An analytical solution for unsteady, inviscid jet formation due to asymmetric 2-d ring collapse

Here we derive a closed form analytical solution for an unsteady inviscid jet caused by the asymmetric collapse of a 2-d ring using linearized, small disturbance, velocity potential theory and classical analytical methods. Use is made of both the Laplace transformation and elementary eigenfunction expansions to solve the associated governing equations. The streamwise diffusion term, e.g. φrr is shown to be second order and is neglected. Jet shape that was computed using the analytical model is compared with CTH (hydrocode) simulations and limited experimental data and shown to provide reasonable agreement. Jet spreading is shown to be consistent with classical turbulent jet scaling in accordance with known shaped charge jet hydrodynamic assumptions. With confidence that the analytical solution is a viable tool we consider the numerical issues associated with rotational symmetry, the effect of boundary loading disturbance to the jet and the effect of finite arrival time detonation wave conditions. Thus we conclude that this model provides a simple, but useful supplement to conventional hydrocode simulation jetting phenomenon due to asymmetric loading of 2-d circular rings.