The extension of the theory for two dimensional turbulent boundary layers into three dimensional flows has met with limited success. The failure of the extended models is attributed to the anisotropy of the turbulence. This is seen by the turbulent shear stress angle lagging the flow gradient angle and by the behavior of the Reynolds shear stresses lagging that of the mean flow. Transport equations for the turbulent shear stresses were proposed to be included in a modeling effort capable of accounting for the lags seen in the flow. This study is aimed at developing algebraic relationships between the various Reynolds-averaged terms in these modeling equations. Particular emphasis was placed on the triple products that appear in the transport equations. Eleven existing experimental data sets were acquired from the original authors and re-examined with respect to developed and existing parameters. A variety of flow geometries were collected for comparison. Emphasis was placed on experiments that included all six components of the Reynolds stress tensor and triple products. Parameters involving the triple products are presented that appear to maintain a relatively constant value across regions of the boundary layer. The variation of these parameters from station to station and from flow to flow is discussed. Part of this study was dedicated to parameters that were previously introduced, but never examined with respect to the data that was collected. Results of these parameters are presented and discussed with respect to agreement or disagreement with the previous results. The parameters presented will aid in the modeling of three dimensional turbulent boundary layers especially with models that employ the transport equations for the Reynolds stresses. / Master of Science

This report documents the measurements of turbulence quantities resulting from vortices embedded in a zero pressure gradient turbulent boundary layer. Turbulent boundary layers are found in most flow regimes over large scale vehicles and have been studied for many years. Various systems to control separation of boundary layers have been proposed, but vortex generators have proven to be an economical choice as they are often used to fix deficiencies in a flow field after large scale production of a vehicle has commenced. In order to better understand the interaction between vortex generators and the boundary layer in which they are embedded, an experiment has been performed using through non-invasive Comprehensive Laser Doppler Velocimeter. The results show that normalization on edge velocity is appropriate for comparison with previous work. The 1/S parameter and vq^2 parameter were found to be most appropriate to correlate the Reynolds stresses and triple products, respectively. The higher inflow edge velocity and greater momentum thickness, creating a lower vortex generator to boundary layer height ratio, result in a more diffuse vortex as compared to previous work conducted in the same wind tunnel, with the same geometry, but with different inflow conditions. / Master of Science

No description available.

The development of aerodynamic boundary layers on wind turbine blades is an important consideration in their performance. It can be quite challenging to replicate full scale conditions in laboratory experiments, and advanced diagnostics become valuable in providing data not available from traditional means. A new variant of Doppler global velocimetry (DGV) known as cross-correlation DGV is developed to measure boundary layer profiles on a wind turbine blade airfoil in the large scale Virginia Tech Stability Wind Tunnel. The instrument provides mean velocity vectors with reduced sensitivity to external conditions, a velocity measurement range from 0ms^-1 to over 3000ms^-1, and an absolute uncertainty. Monte Carlo simulations with synthetic signals reveal that the processing routine approaches the Cramér-Rao lower bound in optimized conditions. A custom probe-beam technique is implanted to eliminate laser flare for measuring boundary layer profiles on a DU96-W-180 wind turbine airfoil model. Agreement is seen with laser Doppler velocimetry data within the uncertainty estimated for the DGV profile. Lessons learned from the near-wall flow diagnostics development were applied to a novel benchmark model problem incorporating the relevant physical mechanisms of the high amplitude periodic turbulent flow experienced by turbine blades in the field. The model problem is developed for experimentally motivated computational model development. A circular cylinder generates a periodic turbulent wake, in which a NACA 63215b airfoil with a chord Reynolds number Re_c = 170, 000 is embedded for a reduced frequency k = (pi)fc/V = 1.53. Measurements are performed with particle image velocimetry on the airfoil suction side and in highly magnified planes within the boundary layer. Outside of the viscous region, the Reynolds stress profile is consistent with the prediction of Rapid Distortion Theory (RDT), confirming that the redistribution of normal stresses is an inviscid effect. The fluctuating component of the phase- averaged turbulent boundary layer profiles is described using the exact solution to laminar Stokes flow. A phase lag similar to that in laminar flow is observed with an additional constant phase layer in the buffer region. The phase lag is relevant for modeling the intermittent transition and separation expected at full scale. / Ph. D.

It is demonstrated that the method for locating a velocity profile origin, or plane of zero velocity, by fitting log profiles to streamwise velocity measurements is applicable to a larger range of roughness scales than previously expected. Five different sets of detailed, experimental velocity measurements were analyzed encompassing sediment-scale roughness elements, roughness caused by rigid vegetation, and large-scale roughness elements comprised of mobile bedforms. The method resulted in similar values of normalized zero-plane displacement for all roughness types considered. The ratios of zero-plane displacement, dh, to roughness height, ks, were 0.20 and 0.26 for the sediment- and vegetation-scale experiments, respectively. The results for the two experiments with bedform dominated roughness were 0.34 and 0.41. An estimate of dh/ks ranging from 0.2 to 0.4 is therefore recommended for a range of roughness types with the higher end of the range being more appropriate for the larger, bedform-scale roughness elements, and the lower end for the sediment-scale roughness elements. In addition, it is demonstrated that the location of the plane of zero velocity is temporally constant even when the bed height is not. The effects of roughness element packing density were also examined with the identification of a possible threshold at 4%, above which zero-plane displacement is independent of packing density. The findings can be applied to field velocity measurements under mobile bed conditions, facilitating the calculation of turbulence parameters such as shear velocity, by using point measurements and providing guidelines for the estimation of an appropriate value for zero-plane displacement. / Master of Science

Experimental investigations were conducted with and without the presence of the surface-mounted obstacle to quantify its effects on the far wake. The obstacle chosen for this study was a 3:2 elliptical nose NACA 0020 tail wing-body (Rood body), approximately of height equal to the boundary layer thickness at one of the measurement locations of the flow. The experiments were performed by varying the Reynolds number of the flow and manipulating the pressure gradient distributions using a NACA 0012 airfoil placed within the wind tunnel test section. The measurements were acquired utilizing a spanwise traversing boundary layer rake and a point pressure sensing microphone array. The findings reveal that the presence of the obstacle introduces disruptions in the flow, such as vortex and jet regions in the wake. However, the overall flow behavior remains consistent with that of an undisturbed turbulent boundary layer, for varying Reynolds numbers and pressure gradients. Notably, an adverse pressure gradient and lower Reynolds number both accentuate the prominence of the jet and vortex region within the wake, with the trend reversing towards the other end of the spectrum. This behavior is akin to the larger turbulent boundary layer under adverse pressure gradients and lower Reynolds numbers. Furthermore, the presence of obstacles induces an increase in the overall level of the wall pressure spectrum by approximately 2 dB, regardless of the flow condition. Additionally, it leads to a deviation in the slope of the mid-frequency range of the autospectra compared to the smooth wall case. Specifically, the mid-slope frequency of an undisturbed turbulent boundary layer is steeper than that observed in the disturbed wake flow caused by the obstacle. / Master of Science / The interaction between turbulence and aerodynamic surfaces gives rise to wall-pressure fluctuations, which in turn induce structural vibrations and acoustic noise. On surfaces turbulent flows meet, antennae, flaps, and other frequently mounted measuring devices. The flow in their wake is impacted by the coherence of a turbulent boundary layer being disrupted by these impediments mounted on aerodynamic surfaces. They also alter the nature of the pressure fluctuations that are generated on the surface of interest. The far wake of a Rood Body obstacle was studied using a point pressure sensing microphone array and a spanwise traversing boundary layer rake. Experimental measurements were taken for a range of Reynolds numbers and pressure gradient environments at the Virginia Tech Stability Wind Tunnel. Results show that the boundary layer rake measurements resolve the presence of the obstacle wake successfully, by characterizing the wake structures and confirming the presence of jet and vortex regions in the wake of the obstacle. Surface pressure measurements reveal that the presence of the obstacle causes the low-frequency content of the wall pressure to be less dominant than the no obstacle case, while the high-frequency content becomes more dominant in the presence of the obstacle. The presence of obstacles also increases the overall levels of the wall pressure spectrum by approximately 2 dB.

<p>The stability and the receptivity of three-dimensional flat plate boundary layers is studied employing parabolised stability equations. These allow for computationally efficient parametric studies. Two different sets of equations are used. The stability of modal disturbances in the form of crossflow vortices is studied by means of the well-known classical parabolised stability equations (PSE). A new method is developed which is applicable to more general vortical-type disturbances. It is based on a modified version of the classical PSE and describes both modal and non-modal growth in three-dimensional boundary layers. This modified PSE approach is used in conjunction with a Lagrange multiplier technique to compute spatial optimal disturbances in three-dimensional boundary layers. These take the form of streamwise oriented tilted vortices initially and develop into streaks further downstream. When entering the domain where modal disturbances become unstable optimal disturbances smoothly evolve into crossflow modes. It is found that non-modal growth is of significant magnitude in three-dimensional boundary layers. Both the lift-up and the Orr mechanism are identified as the physical mechanisms behind non-modal growth. Furthermore, the modified PSE are used to determine the response of three-dimensional boundary layers to vortical free-stream disturbances. By comparing to results from direct numerical simulations it is shown that the response, including initial transient behaviour, is described very accurately. Extensive parametric studies are performed where effects of free-stream turbulence are modelled by filtering with an energy spectrum characteristic for homogeneous isotropic turbulence. It is found that a quantitative prediction of the boundary layer response to free-stream turbulence requires detailed information about the incoming turbulent flow field. Finally, the adjoint of the classical PSE is used to determine the receptivity of modal disturbances with respect to localised surface roughness. It is shown that the adjoint approach yields perfect agreement with results from Finite-Reynold-Number Theory (FRNT) if the boundary layer is assumed to be locally parallel.  Receptivity is attenuated if nonlocal and non-parallel effects are accounted for. Comparisons to direct numerical simulations and extended parametric studies are presented.</p>

Direct Numerical Simulations (DNS) are performed to investigate laminar-turbulent transition in a boundary layer on a sharp cone at Mach 6. The main objective of this dissertation research is to explore which nonlinear breakdown mechanisms may be dominant in a broad--band "natural" disturbance environment and then use this knowledge to perform controlled transition simulations to investigate these mechanisms in great detail. Towards this end, a "natural" transition scenario was modeled and investigated by generating wave packet disturbances. The evolution of a three-dimensional wave packet in a boundary layer has typically been used as an idealized model for "natural" transition to turbulence, since it represents the impulse response of the boundary layer and, thus, includes the interactions between all frequencies and wave numbers. These wave packet simulations provided strong evidence for a possible presence of fundamental and subharmonic resonance mechanisms in the nonlinear transition regime. However, the fundamental resonance was much stronger than the subharmonic. In addition to these two resonance mechanisms, the wave packet simulations also indicated the possible presence of oblique breakdown mechanism. To gain more insight into the nonlinear mechanisms, controlled transition simulations were performed of these mechanisms. Several small and medium scale simulations were performed to scan the parameter space for fundamental and subharmonic resonance. These simulations confirmed the findings of the wave packet simulations, namely that, fundamental resonance is much stronger compared to the subharmonic resonance. Subsequently a set of highly resolved fundamental and oblique breakdown simulations were performed. In these DNS, remarkable streamwise arranged "hot'' streaks were observed for both fundamental and oblique breakdown. The streaks were a consequence of the large amplitude steady longitudinal vortex modes in the nonlinear régime. These simulations demonstrated that both second--mode fundamental breakdown and oblique breakdown may indeed be viable paths to complete breakdown to turbulence in hypersonic boundary layers at Mach 6.

The majority of this work is concerned with the local-linear convective instability analysis of the incompressible boundary-layer flows over prolate spheroids and oblate spheroids rotating in otherwise still fluid. The laminar boundary layer and the perturbation equations have been formulated by introducing two distinct orthogonal coordinate systems. A cross-sectional eccentricity parameter e is introduced to identify each spheroid within its family. Both systems of equations reduce exactly to those already established for the rotating sphere boundary layer. The effects of viscosity and streamline-curvature are included in each analysis. We predict that for prolate spheroids at low to moderate latitudes, increasing eccentricity has a strong stabilizing effect. However, at high latitudes of ϴ ≥ 60, increasing eccentricity is seen to have a destabilizing effect. For oblate spheroids, increasing eccentricity has a stabilizing effect at all latitudes. Near the pole of both types of spheroids, the critical Reynolds numbers approach that for the rotating disk boundary layer. However, in prolate spheroid case near the pole for very large values of e, the critical Reynolds numbers exceed that for the rotating disk. We show that high curvature near the pole of prolate spheroids is responsible for the increase in critical Reynolds number with increasing eccentricity. For both types of spheroids at moderate eccentricity, we predict that the most amplified modes travel at approximately 76% of the surface speed at all latitudes. This is consistent with the existing studies of boundary-layer flows over the related rotating-disk, -sphere and -cone geometries. However, for large values of eccentricity, the traveling speed of the most amplified modes increases up to approximately 90% of the surface speed of oblate spheroids and up to 100% in the prolate spheroid case.

This document addresses problems encountered when establishing the very low air-flow speeds required for experimental investigations of the mechanisms of low-Reynolds-number boundary-layer turbulence. Small-scale motions in the near-wall region are important features of turbulent boundary-layer dynamics, and, if these features are to be resolved by measurements in air with conventionally-sized hot-wire probes, a well-behaved canonical turbulent boundary layer must be developed at free stream flow speeds no higher than 4 m/s. However, at such low speeds, the turbulent boundary layers developed on the walls of a wind tunnel are very susceptible to perturbation by non-turbulent time-dependent flow structures which originate upstream from the test section in the laminar flow at the inlet and in the contraction. Four different non-turbulent flow structures have been identified. The first is a result of quasi-two-dimensional separation of the laminar boundary-layer from the surfaces of the wind-tunnel contraction. Potential flow simulations show that susceptibility to this form of separation is reduced by increasing the degree of axisymmetry in the cross-section geometry and by decreasing the streamwise curvature of the concave surfaces. The second source of time-dependence in the laminar boundary-layer flow is an array of weak streamwise vortices produced by Goertler instability. The Goertler vortices can be removed by boundary-layer suction at the contraction exit. The third form of flow perturbation, revealed by visualisation experiments with streamers, is a weak large-scale forced-vortex swirl produced by random spatial fluctuations of temperature at the wind-tunnel inlet. This can be prevented by thorough mixing of the inlet flow; for example, a centrifugal blower installed at the inlet reduces the amplitude of temperature nonuniformity by a factor of about forty and so prevents buoyancy-driven swirl. When subjected to weak pressure gradients near the start of a wind-tunnel contraction, Goertler vortices in laminar wall layers can develop into three-dimensional separations with strong counter-rotating trailing vortices. These trailing vortices are the fourth source of unsteady flow in the test-section. They can be suppressed by a series of appropriately located screens which remove the low-speed-streak precursors of the three-dimensional separations. Elimination of the above four contaminating secondary flows permits the development of a steady uniform downstream flow and well-behaved turbulent wall layers. Measurements of velocity in the turbulent boundary layer of the test-section have been obtained by hot-wire anemometry. When a hot-wire probe is located within the viscous sublayer, heat transfer from the hot-wire filament to the wall produces significant errors in the measurements of both the mean and the fluctuating velocity components. This error is known as wall-proximity effect and two successful methods are developed for removing it from the hot-wire signal. The first method is based on the observation that, if all experimental parameters except flow speed and distance from the wall are fixed, the velocity error may be expressed nondimensionally as a function of only one parameter, in the form DeltaU^+=f(y^+). The second method, which also accommodates the effect of changing the hot-wire overheat ratio, is based on a dimensional analyis of heat transfer to the wall. Velocity measurements in the turbulent boundary layer at the mid-plane of a nearly square test-section duct have established that, when the boundary-layer thickness is less than one quarter of the duct height, mean-velocity characteristics are indistinguishable from those of a two-dimensional flat-plate boundary layer. In thicker mid-plane boundary layers, the mean-velocity characteristics are affected by stress-induced secondary flow and by lateral constriction of the boundary-layer wake region. A significant difference between flat-plate and duct boundary layers is also observed in momentum-balance calculations. The momentum-integral equation for a duct requires definitions of momentumd and displacement thickness which are different from those given for flat-plate boundary layers. Momentum-thickness growth rates predicted by the momentum-integral equation for a duct agree closely with measurements of the newly defined duct momentum thickness. Such agreement cannot be obtained in terms of standard flat-plate momentum thickness. In duct boundary layers with Reynolds numbers Re_theta between 400 and 2600, similarity in the wake-region distributions of streamwise turbulence statistics has been obtained by normalising distance from the wall with the flat-plate momentum thickness, theta_2. This result indicates that, in contrast with the mean velocity characteristics, the structure of mid-plane turbulence does not depend on the proportion of duct cross-section occupied by boundary layers and is essentially the same as in a flat-plate boundary layer. For Reynolds numbers less than 400, both wall-region and wake-region similarity fail because near-wall turbulence events interact strongly with the free stream flow and because large scale turbulence motions are directly influenced by the wall. In these conditions, which exist in both duct and flat-plate turbulent boundary layers, there is no distinct near-wall or wake region, and the behaviour of turbulence throughout the boundary layer depends on both wall variables and on outer region variables simultaneously. / Thesis (Ph.D.)--School of Mechanical Engineering, 1998.