Finite Element Analysis of the Shock Waves Induced in the Liquid Wall of a Pellet Fusion Reactor

A shock wave induced in liquid metal is analyzed numerically by application of the finite element method. Since the governing equations of motion of the fluid are nonlinear, an incremental method is combined with the finite element method to obtain a convergent solution of the shock wave without an interaction technique. To demonstrate the validity of the method developed, shock wave problems in an inertial confinement spherical reactor with a liquid lithium “waterfall” are solved for two cases of surface heating due to soft x-ray absorption and bulk heating due to 14-MeV neutron absorption. The solution is based on a combination of the conservation equations for mass, energy, and momentum along with the following equation of state for liquid metals: p = P_b[(ρ/ρ₀)ⁿ − 1]. Numerical results show that peak pressure induced in the liquid lithium is very high even for a comparatively small energy release E_T = 700 M J/microexplosion of a pellet. Dynamic stress induced in a 5-cm-thick stainless steel pressure vessel is 1.14 × 10³ MPa for the surface heating. The numerical results also show that the dynamic stress induced by bulk heating is superimposed on that due to surface heating within the same period. Two appropriate ways to reduce the high stress are application of two-phase flow of liquid lithium or an increase in the thickness of the pressure vessel.