A time-dependent model for high-pressure discharges in narrow ablative capillaries

Abstract

A time-dependent quasi-one-dimensional model is developed for studying high- pressure discharges in ablative capillaries used, for example, as plasma sources in electrothermal launchers. The main features of the model are (i) consideration of ablation effects in each of the continuity, momentum and energy equations; (ii) use of a non-ideal equation of state; and (iii) consideration of space- and time-dependent ionization.

A Study on the Efficient Method for the Solution of the Saha Equation in the Numerical Simulation of Capillary Discharge

“…However, if is artificially set to be an empirical value, and might still be obtained by solving (17) with procedures (i)-(vi) as solving (15). Then, a new could be obtained by calculating (5). This is actually an iteration process about which could be expressed as…”

“…In the series researches of Zoler et al [5,14], the energy conversation equation is transformed through the variable substitution which makes it able to give temperature directly. However, couples of partial differential terms would also be introduced into the model which would cause extra computation amount for calculating these terms.…”

“…As key physical processes in the ET or ETC launch system, the research in this field is always focused on the capillary discharge which generates high pressure and high temperature plasma by ablating the wall of the tube to serve as working medium or ignite the propellant [2]. During the last several decades, various mathematical models with different degree of simplification were established based on the Euler equations to study this physical process [3][4][5][6][7][8][9]. As one can find from these models, a characteristic is that those driver terms or transport coefficients, such as conductivity and ablation rate, are all related to the plasma composition, so that one needs to determine the composition of plasma in each computational cell firstly before solving the mathematical model for the plasma properties of next time step.…”

Reliable, highly reproducible plasma injectors for electrothermal and electrothermal-chemical launchers

“…The models for the ablative discharges at high energies [3]- [5], [13] predict that the larger values for the plasma temperature and density are reached near the anode (at the closed end of the discharge tube) and the lower values of these parameters at the capillary exit.…”

“…If we take into consideration the dependence of the ablation rate on plasma temperature and density [3]- [5], [11], [12], the ablation (reflected by the tube diameter after discharge) is expected to be larger in the anode region; e.g., larger diameter should be found close to the anode. This proves that another mechanism, most probably ablative erosion, is a dominant process.…”