Part I: 3DPTV: Advances and Error Analysis. Part II: Extension of Guderley's Solution for Converging Shock Waves

Citation

Ponchaut, Nicolas Frederic (2005) Part I: 3DPTV: Advances and Error Analysis. Part II: Extension of Guderley's Solution for Converging Shock Waves. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/09ZH-9M66. https://resolver.caltech.edu/CaltechETD:etd-05312005-111401

Abstract

This work is divided into two unrelated parts. In the first part, a full three-dimensional particle tracking system was developed and tested. Three images, from three separate CCDs placed at the vertices of an equilateral triangle, permit the three-dimensional location of particles to be determined by triangulation. Particle locations measured at two different times can then be used to create a three-component, three-dimensional velocity field. Key developments are the ability to accurately process overlapping particle images, offset CCDs to significantly improve effective resolution, treatment of dim particle images, and a hybrid particle tracking technique ideal for three-dimensional flows when only two sets of images exist. An in-depth theoretical error analysis was performed, which gives the important sources of error and their effect on the overall system. This error analysis was verified through a series of experiments, and a vortex flow measurement was performed. In the second part, the problem of a cylindrically or spherically imploding and reflecting shock wave in a flow initially at rest was examined. Guderley's strong shock solution around the origin was improved by adding two more terms in the series expansion solution for both the incoming and the reflected shock waves. A series expansion was also constructed for the case where the shock is still very far from the origin. In addition, a program based on the characteristics method was written. Thanks to an appropriate change of variables, the shock motion could be computed from virtually infinity to very close to the reflection point. Comparisons were made between the series expansions, the characteristics program, and the results obtained using an Euler solver. These comparisons showed that the addition of two terms to the Guderley solution significantly increases the accuracy of the series expansion.

Thesis Files