An expression for the static temperature-velocity distribution for a zero pressure gradient turbulent boundary layer is derived based on the differential equations for local heat transfer and shear. The present theoretical method of computation is found to give results that correspond well with available experimental temperature velocity distributions. / Master of Science

The vorticity shedding characteristics in attached and separated regions were investigated over three configurations, namely a backward facing circular arc, an ellipse at an angle of attack and a pitching airfoil. A fully automated data acquisition system was developed, including a two-component Laser-Velocimetry system in backscatter mode, an accurately controlled traversing mechanism and a MINK-11 minicomputer. Two-component velocity measurements were obtained over the above mentioned bodies, with steady and unsteady free streams. Emphasis was concentrated on the separation region, the free-shear layers and the wake downstream of these bodies. Two inviscid vortex models were developed to predict two different flow phenomena, namely the separated flow over a circular cylinder started impulsively from rest and propagating stall over a linear stationary cascade. / Ph. D.

Following the concepts of stability analysis, a study is made of the pre-breakdown stage of transition to turbulence in boundary layers. The first step consists of a ’decoupling’ of the primary and secondary instabilities. A perturbation method is used to solve for the primary wave, in the absence of any secondary disturbances. Once the wave is calculated, it is decomposed into a basic flow portion and an interaction portion. The basic flow portion acts as a parametric excitation for the secondary wave. The interaction portion then captures the resonance effects of the secondary back onto the primary. A perturbation method is also used for the secondary and interaction components. The results obtained are in three principal forms: Landau constants, amplitude growth curves, and velocity functions. While in good agreement with experiments and simulations, these results offer new explanations to the observed processes. In addition, a physically-based transition criteria is established. / Ph. D.

The linear stability equations which govern the growth of small periodic disturbances for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The parallel flow assumption is utilized in the derivation. The system of equations is solved using a finite difference scheme similar to that in a current state-of-the-art stability analysis code, COSAL. The LR method and the inverse Rayleigh iteration procedure are used to calculate the eigenvalues. The stability of the three-dimensional compressible laminar boundary layer including the effects of streamline and surface curvature for flows past swept wings where crossflow type disturbances dominate is calculated. A parametric study is performed varying Reynolds number and sweep angle on an airfoil with a concave cutout in the leading edge region of the lower surface. It is known that convex curvature has a stabilizing effect on the laminar boundary layer. Conversely, concave curvature has a destabilizing effect. The magnitude of these effects for swept wing flows is determined. Non-stationary as well as stationary disturbances are calculated, and the most amplified frequencies are identified. N-factor correlations at the measured location of transition are made utilizing flight test data. Results indicate that amplification rates and hence, N-factors, for swept wing flows over convex surfaces are reduced by about 30 to 50 percent when curvature effects are included in the linear stability analysis. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface. The results of the calculations show that concave curvature destabilizes "crossflow” type disturbances with a 30 percent increase in amplification rate. / Ph. D.

An investigation is conducted into the effect of cooling and suction on the stability of subsonic flows over two-dimensional roughness elements and supersonic flows over flat plates. First, the effect of wall cooling on the two-dimensional linear stability of subsonic flows over two-dimensional surface imperfections is investigated. Results are presented for flows over smooth humps and backward-facing steps with Mach numbers up to 0.8. The results show that, whereas cooling decreases the viscous instability, it increases the shear-layer instability and hence it increases the growth rates in the separation region. The coexistence of more than one instability mechanism makes a certain degree of wall cooling most effective. For the Mach numbers 0.5 and 0.8, the optimum wall temperatures are about 80% and 60% of the adiabatic wall temperature, respectively. Increasing the Mach number decreases the effectiveness of cooling slightly and reduces the optimum wall temperature. Second, the effect of suction on the stability of compressible flows over backward-facing steps is investigated. Mach numbers up to 0.8 are considered. As expected, suction considerably reduces the separation region. The results show that continuous suction stabilizes the flow outside the separation bubble, as expected, but it destabilizes the flow inside it. Nevertheless, the overall N factor decreases as the suction level increases. This is due to the considerable reduction in the separation bubble. For the same suction flow rate, properly distributed suction strips are more effective in stabilizing the flow than continuous-suction distributions. Furthermore, the size of the separation bubble, and hence its effect on the instability, can be considerably reduced by placing strips with high suction velocities in the separation region Third, the effect of suction on the stability of supersonic and hypersonic boundary layers is investigated. Calculations are performed for non-similar and self-similar boundary layers. The variation of the maximum growth rate with Mach number at low levels of suction is different from that at high levels of suction. This is due to the coexistence of viscous and inviscid instability mechanisms in supersonic and hypersonic boundary layers. Suction is more effective in stabilizing the viscous instability, and hence it is more effective at low Mach numbers. Although suction decreases the maximum growth rate of second-mode waves, small levels of suction increase the growth rates of disturbances having certain frequencies. On the other hand, first-mode waves are stabilized by suction at all frequencies. Constant-suction distributions considerably move the critical Reynolds numbers of second-mode waves to higher values while the critical Reynolds numbers of first-mode waves are not sensitive to suction. / Ph. D.

A three dimensional, pressure driven turbulent boundary layer created by an idealized wing-body junction flow is experimentally studied. The body used is a 3 : 2 elliptical nosed NACA 0020 tailed symmetric profile which has a chord length of 30.5 cm (12 inches), maximum thickness of 7.17 cm (2.824 inches) , height of 22.9 cm (9.016 inches). The body was sitting on a flat plate. The nominal reference velocity of the flow is 27 m/sec and the Reynolds number based on the momentum thickness at 0.75 chord upstream of the body on the centerline of the tunnel is ≃ 5936. The data presented include time-mean static pressure, skin friction magnitude and direction on the wall, as well as the mean velocity and all Reynolds stresses at several stations on a line determined with the mean velocity vector component parallel to the wall in the layer where the u²¯ normal stress is maximum. The mean velocity and stress data were obtained both with hot-wire ( HW ) and laser-Doppler-velocimeter ( LDV ) techniques. The LDV measurements were taken twice due to the differences observed between the HW and LDV data, which is also shown with the present study. This gave a chance to study the uncertainties on the mean velocity and the stresses extensively. Pressure distributions on the wing and the on the bottom plate were obtained with a Scanivalve and an inclined manometer. Skin friction vectors at several locations on the wall were measured in another study done by Allinger ( 1990 ) with a laser interferometer technique. The data show that the eddy viscosity of the flow is not isotropic, but the ratio of eddy viscosities perpendicular and parallel to the direction of the mean velocity vector component parallel to the wall at the point in the layer where u²¯ is maximum is close to unity, and the shear-stress vector direction in the flow lags behind the flow gradient vector direction. A₁, Townsend's structural parameter is not a constant of 0.15 as expected. The production of the turbulent kinetic energy and shear stresses are important below the logarithmic regions of the U axial velocity component profiles. The skin friction velocity is not the scale of the turbulence in such a flow. Further, a collection of 3-D turbulent boundary layer data including the present study is used to investigate the concept of the Law of the Wall velocity profile and the limitations of eddy-viscosity turbulence models in 3-D flows. For this purpose, several Law-of-the-Wall velocity profile models and eddy-viscosity models were tested. Johnston's Law-of-the-Wall relation and, for the pressure-driven flows the Johnson-King eddy-viscosity model and for the shear-driven flows Patel's eddy-viscosity model are most promising. / Ph. D.

The transport of small particles across the aerodynamic boundary layer that developed over a smooth, flat, acrylic plate and their subsequent deposition was investigated. The velocity boundary layer over the flat plate was characterized for a wind tunnel mainstream velocity of 2 m/s. Particle deposition was quantified with respect to location on the experimental plate with a microscope. The deposition of 0.8, 0.9, 1.1, and 2.0 micron diameter unit density, polystyrene latex microspheres on to oil-coated, uncoated, upper, and lower surfaces was investigated. Although experimental deposition velocities exhibited run-to-run variation, they were significantly greater than those reported in the literature. A turbulent flow deposition model which included eddy diffusion, Brownian diffusion, inertial, and gravitational deposition mechanisms underestimated the experimental deposition velocities. The experimental plate was nonconductive and could not be electrically grounded. It appears the electrostatic attraction mechanism was responsible for the increased experimental deposition velocities; this mechanism was not included in the deposition model. There was no significant resuspension of 42 micron diameter microspheres deposited to an initially moist experimental plate after 6 hours in the wind tunnel at a mean air velocity of 2 m/s. / Ph. D.

The strongly time variant flow in an incompressible, turbulent junction vortex formed at the base of a streamlined cylinder with a circular leading edge placed normal to a flat surface was investigated. The investigation centered around spectral analysis and time resolved measurements of the velocity fluctuations to characterize the time variant flow on the plane of symmetry. All the measurements were performed with a two-color, two-component, frequency shifted laser Doppler velocimeter. Spectral analysis methods for randomly sampled data occurring from the LDV were evaluated under various simulated and real flow situations. The real flow situations studied were the vortex shedding flow behind a cylinder and the two-dimensional turbulent boundary layer. The spectral estimates obtained from the discretized lag product method were found to be better than those obtained from the direct transform method. It was found that the exact lag product method does not offer significant improvements in the spectral estimates to offset its computational slowness. The mean velocity vectors in the junction vortex showed a single vortex on the plane of symmetry and a singular separation point upstream of the cylinder. The time resolved measurements showed the instantaneous separation point on the plane of symmetry to be randomly oscillating between two limits. Maximum possible excursions of the junction vortex position and size were also obtained form the time resolved measurements. The turbulence intensities in the junction vortex were found to be at least two to three times higher than typical two-dimensional boundary layer values. The histograms of instantaneous velocity fluctuations deviated from the expected Gaussian distributions and were found to have multiple peaks. The spectral content of the junction vortex flow was investigated. The overall character of the junction vortex flow was found to be similar to a two-dimensional turbulent boundary layer, with greater amplification perceived in the lower frequencies relative to the higher frequencies. The spectra at locations above the time mean center of the junction vortex showed distinct peaks around 20-30 Hz, unlike boundary layer flows. / Ph. D.

An experimental study of the incompressible, three-dimensional, turbulent flow separation around the base of a bluff obstacle on a flat surface is described. The bluff obstacle is a streamlined, right circular cylinder mounted with its axis normal to the flat surface. The flow environment is characterized by a body Reynolds number of 183,000, based on the diameter of the circular cylinder. The study includes surface flow visualizations, surface pressure measurements, and mean flow measurements. The mean flow measurements consist of total pressure, static pressure, and velocity distributions in three planes around the base of the streamlined cylinder. The results show the presence of a large, dominant vortex in the junction between the cylinder and the flat surface. This vortex was found to consist of low total pressure fluid from the boundary layer flow upstream of the junction. In addition to the three-dimensional flow measurements, extensive measurements in the two-dimensional turbulent boundary layer on the flat surface are reported. These results show the existence of small, but statistically significant, spanwise variations in the nominally two-dimensional turbulent boundary layer. A systematic approach for estimating the wall shear stress from velocity profile data in a two-dimensional turbulent boundary layer based on the method of least squares is presented. / Ph. D.

Three-dimensional (3D) turbulent boundary layers (TBLs) are ubiquitous in most engineering applications, but most turbulence models used to simulate these flows are built on two-dimensional turbulence theory, limiting the accuracy of simulation results. To improve the accuracy of turbulence modeling capabilities, a better understanding of 3DTBL physics is required. This dissertation outlines the experimental investigation of the attached 3D TBL flow over the Benchmark Validation Experiments for RANS/LES Investigations (BeVERLI) Hill using laser Doppler velocimetry in the Virginia Tech Stability Wind Tunnel. The mean flow and turbulence behavior of the boundary layer are studied and compared with turbulence theories to identify the validity of these assumptions in the BeVERLI Hill flow. It is shown that the pressure gradients and curvature of the hill have a significant effect on the turbulence behavior, including significant history effects at all stations due to the changing pressure gradient impact through the height of the boundary layer. Supplementing the experimental results with analysis from rapid distortion theory and simulations, it is shown that the stations lower on the hill are significantly affected by the non-linear history effects due to the varying upstream origins of the flow passing through those stations. Stations closer to the hill apex pass through a region of extremely strong favorable pressure gradient and hill constriction, resulting in behavior that matches qualitatively with the results from rapid distortion theory and provides insights into the physical mechanisms taking place in these regions of the flow. Despite the misalignment of the mean flow angle (γ_FGA) and turbulent shear stress angle (γ_SSA) throughout all of the profiles, the proposed 3D law of the wall of van den Berg (1975), which incorporates pressure gradient and inertial effects and relies on the assumption that γ_FGA=γ_SSA, is able to predict the flow behavior at more mildly non-equilibrium stations. This suggests that models that currently rely on assumptions founded on the two-dimensional law of the wall could be improved by incorporating van den Berg's model instead. The total shear stress distribution at selected stations on the BeVERLI Hill are all significantly reduced below equilibrium two-dimensional (2D) levels, indicating that turbulence models built on this assumptions will not be able to accurately simulate the 3D turbulence behavior. / Doctor of Philosophy / As an object moves through a fluid or a fluid moves past an obstacle, fluid sticks to the solid boundary of the object because of the fluid's viscosity, resulting in zero velocity on the surface (known as the "no-slip" condition). There then exists a region where the flow velocity increases from zero to the freestream velocity - this region is known as the boundary layer. The nature of the boundary layer developing around a body significantly influences how the body and fluid interact and is critical to practical items of engineering interest, such as estimating how much drag a vehicle will experience. Most bodies of engineering interest are three-dimensional (3D), like an aircraft or a car, and thus induce a three-dimensional boundary layer, but many turbulence theories used in computational fluid dynamics simulations are based on simplified two-dimensional (2D) flow behavior studied in laboratories. To further improve the accuracy of simulations, a better understanding of three-dimensional turbulent boundary layer flows is required. This dissertation outlines a study of three-dimensional turbulent flows by analyzing the three-dimensional turbulent boundary layer over the Benchmark Validation Experiments for RANS/LES Investigations (BeVERLI) Hill using laser Doppler velocimetry (LDV) in the Virginia Tech Stability Wind Tunnel. LDV uses the Doppler shift principle to measure the fluid velocity and turbulence at different points in the flow. Through analysis of the fluid velocity and turbulence in the flow, it is shown that the turbulence and flow behavior at certain stations are heavily influenced on the upstream flow history. Stations closer to the bottom of the hill are more influenced by the upstream flow history, while stations closer to the top of the hill experience such strong acceleration due to the local favorable pressure gradient and hill curvature that the upstream history has a more linear influence. In general, the turbulence on the hill is reduced due to the acceleration over the surface below 2D levels and does not match with the 2D fundamental relationships often used in turbulence theories for simulations. Thus, simulations that rely on these assumptions will not be able to accurately predict the details of the 3D flow. A proposed 3D model for the mean velocity behavior by van den Berg (1975) will perform better in simulations than the typical 2D law used in some turbulence model assumptions.