An experimental parametric sturdy of vane and air-jet vortex generators in a turbulent boundary layer has been carried out. Experiments were carried out in two facilities, one with a free-stream velocity of 20 m/s and a boundary layer thickness (6) of 41.5 mm, and one in a high speed facility at free-stream Mach numbers of between 0.45 and 0.75 and a boundary layer thickness of 20 mm. Cross-stream data were measured at a number of downstream locations using a miniature five-hole pressure probe, such that local cross-stream velocity vectors could be derived. Streamwise vorticity was calculated using the velocity vector data. In the low speed study, vortex generator parameters were as follows: ' Vane vortex generators: thin rectangular vanes with a vane aspect ratio of unity (2h/c = 1), free-stream velocity 20 m/s, incidence (cc = 10', 15', 18', 20'), height-to-boundary- layer- thickness-ratio (h/8 0.554,0.916,1.27,1.639), and strearnwise distance from the vortex generator (x/6 = 3.855,12.048,19.277,26.506). ' Air-jet vortex generators: circular jet nozzles, free-stream velocity = 20 m/s, jet nozzle pitch and skew angles (cc, P= 30', 45', 60'), hole diameter-to-boundary-layer-thickness-ratio (D/5 = 0.098,0.193,0.289), jet-to-free-stream-velocity ratio (VR = 0.7,1.0,1.3,1.6,2.0), and strearnwise distance from the vortex generator (x/8 = 3.855,12.048,19.277,26.506). In the high-speed study, the vortex generator parameters were as follows: Vane vortex generators: thin rectangular vanes with an aspect ratio of unity, incidence ((X 1505 20'), he i ght-to- boundary- I ayer-th i ckne s s-rati o (h/8 = 0.75), strearnwise distance from the vortex generator (x/6 = 8.755 16.25,23.75), and free-stream Mach numbers of 0.45,0.6 and 0.75. Air-jet vortex generators: jet pitch ((x = 30', 45'), jet skew angle (P = 30', 45', 60'), hole diameter-to-boundary-layer-thickness-ratio (D/8 = 0.15,0.3), j et-to- free- strearn-ve loc ity ratio (VR = 1.6), and strearnwise distance from the vortex generator (x/6 = 8.75,16.25,23.75, 31.25), and free-stream Mach numbers of 0.50,0.6 and 0.75. Streamwise vorticity data from the experiment was used to generate prediction techniques that would allow the vorticity profiles, downstream of vane or air-jet vortex generators, to be predicted. Both techniques are based on the approximation of the experimental cross-stream vorticity data to Gaussian distributions of vorticity through the vortex centre. The techniques, which are empirically derived, are simple equations that give the peak vorticity and vortex radius based on the vortex generator parameters. Use of these descriptors allows the assembly of the Gaussian vorticity equation. Both techniques are compared with the experimental data set and were seen to produce peak vorticity results to within 12% and 20% (for the vanes and air-jets respectively), 15% for the radius of the vortex, and 15% and 20% in vortex circulation (for the vanes and air-jets respectively). The two simple prediction techniques allow good prediction of the vortex structure at extremely low computational effort.

This thesis explores the experiences of managers who work flexibly. Flexible working policies are prevalent in all organizations in the UK because of the legislation giving specific groups of parents and carers the right to request flexible working. Many organizations extend the policies to all employees, yet the take-up is not as high as expected, particularly among staff at managerial levels. This thesis explores how managers construe and experience flexible working arrangements while successfully fulfilling their roles as managers of people. The exploratory study consisted of interviews with eight managers with unique flexible working patterns. Analysis of the interview transcripts identified concepts of consistency and adaptability. Consistency refers to meeting fixed needs from the work and non-work domains, and adaptability refers to the adjustment of schedules to meet the changing demands from those domains. The concepts of consistency and adaptability were further explored in the main study which is based on interviews with 24 women and 10 men who held managerial positions and had a flexible working arrangement which reduced their face time in the workplace. The research offers three main contributions to the literature. At a theoretical level, I propose a model which demonstrates how individuals use consistency and adaptability to meet the fixed and changing demands from the work and non-work domains. This model extends understanding of the complexity of the segmentation/integration continuum of boundary theory, explaining how and why managers use flexible working arrangements as a means of managing boundaries and achieving desired goals in both domains. Four distinct clusters emerged among the managerial participants in terms of the type and direction of adaptability, indicating the range of strategies used by managers to ensure the success of their flexible working arrangements. A detailed description of managers’ flexible working experiences is provided, adding to what is known about the role of manager through the exploration of the enactment of that role when working flexibly.

The concept of reciprocal acoustical travel-time measurements as a means of determining path-averaged currents is well established. We have designed an instrument to exploit this principle in studies of the boundary layer just beneath the arctic ice cover. Such measurements are of interest both because of the opportunity provided for comparison with the more commonly acquired point measurements and because of a particular configuration allowing determination of average vorticity, which cannot be achieved with the traditional approach; in addition, their unprecedented sensitivity allows detection of phenomena not observable with traditional sensors. The acoustical instrument was deployed during the spring of 1989 in the sub-ice boundary layer of the Eastern Arctic in order to measure turbulence, path-averaged horizontal current, and relative vorticity. A triangular acoustic array of side 200 m was used to obtain reciprocal transmission measurements at 132 kHz, at 8, 10 and 20 m beneath an ice floe. Pseudo-random coding and real-time signal processing provided precise acoustic travel time and amplitude for each reciprocal path. Mean current along each acoustic path is proportional to travel time difference between reciprocal transmissions. Horizontal velocity normal to the acoustic paths is measured using scintillation drift. The instrument measures horizontal circulation and average vorticity relative to the ice, at length scales characteristic of high frequency internal waves in the region. The rms noise level of the measurements is less than 0.1 mm/s for velocity measurements and 0.01 for vorticity, averaged over one minute. Except near the mechanical resonance frequency of the moorings, the measurement accuracy is limited by multipath interference. Path-averaged horizontal velocity is compared to point measurements and marked differences are observed due to local anomalies of the flow field. The integral measurement of current is particularly sensitive to the passage of internal waves that have wavelengths longer than the horizontal separation of the transducers. A comparison of horizontal velocity at two depths in the boundary layer shows good coherence at internal wave frequencies and some attenuation as the ice is approached. Relative vorticity at internal wave length scales is dominated by horizontal shear caused by flow interaction with ice topography and not by planetary vorticity. Reciprocal acoustical travel time measurements over paths of several hundred meters can be used to probe the statistical behaviour of turbulent velocity fine structure in the ocean. For homogenous isotropic flows, and for long measuring baselines, an analytic expression relating line-averaged and point measurements of velocity is derived. Anisotropic and inhomogeneous flows are also considered. Correction formulas for the spatial and temporal variability of advection velocity along the measuring baseline are obtained. Practical limitations are established, and experimental data from the arctic boundary layer beneath ice is compared with the theory. A new remote sensing technique for measuring turbulent kinetic energy dissipation rate is suggested. / Graduate

No description available.

M.Sc. (Applied Mathematics) / A comparison between the recently developed spectral relaxation method (SRM) and the spectral local linearisation method (SLLM) is done for the first time in this work. Both spectral hybrid methods are employed in finding the solution to the non isothermal mass and heat balance model of a catalytic pellet boundary value problem (BVP) with finite mass and heat transfer resistance, which is a coupled system of singular nonlinear ordinary differential equations (ODEs). The SRM and the SLLM are applied, for the first time, to solve a problem with singularities. The solution by the SRM and the SLLM are validated against the results by bvp4c, a well known matlab built-in procedure for solving BVPs. Tables and graphs are used to show the comparison. The SRM and the SLLM are exceptionally accurate with the SLLM being the fastest to converge to the correct solution. We then construct a new spectral hybrid method which we named the spectral Adomian decomposition method (SADM). The SADM is used concurrently with the standard Adomian decomposition method (ADM) to solve well known models arising in fluid mechanics. These problems are the magneto hydrodynamic (MHD) Jeffery-Hamel flow model and the Darcy-Brinkman- Forchheimer momentum equations. The validity of the results by the SADM and ADM are verified by the exact solution and bvp4c solution where applicable. A simple alteration of the SADM is made to improve the performance.

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.

A simplified model with only 2 degrees of freedom is developed for cavity growth along a grain-boundary by surface and grain-boundary diffusion following a similar model for a row of grains used by Sun et al, (1996). A variational principle for the coupled diffusion problem is used to follow the cavity growth. The approximate solution can be reduced to the well-established equilibrium cavity growth model at the fast surface diffusion extreme. By comparing the 2 degree of freedom model with the full finite element solution by Pan et al, (1997), a 'Validity Map' is constructed in terms of the relative diffusivity and applied stress relative to the capillarity stress. It is found that the simplified model accurately describes the evolution process, in terms of overall cavity profile and propagation rate for engineering alloys subject to normal levels of applied stresses. The 2 degree of freedom model for a single cavity was then extended to allow the modelling of multiple cavities. These cavities can be either pre-existing or nucleated during the lifetime of the system. The relative rotation between the grains is also considered. The initial 2 degrees of freedom were increased to six, and a cavity element has been derived. The cavity elements are assembled together using the classical finite element approach. This allows the evolution of multiple cavities and their interactions to be modelled under different applied loads and material parameters. This simplified multiple cavity finite element model was compared with a model for cavity evolution based on a 'smeared-out' approach. It was shown that the 'smeared-out' model does not accurately predict the creep damage for realistic engineering materials and conditions and results in an under prediction of creep lifetime. Using the simplified finite element model the effect of surface diffusion on the evolution of the creep damage was investigated. The evolution of a large pre-existing 'crack-like' cavity was modelled and the effects of nucleation, surface diffusion and loading were also investigated. It was shown that in the majority of cases as the surface diffusion was increased the rupture time was also increased. The results from the large 'crack-like' cavity simulations showed that there was very little crack propagation through the material and the smaller cavities tended to grow independently of the large 'crack-like' cavity.

In this thesis we develop analytical models for boundary layer flow through a two dimensional group of obstacles , based on the "distributed force" model. An array of obstacles is represented as a region without solid obstructions but with distributed body forces resisting the flow. Linear analyses are presented of inviscid, laminar (or constant eddy viscosity) and turbulent flow through such force distributions. For any group of obstacles, we show how to calculate the model force distribution which becomes the input for the linear analyses. The entire procedure can be iterated to take account of non-linear upstream sheltering effects. In general the model distributed force integrates to equal the actual force exerted by obstacles on the flow divided by the fraction of the array volume not occupied by solid obstacles. Turbulent stresses are modelled using a mixing length that is uniform up to a specified height and increases linearly above. Our physical arguments for a displaced mixing length above the obstacles provide an explanation for the observed coincidence between displacement height and the level of mean momentum absorption. Comparisons of the turbulent analysis results with numerical simulations and experimental data show very encouraging agreement and so support both the distributed force model and the assumptions of the mathematical analysis. From the results of the turbulent flow analysis, effective roughness and displacement heights can be calculated for the flow above the obstacles. When the displacement of the turbulent mixing length is correctly taken into account, the calculated parameters are comparable with those obtained experimentally. An analysis of plume dispersion through a group of obstacles shows how the flow field results can be applied to practical situations, and highlights the dominant effect of enhanced perturbation shear stress, especially in the obstacle roof top layer, on changes to the downstream evolution of the plume.

La caractérisation et la simulation des écoulements internes au sein des moteurs àpropergol solide, en considérant des mécanismes physiques fortement couplés, constituentl’objectif principal de ce mémoire de thèse. Dans cette optique, la conjonction entrefluide/régression de surface/couplage fluide structure a imposé de déployer une stratégiepropre lors du développement de la modélisation numérique. En effet, le modèle intègre untraitement de frontière immergée couplé avec un suivi de frontière mobile afin de pouvoirrendre compte de la formidable variation géométrique interne subie au cours d’un tir. Côtéfluide, un maillage automatique est nécessaire et la gestion de ce dernier s’appuie sur undéveloppement récursif avec structure hiérarchisée de type 2n tree. Une attention particulièrea été portée sur le solveur lui-même avec une approche explicite en temps et un schémanumérique basé sur l’approche de Roe avec limiteur de flux au second ordre. Des cas testsont été réalisés afin de valider le solveur et les différentes conditions aux limites introduites,notamment des conditions spécifiques développées pour les besoins de simulation. Lespremiers résultats soulignent tout l’intérêt du modèle proposé et sauf erreur de notre part,pour la première fois, l’analyse des sources tourbillonnaires responsables des instabilités ausein de ces moteurs a été étudiée en intégrant les effets du changement continu de géométrie.Finalement, la faisabilité d’une interaction forte entre solveur fluide et solveur solide a étéréalisée sur un modèle simplifié d’un moteur segmenté.L’ensemble des développements permet un accès aux mécanismes couplés complexeset aux fortes interactions au sein des moteurs à propergol solide et offre de nouvellesperspectives dans la caractérisation des mécanismes fortement couplés. / Characterization and simulation of internaI flow within the solid rocket motors, considering the physicalmechanisms strongly coupled, are the main focus of this thesis objective. In this context, the conjunctionbetween fluid/regression surface/fluid coupling structure imposed deploy c1ean during the development ofnumerical modeling strategy. Indeed, the model incorporates treatment coupled with an immersed boundarytracking moving boundary in order to realize the tremendous internai geometric variation experienced during ashot. Fluid side, an automatic mesh is required and the management of the latter is based on a recursivehierarchical structure development with type 2" tree. Particular attention was paid to the solver itself with anexplicit approach to time and a numerical scheme based on the approach of Roe with flow limiter in the secondorder. Tests cases were conducted to validate the sol ver and different boundary conditions introduced, inc1udingspecific conditions developed for the purpose of simulation. The first results emphasize the interest of theproposed and unless our error model, for the first time, the analysis of the sources responsible vortex instabilitiesin these engines has been studied by incorporating the effects of continuous change in geometry. Finally, thefeasibility of a strong interaction between fluid and solid solver was conducted on a simplified model of a multiengine.AlI the developments allows access to complex mechanisms coupled and strong interactions in solidrocket motors and off ers new insights into the characterization of strongly coupled mechanisms.

The oceanic surface boundary layer is of great importance and interest as its dynamics provides for the exchange of energy, momentum, heat and matter between the atmosphere and the ocean. It is crucial to have a thorough understanding of physical processes that might have a significant influence on its properties and variability. In this study I consider several different facets of mixed layer/boundary layer dynamics. One aspects concerns the consequences of the nonlinearity of the equation of state in mixed layer models. The nonlinearity of the equation of state gives rise to a term in the averaged surface buoyancy flux which can be comparable in magnitude to other terms. Its magnitude is shown to be proportional to the area enclosed by the seasonal cycle of sea-surface temperature T₅ versus the oceanic heat content H. The term always represents a buoyancy input into the ocean and is compensated exactly by the buoyancy loss via cabbeling (densification on mixing) whenever the mixed layer entrains water with different properties from below. Another problem of interest is the role of the coherent wind-induced vortices, commonly known as Langmuir circulation, in generating the surface mixed layer. A simple parameterization of the mixing due to Langmuir circulation is examined in the light of an oceanic dataset. Some evidence for the validity of the parameterization is found, thus drawing attention to Langmuir's assertion that Langmuir circulation is one of the key physical processes in the oceanic boundary layer. The third aspect of surface boundary layer dynamics explored is the mean effect on mixed layer entrainment of periodic vertical movement of isopycnals in the thermocline due to non-breaking internal waves (referred to as heaving). Seasonal model runs incorporating idealized heaving show that heaving can produce significant seasonal differences in sea-surface temperature compared to a reference case without heaving. It is inferred that by periodically stretching and compressing the mixed layer, heaving causes instabilities that result in additional entrainment of colder water from below. A heaving number RH is proposed, and two parameterizations of heaving for use in mixed layer models are suggested. / Graduate