Modelling high-pressure gas flows through long extended delivery tubes used for massive particle fuelling of tokamaks during a major disruptive instability or a preemptive fast plasma shutdown is presented using analytical theory and simulation. For steady-state flows, expressions were derived and compared with experiments for the transition diameter and inlet Mach number of a straight tube (pipe) attached to a 'nozzle-like' inlet valve, such that increases in pipe diameter have no effect on the flow rate (valve-limited flow), and decreases below the transition diameter cause decreasing flow rates (friction-limited flow). Analytical expressions for the exit outflow rate and other gas dynamic variables during the initial unsteady gas flow buildup were developed from the classical 1D centred expansion wave problem and compared with 2D axisymmetric FLUENT simulations with wall friction, and good agreement was found for sufficiently high-conductance pipes. The intrinsic time delay before steady-state outflow is reached can seriously limit plasma density increases during the disruption, as the disruption time scale is similar to the delay time or 'rise time' of the outflow at the exit plane. Thus, conditions required for strong collisional dissipation of destructive runaway electron currents can be compromised. A unique gas injection scheme 'burst membrane gas injection' is also presented in which a steady-state outflow at the exit plane can be established promptly once the membrane bursts. It is shown that the theoretically ideal rise time of the gas at the exit plane will be zero if the membrane had an instantaneous opening time, therefore the true rise time will be limited only by the rupture time of a real bursting disc. The duration of the initial steady-state gas delivery phase can be matched to the relevant disruption time scales (or runaway formation time) by simply adjusting the tube length.
Modelling penetration and plasma response of a dense neutral gas jet in a post-thermal quenched plasma