scholarly journals Three-dimensional acoustic scattering by vortical flows. I. General theory

2001 ◽  
Vol 13 (10) ◽  
pp. 2876-2889 ◽  
Author(s):  
Stefan G. Llewellyn Smith ◽  
Rupert Ford
Keyword(s):  
General Theory ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Vortical Flows

Theory of Electron Diffraction by Crystals

1967 ◽  
Vol 22 (4) ◽  
pp. 422-431 ◽  
Author(s):  
Kyozaburo Kambe
Keyword(s):  
Integral Equation ◽  
Electron Diffraction ◽  
General Theory ◽  
Green’S Function ◽  
Green's Function ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Two Dimensions ◽  
The Third ◽  
Third Dimension

A general theory of electron diffraction by crystals is developed. The crystals are assumed to be infinitely extended in two dimensions and finite in the third dimension. For the scattering problem by this structure two-dimensionally expanded forms of GREEN’S function and integral equation are at first derived, and combined in single three-dimensional forms. EWALD’S method is applied to sum up the series for GREEN’S function.

Adaptivity and Three Dimensional Hierarchical Boundary Elements for Rigid Acoustic Scattering Problems

1995 ◽  
Author(s):  
Steven J. Newhouse ◽  
Ian C. Mathews
Keyword(s):  
Boundary Element ◽  
Acoustic Analysis ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Error Estimator ◽  
Infinite Domain ◽  
Scattering Problems ◽  
Effective Form ◽  
Mesh Density ◽  
Acoustic Scattering Problems

Abstract The boundary element method is an established numerical tool for the analysis of acoustic pressure fields in an infinite domain. There is currently no well established method of estimating the surface pressure error distribution for an arbitrary three dimensional body. Hierarchical shape functions have been used as a highly effective form of p refinement in many finite and boundary element applications. Their ability to be used as an error estimator in acoustic analysis has never been fully exploited. This paper studies the influence of mesh density and interpolation order on several acoustic scattering problems. A hierarchical error estimator is implemented and its effectiveness verified against the spherical problem. A coarse cylindrical mesh is then refined using the new error estimator until the solution has converged. The effectiveness of this analysis is shown by comparing the error indicators derived during the analysis to the solution generated from a very fine cylindrical mesh.

Mathematical aspects of molecular replacement. IV. Measure-theoretic decompositions of motion spaces

2017 ◽  
Vol 73 (5) ◽  
pp. 387-402 ◽  
Author(s):  
Gregory S. Chirikjian ◽  
Sajdeh Sajjadi ◽  
Bernard Shiffman ◽  
Steven M. Zucker
Keyword(s):  
General Theory ◽  
Rigid Body ◽  
Three Dimensional ◽  
Molecular Replacement ◽  
Translation Group ◽  
Common Occurrence ◽  
Space Group ◽  
Space Groups ◽  
Relevant Case ◽  
The Subject

In molecular-replacement (MR) searches, spaces of motions are explored for determining the appropriate placement of rigid-body models of macromolecules in crystallographic asymmetric units. The properties of the space of non-redundant motions in an MR search, called a `motion space', are the subject of this series of papers. This paper, the fourth in the series, builds on the others by showing that when the space group of a macromolecular crystal can be decomposed into a product of two space subgroups that share only the lattice translation group, the decomposition of the group provides different decompositions of the corresponding motion spaces. Then an MR search can be implemented by trading off between regions of the translation and rotation subspaces. The results of this paper constrain the allowable shapes and sizes of these subspaces. Special choices result when the space group is decomposed into a product of a normal Bieberbach subgroup and a symmorphic subgroup (which is a common occurrence in the space groups encountered in protein crystallography). Examples of Sohncke space groups are used to illustrate the general theory in the three-dimensional case (which is the relevant case for MR), but the general theory in this paper applies to any dimension.

Direct Simulation of Acoustic Scattering by Two- and Three-Dimensional Bodies

2000 ◽  
Vol 37 (1) ◽  
pp. 68-75 ◽  
Author(s):  
Olivier A. Laik ◽  
Philip J. Morris
Keyword(s):  
Three Dimensional ◽  
Acoustic Scattering ◽  
Direct Simulation

scholarly journals Cartesian Mesh Linearized Euler Equations Solver for Aeroacoustic Problems around Full Aircraft

2015 ◽  
Vol 2015 ◽  
pp. 1-18 ◽  
Author(s):  
Yuma Fukushima ◽  
Daisuke Sasaki ◽  
Kazuhiro Nakahashi
Keyword(s):  
Euler Equations ◽  
Complex Geometry ◽  
Time Integration ◽  
Three Dimensional ◽  
Acoustic Scattering ◽  
Shielding Effect ◽  
Immersed Boundary ◽  
Noise Propagation ◽  
Linearized Euler Equations ◽  
Cartesian Mesh

The linearized Euler equations (LEEs) solver for aeroacoustic problems has been developed on block-structured Cartesian mesh to address complex geometry. Taking advantage of the benefits of Cartesian mesh, we employ high-order schemes for spatial derivatives and for time integration. On the other hand, the difficulty of accommodating curved wall boundaries is addressed by the immersed boundary method. The resulting LEEs solver is robust to complex geometry and numerically efficient in a parallel environment. The accuracy and effectiveness of the present solver are validated by one-dimensional and three-dimensional test cases. Acoustic scattering around a sphere and noise propagation from the JT15D nacelle are computed. The results show good agreement with analytical, computational, and experimental results. Finally, noise propagation around fuselage-wing-nacelle configurations is computed as a practical example. The results show that the sound pressure level below the over-the-wing nacelle (OWN) configuration is much lower than that of the conventional DLR-F6 aircraft configuration due to the shielding effect of the OWN configuration.

Production and Development of Secondary Flows and Losses Within a Three Dimensional Turbine Stator Cascade

1985 ◽  
Author(s):  
A. Yamamoto ◽  
R. Yanagi
Keyword(s):  
Three Dimensional ◽  
Quantitative Information ◽  
Secondary Flows ◽  
Suction Surface ◽  
Trailing Edge ◽  
Loss Mechanism ◽  
Flow Measurements ◽  
Aerodynamic Loss ◽  
Vortical Flows ◽  
Turbine Stator

Using five-hole pitot tubes, detailed flow measurements were made before, within and after a low-speed three-dimensional turbine stator blade row to obtain quantitative information on the aerodynamic loss mechanism. Qualitative flow visualization tests and endwall static pressure measurements were also made. An analysis of the tests revealed that many vortical flows promote loss generation. Within a large part of the cascade, a major loss process could be explained simply as the migration of boundary layer low energy fluids from surrounding walls (endwalls and blade surfaces) to the blade suction surface near the trailing edge. On the other hand, complexity exists after the cascade and in the vortical flows near the trailing edge. The strong trailing shedding vortices affect upstream flow fields within the cascade. Detailed flow surveys within the cascade under the effects of blade tip leakage flows are also included.

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