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The aerodynamic flow and fluctuating surface pressure of a plane, turbulent, two-dimensional wall jet flow into still air over smooth and rough surfaces has been investigated in a recently constructed wall jet wind tunnel testing facility. The facility has been shown to produce a wall jet flow with Reynolds numbers based on the momentum thickness, Re<SUB>&delta</SUB> = &deltaU<SUB>m</SUB>/&nu, of between 395 and 1100 and nozzle exit Reynolds numbers, Re<SUB>j</SUB> = U<SUB>m</SUB>b/&nu, of between 16000 and 45000. The wall jet flow properties (&delta, &delta<SUP>*</SUP>, &theta, y<SUB>1/2</SUB>, U<SUB>m</SUB>, u<SUP>*</SUP>, etc.) were measured and characterized over a wide range of initial flow conditions and measurement locations relative to the wall jet source. These flow properties were measured for flow over a smooth flow surface and for flow over roughness patches of finite extent. The patches used in the current study varied in length from 305 mm to 914 mm (between 24 and 72 times the nozzle height, b) and were placed so that the leading edge of the patch was fixed at 1257 mm (x/b = 99) downstream of the wall jet source. These roughness patches were of a random sand grain roughness type and the roughness grain size was varied throughout this experiment. The tests covered roughness Reynolds numbers (k<SUP>+</SUP>) ranging from less than 2 to over 158 (covering the entire range of rough wall flow regimes from hydrodynamically smooth to fully rough). For the wall jet flows over 305 mm long patches of roughness, the displacement and momentum thicknesses were found to vary noticeably with the roughness grain size, but the maximum velocity, mixing layer length scale, y<SUB>/2</SUB>, and the boundary layer thickness were not seen to vary in a consistent, determinable way. Velocity spectra taken at a range of initial flow conditions and at several distinct heights above the flow surface showed a limited scaling dependency on the skin friction velocity near the flow surface. The spectral density of the surface pressure of the wall jet flow, which is not believed to have been previously investigated for smooth or rough surfaces, showed distinct differences with that seen in a conventional boundary layer flow, especially at low frequencies. This difference is believed to be due to the presence of a mixing layer in the wall jet flow. Both the spectral shape and level were heavily affected by the variation in roughness grain size. This effect was most notable in overlap region of the spectrum. Attempts to scale the wall jet surface pressure spectra using outer and inner variables were successful for the smooth wall flows. The scaling of the rough wall jet flow surface pressure proved to be much more difficult, and conventional scaling techniques used for ordinary turbulent boundary layer surface pressure spectra were not able to account for the changes in roughness present during the current study. An empirical scaling scheme was proposed, but was only marginally effective at scaling the rough wall surface pressure. / Ph. D.

A low-speed, axisymmetric turbulent boundary layer under a strong adverse pressure gradient is experimentally studied for its relevance to marine applications, urban air-transportation and turbulence ingestion noise. The combined effect of lateral curvature and streamwise pressure gradient are examined on the mean flow, turbulence structure, velocity correlations and wall pressure fluctuations. Additionally, the upstream influence of a rotor operating in this flow is examined to improve the understanding of the turbulence necessary to develop advanced noise prediction tools. Measurements were made in Virginia Tech Stability tunnel documenting the flow over a 0.432-m diameter body-of-revolution comprised of a forward nose-cone, a constant diameter mid-body and a 20 degree tail-cone, at a length based Reynolds number of 1.2 million. The principal finding of this work is the resemblance of the boundary layer to a free-shear layer where the turbulence far from the wall plays a dominant role, unlike in the canonical case of the flat-plate boundary layer. The mean flow along the tail developed inflection points in the outer regions and the associated velocity and turbulence stress profiles were self-similar with a recently proposed embedded shear layer scaling. As the mean flow decelerates downstream, the large-scale motions energize and grow along with the boundary layer thickness; However, the structure is roughly self-similar with the shear-layer scaling, emphasizing the role of the shear-layer in the large-scale structure. Additionally, the correlation structure is discussed to provide information towards the development of turbulence models and aeroacoustic predictions. The associated wall pressure fluctuations, measured with a longitudinal array of microphones, evolved significantly downstream with the dimensional wall pressure spectra weakening by over 20-dB per Hz. However, the spectra collapsed to within 2-dB with the wall-wake scaling, where the pressure-scale is the wall shear stress, and the time-scale is derived from the boundary layer thickness and edge velocity. The success of this scaling, even in the viscous roll-off regions, suggests the increasing importance of the outer region on the near-wall turbulence and wall-pressure. Investigation of the space-time structure revealed the presence of a quasi-periodic feature with the conditional signature of a roller-eddy. The structure appeared to scale with the wall-wake scaling, and was found to convect downstream at speeds matching those at the inflection points (and outer turbulence peak). It is hypothesized that the outer region turbulence in strong adverse pressure gradient flow strongly drive the near-wall turbulence and therefore both the wall pressure and shear stress. Subsequent measurements made with the rotor operating at the tail, using high-speed particle image velocimetry, provided the space-time structure of the inflow turbulence as a function of the rotor thrust. The impact of the rotor on the mean flow, turbulence and correlation structure in the vicinity of the rotor is discussed to supply information towards validating numerical simulations and developing turbulence models that account for the distortion due to the rotor. This work was sponsored by the Office of Naval Research, in particular Drs. Ki-Han Kim and John Muench under grants N00014-17-1-2698 and N00014-20-1-2650. / Doctor of Philosophy / Understanding turbulent flows adjacent to surfaces placed in fluid flows is necessary to develop efficient technologies to mitigate undesirable drag, vibrations and noise. Particularly, this is of an increased interest with the imminent abundance of urban short-haul air transportation. While several fundamental aspects of these flows have been clarified, certain specific areas still remain to be addressed, including the impact of curved surfaces, like those of submarine hulls and aircraft fuselage, and the impact of mean pressure gradients. This study seeks to fill some of these gaps by studying the flow over a body-of-revolution through wind tunnel experiments. The nature of the velocity and wall-pressure fluctuations are examined in detail. It was found that the boundary layer was significantly different from the canonical case of a flat-plate flow, with the mean velocity and turbulence structure developing the characteristics of a free-shear layer (flows unbounded by surfaces). Specifically, the velocity and turbulence intensity appeared self-similar with a recently proposed embedded shear layer scaling, which is based on the parameters at the inflection point in the mean velocity profile. The large-scale motions in the outer regions, despite energizing and growing as the flow decelerated downstream, appeared self-similar with the shear layer parameters, emphasizing the role of shear layer motions within in the boundary layer. This is important since the turbulence relatively further from the wall are now the important sources of pressure fluctuations and therefore drag, vibrations and noise. The associated wall-pressure fluctuation were studied with a focus on the wall-pressure spectrum and the space-time structure. A quasi-periodic feature was detected in the instantaneous fluctuations, which had a conditional structure reminiscent of a conditional roller, and appeared to convect downstream at speeds matching those at the inflection points in the velocity profile. Therefore it is hypothesized that the large-scale motions in the embedded shear layer play a dominant role on the near-wall turbulence and therefore on the wall pressure and shear-stress. This is different from the behavior of the wall-studied flow past a flat-plate. It is therefore important to factor this into technologies aiming to increase the efficiency and quieten the vehicles

Acoustic metamaterials have been shown to support acoustic surface waves when excited by a broadband signal in a quiescent environment and these waves could be manipulated by varying the geometry of the structure making up the metamaterial. The study presented here demonstrates the generation of trapped acoustic surface waves when excited by a turbulent flow source. The metamaterial and flow were interfaced using a Kevlar covered single cavity whose Kevlar side faced the flow to ensure no significant disturbance to the flow and the other side was open to a quiescent (stationary) environment housing the metamaterial. Acoustic measurements were performed very close to the surface of the metamaterial in the Anechoic Wall Jet Facility at Virginia Tech using two probe-tip microphones and correlation analysis yielded the structure of the surface waves. Two different metamaterials; slotted array and meander array were tested and characterized by their dispersion relations, temporal correlations, and spatial-temporal structure. The measurements proved the existence of surface waves with propagating speeds of a tenth of the speed of sound, when excited by a turbulent boundary layer flow. These waves were much weaker than the overlying flow exciting them but showcased excellent attenuation properties away from the source of excitation. Measurements along the length of the unit-cell geometry of the metamaterial demonstrated high coherence over a range of frequencies limited by the dimension of the cell. This was a surprising behavior provided the cavity was excited by a fully developed turbulent flow over a flat plate and indicated to an area averaging phenomenon. A wall normal two-dimensional particle image velocimetry (2D-PIV) measurement was performed over the Kevlar covered cavity and a smooth surface to study the effects of the cavity on the flow. The field of view was the same for both cases which made direct flow comparison possible. Flow characteristics such as the boundary layer profiles, Reynolds stress profiles and fluctuating velocity spectrum were studied over the cavity and at downstream locations to quantify the differences in the flows. The boundary layer profiles collapsed in the inner region of the boundary layer but there were small differences in the outer region. The Reynolds stress profiles were also very similar with differences within the uncertainties of processing the images and it reflected similar average behavior of the flow over a smooth wall and a Kevlar covered cavity. The fluctuating velocity spectrum studied over the cavity location showed some differences at low frequencies for all wall normal locations while at higher frequencies the differences were within ±3 dB. These measurements showcased the underlying physics behind the interaction of acoustic metamaterials and turbulent boundary layer flows creating possibilities of using these devices for flow control although further analysis/optimization is needed to fully understand the capabilities of these systems. The demonstration of no significant effect on flow by the Kevlar covered cavity stimulated development of sensors which can average over a region of the wall pressure spectrum. / M.S. / In the field of physics, acoustic metamaterials have gained popularity due to their ability to exhibit certain properties such as sound manipulation which cannot be seen in regular materials. These materials have a key feature which is the periodic arrangement of geometric elements in any dimension. These materials can support a phenomenon termed as acoustic surface waves which are essentially pressure disturbances in the medium which behave differently than some known phenomenon such as sound waves when excited by a broadband pressure signal in a stationary medium. Also, it has been shown that these materials can change the nature of the acoustic surface waves if their geometry is changed. Here a successful attempt has been made to link two different fields in physics: acoustic metamaterials (acoustics) and turbulent flows (fluid dynamics). The study here uses turbulent boundary layer flows to excite these metamaterials to show the existence of acoustic surface waves. This is done by creating an interface between the flow and the metamaterial using a Kevlar covered through cavity which is essentially a through hole connecting to different sides: flow side and the stationary air/quiescent side. This cavity acted as the source of excitation for the metamaterial. The Kevlar covering ensures that the flow does not get disturbed due to the cavity which was also proved in this study using a visualization technique: Particle Image Velocity (PIV). Two microphones were used to study the pressure field very close to two metamaterials; one was referred to as the slotted array comprised of slot cavities arranged in one dimension (along the direction of the flow), while the other was termed as the meander array and it comprised of a meandering channel. The pressure field was well characterized for both the acoustic metamaterials and it was proved that these metamaterials could support acoustic surface waves even when excited by a turbulent flow. The idea here was to fundamentally understand the interaction of acoustic metamaterials and turbulent flows, possibly finding use in applications such as trailing edge noise reduction. The use of these metamaterials in direct applications needs further investigation. A finding from the pressure field study showed that the pressure measured along the length of the Kevlar covered cavity was uniform. The flow visualization study looked at the turbulent flow on a smooth wall and over a Kevlar covered cavity. This was done by injecting tiny particles in air and shooting a laser sheet over these to illuminate the flow. Images were recorded using a high-speed camera to track the movement of these particles. It was found that the flow was unaffected with or without the presence of a Kevlar covered cavity. This result coupled with the pressure field uniformity could have some wide applications in the field of pressure sensing.

The behavior of a junction vortex formed around an obstacle in a boundary layer flow was studied experimentally in a water tunnel for two low speed cases. A wing consisting of a 3 : 2 elliptical nose and an NACA 0020 tail was used to simulate the junction vortex. A visual study using a hydrogen bubble technique was extensively conducted to investigate the flow structures in the stagnation region of the wing. It was observed that a multiple vortex system exists in this region and shows an acyclic flow pattern. LDV measurements were performed in the plane of symmetry upstream of the wing. The general behavior of the flow agrees with an earlier wind tunnel test of Devenport and Simpson which was conducted at higher speed. A low frequency, bistable flow structure was observed as in the wind tunnel measurements. The switching between two flow modes (a backfiow mode and a zero flow mode) was analyzed using LDV signals in the zone of a bimodal structure. A dimensionless frequency group (StT) was found to represent the average frequency of successive switches from a given mode to the other. The visual evidence of acyclic flow pattern was consistent with the LDV measurements, and revealed that aperiodic stretching of the junction vortex appears responsible for the bimodal (double-peaked) structure in the velocity histograms. An attempt to measure the three-dimensional instantaneous velocity field in this region was made. A unique PIDV (particle image displacement velocimetry) technique was developed using a multiple wire hydrogen bubble method and a high speed video system. A stereo vision approach was implemented to capture two orthogonal views simultaneously for the three-dimensional motion analysis. / Ph. D.

Three new computational procedures are presented for the simulation of incompressible wall-bounded turbulent flows. First, an integral method based on the strip integral method has been developed for the solution of three-dimensional turbulent boundary-layer flows. The integral equations written in a general form using non-orthogonal streamline coordinates include the turbulent shear stress at the upper limit of an inner strip inside the boundary-layer. The shear stress components are modeled using the Boussinesq assumption, and the eddy viscosity is defined explicitly as in differential methods. The turbulence modeling is not hidden in opaque empirical correlations as in conventional integral methods. A practical four-parameter velocity profile has been established based on the Johnston Law of the Wall using a triangular model for the crosswise velocity. Two strips are used to solve for the four unknowns: skin friction coefficient, wall crossflow angle, boundary-layer thickness, and location of maximum crosswise velocity. The location of maximum crosswise velocity proves to be a natural and adequate parameter in the formulation, but it is numerically sensitive and has a strong influence on the wall crossflow angle. Good results were obtained when compared to predictions of other integral or differential methods. Secondly, two computational procedures solving the Reynolds Averaged Navier-Stokes equations for 20 and 3D flows respectively have also been developed using a new treatment of the near-wall region. The flow is solved down to the wall with a slip velocity based on Clauser's idea of a pseudolaminar velocity profile. The present idea is different from the wall-function methods and does not require a multi-layer eddy viscosity model. The solution of the equations of motion is obtained by the Finite Element Method using the wall shear stress as a boundary condition along solid surfaces, and using the Clauser outer region model for the eddy viscosity. The wall shear stress distribution is updated by solving integral equations obtained from the enforcement of conservation of mass and momentum over an inner strip in the near-wall region. The Navier-Stokes solution provides the necessary information to the inner strip integral formulation in order to evaluate the skin friction coefficient for 2D flows, or the skin friction coefficient and the wall crossflow angle for 3D flows. The procedures converge to the numerically "exact" solution in a few iterations depending on the accuracy of the initial guess for the wall shear stress. A small number of nodes is required in the boundary-layer to represent adequately the physics of the flow, which proves especially useful for 3D calculations. Excellent results were obtained for the 2D simulations with a simple eddy viscosity model. 3D calculations gave good results for the turbulent boundary-layer flows considered here. The present methods were validated using well-known experiments chosen for the STANFORD conferences and EUROVISC workshop. The 2D numerical predictions are compared with the experimental measurements obtained by Wieghardt-Tillmann, Samuel-Joubert, and Schubauer-Klebanoff. For the 3D analyses, the numerical predictions obtained by the strip-integral method and the Finite Element Navier-Stokes Integral Equation procedure are validated using the Van den Berg-Elsenaar and Müller-Krause experiments. / Ph. D.

The equations and numerics necessary for the analysis of dense-gas boundary-layer flows over arbitrarily shaped two-dimensional bodies are developed. The governing equations are derived from the Navier-Stokes-Fourier equations for a general fluid. A numerical method based on the second-order Davis-coupled scheme is employed to solve for mean flows over flat plates. Flows of nitrogen, sulfur hexafluoride, and toluene over adiabatic walls are examined; in addition, flows of nitrogen over heated and cooled walls are studied. Results indicate a breakdown of the standard correlations for the recovery factor and the Nusselt number due primarily to the substantial variations of the Prandtl number and the Chapman-Rubesin parameter throughout the boundary layer. The stability equations for two-dimensional inviscid disturbances in a general fluid are derived. The temporal stability of the mean flows of nitrogen is subsequently examined using the generalized inflection-point criterion extracted from these equations. Results reveal significant variations from standard ideal-gas predictions including the existence of flows for which neither heating nor cooling of the wall has a stabilizing effect. / Master of Science

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.