Eddy genesis and manipulation in plane laminar shear flow

Eddy formation and presence in a plane laminar shear flow configuration consisting of two infinitely long plates orientated parallel to each other is investigated theoretically. The upper plate, which is planar, drives the flow; the lower one has a sinusoidal profile and is fixed. The governing equations are solved via a full finite element formulation for the general case and semi-analytically at the Stokes flow limit. The effects of varying geometry (involving changes in the mean plate separation or the amplitude and wavelength of the lower plate) and inertia are explored separately. For Stokes flow and varying geometry, excellent agreement between the two methods of solution is found. Of particular interest with regard to the flow structure is the importance of the clearance that exists between the upper plate and the tops of the corrugations forming the lower one. When the clearance is large, an eddy is only present at sufficiently large amplitudes or small wavelengths. However, as the plate clearance is reduced, a critical value is found which triggers the formation of an eddy in an otherwise fully attached flow for any finite amplitude and arbitrarily large wavelength. This is a precursor to the primary eddy to be expected in the lid-driven cavity flow which is formed in the limit of zero clearance between the plates. The influence of the flow driving mechanism is assessed by comparison with corresponding solutions for the case of gravity-driven fluid films flowing over an undulating substrate. When inertia is present, the flow generally becomes asymmetrical. However, it is found that for large mean plate separations the flow local to the lower plate becomes effectively decoupled from the inertia dominated overlying flow if the wavelength of the lower plate is sufficiently small. In such cases the local flow retains its symmetry. A local Reynolds number based on the wavelength is shown to be useful in characterising these large-gap flows. As the mean plate separation is reduced, the form of the asymmetry caused by inertia changes, and becomes strongly dependent on the plate separation. For lower plate wavelengths which do not exhibit a cinematically induced secondary eddy, an inertially induced secondary eddy can be created if the mean plate separation is sufficiently small and the global Reynolds number sufficiently large

Studying Flow Close to an Interface by Total Internal Reflection Fluorescence Cross Correlation Spectroscopy: Quantitative Data Analysis

Total Internal Reflection Fluorescence Cross Correlation Spectroscopy (TIR-FCCS) has recently (S. Yordanov et al., Optics Express 17, 21149 (2009)) been established as an experimental method to probe hydrodynamic flows near surfaces, on length scales of tens of nanometers. Its main advantage is that fluorescence only occurs for tracer particles close to the surface, thus resulting in high sensitivity. However, the measured correlation functions only provide rather indirect information about the flow parameters of interest, such as the shear rate and the slip length. In the present paper, we show how to combine detailed and fairly realistic theoretical modeling of the phenomena by Brownian Dynamics simulations with accurate measurements of the correlation functions, in order to establish a quantitative method to retrieve the flow properties from the experiments. Firstly, Brownian Dynamics is used to sample highly accurate correlation functions for a fixed set of model parameters. Secondly, these parameters are varied systematically by means of an importance-sampling Monte Carlo procedure in order to fit the experiments. This provides the optimum parameter values together with their statistical error bars. The approach is well suited for massively parallel computers, which allows us to do the data analysis within moderate computing times. The method is applied to flow near a hydrophilic surface, where the slip length is observed to be smaller than 10nm, and, within the limitations of the experiments and the model, indistinguishable from zero.Comment: 18 pages, 12 figure

Design and Characterization of a Hypervelocity Expansion Tube Facility

We report on the design and characterization of a 152 mm diameter expansion tube capable of accessing a range of high enthalpy test conditions with Mach numbers up to 7.1 for aerodynamic studies. Expansion tubes have the potential to offer a wide range of test flow conditions as gas acceleration is achieved through interaction with an unsteady expansion wave rather than expansion through a fixed area ratio nozzle. However, the range of test flow conditions is in practice limited by a number of considerations such as short test time and large amplitude flow disturbances. We present a generalized design strategy for small-scale expansion tubes. As a starting point, ideal gas dynamic calculations for optimal facility design to maximize test time at a given Mach number test condition are presented, together with a correction for the expansion head reflection through a non-simple region. A compilation of practical limitations that have been identified for expansion tube facilities such as diaphragm rupture and flow disturbance minimization is then used to map out a functional design parameter space. Experimentally, a range of test conditions have been verified through pitot pressure measurements and analysis of schlieren images of flow over simple geometries. To date there has been good agreement between theoretical and experimental results

A note on the Kutta condition in Glauert's solution of the thin aerofoil problem

Glauert's classical solution of the thin aerofoil problem (a coordinate transformation, and splitting the solution into a sum of a singular part and an assumed regular part written as a Fourier sine series) is usually presented in textbooks on aerodynamics without a great deal of attention being paid to the rôle of the Kutta condition. Sometimes the solution is merely stated, apparently satisfying the Kutta condition automatically. Quite often, however, it is misleadingly suggested that it is by the choice of a sine series that the Kutta condition is satisfied. It is shown here that if Glauert's approach is interpreted in the context of generalised functions, (1) the whole solution, i.e. both the singular part and any non-Kutta condition solution, can be written as a sine-series, and (2) it is really the coordinate transformation which compels the Kutta condition to be satisfied, as it enhances the edge singularities from integrable to non-integrable, and so sifts out solutions not normally representable by a Fourier series. Furthermore, the present method provides a very direct way to construct other, more singular solutions. A practical consequence is that (at least, in principle) in numerical solutions based on Glauert's method, more is needed for the Kutta condition than a sine series expansion

Self-authorship and creative industries workers’ career decision-making

Career decision-making is arguably at its most complex within professions where work is precarious and career calling is strong. This article reports from a study that examined the career decision-making of creative industries workers, for whom career decisions can impact psychological well-being and identity just as much as they impact individuals’ work and career. The respondents were 693 creative industries workers who used a largely open-ended survey to create in-depth reflections on formative moments and career decision-making. Analysis involved the theoretical model of self-authorship, which provides a way of understanding how people employ their sense of self to make meaning of their experiences. The self-authorship process emerged as a complex, non-linear and consistent feature of career decision-making. Theoretical contributions include a non-linear view of self-authorship that exposes the authorship of visible and covert multiple selves prompted by both proactive and reactive identity work

Fluid mechanics: problems and solutions

his collection of over 200 detailed worked exercises adds to and complements the textbook Fluid Mechanics by the same author, and illustrates the teaching material through examples. In the exercises the fundamental concepts of Fluid Mechanics are applied to obtaining the solution of diverse concrete problems, and in doing this the student's skill in the mathematical modeling of practical problems is developed. In addition, 30 challenging questions without detailed solutions have been included, and while lecturers will find these questions suitable for examinations and tests, the student himself can use them to check his understanding of the subject