The pressure fluctuations under a high Reynolds Number, rough-wall, turbulent, boundary layer have been studied in the Virginia Tech Stability Wind Tunnel. Rough surfaces of varying element height (1-mm, 3-mm), shape (hemispheres, cylinders) and spacing (5.5-mm, 10.4-mm, 16.5-mm) were investigated in order to ascertain how the turbulent pressure fluctuations change with changes in roughness geometry. Rough surfaces which contain two types of elements are investigated and relationships between the combination surface and the individual surfaces have been uncovered. Measurements of the wall pressure fluctuations were made using pinhole microphones and hotwire measurements were made to obtain the velocity and turbulence field. Among the principal findings is the development of two scaling laws for the low frequency pressure fluctuations. Both of these are based on the idea that the defect between the edge velocity and some local boundary layer velocity sustains the pressure fluctuations in the outer regions of the flow. The first scaling uses the broadband convection velocity as the local velocity of the large scale pressure fluctuations. The second scaling uses the mean boundary layer velocity. Both these scalings appear more robust than the previously proposed scalings for the low frequency region and are able to scale the pressure spectra of all the data to within 3.5-dB. In addition, it was proven that the high frequency shear friction velocity scaling of Meyers et al. (2015) is universal to rough surfaces of different element shape and density. Physical insights into the shear friction velocity, on which this scaling is based, have been revealed. This includes an empirical formula which estimates the element pressure drag coefficient from the roughness density and the Reynolds number. The slopes in the mid-frequency region were found to vary with element density and microphone location such that a useful scaling could not be determined for this region. The possibility of an overlap region is explored and the expectation of a -1 slope is disproved. It is hypothesised that an evanescent decay of the mid-frequency pressure fluctuations occurs between their actual location and the wall where they are measured. A method for accounting for this decay is presented in order to scale the pressure fluctuations in this region. Lastly, a piecewise interpolation function for the pressure spectrum of rough wall turbulent boundary layers was proposed. This analytical function is based on the low frequency scaling on mean velocity and the high frequency scaling of Meyers et al. (2015) The mid-frequency is estimated by a spline interpolation between these two regions. / Ph. D. / Most flows of practical interest are turbulent in nature, typically occurring next to a rigid surface such as a submarine hull or aircraft wing. This boundary layer flow is of engineering importance because its pressure fluctuations are the source of unwanted structural vibrations and undesired acoustic noise. From a purely scientific perspective, it is useful to study the turbulent pressure fluctuations in order to learn more about the workings of the region of the flow closest to the surface. Turbulent flow over smooth walls has been researched extensively. However, one cannot ignore the fact that surfaces of practical interest are not smooth. Thus, it is important to account for the effect of roughness on the turbulent boundary layer. It has been found that there are significantly greater pressure fluctuations over rough walls when compared to smooth walls. Consequently the extent of vibrations and noise which occur in rough walls is larger than that experienced in smooth walls. The present study seeks to shed light on the nature of the rough-wall turbulent boundary layer through wind tunnel experiments. The nature of the velocity, pressure fluctuations, and turbulence within the boundary layer are examined as well as the existence of universal relationships which are applicable to all rough-wall turbulent boundary layers. A method for predicting the pressure fluctuations (to within 4-dB) over a specific rough wall is also proposed.

A study on the behaviour of wave-packets and random disturbances, introduced by the vibrating-ribbon technique in a Blasius boundary layer, is presented. The experiments were conducted in the VPI & SU low turbulence wind tunnel. The flat plate model was constructed from an aluminum-paper honeycomb laminate and an aluminum leading edge with an elliptical profile. A theoretical model was developed to verify the random and step-function-form motion of the vibrating ribbon. In the case of random disturbance introduction it was found that the random disturbances behave like infinite number, single-frequency waves and measurements of their growth made possible to verify regions of the neutral-stability curve. In the case of wave-packet creation it was found that the wave packets behave like a structure that consists of waves of certain frequencies that grow or decay not necessarily according to the stability curve but in that way as to maintain the wave-packet structure. Their growth as they move downstream and their quick destruction into turbulence was compared to previously published data. / Master of Science

Turbulence research in the laboratory over the past three decades has confirmed the existence of quasi-coherent structures amidst the chaos of a turbulent boundary layer. It has been observed that a quasi-periodic phenomena called "bursting" accounts for a major contribution to the turbulent Reynolds stress and the production of turbulent kinetic energy. Bursting is the term used for a sequence of events, where a low-speed streak of fluid from the near wall region lifts away from the wall, slowly at first, and then rapidly moves away from the wall as it convects downstream where it becomes unstable and breaks up violently upon interaction with the outer flow. This ejection of low speed fluid into the mean flow is responsible for locally high values of turbulent kinetic energy. Though a great deal is known about these structures in laboratory flows, little has been done to investigate their existence in the turbulent air flow over the ocean. It would seem, intuitively, that such structures, if present in the marine atmospheric boundary layer, would playa major role in the transfer of momentum, mass and heat across the air-sea interface. The present study is aimed at identifying the existence of burst structures in the marine atmospheric boundary layer. The standard ejection detection schemes like the quadrant, the VITA and the modified u-level techniques were applied to the turbulent wind data measured over the ocean. It was found that the proportion of contribution to the Reynolds stress from the four quadrants of the u'w' plane is in close agreement with the corresponding contributions for a laboratory flow. Ejection detection followed by the grouping of ejections into bursts yielded a mean burst period of 47 sec., at a height of 8.2 m above the water surface, where the mean wind velocity was 6.74 m/s. This burst period corresponds well with the peaks obtained from the autocorrelation of the streamwise velocity signal and the first moment of the stress spectrum. Furthermore, phase averages of these events show a structure which is similar to the structure of the events detected in the laboratory flows. / Master of Science

Turbulent boundary layer and metamaterial properties were explored to initiate the viability of controlling acoustic waves driven by pressure fluctuations from flow. A turbulent boundary layer scaling analysis was performed on zero-pressure-gradient turbulent boundary layers over rough surfaces, for 30,000≤〖Re〗_θ≤100,000. Relationships between fluctuating pressures and velocities were explored through the pressure Poisson equation. Certain scaling laws were implemented in attempts to collapse velocity spectra and turbulence profiles. Such analyses were performed to justify a proper scaling of the low-frequency region of the wall-pressure spectrum. Such frequencies are commonly associated with eddies containing the largest length scales. This study compared three scaling methods proposed in literature: The low-frequency classical scaling (velocity scale U_τ, length scale δ), the convection velocity scaling (U_e-U ̅_c, δ), and the Zagarola-Smits scaling (U_e-U ̅, δ). A default scaling (U_e, δ) was also selected as a baseline case for comparison. At some level, the classical scaling best collapsed rough and smooth wall Reynolds stress profiles. Low-pass filtering of the scaled turbulence profiles improved the rough-wall scaling of the Zagarola-Smits and convection velocity laws. However, inconsistent scaled results between the pressure and velocity requires a more rigorous pressure Poisson analysis. The selection of a proper scaling law gives insight into turbulent boundary layers as possible sources for acoustic metamaterials. A quiescent (no flow) experiment was conducted to measure the capabilities of a metamaterial in retaining acoustic surface waves. A point source speaker provided an acoustic input while the resulting sound waves were measured with a probe microphone. Acoustic surface waves were found via Fourier analysis in time and space. Standing acoustic surface waves were identified. Membrane response properties were measured to obtain source condition characteristics for turbulent boundary layers once the metamaterial is exposed to flow. / Master of Science / Aerodynamicists are often concerned with interactions between fluids and solids, such as an aircraft wing gliding through air. Due to frictional effects, the relative velocity of the air on the solid-surface is negligible. This results in a layer of slower moving fluid near the surface referred to as a boundary layer. Boundary layers regularly occur in the fluid-solid interface, and account for a sufficient amount of noise and drag on aircraft. To compensate for increases in drag, engines are required to produce increased amounts of power. This leads to higher fuel consumption and increased costs. Additionally, most boundary layers in nature are turbulent, or chaotic. Therefore, it is difficult to predict the exact paths of air molecules as they travel within a boundary layer. Because of its intriguing physics and impacts on economic costs, turbulent boundary layers have been a popular research topic. This study analyzed air pressure and velocity measurements of turbulent boundary layers. Relationships between the two were drawn, which fostered a discussion of future works in the field. Mainly, the simultaneous measurements of pressure on the surface and boundary layer velocity can be performed with understanding of the Pressure Poisson equation. This equation is a mathematical representation of the boundary layer pressure on the surface. This study also explored the possibility of turbulent-boundary-layer-driven-acoustic-metamaterials. Acoustic metamaterials contain hundreds of cavities which can collectively manipulate passing sound waves. A facility was developed at Virginia Tech to measure this effect, with aid from a similar laboratory at Exeter University. Microphone measurements showed the reduction of sound wave speed across the metamaterial, showing promise in acoustic manipulation. Applications in metamaterials in the altering of sound caused by turbulent boundary layers were also explored and discussed.

Various researchers are interested in the structure of the surface pressure fluctuations for the development and use of noise prediction techniques for helicopter and turbomachinery rotors. This study, conducted in the Virginia Tech low speed boundary layer wind tunnel, covered the effects of zero and favorable streamwise pressure gradient flows on the surface pressure fluctuation spectra, coherence and convective wave speeds in turbulent boundary layers for momentum Reynolds numbers from 3000 to 18,800. The acceleration parameter, pressure gradient flow. K is near 2x10⁻⁷ for the favorable Small pinhole condenser microphones were used to obtain the surface pressure fluctuation data for all test cases. The longitudinal and lateral coherence functions and the convective wave speeds were obtained for both streamwise pressure gradient flows. The results presented are for the surface pressure fluctuation spectra nondimensionalized by different groupings of the outer and inner boundary layer variables. The grouping using the outer variables, U_e, π_w and δ₁ collapse the spectra for the low to middle range of frequencies for most test cases. The grouping using the inner variables, U_π and ν, collapse the spectra for the middle to high range of frequencies for all test cases. The value of p¹/r_w was near 3.8 and 2.8 for the smallest values of d⁺ in the zero and favorable pressure gradient flows, respectively. The spectral data was corrected using the correction developed by G.M. Corcos, but the pinhole correction developed by Bull and Thomas was not used in the data reduction process. However, some discussion is included on the effects of the pinhole correction for the results of this study. The coherence exhibits a decay that is not exponential in some cases, but the Corcos similarity parameters ωΔx/U_c and ωΔz/U_c collapse the data for all test cases. C The ratio of U_c/U_e shows an increase with increasing ωδ₁/U_e up to a certain value of ωδ₁/U_e where U_c/U_e becomes constant. This was observed in the present results for both streamwise pressure gradient flows. The experimental results presented show good agreement with previous research. / M.S.

This study focuses on measuring and normalizing the roughness noise of multiple roughness types across numerous layouts and flow speeds. Using the Virginia Tech Anechoic Wall Jet Facility, far field noise was recording for the flow of a turbulent wall jet boundary layer over cubes, hemispheres, and gravel, with element heights in the range of 14.3 - 55.2% of the boundary layer thickness. The sound radiated from the various layouts showed that the elements acted as independent sources when separated by three element diameters center-to-center or more. When the elements were placed shoulder to shoulder, interaction between the elements and shielding of the higher velocity flow lowered the noise per element produced. The far field roughness noise was then normalized using the theory of Glegg et al. (2007), which assumes a dipole efficiency factor. Comparisons were made between the theoretical drag spectrum model proposed by Glegg et al. (1987) and a modified version of this model made using the empirical data gathered. Overall, the theory of Glegg et al. (2007) succeeds greatly in collapsing the data into its non-dimensional drag spectra, but the original model spectrum did not fit well. The modified spectrum showed much greater fit with the data at all layouts and speeds. The collapse of the data using the theory of Glegg et al. (2007) confirms that roughness noise is dipole in nature. / Master of Science

Recent studies have utilized spanwise traveling waves to alter the turbulent boundary layer with the aim of reducing skin friction drag. Spanwise traveling waves are a promising active drag reduction technique; however, the wave generation methods used in previous studies are bulky and could not be practically implemented. This research has developed an implementable traveling wave generation method and then fundamentally demonstrated how it changes the turbulent boundary layer, which is in a manner consistent with skin friction/shear stress reduction. Traveling waves were generated on a two-dimensional surface using low-profile piezoelectric actuators, in an open-loop fashion, and with minimal frequency limitations. The wave generation method was developed to generate tailored traveling wave patterns; thus, yielding control over the propagation direction, number of wave-fronts, and regions of the surface containing traveling waves. These tailored traveling waves have the capacity not just for affecting the boundary layer, but also for other applications such as propulsion. The implementable traveling wave generation method was then tested in a low-speed wind tunnel and shown to alter the structure of the turbulent boundary layer. The boundary layer is pushed off the wall, and the viscous sublayer is thickened, indicating a reduction in shear stress. Analysis of the boundary layer at positions phase-locked to the wave oscillation suggests that the traveling waves induce a phase-lag effect in the flow. This phase-lag produces a stretching of the viscous sublayer and may contribute to the skin friction reduction. The effects of standing waves on the turbulent boundary layer were also investigated and compared with traveling waves. The results indicate that both wave types alter the boundary layer in the same manner. Standing waves are simpler to generate than traveling waves, suggesting that standing waves may be an effective skin friction reduction method. Before traveling or standing waves can be implemented, further research is necessary to investigate the interaction between the wave pattern and the turbulent phenomena and also to quantify the skin friction reduction and overall net energy usage. / Ph. D. / Recent studies have utilized spanwise traveling waves to alter the turbulent boundary layer with the aim of reducing skin friction drag. Spanwise traveling waves are a promising active drag reduction technique; however, the wave generation methods used in previous studies are bulky and could not be practically implemented. This research has developed an implementable traveling wave generation method and then fundamentally demonstrated how it changes the turbulent boundary layer, which is in a manner consistent with skin friction/shear stress reduction. Traveling waves were generated on a two-dimensional surface using low-profile piezoelectric actuators, in an open-loop fashion, and with minimal frequency limitations. The wave generation method was developed to generate tailored traveling wave patterns; thus, yielding control over the propagation direction, number of wave-fronts, and regions of the surface containing traveling waves. These tailored traveling waves have the capacity not just for affecting the boundary layer, but also for other applications such as propulsion. The implementable traveling wave generation method was then tested in a low-speed wind tunnel and shown to alter the structure of the turbulent boundary layer. The boundary layer is pushed off the wall, and the viscous sublayer is thickened, indicating a reduction in shear stress. Analysis of the boundary layer at positions phase-locked to the wave oscillation suggests that the traveling waves induce a phase-lag effect in the flow. This phase-lag produces a stretching of the viscous sublayer and may contribute to the skin friction reduction. The effects of standing waves on the turbulent boundary layer were also investigated and compared with traveling waves. The results indicate that both wave types alter the boundary layer in the same manner. Standing waves are simpler to generate than traveling waves, suggesting that standing waves may be an effective skin friction reduction method. Before traveling or standing waves can be implemented, further research is necessary to investigate the interaction between the wave pattern and the turbulent phenomena and also to quantify the skin friction reduction and overall net energy usage.

Two rotor configurations with different non-uniform inflows were studied: a rotor ingesting the wake of an upstream cylinder and a rotor ingesting a thick axially symmetric boundary layer from an upstream centerbody. In both cases, the undisturbed inflow was measured without the rotor present in order to characterize the inflow, in particular to calculate the unsteady upwash velocity distribution at the location of the rotor. In addition, detailed acoustic measurements were completed using a 251-channel large-area microphone array. In all, over 400 conditions covering different advance ratios, angles of yaw, and inflow conditions were measured. Measurements of the sound show that the source has a complex directivity, different from that of a streamwise aligned dipole, due to the inhomogeneous unsteady upwash distribution. In addition, observers at different far field locations will perceive sources from different locations on the rotor disk. The directivity is a function of both the rotor geometry and turbulent inflow. A simplified model of the sound source was developed using these inputs and accurately predicts trends observed in the far field noise. For the cylinder wake ingestion case, on-blade measurements of the flow field show that the wake is drawn to the center of the rotor disk with increasing thrust. This is particularly noticeable if the wake does not strike the center of the rotor disk. The effects of this flow distortion on the far field directivity are well predicted by the model. The effects of yaw to rotate the produced sound field can be inferred from this model as well. A novel beamforming procedure was used to isolate sources across the face of the rotor for the cylinder wake ingestion case for an upstream observer position. This method may be used to isolate different sound sources on a rotor if multiple sources are present or if different regions of the rotor disk need to be isolated. The directivity of a rotor ingesting an axially symmetric boundary layer is far less complex than the ingestion of a two-dimensional cylinder wake, but measurements still show the perceived source location shift with observer location. Overall, the proposed noise modeling technique is an efficient method to predict the directivity of turbulence ingestion noise for inhomogeneous inflows. This can enable quick absolute noise predictions at all far field locations using only a single point measurement or far field noise prediction to establish absolute levels. / Doctor of Philosophy / In many engineering applications, rotors interact with turbulence. Aircraft and ships with rear mounted propellers can have upstream appendages or discontinuities that generate turbulence that travels downstream and is drawn into the propeller. Wind turbines interact with turbulence in the atmosphere and with turbulent wakes from other turbines. Interaction of a rotor with turbulence results in unsteady loading on the rotor blades that can radiate as sound, causing unwanted community noise or vehicle detection. As such, prediction and reduction of noise due to turbulence ingestion is highly desirable and remains an active area of research. Turbulence ingestion noise is well understood from first principles and can be successfully predicted provided an accurate description of the turbulent inflow and unsteady aerodynamic response of the rotor blades. Much work has focused on homogenous, isotropic turbulence ingestion noise, however, in practical applications, the rotor inflow is often non-uniform, anisotropic, and can change dramatically with the thrusting condition of the rotor. Research efforts to develop noise predictions considering these more complex, but practical inflows have focused on the inflow modeling and measurement and have relied on a small subset of sound measurements for validation. The present study seeks to provide new physical insight into inhomogeneous, anisotropic turbulence ingestion noise through wind tunnel experiments. In particular, two rotor configurations with different practical non-uniform inflows are studied: a rotor ingesting the wake of an upstream cylinder and a rotor ingesting a thick axially symmetric boundary layer from an upstream center body. In both cases, the undisturbed inflow was measured without the rotor present in order to characterize the inflow, and detailed acoustic measurements were completed using a 251-channel large-area microphone array. In all, over 400 rotor operating conditions were measured. The acoustic directivity in each case is examined in detail as a function of rotor operating condition. A simplified directivity model is developed and validated with measurements. Ultimately, the directivity model can provide a good engineering approximation of the full directivity with reduced computational time or can be used to extrapolate measured results to positions in the far field where placement of sensors is not possible. The results can also be used to guide the analysis and interpretation of single point or microphone array measurements in the acoustic far field of a rotor.

The structure and behavior of the bimodal flow of the horseshoe vortex at the nose of a wing-body junction flow was studied. The wing consists of a 3:2 elliptic nose and a NACA 0020 tail joined at the maximum thickness (t). Measurements were performed with an approach flow conditions of U_ref = 27.5 m/s, Re_θ = 6700 at x/t=-2.15, and δ/t=0.5. A rapidly-scanning two-velocity-component laser-Doppler anemometer system was developed for use in investigating this flow. U and V velocity components were measured simultaneously with surface pressure measurements at the location of the most bimodal pressure histogram (x/t=-0.26). Mean (U, V) and rms (u’, v’) velocity components were obtained at four x locations, x/t= -0.15, -0.20, -0.25, -0.30, and show the same flow features measured in previous studies at this facility. Cross-correlations between the velocity and the surface pressure fluctuations were obtained. Large correlations were found between the u fluctuations (x/t= -0.15, -0.25, and -0.30) near the wall, y/t < 0.05, and the surface pressure fluctuations. The z fluctuations for y/t > 0.1 at all four x-locations lead the surface pressure fluctuations. Space-time correlations between the velocity fluctuations near the wall with the velocity fluctuations along the scan were also obtained. The correlations at x/t=-0.25 and x/t=-0.30 show that the fluctuations in the outer region, y/t > 0.1, are significantly correlated with and lead the velocity fluctuations near the wall. These measurements support a model of a single primary junction vortex that changes size and location in front of the wing. The strength or circulation of this vortex varies by only 20%. Event-threshold conditional-averages of velocity were obtained based on the surface pressure signal, which is sensitive to the movement of the junction vortex. These show that the junction vortex is concentrated near the nose, with large backflow, when the surface pressure signal is above the mean. The junction vortex is larger, with smaller backflow near the nose, when the surface pressure signal is below the mean. The velocity-pressure cross-correlations and space-time correlations indicate that the behavior of the junction vortex is influenced by fluctuations originating upstream and propagating inward and downward toward the wing. / Ph. D.

A pressure-driven three-dimensional turbulent boundary layer flow upstream and around a junction vortex was experimentally studied and is offered for use as a benchmark flow for testing and evaluating the predictive ability of state-of-the-art three-dimensional turbulent boundary layer codes. The pressure-driven flow and junction vortex system was generated by a streamlined cylinder placed normal to a flat surface. Measurements of wall static pressure, wall shear stress, mean velocity, and Reynolds stress tensor field are reported at several stations in the three-dimensional turbulent boundary layer region. Documentation of the flow edge conditions is provided as well as upstream initial conditions along a plane with measured mean velocity and Reynolds stress tensor to permit the testing of intermediate and higher order turbulence models. Measurements of wall shear stress magnitude were made with a Preston tube and the wall shear stress directions were taken from an oil streak flow visualization. These results are compared with earlier direct force wall shear measurements of both magnitude and direction. Mean velocity magnitude and direction were measured with a single hot film probe. Measurements of the complete Reynolds stress tensor were carried out with three hot film x-array probes. Supporting work includes a wind tunnel calibration which examined the sensitivity and effects of spanwise nonuniformities and a two-dimensional momentum integral calculation along the tunnel center plane; the development of a calibration technique to determine individual sensor yaw characteristics in more complex probe geometries; and a generalized response analysis for a sensor with arbitrary orientation to the flow which allows for the use of an arbitrary yaw cooling law, allows for modest amounts of probe misalignment and yields a precise definition of matched sensors, geometric guidelines for constructing x-array probes, and a general mean velocity correction for turbulence where several existing formulas are compared. In addition, two popular cooling laws are studied, comparisons are made with other response equations, and an extensive discussion of the errors associated with the matched sensor approximations is given. Comparisons are made of several mean velocity measurements using different probes and redundant normal and shear stresses measured by the different x-array film probes, a single wire, and single film probe are compared. / Ph. D.