Joule Heating Driving Hydrodynamic Explosions from an Electrostatic Discharge Event*

An electrostatic discharge (ESD) spark in ambient air involves electric fields strong enough to ionize air; it also creates enough Joule heating to generate a shock wave. Modeling this transient process requires an intricate coupling between Joule heating and hydrodynamic flow, with spatial and time-dependent feedback between the plasma kinetics of the ESD spark creating Joule heating and fluid flow. Within this work, a Joule heating source modeling plasma chemistry is parameterized and mapped via a high-fidelity shock-physics code to obtain physical characteristics on fluid flow, simulating an 'infinite' axial line source explosion. Shockwave generation, propagation, and energy consumption exemplify hydrodynamic phenomena observed and calculated. Energy consumption by the hydrodynamics is 'earmarked' for advection away from the axial line source, and is guaranteed to be unavailable for other physical processes within the ESD event. Comparison to experimental validation data is performed and theoretical verification over a complete range of shock regimes is executed. Excellent agreement between hydrodynamic flow generated by simulation and collected from experiment in the strong and intermediate shock regimes is observed, substantiating the assumed form of the heat source.