962 resultados para Spherical trigonometry.


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This paper demonstrates the application of laser Doppler velocimetry (LDV) and particle image velocimetry (PIV) techniques to a particle-laden reacting flow of pulverized coal. A laboratory-scale open-type annular burner is utilized to generate velocity profiles of coal particles and micrometric alumina particles. Pair-wise two-component LDV measurements and high-speed stereo PIV measurements provide three-dimensional velocity components of the flow field. A detailed comparison of velocities for alumina and coal particle seeding revealed differences attributed to the wide size distribution of coal particles. In addition, the non-spherical shape and high flame luminosity associated with coal particle combustion introduces noise to the Mie scatter images. The comparison of mean and RMS velocities measured by LDV and PIV techniques showed that PIV measurements are affected by the wide size distribution of coal particles, whereas LDV measurements become biased toward the velocity of small particles, as signals from large particles are rejected. This small-particle bias is also reflected in the spectral characteristics for both techniques, which are in good agreement within the range of frequencies accessible. PIV measurements showed an expected lack of response of large coal particles to the turbulence fluctuations. The overall good agreement between LDV and PIV measurements demonstrates the applicability of the high-speed PIV technique to a particle-laden, high luminosity coal flame while highlighting some of its limitations. © 2013 Springer-Verlag Berlin Heidelberg.

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The impact of a slug of dry sand particles against a metallic sandwich beam or circular sandwich plate is analysed in order to aid the design of sandwich panels for shock mitigation. The sand particles interact via a combined linear-spring-and-dashpot law whereas the face sheets and compressible core of the sandwich beam and plate are treated as rate-sensitive, elastic-plastic solids. The majority of the calculations are performed in two dimensions and entail the transverse impact of end-clamped monolithic and sandwich beams, with plane strain conditions imposed. The sand slug is of rectangular shape and comprises a random loose packing of identical, circular cylindrical particles. These calculations reveal that loading due to the sand is primarily inertial in nature with negligible fluid-structure interaction: the momentum transmitted to the beam is approximately equal to that of the incoming sand slug. For a slug of given incoming momentum, the dynamic deflection of the beam increases with decreasing duration of sand-loading until the impulsive limit is attained. Sandwich beams with thick, strong cores significantly outperform monolithic beams of equal areal mass. This performance enhancement is traced to the "sandwich effect" whereby the sandwich beams have a higher bending strength than that of the monolithic beams. Three-dimensional (3D) calculations are also performed such that the sand slug has the shape of a circular cylindrical column of finite height, and contains spherical sand particles. The 3D slug impacts a circular monolithic plate or sandwich plate and we show that sandwich plates with thick strong cores again outperform monolithic plates of equal areal mass. Finally, we demonstrate that impact by sand particles is equivalent to impact by a crushable foam projectile. The calculations on the equivalent projectile are significantly less intensive computationally, yet give predictions to within 5% of the full discrete particle calculations for the monolithic and sandwich beams and plates. These foam projectile calculations suggest that metallic foam projectiles can be used to simulate the loading by sand particles within a laboratory setting. © 2013 Elsevier Ltd.