Far field approximation for a nozzle exhausting into a vacuum.

1969 ◽  
Vol 6 (5) ◽  
pp. 626-628 ◽  
Author(s):  
JOHN W. BROOK
Keyword(s):  
Field Approximation ◽  
Far Field

scholarly journals Far-field approximation for hydrodynamic interactions in parallel-wall geometry

2006 ◽  
Vol 212 (2) ◽  
pp. 718-738 ◽  
Author(s):  
S. Bhattacharya ◽  
J. Bławzdziewicz ◽  
E. Wajnryb
Keyword(s):  
Field Approximation ◽  
Hydrodynamic Interactions ◽  
Far Field ◽  
Parallel Wall ◽  
Wall Geometry

A far-field scattering model in textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry

2020 ◽  
Vol 25 (5) ◽  
pp. 1155-1171
Author(s):  
Gaofeng Sha
Keyword(s):  
Elastic Waves ◽  
Field Approximation ◽  
Crystal Symmetry ◽  
Polycrystalline Materials ◽  
Far Field ◽  
Efficient Tool ◽  
Practical Applications ◽  
Full Wave ◽  
Non Destructive ◽  
High Computational Efficiency

Modeling the scattering-induced attenuation of elastic waves in heterogeneous polycrystals has practical applications in seismology and non-destructive evaluation. However, attenuation modeling for polycrystals with preferred crystallographic orientation (statistically anisotropic or textured polycrystals) has not been well studied. The far-field approximation (FFA) model, which is applicable for arbitrary crystal (triclinic) symmetry and valid for the whole frequency range (Rayleigh region, stochastic regime, and geometric region), has been reported for texture-free polycrystalline materials. This paper extends the FFA model to textured polycrystals with ellipsoidal grains of arbitrary crystal symmetry. This FFA model for textured polycrystals encompasses two advantages: a simple form of dispersion equation and high computational efficiency. Furthermore, this FFA model can predict both the attenuation and phase velocity of elastic waves in textured polycrystals. The FFA model in this study has also been validated by comparison with the full-wave second-order attenuation model on textured polycrystals of triclinic grains. This work provides a simple and efficient tool to predict the elastic wave behavior in heterogeneous polycrystalline materials.

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