Experimental studies were conducted to obtain direct measurements of skin friction, mean velocity profiles, axial and normal turbulence intensity profiles, and Reynolds stress profiles in the boundary layer on a large diameter, axisymmetric body with a smooth, solid surface; a sandpaper-roughened, solid surface; a sintered metal, porous surface; a"smooth", perforated titanium surface, a solid, rough Dynapore surface made of diffusion-bonded screening, and a porous, rough Dynapore surface. The roughness values were in the low range (k⁺ = 5-7) just above what is normally considered"hydraulically smooth. 11 Measurements were taken at several axial locations and two different freestream velocities corresponding to dynamic pressures of 12.7 and 17.8 cm. of H₂O, which gives a Re_𝓁 range of 2.93 x 10⁶ to 3.38 x 10⁶. For the Law of the Wall, Defect Law, and the turbulence quantities, very good agreement was found between the present results and those from well-established studies for a solid, smooth surface. The sandpaper-roughened, solid wall and solid, rough Dynapore wall tests showed a 20%~30% increment in local skin friction and a slight shift in the log region of the Wall Law, as well as an increase in turbulence quantities over the smooth wall results. These results were in accord with the classical results collected by Clauser for rough, solid surfaces in this range. The effect of porosity can be shown by comparing the sintered metal, porous wall results to the sand-roughened, solid wall results. Although there is a difference in roughness patterns for these two cases, the average k⁺ is in the same range of 5 ~ 7. To check the effect of porosity directly without any interference of different surface roughness patterns, one can compare the results between the 11 smooth 11 perforated titanium wall and the solid, smooth wall, or between the porous Dynapore and solid Dynapore walls. The effect of porosity showed a 30%~40% increment in local skin friction and a marked downward shift of the logarithmic portion of the Wall Law, as well as an increase in turbulence quantities over the smooth wall results. The combined effects of small roughness and porosity could be seen by comparing the results between the sintered metal, porous wall and the smooth, solid wall, or between the porous Dynapore wall and the smooth, solid wall. It was observed that the combined effects of small roughness and porosity are roughly additive. The effect of porosity due to the existence of the penetration of turbulence through the porous surfaces was detected experimentally by a hot-wire underneath the porous walls. All these results demonstrate that a rough, porous wall simply does not influence the boundary layer in the same way as a solid, rough wall. Therefore, turbulent boundary layer models with injection or suction must include both surface roughness and porosity effects. / Ph. D.

An examination of selected two- and three-dimensional turbulent boundary layer data sets was made to determine the consistency of these data sets with their appropriate momentum integral equations. Several turbulent boundary layer experiments were reviewed to determined which of these provided adequate data so that they could be examined using this method. The selected data sets were used to numerically integrate and compare the two sides of the appropriate momentum integral equations in an extension of the Coles' momentum integral (PL-PR) method originally derived for two-dimensional flow. The effects of small three-dimensionality in a nominally two-dimensional flow were also studied. Three-dimensionality due to converging or diverging collateral flow and converging or diverging skewed flow about a plane of symmetry was investigated. The momentum integral examination of two-dimensional and quasi two-dimensional data sets was verified to be a useful and convenient means of data set validation. Very small amounts of three dimensionality in a nominally two-dimensional flow could have large effects on and adversely affect the outcome of a momentum integral validation of the data set. Three-dimensionality of the order of magnitude of experimental uncertainty, in the form of collateral or skewed convergence/divergence of the flow at a plane of symmetry, was shown to have large adverse effects on the momentum integral validation. Investigations of arbitrary.three-dimensional flows were generally found to lack sufficient data to perform an accurate validation using this PL-PR technique extended to such flows. / Master of Science

Three-dimensional wind measurements and temperature measurements were obtained on a 250-foot meteorological tower located near the Atlantic Ocean at Wallops Island, Virginia. The type of flow measured approached the tower from the ocean resulting in a complex three-dimensional type of flow as it sees a change in roughness and a possible change in surface temperature when passing the shoreline. During warm summer afternoons, the stable air is heated from below, and an internal boundary layer (IBL) with an unstable stratification develops within the stable layer which originated over the ocean. As this flow moves inland the IBL grows vertically depending on changes in surface roughness and surface temperature. Eventually, far enough inland, the IBL replaces the original stable layer. The vertical heat flux is positive in the IBL and negative in the overlying inversion. The point where the heat flux changes sign corresponds to the height of the IBL. Measurements of the mean and turbulent flow quantities were made with a special computer-controlled data-acquisition system for the aforementioned type of flow. Data analysis includes the following statistical parameters: mean values, variances, covariances (heat flux and Reynold's stresses), spectra and cospectra. Nine, one-hour runs were analyzed and the results agreed closely with the suggested model. In addition, the spectra and cospectra measured in the IBL, as well as those from the overlying inversion layer, reduce to a family of curves when expressed in appropriate similarity coordinates. These results for moderately, thermally stratified flows compare quite well with the Kansas data which were obtained in the surface layer. The results for very stable flow (z/L > 2.0) do not follow the same trend as was established in the moderately stable range. / Master of Science

A review of the existing, more prominent velocity profile models for two and three-dimensional incompressible flows was presented, with emphasis placed on those that had previously shown their ability to correlate experimental data taken under various conditions. This review included velocity profile models that seemingly could represent flows in which the cross flow velocity vector reverses direction. The various methods of determining a wall shearing stress by semi-empirical considerations for two and three-dimensional flows was discussed. A direct measurement of the wall shearing stress in a three-dimensional flow field was used to infer the most accurate method of applying two-dimensional techniques to three-dimensional conditions in order to obtain reasonable values for the friction losses in a boundary layer. A discussion of the error in the determination of the skin friction coefficient by use of the Glauser Chart was presented. The experimental constants in the law of the wall formulation are shown to be the basis for an error which may be in excess of 15 per cent in the determination of the skin friction coefficient. Finally, a thorough comparison of the previously reviewed two and three-dimensional velocity profile models was made with some of the most complete sets of experimental data available to date. / Master of Science

Presented in this paper are experiments to test the hypothesis that drag reduction is possible over hydrophobic surfaces in the Wenzel state during laminar and turbulent flows. Quantification of surface drag reduction in rectangular channel flow over walls with specific hydrophobic or hydrophilic properties was obtained with pressure drop measurements along the channel for a range of Reynolds numbers between 350 and 5900. Several commercially available materials and coatings were chosen in order to span a range of contact angles between 30° and 135°. The results are within the bounds of the theoretical values calculated with the Colebrook equation, and do not show any reduction in wall shear stress as a function of material properties or surface chemistry. The differences between this experiment and others measuring pressure drop over hydrophobic surfaces is the macro-scale conditions and the hydrophobic surfaces being fully wetted. These experiments are further proof of the importance of a liquid-vapor interface for increasing the shear free area to produce drag reduction. / Master of Science

The present investigation was undertaken to determine experimentally whether or not instability of the laminar boundary layer on blunt convex bodies exists when the wall-to-stagnation temperature is lowered. It was found that instability existed and theoretical considerations are given to the transition being associated with the formation of ice on the model surface and with an increase in roughness Reynolds numbers due to thinning of the laminar boundary layer at low wall-to-stagnation temperature ratios. The experimental tests were conducted on two-inch diameter spheres at M = 4.95 and free-stream Reynolds numbers per foot of approximately 72. 5 x 10⁶ or 12.1 x 10⁶ based on the model base diameter. Data were obtained tor both the hot wall and cold wall case. The stagnation temperature was approximately 400° F. Initial model wall temperatures were 97°F, for the hot wall test and -320° F for the cold wall tests. / M.S.

Instability waves in a free shear layer formed by two parallei compressibie streams are analyzed using the linear spatial stability theory. Both viscous and inviscid disturbances are considered. The basic state is obtained by solving the compressibie laminar boundary-layer equations or is specified by the hyperbolic tangent velocity profile. The effects of viscosity, Mach number, the velocity and temperature ratios on the growth rate are determined. Unlike the boundary layer flow, viscosity has a stabilizing effect on the mixing layer flow. Increasing the temperature ratio produces a strong stabilizing effect on the growth of the mixing flow; this stabilization does not, however, persist at higher Mach numbers. Whereas the maximum growth rate of the Incompressible mixing layer varies linearly with the velocity ratio, the maximum growth rate of the compressible mixing flow varies nonlinearly with the velocity ratio. The numerical results substantiate the fact that the convective Mach number Is the appropriate parameter for correlating the compressibility effects on the spreading rate of the mixing layer. The ratio of the spreading rate of a compressible layer to that of an incompressible layer at the same velocity and density ratios depends primarily on the convective Mach number. Three-dimensional waves become important when the convective Mach number is greater than 0.6. The influence of nonparallelism on the spatial growth rate of two-dimensional disturbances is evaluated and is found to be negligible. Linear subharmonic Instabilities of a compressible mixing layer, which Is spatially periodic in a translating frame of reference, are analyzed by using Floquet theory. The basic state is obtained by the linear superposition ofa steady mean flow, which is given by a solution to the compressible boundary-layer equations or by a hyperbolic tangent velocity profile approximation, and the neutral primary wave of that mean flow. The results show that the growth rates of two-dimensional subharmonic instabilities (pairing mode) increase with increasing amplitude of the periodicity but decrease with increasing the convective iVIach number. In the incompressible flow case, the most amplified subharmonic wave is a two-dimensional mode, which is in agreement with the published results. For subsonic convective Mach numbers, the presence of the periodicity enhances the growth rates of three-dimensional subharmonic waves over a wide range of spanwise wavenumber which shows a preferred band over which the growth rate is maximum. However, when the convective IVIach number is greater than one, the interaction between the subharmonic wave and the primary wave marginally increases the maximum growth rate of the subharmonic. Nevertheless, that interaction dramatically increases the range of amplified spanwise wave numbers. Fourth-order compact finite-difference codes are developed for solving the compressible boundary-layer equations and investigating their primary and subharmonic instabilities. The codes proved to be very accurate and versatile. / Ph. D.

Static pressure and mean velocity data were obtained in a relaxing shear driven three-dimensional incompressible turbulent boundary layer flow produced by a swept rectangular step. The nominally 10 cm (4 in.) thick boundary layer had a freestream velocity of approximately 25 m/sec (80 ft/sec). The two steps investigated were each 3.8 cm (1.5 in.) high by 18.4 cm (7 .25 irt.) long and at angles of 30° and 45° to the transverse wind tunnel direction. Pressure gradients were determined by taking the derivative of least-squares curve fits to the static pressure data. Close to the trailing edge reattachment region, the maximum·gradient was·0.8 kPa/m (5 psf/f) for the 30° step and 0.4 kPa/m (2.5 psf/f) for the 45°step. As expected, a region of nominal pressure gradient (0.03 kPa/m or 0.2 psf/f compared to 1.6 kPa/m or 10 psf/f for a pressure driven flow) was found at greater than 36 cm (14 in.) down.stream of the trailing edge of each step. The wall crossflow angle decayed from 67° at 15 cm (6 in.) behind the trailing edge to 9° at 66 cm (26 in.) for the 30° step. In the same region, the crossflow angle decayed from 45° to 6° for the 45° step. The decay or relaxation was found to be much faster in the near-wall region and in the region close to the trailing edge. A defect in the streamwise velocity profiles indicated that the flow was dominated by the separation and reattachment over the step. For future shear driven investigations, a lower, more streamlined wing-type body is recommended to produce a moderately skewed boundary layer without dominant separation effects. / Master of Science

Static pressure, mean velocity, indirect wall shear from Preston tubes, direct wall shear using a two-dimensional (single line of action) floating element device, and direct wall shear measurements from an omnidirectional floating element capable of simultaneously determining magnitude and direction of a wall shear vector were completed over a modest range of two-dimensional, (near-zero) pressure gradient flows. Static pressure, mean velocity, and direct wall shear measurements using the omnidirectional meter were completed in a pressure driven, and two different shear driven three-dimensional flows. These data were combined to evaluate ten of eleven three-dimensional similarity models found in the literature. Uncertainty estimates on all the data are presented. Two-dimensional experimental results show that the constants in the two-dimensional law of the wall formula appear to be slightly dependent on Reynolds number, and the Patel calibration formulas for Preston tubes to be better than any other available formulas. Three-dimensional results show (1) the Perry and Joubert and the White, Lessmann, and Christoph three-dimensional similarity models to give limited but overall better agreement with experimental data, (2) none of the proposed models adequately model experimental results for y⁺ < 50, (3) near-wall collateral flow does not exist, and (4) pressure gradient effects on the omnidirectional meter appear to be negligible. / Ph. D.

Wind speed data of multi-heights have been examined to investigate the spatial and temporal characteristics of coherent structures in the near neutral marine atmospheric surface layer. With Taylor's hypothesis, the temporal velocity signals have been transformed to spatial fluctuations and then visualize these spatial velocity fluctuations to identify the coherent structures. It has been confirmed that there exist similar coherent structures in the marine atmospheric surface layer to those in laboratory turbulent boundary layer. These similar coherent structures include ejections, sweeps, shear layers, transverse vortices, and combined events of the shear layers and transverse vortices. Besides these similar coherent structures, there exist the plume and downdraft motions in the unstable marine atmospheric surface layer. It has been observed that the streamwise spatial length of the ejections and sweeps is 20-250 m and their mean frequency is of order of 0.01-0.001 /s at mean wind speed of 5-12.6 m/s. Between the region of the upstream ejection and downstream sweep motions an inclined shear layer is often seen. The inclined angle of the shear layer has been observed to vary from 30 to 70 degree with the height and length of the the shear layer. The transverse vortices are seen to exist in every region from the wall up to a height of 45 m and their diameter is up to 40 m. The mean frequency of the shear layers and the transverse vortices is of order of 0.001 /s. In the fully developed stage of the combined event of the shear layer and transverse vortex, the shear layer is generally longer and the diameter of the transverse vortex is larger. The mean frequency of the combined event of the shear layers and the transverse vortices is of order of 0.001 /s. The streamwise spatial length of the plume and downdraft motions is generally from 20 m to 50 m. Analysis indicates that the mean wind speed is a dominant factor in affecting the spatial and temporal characteristics of the coherent structures in the near neutral marine atmospheric surface layer. As the mean wind speed increases, the frequency of the shear related coherent events will increase, while the frequency of the buoyancy related coherent events (plumes and downdrafts) will decrease. The temperature difference between higher level of the surface layer and sea surface is the second main factor in affecting the spatial and temporal characteristics of the coherent structures. As the marine atmospheric surface layer becomes more stable the coherent motions will be suppressed. The effect of the temperature difference on the buoyancy related plume and downdraft motions is more evident than on the other shear related coherent motions. / Master of Science