In canonical boundary layer transition, a uniform laminar flow perturbed by 2-d T-S waves develops downstream into 3-d waves, which eventually break down with turbulent spots appearing. Previous experimental studies have established that this kind of development is absent, is by-passed, in transition induced by free-stream turbulence or surface roughness. However a common, characteristic feature of the late, three-dimensional stage is the prevalence of streamwise vorticity and streaks. Isolated and multiple streamwise vortices are present in both, canonical transition and bypass transition. This thesis de-scribes an experimental study of the late stages of boundary layer transition after a single or a pair of streamwise vortices have formed. The present work can be considered both as a study of transition induced by surface roughness and as a study of the late stages of transition in general. The experiments were made on a zero-pressure-gradient boundary layer in a low speed wind tunnel. Various hill configurations, mounted on a flat plate, were used to create isolated and multiple streamwise vortices. Particle image velocimetry (PIV) and hot-wire anemometry used for measurements. Numerical simulations of the initial laminar stage were carried out to understand the vortex formation at the edge of the hills. Computations have shown that the streamwise vorticity induced by the spanwise asymmetry of the hill rolls up into a single streamwise vortex. The streamwise vortex causes high speed fluid to be brought close to the wall and low speed fluid to move away. In turn, streamwise velocity profiles acquire inflections in both the spanwise and wall-normal directions. Previous studies have concluded that the inviscid instability of inflectional profiles are essential, or at least common, precursors to transition. Another view of the structure of bypass transition induced involves a secondary instability of streaks that can be sinuous or varicose. These two types follow from instabilities of the inflectional spanwise and wall-normal profiles of the streamwise velocity, respectively. However the present study confirms that the occurrence of inflections is not sufficient for transition. The first series of experiments were with smooth Gaussian shaped hills that spanned one-half of the tunnel. Two hill shapes were taken, steep and shallow. Isolated streamwise vortices formed by the side of the hill. Hill heights were less than that of the incoming boundary layer, and they were mounted within the subcritical part of the boundary layer. At low free stream speeds, streaks formed, with inflectional wall-normal and spanwise velocity profiles, but without effecting transition. The necessary conditions for inviscid instability Rayleigh’s inflexion-point theorem and Fjortoft’s theorem are satisfied for these low-speed non-transitional cases. Transition observed at higher speeds show two kinds of development. With the steep hill, the streamwise vortex is not too close to the plate and it exhibits oscillations over some distance before flow breaks down to turbulence; streamwise velocity signals exhibited the passage of a wave packet which intensified before break-down to turbulence. This dominant mode persists far downstream from the hill even while the flow breaks down and frequency content grows over a range of scales. With the shallow hill, the breakdown develops continuously without such a precursor stage; there was a broad range of frequencies present immediately downstream of the hill. For the steep hill the maximum fluctuation is observed on the upwash side of the vortex. With the shallow hill, the fluctuation level is maximum at the location between low and high speed streak. Features of breakdown to transition caused by these single streamwise vortices are found to be similar to those in transition by other causes such as surface roughness, freestream turbulence etc. With the steep hill, the growth of fluctuations(urms, the peak levels of streamwise velocity component fluctuations) is remarkably similar to that in the K-type transition. Unlike in freestream induced transition, the initial growth of u2 rms,max with downstream distance was not linear. Profiles of urms/urms,max vs. y/δ∗where δ∗,is the displacement thickness is partially matching with the optimal disturbances, for the steep hill case. The phase velocity matches as in previous measurements of roughness induced transition. The flow exhibits the breakup of a shear layer near the outer edge of the boundary layer into successive vortices. This breakdown pattern resembles to those in the recent numerical simulations. The passing frequency of these vortices scales with freestream velocity, similar to that in single-roughness induced transition. Quadrant analysis of streamwise and wall-normal velocity fluctuations show large ejection events in the outer layer. The difference in the route to transition between the steep and shallow hills was considered to the relative proximity of the initial streamwise vortex to the flat plate and its interaction with the wall. To examine this conjecture, two configurations were prepared to produce two types of counter-rotating streamwise vortices. One is a hill that span the tunnel except for a short gap, and the other, its complement, is a short span hill. The short-gap hill produce a pair of vortices with the common flow directed away from the wall. This resulted in a separation bubble that formed a short distance downstream and breakdown to turbulence. The short-span hill configuration seems to have a stabilizing effect. With the short gap hill, transition occurs for lower freestream speeds than with the isolated vortices considered before. Also, the breakdown location is further downstream when the gap is larger. The initial velocity profiles look similar for transitional and non-transitional flow cases, and are inflectional, which clearly indicates that inflectional instabilities are not effective here. A separation index was computed to identify unsteadiness of the separated flow region. The separation is itself steady, where as the reattachment is unsteady. Fluctuations grow near this reattachment zone. The unsteadiness of the reattachment coexists with the appearance of strong fluctuations and transition. It is likely that the this last stage of breakdown results when the shear layer, lifted up by the separation bubble, breaks down near the edge of the boundary layer and the consequent unsteadiness is in the reattachment also. Coherent cat’s-eye-like patterns were observed in a longitudinal, plane normal to the wall. With isolated vortices sinuous oscillations and with stream-wise vortex pairs varicose oscillations were observed in wall-parallel planes. In both cases passing frequency of these vortices scales with freestream velocity. Λ-type vortices were identified in spanwise plane with counter-rotating legs. These experiments have identified some possible roles of streamwise vortices in the last stages of boundary layer transition. Vortices may undergo their own instability in the background shear layer, evident as oscillations, if they are not too close to the wall. Otherwise the breakdown is without such a stage. Wall interaction of these vortices seems to be a necessary last stage. Inflectional instability is not indicated. Wall interaction that results in separation results in break-down in the unsteady reattachment zone. Breakdown coexists with the reattachment and not at separation, even though it may be the separating shear layer that breaks down.

This research focuses on measurements of a convective shear-layer instability seen naturally in quiet hypersonic flow. Experiments were carried out in the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University. The BAM6QT provides low-disturbance hypersonic flow with freestream noise levels similar to what would be experienced by a flight vehicle. To obtain high-speed, off-the-surface measurements of the instability, a modified focused laser differential interferometer (FLDI) was first designed to work with the contoured Plexiglas windows available in the tunnel.<div><br>A cone-cylinder-flare geometry was then selected to study the instabilities related to an axisymmetric separation bubble at Mach 6. The sharp cone had a 5-degree half-angle, while flare angles of 10 degrees and 3.5 degrees were tested to compare axisymmetric compression with and without separation, respectively. Under quiet flow, laminar separation and reattachment was confirmed by schlieren and surface pressure-fluctuation measurements. Coherent traveling waves were observed. These were attributed to both the second-mode instability, as well as a shear-generated instability from the separation bubble. The symmetry of the bubble was found to be highly sensitive to angle of attack. Additionally, by introducing controlled disturbances on the cone upstream of the separation, larger-amplitude shear-generated waves were measured while the second-mode amplitudes remained unchanged. Therefore, the shear-generated waves were amplified moving through the shear layer, while the second mode remained neutrally stable. These appear to be the first measurements of traveling waves that are generated in the shear layer of a separation bubble in hypersonic flow. <br></div>

Boundary-layer transition from a laminar to a turbulent regime is a critical driver in the design of high-speed vehicles. The aerothermodynamic loads associated with transitional or fully turbulent hypersonic boundary layers are several times higher than those associated with laminar flow. The presence of isolated roughness elements on the surface of a body can accelerate the growth of incoming disturbances and introduce additional instability mechanisms in the flow field, eventually leading to a premature occurrence of transition. This dissertation studies the instabilities induced by three-dimensional discrete roughness elements located inside a high-speed boundary layer developing on a flat plate. Two-dimensional local linear stability theory (2D-LST) is employed to identify the instabilities evolving in the three-dimensional flow field that characterizes the wake induced by the roughness elements and to investigate their evolution downstream. A formulation of the disturbance energy evolution equation available for base flows depending on a single spatial direction is generalized for the first time to base flows featuring two inhomogeneous directions and perturbations depending on three spatial directions. This generalization allows to obtain a decomposition of the temporal growth rate of 2D-LST instabilities into the different contributions that lead to the production and dissipation of the total disturbance energy. This novel extension of the formulation provides an additional layer of information for understanding the energy exchange mechanisms between a three-dimensional base flow and the perturbations resulting from 2D-LST. Stability computations for a calorically perfect gas illustrate that the wake induced by the roughness elements supports the growth of different sinuous and varicose instabilities which coexist together with the Mack-mode perturbations that evolve in the flat-plate boundary layer, and which become modulated by the roughness-element wake. A single pair of sinuous and varicose disturbances is found to dominate the wake instability in the vicinity of the obstacles. The application of the newly developed decomposition of the temporal growth rate reveals that the roughness-induced wake modes extract most of their potential energy from the transport of entropy fluctuations across the base-flow temperature gradients and most of their kinetic energy from the work of the disturbance Reynolds stresses against the base-flow velocity gradients. Further downstream, the growth rate of the wake instabilities is found to be influenced by the presence of Mack-mode disturbances developing on the flat plate. Strong evidence is observed of a continuous synchronization mechanism between the wake instabilities and the Mack-mode perturbations. This phenomenon leads to an enhancement of the amplification rate of the wake modes far downstream of the roughness element, ultimately increasing the associated integrated amplification factors for some of the investigated conditions. The effects of vibrational molecular excitation and chemical non-equilibrium on the instabilities induced by a roughness element are studied for the case of a high-temperature boundary layer developing on a sharp wedge configuration. For this purpose, a 2D-LST solver for chemical non-equilibrium flows is developed for the first time, featuring a fully consistent implementation of the thermal and transport models employed for the base flow and the perturbation fields. This is achieved thanks to the automatic derivation and implementation tool (ADIT) available within the von Karman Institute extensible stability and transition analysis (VESTA) tool-kit, which enables an automatic derivation and implementation of the 2D-LST governing equations for different thermodynamic flow assumptions and models. The stability computations for this configuration show that sinuous and varicose disturbances also dominate the wake instability in the presence of vibrational molecular energy mode excitation and chemical reactions. The resulting base-flow cooling associated with the modeling of such high-temperature phenomena is found to have opposite stabilizing and destabilizing effects on the streamwise evolution of the sinuous and varicose instabilities. The modeling of vibrational excitation and chemical non-equilibrium acting exclusively on the perturbations is found to have a stabilizing influence in all cases. / Doctorat en Sciences de l'ingénieur et technologie / info:eu-repo/semantics/nonPublished

<p>Accurate and reliable prediction of laminar-turbulent boundary layer transition at hypersonic velocities is important for the development of a variety of practical high-speed flight systems currently under development. Boundary layer transition can cause up to an order of magnitude increase in skin friction and heat flux on a flight vehicle, meaning that understanding boundary layer behavior is critical to the design of weight-efficient thermal protection systems. Despite the importance of the topic, significant gaps remain in the community's current understanding of boundary layer transition and control. </p> <p>One of the biggest areas of concern in the field of high-speed boundary layer transition is the effect of facility noise on wind tunnel measurements. Conventional hypersonic wind tunnels are contaminated by freestream fluctuations which can be as much as two orders of magnitude higher than free-flight atmospheric conditions. These disturbances are typically produced by turbulent boundary layers on the tunnel walls; they are acoustic in nature and consist of pressure waves which radiate into the test section. This facility noise plays a leading role in high-speed transition phenomena in conventional hypersonic tunnels.</p> <p><br></p> <p>The current work studies the effects of facility noise on hypersonic transition using both linear stability theory and direct numerical simulation. A model for the freestream disturbance environment of the von Karman Facility's Tunnel B based on experimental measurements of the disturbance spectra present in the tunnel is created and used to study a past experiment performed in the same wind tunnel using a sharp cone and hollow cylinder. The results show that while linear stability theory accurately captures the behavior of second-mode instability growth, it fails to predict the growth of low-frequency instabilities recorded in the experiments. The stability theory analysis also suggests that very fine scale variation in nose tip geometry can play an outsize role in the development of boundary layer instabilities significantly farther downstream.</p> <p><br></p> <p>The direct numerical simulation demonstrates that, using an artificial body forcing term to implement the constructed tunnel noise model, the experimental effects of facility noise can be adequately captured with a sufficiently dense computational grid. For the conical geometry used in the experiments, calculations of surface heat flux indicate good experimental agreement with in prediction of transition location, and total temperature spectra extracted from the flow compare favorably with the experimental data as well. Visualizations of the flowfield confirm the onset of turbulence as a result of the freestream forcing. The computations also suggest that nonlinear interactions may be present in the turbulent breakdown region, leading to the production of streamwise streaks along the cone's surface. Transition on the hollow cylinder was not achieved due to suspected resolution issues, so detailed physical comparison of the two cases was not possible.</p> <p><br></p> <p>Overall, the results of this work suggest that direct numerical simulation is a capable tool for studying the effects of facility noise on hypersonic transition for simple geometries, albeit one which can be difficult to practically realize considering the required computational cost. Computational results indicate that two phenomena may play a role in the development of boundary layer instabilities for a sharp cone --- the fine-scale shape of the tip, which may change the behavior of the entropy layer near the nose; and the interactions between low- and high-frequency waveforms, which seems to cause nonlinear breakdown in line with current experimental understanding.</p>

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