Optimal Vortex Ring Formation at the Exit of a Shock Tube

Formation of vortex rings at the exit of a shock tube is studied theoretically. A model for predicting the maximum circulation that a vortex ring can attain at the exit of a shock tube is offered. To achieve maximum circulation the initial conditions and the design of the driver and driven sections must be such that the generated shock wave reaches the shock tube exit at least 4Dn/^2 time units (Dn is the nozzle diameter and U2 is the fluid velocity behind the shock wave) before the leading front of the expansion waves arrives at the shock tube exit. A simple way to satisfy this condition is to design a shock tube with long driver and short driven sections. The model is verified by comparison with available computational and experimental data.