Acoustical response of shear layers

In the present work the linear acoustical response of shear layers is investigated for two different geometrical configurations. Both theoretical modelling and experiments are carried out. The first studied configuration is a sudden area expansion in a duct with mean flow. Here, a shear layer, separating a region with mean flow from a region where the fluid is quiescent, is formed downstream of the area discontinuity. Theoretical modelling for this configuration is done by means of a modal analysis method. The geometry is split into a duct upstream and a duct downstream of the area expansion. The acoustical field in both ducts is found as an expansion of eigenmodes by solving a generalized eigenvalue problem, derived from the linearized Euler equations for conservation of mass and momentum. Here, a discretization in the transverse direction of the duct is employed. By mode matching, a procedure in which continuity of massand momentum flux at the interface between the two ducts is applied, the aeroacoustical behaviour is found in the form of a scattering matrix. This scattering matrix relates the modes propagating away from the area discontinuity to the modes propagating towards the area discontinuity. The influence of the mean flow profile, and in particular the application of an acoustical Kutta condition at the edge, on the scattering at the area expansion is investigated. A relatively small influence is observed, and a smooth transition from the case where a Kutta condition is not imposed to the case where it is imposed is seen. Scattering results for plane waves have also been compared to results of an alternative model proposed by Boij and Nilsson, as well as to experimental data of Ronneberger. The alternative model considers an area expansion in a rectangular duct and an infinitely thin shear layer. The experimental data of Ronneberger are obtained for an expansion in a cylindrical tube. In this context, the scaling rule, proposed by Boij and Nilsson, for the comparison of results obtained in a rectangular and a cylindrical geometry, is examined. For this purpose both modal analysis calculations are carried out for rectangular and cylindrical geometry. The scaling rule appears to be reasonably valid in a wide Strouhal number range. However, it is found that a deviation can occur around a certain critical Strouhal number. Here, a specific behaviour of the scattering is found, which depends on the ratio of the upstream and downstream duct heights or duct radii. Furthermore, comparison of results of the modal analysis method with those of the alternative model and the experimental data provided by Ronneberger shows fairly good correspondence. Also, an improved prediction of the experimental results by the modal analysis method is obtained in some cases when accounting for the non-uniform mean flow profile. The second configuration studied is that of a shear layer formed in a rectangular orifice in a wall due to the presence of mean grazing flow. Experimentally, the acoustical response of such a shear layer in an orifice is investigated by means of a multi-microphone impedance tube set-up. Care was taken to remain in the regime of linear perturbations. The acoustical behaviour is expressed as a change of orifice impedance due to the grazing flow. Here, the real and imaginary part of the difference of the non-dimensional impedance with flow and the non-dimensional impedance without flow are scaled to the Mach number and the Helmholtz number respectively. The obtained quantities are denoted as the non-dimensional scaled resistance due to the mean flow, respectively the non-dimensional scaled reactance due to the mean flow. This procedure was originally proposed by Golliard on basis of the theory of Howe. The influence of the boundary layer characteristics is investigated. For this purpose boundary layer characterization is performed by means of hot-wire measurements. The Strouhal number dependency of the non-dimensional scaled resistance and reactance due to the flow shows an oscillatory shape. When the Strouhal number is based on the phase velocity of the hydrodynamic instability in the shear layer, rather than the mean flow velocity, these oscillations coincide for different boundary layer flows. The phase velocity is deduced from the shear layer profiles, measured with a hot-wire, using the spatial instability analysis for parallel flows by Michalke. For laminar boundary layer flows the amplitudes of the oscillations increase with decreasing boundary layer thickness. Furthermore, the oscillating behaviour appears to vanish around a Strouhal number, at which the shear layer becomes stable. Since the instability of a shear layer depends on the Strouhal number based on its momentum thickness, the ratio of shear layer momentum thickness and orifice width determines the number of observed oscillations in impedance. The influence of the edge geometry of the orifice on the impedance with grazing flow is examined. It was found that the amplitudes of oscillations in the impedance increase when using sharp edges. Especially the downstream edge of the orifice is important. Similar to the configuration of an area expansion in a duct, theoretical modelling for the aeroacoustical response of a shear layer in an orifice is done by means of the modal analysis method. In this case the considered geometry is that of two parallel rectangular ducts, of which one carries mean flow. The orifice is represented by an interconnection between the two ducts. This geometry is split into five ducts, in each of which the acoustic field is solved as an expansion of eigenmodes. Mode matching at the relevant interfaces gives the acoustical behaviour in terms of a scattering matrix, which relates the modes propagating away from the orifice to the modes propagating towards the orifice. From the scattering matrix an orifice impedance is calculated. Modal analysis results are compared with those from an analytical model, proposed by Howe, which considers the low Helmholtz number, low Mach number acoustical response of an infinitely thin shear layer in an orifice in a thin wall separating unbounded uniform grazing flows. Qualitatively, good correspondence is seen between the two models. However, an unexpected influence of the geometrical ratios in the duct configuration on the non-dimensional scaled resistance and reactance is present in case of the modal analysis method. Also, the results both obtained by Howe’s theory and by the modal analysis method seem to display non-physical behaviour, especially in the high Strouhal number limit. For non-uniform grazing flow over an orifice convergence of the modal analysis method is a problematic issue. However, a tentative comparison with experimental results shows that the model at least qualitatively predicts the behaviour of the impedance with grazing flow fairly well. In particular, the oscillations in Strouhal number dependency of the non-dimensional scaled resistance and reactance due to the flow, and the related influence of the boundary layer thickness of the flow, are accurately predicted

Audio driver

An audio driver comprising a diaphragm (101, 103) with a first side and a second side. The diaphragm (101, 103) is coupled to a transducer element (109, 111) on the second side and is arranged to radiate sound. The transducer element (109, 111) converts an electrical input signal into movement of the diaphragm (101, 103). The diaphragm (101, 103) is arranged such that a part of the diaphragm (103) at least partly forms a cavity (113) at the second side and an air conduit (115) is coupled to the cavity (113). The air conduit (115) has a first opening (117) into the cavity and a second opening (119) outside the cavity (113). The air conduit (115) and cavity (113) form a resonator which has a resonance frequency that is less than half a free air acoustic resonance frequency of the audio driver.; The invention may allow simultaneous sound production and an acoustic air flow generation while maintaining an efficient decoupling between the two functionalities

Modes of Growth in Dynamic Systems

Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct modes that depend on the availability of material and energetic resources. These modes include a law of diminishing returns, logistic behavior and, if resources are expanding very rapidly, super-exponential growth. For a case where a system has a resolved sink as well as a source, growth and decay can be characterized in terms of a slightly modified form of the predator-prey equations commonly employed in ecology, where the perturbation formulation of these equations is equivalent to a damped simple harmonic oscillator. Thus, the framework presented here suggests a common theoretical under-pinning for emergent behaviors in the physical and life sciences. Specific examples are described for phenomena as seemingly dissimilar as the development of rain and the evolution of fish stocks.Comment: 16 pages, 6 figures, including appendi

Neuroprotection by Insulin-like Growth Factor-1 in Rats with Ischemic Stroke is Associated with Microglial Changes and a Reduction in Neuroinflammation

We and others have shown that insulin-like growth factor-1 (IGF-1) is neuroprotective when administered systemically shortly following stroke. In the current study, we addressed the hypothesis that microglia mediate neuroprotection by IGF-1 following ischemic stroke. Furthermore, we investigated whether IGF-1 modulates pro- and anti-inflammatory mediators in ischemic brain with a special reference to microglia. Ischemic stroke was induced in normal conscious Wistar rats by infusing the vasoconstrictor, endothelin-1 (Et-1), next to middle cerebral artery (MCA). IGF-1 (300 μg) was injected subcutaneously (SC) at 30 and 120 min following stroke. Microglial inhibitor, minocycline, was injected intraperitoneally (IP) at 1 h before stroke (25 mg/kg) and 11 h after stroke (45 mg/kg). Post-stroke IGF-1 treatment reduced the infarct size and increased the sensorimotor function which coincided with an increase in the number of ameboid microglia in the ischemic cortex. Minocycline treatment abrogated the increase in ameboid microglia by IGF-1, while the effect of IGF-1 in the reduction of infarct size was only partially affected. IGF-1 suppressed mRNA expression of inducible nitric oxide synthase (iNOS) and interleukin (IL)-1β in the ischemic hemisphere, while in purified microglia, only iNOS expression levels were reduced. Our findings show that microglia are a target for IGF-1 and that neuroprotection by IGF-1 coincides with down-regulation of inflammatory mediators which could be instrumental to the beneficial effects

Determination of Inter-Phase Line Tension in Langmuir Films

A Langmuir film is a molecularly thin film on the surface of a fluid; we study the evolution of a Langmuir film with two co-existing fluid phases driven by an inter-phase line tension and damped by the viscous drag of the underlying subfluid. Experimentally, we study an 8CB Langmuir film via digitally-imaged Brewster Angle Microscopy (BAM) in a four-roll mill setup which applies a transient strain and images the response. When a compact domain is stretched by the imposed strain, it first assumes a bola shape with two tear-drop shaped reservoirs connected by a thin tether which then slowly relaxes to a circular domain which minimizes the interfacial energy of the system. We process the digital images of the experiment to extract the domain shapes. We then use one of these shapes as an initial condition for the numerical solution of a boundary-integral model of the underlying hydrodynamics and compare the subsequent images of the experiment to the numerical simulation. The numerical evolutions first verify that our hydrodynamical model can reproduce the observed dynamics. They also allow us to deduce the magnitude of the line tension in the system, often to within 1%. We find line tensions in the range of 200-600 pN; we hypothesize that this variation is due to differences in the layer depths of the 8CB fluid phases.Comment: See (http://www.math.hmc.edu/~ajb/bola/) for related movie

Poder y escritura : el Príncipe, la biblioteca y la dedicatoria (siglos XV-XVII)

Se muestra cómo la lectura y la escritura son actos sociales perfectamente normativizados en la cultura de la Edad Moderna. Se exponen los ejemplos de la biblioteca, una institución en la que tan importante como el material que conserva son las relaciones sociales que se establecen entorno a ella (así en las "bibliotecas reales" como en las particulares), y de la dedicatoria de libros, en la que los autores desarrollan un lenguage muy sutil que les permitía relacionarse de forma especial con el destinatario.Roger Chartier shows how reading and writing were perfectly normativized social acts in the culture of Modern Age. As a demonstration of his assertions, he sets two examples: the first concerning libraries, institutions where materials preserved there were as important as social relationship established round it (both in regal libraries and in private ones), the second about the dedications written in books, through which their authors developed a very subtle language that allowed them to set up a kind of especial relation with their final addressees

Columnar Molecular Aggregation In The Aqueous Solutions Of Disodium Cromoglycate

Stack, chimneylike, and threadlike assemblies have previously been proposed for the structure of disodium cromoglycate (DSCG) aggregates in aqueous solutions. The results of the synchrotron x-ray scattering investigations reported here reveal the formation of simple columnar assemblies with pi-pi stacking at a separation of 3.4 angstrom between the DSCG molecules. Lateral separation between the assemblies is concentration and temperature dependent, varying from similar to 35 to 42 angstrom in the orientationally ordered nematic (N) phase and from 27 to 32 angstrom in the columnar or middle (M) phase having long range lateral positional order. The assemblies\u27 length depends on concentration and consists of similar to 23 molecules in the N phase, becoming three to ten times larger in the M phase. The scission energy is concentration dependent in the N phase with values similar to 7.19 +/- 0.14 k(B)T (15 wt%), 2.73 +/- 0.4 k(B)T (20 wt%), and 3.05 +/- 0.2 k(B)T (25 wt%). Solutions of all concentrations undergo a spinodal decomposition at temperatures above similar to 40 degrees C, resulting in DSCG-rich regions with the M phase and water-rich regions in the N and isotropic phases