thesis presents measurements of the three-dimensional flow due to the horseshoe vortex formed at the junction of a flat wall and the leading edge of a Rankine half body. The half body is located between the parallel end walls of a duct to model the situation in turbomachinery where struts and vanes, which generate performance losses due to horseshoe vortices and other secondary flow mechanisms, extend over the total flow passage height. The boundary layer on the duct end wall is artificially thickened to produce a large horseshoe vortex. Flow measurements are presented showing the inlet flow and the three-dimensional flow just downstream of the leading edge of the body. Sufficient data is presented to provide a means for testing the validity of three-dimensional viscous flow calculations. A three-dimensional flow measurement technique using a single slanted hotwire anemometer is evaluated. The hotwire anemometer measurements are compared with measurements of the same flow made with a five-hole pressure probe. A two-dimensional laminar and turbulent boundary layer analysis is performed at mid-height on the body. / M.S.

Wind energy industry thrived in the last three decades, environmental concerns and government regulations stimulate studies on wind farm location selection and wind turbine design. Full-scale experiments and high-fidelity simulations are restrictive due to the prohibitively high cost, while the model-scale experiments and low-fidelity calculations miss key flow physics of unsteady high Reynolds number flows. A hybrid RANS/LES turbulence model integrated with transition formulation is developed and tested by a surrogate model problem through joint experimental and computational fluid dynamics approaches. The model problem consists of a circular cylinder for generating coherent unsteadiness and a downstream airfoil in the cylinder wake. The cylinder flow is subcritical, with a Reynolds number of 64,000 based upon the cylinder diameter. The quantitative dynamics of vortex shedding and Reynolds stresses in the cylinder near wake were well captured, owing to the turbulence-resolving large eddy simulation method that was invoked in the wake. The power spectrum density of velocity components showed that the flow fluctuations were well-maintained in cylinder wake towards airfoil and the hybrid model switched between RANS/LES mode outside boundary layer as expected. According to the experimental and simulation results, the airfoil encountered local flow angle variations up to ±50 degrees, and the turbulent airfoil boundary layer remained attached. Inspecting the boundary layer profiles over one shedding cycle, the oscillation about mean profile resembled the Stokes layer with zero mean. Further processing the data through phase-averaging technique found phase lags along the chordwise locations and both the phase-averaged and mean profiles collapsed into the Law of Wall in the range of 0 < y+ < 50. The features of high blade loading fluctuations due to unsteadiness and transitional boundary layers are of interest in the aerodynamic studies of full-scale wind turbine blades, making the model problem a comprehensive benchmark case for future model development and validation. / Ph. D. / Wind energy industry thrived in the last three decades, environmental concerns and government regulations stimulate studies on wind farm location selection and wind turbine design. Full-scale experiments and high-fidelity simulations are restrictive due to the prohibitively high cost, while the model-scale experiments and low-fidelity calculations miss key flow physics of of the full-scale models. The current study adopted a joint experimental and computational fluid dynamic approach to design a surrogate problem that features the unsteady flow physics presented in the full-scale wind turbine blades. A new hybrid turbulence model was implemented and validated against the complementary experimental results. The new model improves the accuracy of the current industry-standard turbulence models without excessive computational cost, making it a viable solution to the high-fidelity full-scale simulations in the future.

The subject of this dissertation is the analysis and solution of the equations describing the laminar boundary layer on axisymmetric bodies immersed in an oncoming stream and spinning at a constant rate about their axis of revolution. The flow is allowed to be compressible or incompressible and the geometries for which solutions are obtained include the sphere, cone, paraboloid, hyperboloid and tangent ogive. The only limitation on spin rate involves the assumption that the pressure across the boundary layer remain essentially constant. The method of solution for the set of parabolic nonlinear partial differential equations which describe the boundary layer is an implicit finite difference technique. A study of step size and convergence criteria is included to determine the accuracy of the numerical method. Comparisons with previous approximate methods are also presented in an effort to establish confidence in these results. Boundary layer characteristics in the form of shear stress, heat transfer, velocity and temperature profiles, displacement thickness and frictional drag and moment coefficients are presented for each geometry over a wide range of spin rates. / Ph. D.

Significant differences involving near-wall velocity profiles in two-dimensional turbulent boundary layers when such data was plotted on law of the wall coordinates were reported by D. Coles in the Stanford Conference. These discrepancies can be especially important when near-wall velocity data is used to infer the local wall shear stress from law of the wall similarity laws. With emphasis on the near-wall measurements, this study systematically investigated the effects of the following parameters on the velocity profile: probe type (straight-stem claw probe, gooseneck probe, and hot-wire probe), probe tip diameter, streamwise pressure gradient, and boundary layer tripping. In addition, the local wall shear stress was inferred from the near-wall data, and the effects from the previously mentioned parameters and the choice of both the law of the wall constants and formulas on the inferred wall shear stress were examined. / M. S.

The transition from laminar to turbulent flow in boundary-layers occurs in three stages: onset of two-dimensional TS waves, onset of three-dimensional secondary disturbances of fundamental or subharmonic type, and onset of the turbulent regime. In free flight conditions, subharmonic disturbances are the most amplified. Recent modeling of the subharmonic disturbance as a parametric instability arising from the presence of a finite amplitude TS wave has given results in quantitative agreement with experiments conducted in a Blasius boundary-layer. The present work extends the analysis to the Falkner-Skan family of profiles, and develops a formulation for spatially growing disturbances to exactly match the experimental observations. Results show that subharmonic disturbances in Falkner-Skan flows behave similarly to those in a Blasius flow. The most noticeable effect of the pressure gradient is a decrease (favorable) or an increase (adverse) of the disturbance's growth rate. Due to the lack of experimental data, a comparison of subharmonic growth rates from theory and experiment is limited to the Blasius boundary-layer. A comparison of results from the spatial formulation with those previously obtained from a temporal formulation shows the difference to be small. A connection between disturbance growth in a separating boundary-layer profile and a free shear layer is presented. A modification of Caster's transformation from temporal to spatial growth rates for secondary disturbances is given. / M.S.

It was found in this investigation that the testing of supersonic airfoils at subsonic speeds to obtain pressure distributions will result in considerable error if the models are tested at very low Reynolds Numbers. The thickness of the boundary layer is critical at low Reynolds Numbers and causes a decrease in the overpressure region. This, coupled with the fact that the overpressure region increases more with Mach Number than predicted by the theory, could lead to erroneous calculations of the drag. / Master of Science

The accuracy of the compressible interacting boundary-layer computations is investigated and their limitations are established by comparison with solutions to the Navier-Stokes equations both for the mean flow profiles and for the stability characteristics. The instabilities of flows around smooth forward and backward facing steps are investigated. Results presented include the effect of computational grid refinement, geometrical parametres such as heights and slopes of steps, Mach number and Reynolds number on the mean flow as well as the stability characteristics. A proper grid should be chosen to predict accurately the mean flow profiles, including their first and second derivatives. The study has shown that the heights of the steps are more influential in triggering transition than their slopes. Increasing the Mach number reduces the growth rates and amplification factors but the presence of small separation bubbles, which increase in size with increasing Mach number, partially offset this benefit. / M.S.

The laminar boundary layer over a semi-infinite flat plate which is impulsively set in motion in an incompressible fluid and which has a simultaneous step change in surface temperature was studied. An approximate method was derived which can be used to determine the thermal boundary layer thickness as a function of the distance from the leading edge and of time. From the thermal boundary layer thickness the temperature of the fluid can be determined at any position in the boundary layer and at any time. The local Nusselt number can also be determined from the thermal boundary layer thickness. The approximate solution was compared with exact steady-state and infinite-plate solutions of the energy equation and with a finite-difference solution of the unsteady continuity, momentum and energy equations. Agreement between the solutions was close enough to indicate that the approximate solutions for the temperature in the boundary layer and for the Nusselt number approximate the actual situation with reasonable accuracy. / Master of Science