Modeling and simulation of fragmentation of suddenly heated liquid metal jets.

Abstract

Thermoelastic response of liquid metal targets exposed to high-volumetric-energy deposition in times shorter than the target hydrodynamic response time (i.e., sound travel time) is of interest to several research areas, including first walls of fusion reactors (especially inertially confined fusion reactors), targets for high-power accelerators such as the Spallation Neutron Source, muon collider targets, etc. Under conditions that exist in these reactors, accelerators, etc., the deposited energy is considered instant in time from the hydrodynamic point of view. Because thermal heat conduction requires a longer than instant response time for energy redistribution, only hydrodynamic phenomena should be taken into account when modeling and simulating the fragmentation of suddenly heated liquid metal jets. Sudden energy deposition causes an instant rise in temperature that leads to a corresponding rise in the thermal pressure that causes excitation of sound waves, i.e., shock waves and rarefaction waves. During this excitation of sound waves, pressure oscillates with magnitude {+-} {Delta}P that corresponds to an initial thermal pressure of tens of katm. Liquids are frequently observed to withstand significant negative pressures (hydrostatic tensile stresses). Yet, a liquid subjected to a negative pressure is metastable. The formation and behavior of cavities (empty voids) under negative pressures was previously studied. Theoretically, the obtained fracture (failure) pressure of mercury is in good agreement with experimental results. Cavitation, or spontaneous formation of cavities, in stressed liquid metal targets is of interest to engineers and physicists who operate high-power targets in fusion reactors, nuclear accelerators, and particle colliders. The problems of liquid target oscillation in the presence of large magnitudes of negative pressure, and the mechanism of fragmentation and its consequences are considered in this analysis. It is shown that a cavity coming into existence will initiate a shock wave that is actually a relaxation shock wave initiated when the stretched medium reverts to normal density from the low-density state. The nature of this relaxation wave is similar to that of the detonation wave. It is also shown that a cavity born at the high-negative-pressure stage expands permanently and does not disappear. This permanent expansion and failure to disappear is a major difference between the cavity dynamics in stretched media and the dynamics observed in the usual cavitation processes that occur when vapor bubbles collapse during a phase of increased pressure, and is the result of ''unloading'' or ''discharging'' of the medium by the relaxation shock wave initiated by the appearance of the cavity. Detailed calculations of cavity dynamics are presented for both spherical and cylindrical liquid metal target systems.