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We propose a novel mesh refinement scheme based on signal processing for boundary integral simulations of inviscid droplet dynamics with axial symmetry. A key idea is to directly access the Fourier coefficients of a principal curvature as a function of the arclength through a natural change of variables. The trapezoidal rule is applied to those Fourier-type integrals and the resulting formula fits in the framework of the non-uniform fast Fourier transform. This observation enables to efficiently use an envelope analysis and smoothing filter to generate guidelines for mesh refinement in two singularity formation scenarios. Applications also include a non-iterative construction of the uniform parametrization for an important class of plane curves, which is used in a convergence study of the time-stepping procedure implemented in the previous work by Nitsche and Steen (2004).

In an incompressible inviscid flow system, helical symmetry means invariance though combined axial translation and rotation about the same axis. In helical symmetry, the axial vorticity is materially conserved if the velocity components along the helical lines are proportional to 1/(1+epsilon^2r^2), where e is the pitch and r is the distance from the z-axis. Linear instability analysis shows that a circular helical vortex patch centered at the origin is neutrally stable. We present the evolution of a family of helically symmetric vortices using contour dynamics, a Lagrangian technique to compute the motion of vortices via contour integrals. For contours perturbed by both lower and high modes, the first mode always becomes the most unstable mode for large time. We can inspect the features induced by the lower perturbed mode. We take mode 4 and mode 9 as examples in this work. Adding a vortex sheet on the boundary of the shifted contour accelerates the twisting and rotating process. The distribution of vortex sheet forms a sharpening shock in the evolution and may lead to the discontinuity.

In an incompressible inviscid flow system, helical symmetry means invariance though combined axial translation and rotation about the same axis. In helical symmetry, the axial vorticity is materially conserved if the velocity components along the helical lines are proportional to 1/(1+epsilon^2r^2), where e is the pitch and r is the distance from the z-axis. Linear instability analysis shows that a circular helical vortex patch centered at the origin is neutrally stable. We present the evolution of a family of helically symmetric vortices using contour dynamics, a Lagrangian technique to compute the motion of vortices via contour integrals. For contours perturbed by both lower and high modes, the first mode always becomes the most unstable mode for large time. We can inspect the features induced by the lower perturbed mode. We take mode 4 and mode 9 as examples in this work. Adding a vortex sheet on the boundary of the shifted contour accelerates the twisting and rotating process. The distribution of vortex sheet forms a sharpening shock in the evolution and may lead to the discontinuity.

In this paper, we study the influence of the exit conditions on the acoustic reflections at a jet pipe opening. For the flow exit conditions, the model of Munt assuming a vortex sheet at the exit of a semi-infinite jet pipe is improved by considering more general coupling conditions. We focus on modelling the acoustic properties at the shear layer in general and the stability properties in particular. Experimental methods are used for studying primarily the geometric exit conditions. Both theoretical and experimental results are presented and discussed. Numerical results related to the theory show that the thickness of the shear layer causes an expected increase in the magnitude of the reflection coefficient compared to the original infinitely thin shear layer in the Munt model. The experimental results, on the other hand, show that there are additional effects due to the presence of thick walls at the exit of the straight pipes used in the experiments. These effects are observed to be more dominant than the effects due to the shape of the edges. Based on the discussions, further theoretical and experimental investigations are proposed., QC 20140829 QC 20160929

Modelling the acoustic scattering and absorption at an area expansion in a flow duct requires the incorporation of the flow-acoustic interaction. One way to quantify the interaction is to study the energy in the incident and the scattered field respectively. If the interaction is strong, energy may be transferred between the acoustic and the main flow field. In particular, shear layers, that may be transferred between the acoustic and the main flow field. In particular, shear such as acoustic waves. The vortex sheet model is an analytical linear acoustic model, developed to study scattering of acoustic waves in duct with sharp edges including the interaction with primarily the separated flows that arise at sharp edges and corners. In the model the flow field at an area expansion in a duct is described as a jet issuing into the larger part of the duct. In this paper, the flow-acoustic interaction is described in terms of energy flow. The linear convective wave equation is solved for a two-dimensional, rectangular flow duct geometry. The resulting modes are classified as "hydrodynamic" and "acoustic" when separating the acoustic energy from the part of the energy arising from the steady flow field. In the downstream duct, the seat of modes for this complex flow field are not orthogonal. For small Strouhal numbers, the plane wave and the two hydrodynamic waves are all plane, although propagating with different wave speeds. As the Strouhal numbers increases, the hydrodynamic modes changes to get a shape where the amplitude is concentrated near the vortex sheet. In an intermediate Strouhal number region, the mode shape of the first higher order mode is very similar to the damped hydrodynamic mode. A physical interpretation of this is that we have a strong coupling between the flow field and the acoustic field when the modes are non-orthogonal. Energy concepts for this duct configuration and mean flow profile are introduced. The energy is formulated such that the vortex s, QC 20110325

A fast and accurate algorithm to compute interactions between N point vortices and between N vortex blobs on a sphere is proposed. It is an extension of the fast tree-code algorithm developed by Draghicescu for the vortex method in the plane. When we choose numerical parameters in the fast algorithm suitably, the computational cost of O(N2) is reduced to O(N(logN)4) and the approximation error decreases like O(1/N) when N→∞, as demonstrated in the present article. We also apply the fast method to long-time evolution of two vortex sheets on the sphere to see the efficiency. A key point is to describe the equation of motion for the N points in the three-dimensional Cartesian coordinates.

A fast and accurate algorithm to compute interactions between N point vortices and between N vortex blobs on a sphere is proposed. It is an extension of the fast tree-code algorithm developed by Draghicescu for the vortex method in the plane. When we choose numerical parameters in the fast algorithm suitably, the computational cost of O(N2) is reduced to O(N(logN)4) and the approximation error decreases like O(1/N) when N→∞, as demonstrated in the present article. We also apply the fast method to long-time evolution of two vortex sheets on the sphere to see the efficiency. A key point is to describe the equation of motion for the N points in the three-dimensional Cartesian coordinates.

A fast and accurate algorithm to compute interaction between N point vortices on a sphere is proposed. It is an extension of the fast tree-code algorithm based on the Taylor expansion developed by Draghicescu for the point vortices in the plane. When we choose numerical parameters in the fast algorithm suitably, the computational cost of O(N2) is reduced to O(N(logN)4) and the approximation error decreases like O(1=N) as N ! 1, which are clearly con rmed in the present article. We also apply the fast method to a long-time evolution of two vortex sheets on the sphere. A key device is to embed the sphere into the three-dimensional space, in which we reformulate the equation of motion for the N point vortices.

The subject of this thesis is the acoustic properties offlow duct area expansions and the influence of flow-acousticcoupling at sharp edges. For low Mach number flow, significantinteraction between the sound field and the flow field canoccur at such points of flow separation. A linear analyticalmodel is used to describe the sound field, whereas the meanflow field is modelled as a jet issuing into the larger duct.The scattering coefficients for sound waves incident on thearea expansion are determined by the Wiener-Hopf techniquetogether with a building block method. To achieve a uniquesolution, the unsteady Kutta condition is applied at the sharpedge. The results have been verified through comparison withexperimental data, and the agreement is excellent. Thereflection and transmission coefficients for the plane wave, aswell as the absorption coefficient have been studied, and aquasi-stationary model for the scattering coefficient have beenderived from the analytical model. The shear layer emanating from the edge is modelled as avortex sheet, with zero thickness. The vortex sheet is unstablefor all frequencies, and as a real shear layer is unstable onlyup to a critical frequency disturbances, it is a low frequencymodel. In fact, it is the Strouhal number, based on thethickness of the shear layer that determines the stabilityproperties of the shear layer. The dynamics of a finite shearlayer is included in the model by adjusting the edge condition,thus extending the model to higher Strouhal numbers. Inaddition, a method to calculate the absorption of sound due tothe vortex shedding gives a good prediction of experimentaldata. The promising result for the adjusted edge condition andthe possibility to predict the transmitted acoustic far fieldimplies that the jet expansion region, which is neglected inthe model, has indeed a negligible influence on the plane wavesound transmission. Apparently, linear theory is sufficient topredict these phenomena, at least in the low freq, QC 20100426 NR 20140805

QC 20100426

The problem of separated slow about a circular cylinder is studied analytically through the use of two potential flow models. Following a detailed review of the present state of knowledge, mathematical formulation of the models and appropriate computer programs are presented These models are shown to be capable of simulating the asymmetric vortex shedding, http://archive.org/details/annalyticalstudy1094511642, Lieutenant, United States Navy, Approved for public release; distribution is unlimited.