This thesis is an experimental study of turbulent flows over smooth and rough walls in a channel that consists of an upstream parallel section to produce a fully developed channel flow and a diverging section to produce an adverse pressure gradient (APG) flow. The roughness elements used were two-dimensional square ribs of nominal height k = 3 mm. The ribs were secured to the lower wall of the channel and spaced to produce the following three pitches: 2k, 4k and 8k, corresponding to d-type, intermediate and k-type rough walls, respectively. For each rough wall type, the ribs were inclined at 90°, 45° and 30° to the approach flow. The velocity measurements were performed using a particle image velocimetry technique. The results showed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. The level of turbulence production and Reynolds stresses were significantly increased by roughness beyond the roughness sublayer. It was observed that the population, sizes and the level of organization of hairpin vortices varied with roughness and more intense quadrant events were found over the smooth wall than the rough walls. APG reinforced wall roughness in augmenting the equivalent sand grain roughness height, turbulence production and Reynolds stresses. APG also reduced the sizes of the hairpin packets but strengthened the quadrant events in comparison to the results obtained in the parallel section. The secondary flow induced by inclined ribs significantly altered the distributions of the flow characteristics across the span of the channel. Generally, the mean flow was less uniform close to the trailing edge of the ribs compared to the flows at the mid-span and close to the leading edge of the ribs. The Reynolds stresses and hairpin packets were distinctly larger close to the trailing edge of the ribs. Rib inclination also decreased the drag characteristics and significantly modified the distributions of the Reynolds stresses and quadrant events. In the parallel section, the physical sizes of the hairpin packets were larger over 45° ribs whereas in the diverging section, the sizes were larger over perpendicular ribs.

This thesis is an experimental study of turbulent flows over smooth and rough walls in a channel that consists of an upstream parallel section to produce a fully developed channel flow and a diverging section to produce an adverse pressure gradient (APG) flow. The roughness elements used were two-dimensional square ribs of nominal height k = 3 mm. The ribs were secured to the lower wall of the channel and spaced to produce the following three pitches: 2k, 4k and 8k, corresponding to d-type, intermediate and k-type rough walls, respectively. For each rough wall type, the ribs were inclined at 90°, 45° and 30° to the approach flow. The velocity measurements were performed using a particle image velocimetry technique. The results showed that rib roughness enhanced the drag characteristics, and the degree of enhancement increased with increasing pitch. The level of turbulence production and Reynolds stresses were significantly increased by roughness beyond the roughness sublayer. It was observed that the population, sizes and the level of organization of hairpin vortices varied with roughness and more intense quadrant events were found over the smooth wall than the rough walls. APG reinforced wall roughness in augmenting the equivalent sand grain roughness height, turbulence production and Reynolds stresses. APG also reduced the sizes of the hairpin packets but strengthened the quadrant events in comparison to the results obtained in the parallel section. The secondary flow induced by inclined ribs significantly altered the distributions of the flow characteristics across the span of the channel. Generally, the mean flow was less uniform close to the trailing edge of the ribs compared to the flows at the mid-span and close to the leading edge of the ribs. The Reynolds stresses and hairpin packets were distinctly larger close to the trailing edge of the ribs. Rib inclination also decreased the drag characteristics and significantly modified the distributions of the Reynolds stresses and quadrant events. In the parallel section, the physical sizes of the hairpin packets were larger over 45° ribs whereas in the diverging section, the sizes were larger over perpendicular ribs.

The discrete-element method for predicting skin friction for turbulent flow over rough surfaces considers the drag on the surface to be the sum of the skin friction on the flat part of the surface and the drag on the individual roughness elements that protrude into the boundary layer. The discrete-element method considers heat transfer from a rough surface to be the sum of convection through the fluid on the flat part of the surface and the convection from each of the roughness elements. The discrete-element method has been widely used and validated for roughness composed of sparse, ordered, and deterministic elements. Modifications made to the discrete-element roughness method to extend the validation to real surface roughness are detailed. These modifications include accounting for the deviation of the roughness element cross sections from circular configurations, determining the location of the computational "surface" that differs from the physical surface, and accounting for temperature changes along the height of the roughness elements. Two randomly-rough surfaces found on high-hour gas-turbine blades were characterized using a Taylor-Hobson Form Talysurf Series 2 profilometer. A method for using the three-dimensional profilometer output to determine the geometry input required in the discrete-element method for randomly-rough surfaces is presented. Two randomly-rough surfaces, two elliptical-analog surfaces, and two cone surfaces were generated for wind-tunnel testing using a three-dimensional printer. The analog surfaces were created by replacing each random roughness element from the original randomly-rough surface with an elliptical roughness element with the equivalent planorm area and eccentricity. The cone surfaces were generated by placing conical roughness elements on a flat plate to create surfaces with equivalent values of centerline-averaged height or root-mean-square (RMS) height as the randomly-rough surfaces. The results of the wind tunnel skin friction coefficient and Stanton number measurements and the discrete-element method predictions for each of the six surfaces are presented and discussed. For the randomly-rough surfaces studied, the discrete-element method predictions are within 7% of the experimentally measured skin friction coefficients. The discrete-element predictions are within 16% of the experimentally measured Stanton numbers for the randomly-rough surfaces.

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

Roughness noise can be a significant contributor of sound in low Mach number, high Reynolds number flows. Only a small amount of experimental research has been conducted to analyze roughness noise because of its often low energy levels that are hard to isolate even in a laboratory setting. This study details efforts to scale the roughness noise while independently varying roughness size and edge velocity. Measurements were taken in the Virginia Tech Anechoic Wall Jet Facility for stochastic rough surfaces varying from hydrodynamically smooth to fully rough as well as deterministic rough surfaces including 1mm and 3mm hemispheres and a 2D wavy wall. Inner and outer variable normalizations were applied to recorded far field data in an attempt to find specific driving variables of the roughness noise. Also, a newly formulated derivation that attempts to scale the far field sound from a single point wall pressure measurement was used to collapse the far field noise. From the results, the inner and outer variable scalings were unable to collapse the noise generated by all velocities and roughness sizes. The changing spectral shapes of noise generated by rough surfaces with significantly varying wavenumber spectra make it impossible to scale the produced noise using the proposed inner and outer variable scalings. They use only one a single scaling value for the entire frequency range of each spectrum. The analyzed wall pressure normalization, which is inherently frequency dependent, produces a tight collapse within the uncertainty of the measurements for all rough surfaces studied except the larger hemispherical roughness which had individual elements that dominated the surrounding region of the wall pressure microphone. This indicates that the roughness generated noise is directly proportional to the wall pressure spectrum. The collapsed data displayed a slope of Ï ^2, the expected dipole efficiency factor. This is the clearest confirmation to date that the roughness noise source is of a dipole nature. / Master of Science

The present study deals with the effects of sparsely distributed three-dimensional elements on two-dimensional (2-D) and three-dimensional (3-D) turbulent boundary layers (TBL) such as those that occur on submarines, ship hulls, etc. This study was achieved in three parts: Part 1 dealt with the cylinders when placed individually in the turbulent boundary layers, thereby considering the effect of a single perturbation on the TBL; Part 2 considered the effects when the same individual elements were placed in a sparse and regular distribution, thus studying the response of the flow to a sequence of perturbations; and in Part 3, the distributions were subjected to 3-D turbulent boundary layers, thus examining the effects of streamwise and spanwise pressure gradients on the same perturbed flows as considered in Part 2. The 3-D turbulent boundary layers were generated by an idealized wing-body junction flow. Detailed 3-velocity-component Laser-Doppler Velocimetry (LDV) and other measurements were carried out to understand and describe the rough-wall flow structure. The measurements include mean velocities, turbulence quantities (Reynolds stresses and triple products), skin friction, surface pressure and oil flow visualizations in 2-D and 3-D rough-wall flows for Reynolds numbers, based on momentum thickness, greater than 7000. Very uniform circular cylindrical roughness elements of 0.38mm, 0.76mm and 1.52mm height (k) were used in square and diagonal patterns, yielding six different roughness geometries of rough-wall surface. For the 2-D rough-wall flows, the roughness Reynolds numbers, based on the element height (k) and the friction velocity, range from 26 to 131. Results for the 2-D rough-wall flows reveal that the velocity-defect law is similar for both smooth and rough surfaces, and the semi-logarithmic velocity-distribution curve is shifted by an amount depending on the height of the roughness element, showing that this amount is a function of roughness Reynolds number and the wall geometry. For the 3-D flows, the data show that the surface pressure gradient is not strongly influenced by the roughness elements. In general, for both 2-D and 3-D rough-wall TBL, the differences between the two roughness patterns (straight and diagonal), as regards the mean velocities and the Reynolds stresses, are limited to about 3 roughness element heights from the wall. The study on single elements revealed that the separated shear layers emanating from the top of the elements form a pair of counter rotating vortices that dominate the downstream flow structure. These vortices, termed as the roughness top vortex structure (RTVS), in conjunction with mean flow, forced over and around the elements, are responsible for the production of large Reynolds stresses in the neighborhood of the element height aft of the elements. When these elements are placed in a distribution, the effects of RTVS are not apparent. The roughness elements create a large region of back flow behind them which is continuously replenished by faster moving fluid flowing through the gaps in the rough-wall. The fluid in the back flow region moves upward as low speed ejections where it collides with the inrushing high speed flow, thus, leading to a strong mixing of shear layers. This is responsible for the generation of large levels of turbulent kinetic energy (TKE) in the vicinity of the element height which is transported, primarily, by turbulent diffusion. As regards the 3-D rough-wall TBL, the effect of flow three-dimensionality is seen in the large skewing of the distributions of mean velocities, Reynolds stresses and TKE, aft of the elements. In general, the regions of large TKE production-rates seem to propagate in the direction of the local velocity vector at the element height. The data-sets also enable the extraction of the turbulent flow structure to better describe the flow physics of these rough-wall turbulent boundary layers. / Ph. D.

In this thesis, wall-resolved and wall-modeled large-eddy simulation (LES) have been employed to investigate turbulent flow and dispersion around a single and a group of wall-mounted bluff bodies which are partially and fully submerged in developing boundary layers, respectively. The dispersion is caused by a continuous release of a passive scalar from a ground-level point source located within the matrix of obstacles. The results have been validated through comparisons against the available experimental measurement data. Thorough physical analysis including investigation of the spatial evolution and temporal cascades of the kinetic and scalar energies, flow structures and their influences on dispersion of the concentration plume in the context of highly disturbed flows, and study of turbulence statistics for the flow and concentration fields have been performed to provide deeper insights into turbulent flow and dispersion in domains with complex geometries. An in-house code based on FORTRAN programming language, parallelized with MPI libraries has been developed, modified and optimized for conducting the simulations. The simulations have been conducted on public-domain supercomputers ofWest-Grid, specifically Orcinus and Grex, and also the local 256-core cluster system of the CFD LAB at the University of Manitoba.

The velocity fields of high Reynolds number, turbulent, wall boundary layers in non-equilibrium pressure gradients are experimentally investigated. Experiments in two wall configurations were performed; one with a hydrodynamically smooth test wall composed of flat aluminum panels, and the other with a rough surface consisting of 2 mm tall, staggered, circular cylindrical elements. A representative set of pressure gradient distributions were generated on the research wall by a systematically rotated NACA 0012 airfoil placed in a wind tunnel section to determine the functional dependence of the boundary layer formation on pressure gradient. Particle image velocimetry (PIV) was the primary measurement technique used to determine time-resolved features of the velocity flow field. newline{}newline{} It is shown that regardless of wall condition and Reynolds number, the non-equilibrium turbulent boundary layers exhibit increasingly non-local behavior with streamwise development. This is apparent as a lag to the pressure gradient distribution observed in the streamwise developing integrated boundary layer parameters. These ``history effects" are also prevalent in mean velocity profiles which are exhibited as a cross-over of the favorable and adverse pressure gradient profiles in the logarithmic layer. Similar cross-over points are observed in the Reynolds shear and normal stresses, particularly at the streamwise station downstream of the pressure gradient switch. The primary effect of the rough wall is to increase the magnitude of flow scales, and, while they exhibit the same qualitative history effects as the smooth wall, the rough wall flows show an earlier relaxation to equilibrium. Despite inherent uncertainties of indirect skin friction methods for the rough wall, the effective sandgrain roughness parameter k_s does not show a functional dependency to pressure gradient history. An evaluation of the wall-similarity hypothesis solely based on boundary layer thickness to roughness parameter ratios delta/k_s is insufficient and additional parameters such as pressure gradient histories, local roughness Reynolds numbers, and bias uncertainties due to instrument spatial resolution must be considered. / Doctor of Philosophy / In the interface between a surface and a moving fluid is the boundary layer where high shear and viscous stresses cause the bulk velocity to decrease to zero. When turbulent, this region of fluid is characterized by random, chaotic, and fluctuating motions of varying sizes. Parameters such as pressure gradients and geometric irregularities of the surface, referred to as roughness, can increase fluctuating pressures and velocities within the boundary layer and cause unwanted noise, vibration, and increased drag. Although many studies have evaluated boundary layers with either roughness or pressure gradient independently, most surfaces in practical application are susceptible to the compounding influences of both of these parameters. Thus, it is necessary to expand the current knowledge database to include complex flow fields necessary to improve data driven modeling and vehicle design.newline{}newline{} This study focuses on experimental observations of the turbulent velocity field developing in both a rough and smooth wall boundary layer that is induced to a family of bi-directional pressure gradients generated by the pressure field of a rotating airfoil inside in a wind tunnel. Through statistical observations of the velocity field it was found that the varying pressure gradients caused the flow to develop non-local dependencies such that the response of the downstream boundary layer was dependent on the upstream flow history. The principal effect of roughness was to increase the magnitude of turbulent scales, but to show the same qualitative response to the pressure gradient history as seen in a smooth wall flow. However, direct comparison of rough and smooth wall turbulence statistics by means of the ``wall-similarity hypothesis" requires careful consideration of multiple parameters including these flow histories, scales prescribed by roughness parameters, and bias errors from experiment under-resolution of the velocity field.

The far field acoustics generated by turbulent flow over rough surfaces has been experimentally investigated in an acoustically treated wall jet facility. The facility allows direct measurement of the far field sound from small patches of surface roughness, without contamination from edge or other aerodynamic noise sources. The facility is capable of generating turbulent boundary layer flows with momentum thickness Reynolds numbers between 450 and 1160. The variation of surface conditions tested cover the range from hydrodynamically smooth surfaces through most of the transitional range, with h+ variations from 3 to 85. Single microphone narrow band acoustic spectra, measured in the far field, show sound levels as much as 15 dB above the background from 0.186 m2 roughness patches. The measurements revealed the spectral shape and level variations with flow velocity, boundary layer thickness, and roughness size; providing the first data set large enough to assess the affects of many aerodynamic properties on the acoustic spectra. Increases in the size of grit type roughness produced significant increases in acoustic levels. Patches of hydrodynamically smooth roughness generated measurable acoustic levels, confirming that acoustic scattering is at least one of the physical mechanisms responsible for roughness noise. The shapes of the measured spectra show a strong dependence on the form of the surface roughness. The acoustic spectra generated by periodic two-dimensional surfaces have a much narrower louder peak than that generated by three-dimensional grit type roughness. Measurements also show the orientation of the two-dimensional surface significantly affects the acoustic levels and directivity. The variation of sound levels with flow velocity and roughness size suggests the acoustic field is significantly affected by changes in the near wall flow due to the presence of the roughness. Current models of noise generated by rough surfaces predict the general trends seen in measurements for flows over grit and two-dimensional roughness in the range of 20<h+<50. However, in cases with a low Reynolds number or large grit size, where the roughness is likely to significantly affect the hydrodynamic pressure field, the scattering models did not perform as well. / Ph. D.

There have been very few studies investigating the rough wall pressure spectra under fully rough flows, which are relevant to many common engineering applications operating within this regime. This investigation uses the Virginia Tech Stability Wind Tunnel to perform experiments on a series of high Reynolds number zero pressure gradient turbulent boundary layers formed over rough walls in an effort to better understand and characterize the behavior of the rough wall pressure spectrum. The boundary layers were fully rough, and the boundary layer height remained sufficiently larger than the height of the roughness elements. Two rough surfaces were tested. One consisted of an array of 1-mm ordered hemispherical elements spaced 5.5-mm apart, and the other contained 3-mm hemispherical elements randomly spaced, but with the same element density as 1/3 of the 1-mm ordered roughness. The wall pressure spectrum and its scaling were then studied in detail, and it was found that the rough wall turbulent pressure spectrum at vehicle relevant conditions is defined by three scaling regions. One of which is a newly discovered high frequency scaling defined by viscosity, but controlled by the friction velocity adjusted to exclude the pressure drag on the roughness elements. Based on these three scaling regions an empirical model describing the wall pressure spectra for hydraulically smooth, traditionally rough, and fully rough flows was explored. Two point wall pressure fluctuations were also analyzed for each surface condition, and it was found that the roughness inhibits the convective velocities within the inner portions of the boundary layer. / Master of Science