Two-phase flow model for energetic proton beam induced pressure waves in   mercury target systems in the planned European Spallation Source
  Two-phase flow calculations are presented to investigate the thermo-hydraulical effects of the interaction between 300 kJ proton pulses (2 ms long, 1.3 GeV) with a closed mercury loop which can be considered as a model system of the target of the planned European Spallation Source(ESS) facility. The two-fluid model consists of six first-order partial differential equations that present one dimensional mass momentum and energy balances for mercury vapour and liquid phases are capable to describe quick transients like cavitation effects or shock waves. The absorption of the proton beam is represented as instantaneous heat source in the energy balance equations. Densities and internal energies of the mercury liquid-vapour system are calculated from van der Waals equation, and the general method how to obtain such properties is also presented. A second order accurate high-resolution shock-capturing numerical scheme is applied with different kinds of limiters in the numerical calculations. %Our two-fluid model is very similar to the RELAP5 thermo-hydraulical code %which is used in the nuclear industry to simulate nuclear power plant accidents. Our analysis show that even 75 degree temperature heat shocks cannot cause considerable cavitation effects in mercury in 2ms long pulses 
Imre Ferenc Barna, Attila Richard Imre, Laszlo Rosta, Ferenc Mezei