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Several aspects of the subharmonic instability of boundary layers are studied. First, the subharmonic instability of incompressible flows over a flat plate is investigated using the resonant triad model and the Floquet model. The primary wave is taken in the form of a two-dimensional (2-0) Tollmien-Schlichting (T-S) wave. The subharmonic wave is taken in the form of a three-dimensional (3-D) wave. Results from both models are presented and compared with the experimental data and numerical simulation. It is found that the results of the Floquet model are in good agreement with the experimental data and numerical simulation, whereas the results of the resonant triad model agree only qualitatively with the experimental data. Second, the subharmonic instability of incompressible flows over a 2-0 hump is studied using the Floquet model. The mean flow over the hump is calculated by using interacting boundary layers, thereby accounting for viscid/inviscid interactions. The results show that increasing the hump height results in an increase in the amplification factors of the primary and subharmonic waves. When the hump causes separation, the growth rates of both the primary and subharmonic waves are considerably larger than those obtained in the case of no separation. Third, the subharmonic instability of compressible boundary layers over a flat plate is studied using the Floquet model. Results are presented for adiabatic wall boundary conditions and subsonic, transonic, and supersonic flows. For supersonic flows results are presented for first- and second-mode primary waves. The effect of Mach number, spanwise wavenumber, primary-wave amplitude, Reynolds number, and frequency are studied. Fourth, results for the effect of heat transfer on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented for different Mach numbers. For supersonic flows results are presented for first- and second-mode waves. The effect of different levels of heat transfer on changing the features of the subharmonic compressible instability is evaluated. Fifth, results for the effect of suction on the subharmonic instability of a two-dimensional compressible boundary layer over a flat plate are presented. It is found that when the primary wave is a first-mode merging with a second-mode, the subharmonic wave is strongly destabilized by suction. Sixth, the effect of a bulge on the subharmonic instability of compressible boundary layers is studied. It is found that the effect of compressibility on reducing the growth rate of the disturbances weakens as the hump height increases. / Ph. D.

An experiment has been conducted to examine the generation and subsequent evolution of boundary-layer disturbances on a two-dimensional airfoil up through transition to turbulent flow. The experiment was conducted at the NASA Langley Research Center "2 ft by 3 ft Low Speed Wind Tunnel Facility." The primary objective of the experiment was to generate a comprehensive database that includes the effect of the external disturbance environment on the transition process and can be used as a benchmark for future transition prediction tools. The airfoil used for this experiment was custom designed. The model was a 6% thick, 4-ft chord unswept symmetric wing. A description of the design procedure, along with the theoretical stability characteristics of the airfoil will be presented in this paper. The experiment consisted of establishing the mean flow conditions, forcing two-dimensional Tollmien-Schlichting (T-S) waves in the boundary layer using modulated acoustic bursts in the free-stream, and acquiring the mean boundary-layer data and fluctuating disturbance data using hot-wire probes. The acoustic receptivity due to surface roughness near Branch I has been examined. The surface roughness consisted of two-dimensional strips of tape applied at and symmetrically spaced about Branch I. Repeated roughness elements were spaced one wavelength apart based upon the wavelength of the primary forcing frequency as determined by linear-stability theory. The test conditions consisted of mean flow velocities of 15 and 20 m/s, which correspond to chord Reynolds numbers of 1.25 and 1.68 million, respectively. Boundary-layer disturbance profiles and constant boundary-layer height chordwise traverses were acquired and examined at individual frequencies and in total energy amplitude / broadband forms. The experimental results match well with linear stability theory and linear parabolized stability equations, indicating breakdown of disturbances between N-factors of 7 and 11 with surface roughness on the model. It was observed that when the flow physics change, differences between linear-stability theory and experiment are strongly apparent. An amplitude-based breakdown criterion was defined for the developing boundary-layer responses, which were burst-type packets like the acoustic forcing signal. A criterion was defined for the breakdown of both maxima of the T-S-like disturbance profile. Overall, the effects of surface roughness and free-stream acoustic forcing on boundary-layer receptivity and stability were examined in a well-documented disturbance environment. These results will be used to validate and refine non-linear flow theories as well as help to provide an improved understanding and improved methods to control flow transition. / Ph. D.

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

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.