Self-similar turbulent vortex rings: interaction of propellant gases with blood backspatter and the transport of gunshot residue

Abstract

Self-similar turbulent vortex rings are investigated theoretically in the framework of the semi-empirical turbulence theory for the modified Helmholtz equation. The velocity and vorticity fields are established, as well as the transport of passive admixture by turbulent vortex rings. Turbulent vortex rings of propellant gases originating from the muzzle of a gun after a gunshot are an important phenomenon to consider in crime scene reconstruction. In this work, it is shown that this has a significant repercussion on the outcome of backward blood spatter resulting from a gunshot. Turbulent vortex rings of propellant gases skew the distribution of bloodstains on the ground and can either propel blood droplets further from the target, or even turn them backwards towards the target. This is revealed through the final bloodstain locations and the respective distributions of the number of stains and their area as a function of distance from the target for two different shooter-to-target distances. An image of the propagating muzzle gases after bullet ejection is overlaid with the predicted flow field, which reveals satisfactory agreement. Gunshot residue is an important factor in determining the events of a violent crime due to a gunshot and are considered to be entrained and transported by the propellant gases. The self-similar solutions for the flow, vorticity and concentration of gunpowder particles are predicted and the results are shown to be within the measured range of a limited set of experimental data.