Relationship Between Perturbation Size and Structure of the Vortex Pair for Converging Cylindrical Shocks
Converging cylindrical shock front shapes, bearing small and large perturbations, were examined via spark Schlieren photography taken near the geometric center. The perturbation parameter was found to increase with shock travel, according to r −n but with fluctuations that are found to be linearly proportional to its initial value. Based on the hypothesis that the distance between the vortex pairs is proportional to the radius where breakdown in shock front curvatures takes place, a relationship was obtained between the distance separating the two vortex pairs and the initial value of the perturbation. This relationship was found to be in excellent agreement with those experimentally measured. Both theory and experiments were also found to approach a constant value as the perturbation on the shock front increases beyond a certain limit.
Key WordsConverging cylindrical shocks Stability of converging shocks Vortex growth
Unable to display preview. Download preview PDF.
- Butler DS (1956) The stability of converging spherical and cylindrical shock waves. Armament Research and Development Establishment, Report No.(B) 18 /56Google Scholar
- Neemeh RA, Le DT (1989) Stability analysis of initially weak converging cylindrical shock waves. In: Kim YW (ed) Proc. 17th Intl. Symp. on Shock Tubes and Shock Waves, Bethlehem, Penn., July 17–21, pp 957–962Google Scholar