Two-phase Equation Of State Research Articles

Prediction of shock-induced cavitation in water

Fluid-structure interaction problems that require estimating the response of thin structures within fluids to shock loading have wide applicability. For example, these problems may include underwater explosions and the dynamic response of ships and submarines; and biological applications such as Traumatic Brain Injury (TBI) and wound ballistics. In all of these applications the process of cavitation, where small cavities with dissolved gases or vapor are formed as the local pressure drops below the vapor pressure due to shock hydrodynamics, can cause significant damage to the surrounding thin structures or membranes if these bubbles collapse, generating additional shock loading. Hence, a two-phase equation of state (EOS) with three distinct regions of compression, expansion, and tension was developed to model shock-induced cavitation. This EOS was evaluated by comparing data from pressure and temperature shock Hugoniot measurements for water up to 400 kbar, and data from ultrasonic pressure measurements in tension to -0.3 kbar, to simulated responses from CTH, an Eulerian, finite volume shock code. The new EOS model showed significant improvement over preexisting CTH models such as the SESAME EOS for capturing cavitation.

Ion-beam-driven warm dense matter experiments

As a technique for heating matter to high energy density, intense beams of heavy ions are capable of delivering precise and uniform beam energy deposition to a relatively large sample. The US heavy ion fusion science program has developed techniques for heating and diagnosing warm dense matter (WDM) targets. We have developed a WDM target chamber and a suite of target diagnostics including a fast multi-channel optical pyrometer, optical streak camera, VISAR, and high-speed gated cameras. Initial WDM experiments heat targets by both the compressed and uncompressed parts of the NDCX-I beam, and explore measurement of temperature, droplet formation and other target parameters. Continued improvements in beam tuning, bunch compression, and other upgrades are expected to yield higher temperature and pressure in the WDM targets. Future experiments are planned in areas such as dense electronegative targets, porous target homogenization and two-phase equation of state.

High-energy density physics experiments with intense heavy ion beams

The US heavy ion fusion science program has developed techniques for heating ion-beam-driven warm dense matter (WDM) targets. The WDM conditions are to be achieved by combined longitudinal and transverse space-charge neutralized drift compression of the ion beam to provide a hot spot on the target with a beam spot size of about 1 mm, and pulse length about 1–2 ns. As a technique for heating volumetric samples of matter to high-energy density, intense beams of heavy ions are capable of delivering precise and uniform beam energy deposition d E/d x, in a relatively large sample size, and the ability to heat any solid-phase target material. Initial experiments use a 0.3 MeV K + beam (below the Bragg peak) from the NDCX-I accelerator. Future plans include target experiments using the NDCX-II accelerator, which is designed to heat targets at the Bragg peak using a 3–6 MeV lithium ion beam. The range of the beams in solid matter targets is about 1 μm, which can be lengthened by using porous targets at reduced density. We have completed the fabrication of a new experimental target chamber facility for WDM experiments, and implemented initial target diagnostics to be used for the first target experiments in NDCX-1. The target chamber has been installed on the NDCX-I beamline. The target diagnostics include a fast multi-channel optical pyrometer, optical streak camera, VISAR, and high-speed gated cameras. Initial WDM experiments will heat targets by compressed NDCX-I beams and will explore measurement of temperature and other target parameters. Experiments are planned in areas such as dense electronegative targets, porous target homogenization and two-phase equation of state.

Richtmyer–Meshkov instability in liquid metal flows: influence of cavitation and magnetic fields

The influence of magnetic fields and cavitation on the Richtmyer-Meshkov (RM) instability in liquid mercury has been studied numerically in 2D geometry. Numerical results shed light on the evolution of the Muon Collider target proposed as a pulsed jet of mercury interacting with high intensity proton beams in a strong magnetic field. We have shown that a uniform longitudinal magnetic field significantly reduces amplitudes and velocities of surface instabilities and is able to stabilize the jet during period of time typical for the jet breakup at zero magnetic field. We have developed a simple homogeneous two-phase equation of state for modeling of liquids with cavitation bubbles and applied it to the study of the evolution of mercury due to the interaction with proton pulses.

The impact of compressible liquid droplet on hot rigid surface

The processes arising when a high-velocity liquid nitrogen drop impacts a hot rigid wall have been studied by means of numerical simulation. An extremely thin near-wall layer of fluid undergoing heating and liquid–vapor phase transition is clearly distinguished in the droplet, the rest of the liquid remaining cold. A model for the layer, based on the reduced compressible Navier–Stokes equations with a two-phase equation of state, has been constructed and adjusted to the known model for the cold liquid part of the drop, based on the barotropic liquid Lagrangian equations with the Tait equation of state. A predictor-corrector finite-difference scheme for the thin layer equations has been devised and coupled with the finite-element method for the barotropic liquid. Drop shapes and flow field distributions in the layer have been obtained for the impacts of nitrogen droplets of different sizes with an initial velocity 186 m/s and different wall temperatures. The influence of the vapor layer on the drop has been analyzed. The heat flux on the wall has been calculated. An analytic formula has been derived for the heat flux, which is in agreement with the calculations for droplets up to 0.1 mm radius.