Modelling of time development of cylindrical underwater spark channel in compressible viscous liquid

In this study, a new finite-difference cylindrical model of long underwater spark is developed that allows us to numerically calculate the time evolution of the underwater spark channel from a given power input. A one dimensional simulation starts in the breakdown moment. The whole time development is divided into time steps of equal duration. The investigated region consists of a homogeneous cylindrical central column filled with weakly ionized vapour and its atomic fragments, and co-axial cylindrical liquid slabs of equal thickness in the beginning. In each time step, some energy (experimentally given and reduced by losses spent on dissociation, excitation, and ionization) is delivered into the central plasma column. This energy is partly irradiated, out-conducted, spent on mechanical work, and/or used for an increase of inner energy of the plasma column. This ambiguity enables us in future to fit, e.g. the plasma column diameter at the end of energy input to its experimental value. The model shows that plasma channel expansion generates a primary pressure wave propagating with supersonic velocity, and a subsequent secondary pressure wave that propagates with sound velocity. An advantage of this approach is that the present solution with constant coefficients can be relatively easily upgraded to a solution with variable coefficients.