Parabolized stability equation models for predicting large-scale mixing noise of turbulent round jets

Parabolized stability equation (PSE) models are being deve loped to predict the evolu-tion of low-frequency, large-scale wavepacket structures and their radiated sound in high-speed turbulent round jets. Linear PSE wavepacket models were previously shown to be in reasonably good agreement with the amplitude envelope and phase measured using a microphone array placed just outside the jet shear layer. 1,2 Here we show they also in very good agreement with hot-wire measurements at the jet center line in the potential core,for a different set of experiments. 3 When used as a model source for acoustic analogy, the predicted far field noise radiation is in reasonably good agreement with microphone measurements for aft angles where contributions from large -scale structures dominate the acoustic field. Nonlinear PSE is then employed in order to determine the relative impor-tance of the mode interactions on the wavepackets. A series of nonlinear computations with randomized initial conditions are use in order to obtain bounds for the evolution of the modes in the natural turbulent jet flow. It was found that n onlinearity has a very limited impact on the evolution of the wavepackets for St≥0. 3. Finally, the nonlinear mechanism for the generation of a low-frequency mode as the difference-frequency mode 4,5 of two forced frequencies is investigated in the scope of the high Reynolds number jets considered in this paper.

An Outward-Wave-Favouring Finite Element-Based Strategy for Exterior Acoustical Problems

This work presents a finite element-based strategy for exterior acoustical problems based on an assumed pressure form that favours outgoing waves. The resulting governing equation, weak formulation, and finite element formulation are developed both for coupled and uncoupled problems. The developed elements are very similar to conventional elements in that they are based on the standard Galerkin variational formulation and use standard Lagrange interpolation functions and standard Gaussian quadrature. In addition and in contrast to wave envelope formulations and their extensions, the developed elements can be used in the immediate vicinity of the radiator/scatterer. The method is similar to the perfectly matched layer (PML) method in the sense that each layer of elements added around the radiator absorbs acoustical waves so that no boundary condition needs to be applied at the outermost boundary where the domain is truncated. By comparing against strategies such as the PML and wave-envelope methods, we show that the relative accuracy, both in the near and far-field results, is considerably higher.

EFFECT OF CORE-SHELL STRUCTURE OF HYDROGEL BEADS ON THE THRESHOLD CONCENTRATION OF WATER FOR SWELLING AND ITS PH SENSITIVITY

In this paper we investigate the effect of core-shell structure of Sodium Alginate based hydrogel beads and their size on certain activation threshold concentration of water for applications in swelling and pH sensing. This type of hydrogel experiences diffusive pressure due to transport of certain free charges across its interface with a solvent or electrolyte. This process is essentially a dynamic equilibrium of the electric force field, stress in the polymeric network with cage like structure and molecular diffusion including phase transformation due to pressure imbalance between the hydrogel and its surroundings. The effect of pH of the solvant on the swelling rate of these beads has been studied experimentally. A mathematical model of the swelling process has been developed by considering Nernst-Planck equation representing the migration of mobile ions and Er ions, Poisson equation representing the equilibrium of the electric field and mechanical field equation representing swelling of the gel. An attempt has been made to predict the experimentally observed phenomena using these numerical simulations. It is observed experimentally that certain minimum concentration called activation threshold concentration of the water molecules must be present in the hydrogel in order to activate the swelling process. For the required activation threshold concentration of water in the beads, the pH induced change in the rate of swelling is also investigated. This effect is analyzed for various different core-shell structures of the beads.

Effect of contact stresses on shape recovery of NiTiCu thin films

Permanent plastic deformation induced by mechanical contacts affects the shape recovery of shape memory alloys. To understand the shape recovery of NiTiCu thin films subjected to local contact stresses, systematic investigations are carried out by inducing varying levels of contact stresses using nanoindentation. The resulting indents are located precisely for imaging using a predetermined array consisting of different sized indents. Morphology and topography of these indents before and after shape recovery are characterized using Scanning Electron Microscope and Atomic Force Microscope quantitatively. Shape recovery is found to be dependent on the contact stresses at the low loads while the recovery ratio remains constant at 0.13 for higher loads. Shape recovery is found to occur mainly in depth direction of the indent, while far field residual stresses play very little role in the recovery. (C) 2014 Elsevier B.V. All rights reserved.

Digital image analysis around isotropic points for photoelastic pattern recognition

Fringe tracking and fringe order assignment have become the central topics of current research in digital photoelasticity. Isotropic points (IPs) appearing in low fringe order zones are often either overlooked or entirely missed in conventional as well as digital photoelasticity. We aim to highlight image processing for characterizing IPs in an isochromatic fringe field. By resorting to a global analytical solution of a circular disk, sensitivity of IPs to small changes in far-field loading on the disk is highlighted. A local theory supplements the global closed-form solutions of three-, four-, and six-point loading configurations of circular disk. The local theoretical concepts developed in this paper are demonstrated through digital image analysis of isochromatics in circular disks subjected to three-and four-point loads. (C) 2015 Society of Photo-Optical Instrumentation Engineers (SPIE)

Elastic fields of interacting elliptic inhomogeneities

This paper presents a method for the calculation of two-dimensional elastic fields in a solid containing any number of inhomogeneities under arbitrary far field loadings. The method called 'pseudo-dislocations method', is illustrated for the solution of interacting elliptic inhomogeneities. It reduces the interacting inhomogeneities problem to a set of linear algebraic equations. Numerical results are presented for a variety of elliptic inhomogeneity arrangements, including the special cases of elliptic holes, cracks and circular inhomogeneities. All these complicated problems can be solved with high accuracy and efficiency.

On applications of high-frequency asymptotics in aeroacoustics.

The aim of this paper is to survey a range of applications of high-frequency asymptotic methods in aeroacoustics. Specifically, we are concerned with problems associated with noise generation, propagation and scattering as found in large modern aeroengines. With regard to noise generation, we consider the interaction between high-frequency vortical waves and thin aerofoils, with particular emphasis being placed on the way in which the vortical waves act on the non-uniform mean flow around the aerofoil. A ray-theoretic description of the resulting sound as it propagates along the engine intake is then presented, followed by consideration of the diffraction of these rays by the (possibly asymmetric) intake lip to produce sound in the far field. A range of more detailed possible extensions is also presented.

Weak Zone Related Seismic Cycles in Progressive Failure Leading to Collapse in Brittle Crust

Until quite recently our understanding of the basic mechanical process responsible for earthquakes and faulting was not well known. It can be argued that this was partly a consequence of the complex nature of fracture in crust and in part because evidence of brittle phenomena in the natural laboratory of the earth is often obliterated or obscured by other geological processes. While it is well understood that the spatial and temporal complexity of earthquakes and the fault structures emerge from geometrical and material built-in heterogeneities, one important open question is how the shearing becomes localized into a band of intense fractures. Here the authors address these questions through a numerical approach of a tectonic plate by considering rockmass heterogeneity both in microscopic scale and in mesoscopic scale. Numerical simulations of the progressive failure leading to collapse under long-range slow driving forces in the far-field show earthquake-like rupture behavior. $En Echelon$ crack-arrays are reproduced in the numerical simulation. It is demonstrated that the underlying fracturing induced acoustic emissions (or seismic events) display self-organized criticality------from disorder to order. The seismic cycles and the geometric structures of the fracture faces, which are found greatly depending on the material heterogeneity (especially on the macroscopic scale), agree with that observed experimentally in real brittle materials. It is concluded that in order to predict a main shock, one must have extremely detailed knowledge on very minor features of the earth's crust far from the place where the earthquake originated. If correct, the model proposed here seemingly provides an explanation as to why earthquakes to date are not predicted so successfully. The reason is not that the authors do not understand earthquake mechanisms very well but that they still know little about our earth's crust.

Assessment of the contribution of surface roughness to airframe noise

The generation of sound by turbulent boundary-layer flow at low Mach number over a rough wall is investigated by applying a theoretical model that describes the scattering of the turbulence near field into sound by roughness elements. Attention is focused on the numerical method to approximately quantify the absolute level of far-field radiated roughness noise. Models for the source statistics are obtained by scaling smooth-wall data by the increased skin friction velocity and boundary-layer thickness for a rough surface. Numerical integration is performed to determine the roughness noise, and it reproduces the spectral characteristics of the available empirical formula and experimental data. Experiments are conducted to measure the radiated sound from two rough plates in an open jet The measured noise spectra of the rough plates are above that of a smooth plate in 1-2.5 kHz frequency and exhibit reasonable agreement with the predicted level. Estimates of the roughness noise for a Boeing 757 sized aircraft wing with idealized levels of surface roughness show that hi the high-frequency region the sound radiated from surface roughness may exceed that from the trailing edge, and higher overall sound pressure levels are observed for the roughness noise. The trailing edge noise is also enhanced by surface roughness somewhat A parametric study indicates that roughness height and roughness density significantly affect the roughness noise with roughness height having the dominant effect The roughness noise directivity varies with different levels of surface roughness. Copyright © 2007 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Effects of surface roughness on airframe noise

The generation of sound by turbulent boundary layer flow at low Mach number over a rough wall is investigated by applying the theoretical model which describes the scattering of the turbulence near field into sound by roughness elements. Attention is focused on the numerical method to approximately quantify the absolute level of the roughness noise radiated to far field. Empirical models for the source statistics are obtained by scaling smooth-wall data through increased skin friction velocity and boundary layer thickness for the rough surface. Numerical integration is performed to determine the roughness noise, and it reproduces the spectral characteristics of the available empirical formula and experimental data. Experiments are conducted to measure the radiated sound from two rough plates in an open jet by four 1/2'' free-field condenser microphones. The measured noise spectra of the rough plates are above that of a smooth plate in 1-2.5 kHz frequency and exhibits encouraging agreement with the predicted spectra. Also, a phased microphone array is utilized to localize the sound source, and it confirms that the rough plates generate higher source strengthes in this frequency range. A parametric study illustrates that the roughness height and roughness density significantly affect the far-field radiated roughness noise with the roughness height having the dominant effect. The estimates of the roughness noise for a Boeing 757 sized aircraft wing show that in high frequency region the sound radiated from surface roughness may exceed that from the trailing edge, and higher overall sound pressure levels for the roughness noise are also observed.

Models for acoustic propagation through turbofan exhaust flows-lined ducts

Turbomachinery noise radiating into the rearward arc is an important problem. This noise is scattered by the trailing edges of the nacelle and the jet exhaust, and interacts with the shear layers between the external flow, bypass stream and jet, en route to the far field. In the past a range of relevant model problems involving semi-infinite cylinders have been solved. However, one limitation of these previous solutions is that they do not allow for the jet nozzle protruding a finite distance beyond the end of the nacelle (or in certain configurations being buried a finite distance upstream). With this in mind, we have used the matrix Wiener-Hopf technique to allow precisely this finite nacelle-jet nozzle separation to be included. We have previously reported results for the case of hard-walled ducts, which requires factorisation of a 2 × 2 matrix. In this paper we extend this work by allowing one of the duct walls, in this case the outer wall of the jet pipe, to be acoustically lined. This results in the need to factorise a 3 × 3 matrix, which is completed by use of a combination of pole-removal and Pad́e approximant techniques. Sample results are presented, investigating in particular the effects of exit plane stagger and liner impedance. Here we take the mean flow to be zero, but extension to nonzero Mach numbers in the core and bypass flow has also been completed. Copyright © 2009 by Nigel Peake & Ben Veitch.

Numerical Investigation On Evolution Of Cylindrical Cellular Detonation

Cylindrical cellular detonation is numerically investigated by solving two-dimensional reactive Euler equations with a finite volume method on a two-dimensional self-adaptive unstructured mesh. The one-step reversible chemical reaction model is applied to simplify the control parameters of chemical reaction. Numerical results demonstrate the evolution of cellular cell splitting of cylindrical cellular detonation explored in experimentas. Split of cellular structures shows different features in the near-field and far-field from the initiation zone. Variation of the local curvature is a key factor in the behavior of cell split of cylindrical cellular detonation in propagation. Numerical results show that split of cellular structures comes from the self-organization of transverse waves corresponding to the development of small disturbances along the detonation front related to detonation instability.

Quasi-Dammann Grating With Proportional Intensity Array Spots

A quasi-Dammann grating is proposed to generate array spots with proportional-intensity orders in the far field. To describe the performance of the grating, the uniformities of the array spots are redefined. A two-dimensional even-sampling encode scheme is adopted to design the quasi-Dammann grating. Numerical solutions of the binary-phase quasi-Dammann grating with proportional-intensity orders are given. The experimental results with a third-order quasi-Dammann grating, which has an intensity proportion of 3:2:1 from zero order to second order, are presented. (C) 2008 Optical Society of America

Compact difference approximation with consistent boundary condition

For simulating multi-scale complex flow fields it should be noted that all the physical quantities we are interested in must be simulated well. With limitation of the computer resources it is preferred to use high order accurate difference schemes. Because of their high accuracy and small stencil of grid points computational fluid dynamics (CFD) workers pay more attention to compact schemes recently. For simulating the complex flow fields the treatment of boundary conditions at the far field boundary points and near far field boundary points is very important. According to authors' experience and published results some aspects of boundary condition treatment for far field boundary are presented, and the emphasis is on treatment of boundary conditions for the upwind compact schemes. The consistent treatment of boundary conditions at the near boundary points is also discussed. At the end of the paper are given some numerical examples. The computed results with presented method are satisfactory.

Three-dimensional finite element analysis of composites with coated spherical inclusions

A three-dimensional finite element analysis has been used to determine the internal stresses in a three-phase composite. The stresses have been determined for a variety of interphase properties, the thicknesses of the interphase and the volume fractions of particles. Young's modulus has been calculated from a knowledge of these stresses and the applied deformation. The calculations show that stress distributions in the matrix and the mechanical properties are sensitive to the interphase property in the three-phase composites. The interfacial stresses in the three-dimensional analysis are in agreement with results obtained by an axisymmetric analysis. The predicted bulk modulus in three-dimensional analysis agrees well with the theoretical solution obtained by Qui and Weng, but it presents a great divergence from that in axisymmetric analyses. An investigation indicates that this divergence may be caused by the difference in the unit cell structure between two models. A comparison of the numerically predicted bulk and shear modulus for two-phase composites with the theoretical results indicates that the three-dimensional analysis gives quite satisfactory results.