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 2 ms long 1.3 GeV proton pulses 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 vapor 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-vapor system is calculated from the van der Waals equation, but general method how to obtain such properties using arbitrary equation of state is also presented. A second order accurate high-resolution shock-capturing numerical scheme is applied with different kind of limiters in the numerical calculations. Our analysis show that even 75 degree temperature heat shocks cannot cause considerable cavitation effects in mercury.