Stationary supersonic plasma expansion: continuum fluid mechanics versus direct simulation Monte Carlo method

Abstract

Supersonically expanding stationary thermal plasma, formed by a thermal cascaded arc is studied. Due to the low chamber pressure (20-100 Pa) the results of continuum mechanics model can be doubtful. This is why these results are validated against kinetic Monte Carlo simulation and experimental data obtained by means of laser induced fluorescence. The analysis proves that continuum mechanics is still applicable for the velocity and temperature field predictions downstream of the shock region. However, the shock formation and some non-equilibrium effects typical for supersonic flow can be correctly studied only with the help of kinetic simulations. We show that the errors in the results using continuum mechanics can be attributed to the presence of flow gradients. These errors diminish when the shock regions are thickened due to rarefaction, viscosity and heat conductivity. Besides, both methods show that the effect of the chamber geometry on the plasma flow field is important.

Measurement and modeling of a diamond deposition reactor: Hydrogen atom and electron number densities in an Ar∕H2 arc jet discharge

“…The conservation equations 35 for mass, species, energy, and radial and axial momentum were numerically integrated, simultaneously, using thermal and caloric equations of state and initial and boundary conditions in 2D, i.e., the cylindrical ͑r , z͒, coordinate space. The explicit conservative numerical integration scheme employed a time step of 20 ns and a grid size of 0.5 mm in r and 2 mm in z, and continued until steady-state conditions were attained.…”

Multi-scale Modelling of the Two-Dimensional Flow Dynamics in a Stationary Supersonic Hot Gas Expansion

“…In Fig. 3(b)-(e) a comparison between experimental data from [6], results from the present hybrid method, results from full DSMC simulations performed by Selezneva et al [5], and results from present continuum simulations for the 2-dimensional velocity field in the expansion-shock region is presented. The velocity contours in Fig.…”

“…Although several studies have been devoted to supersonic expansion of gas jets in a low pressure environment [3,4,5,6], full understanding of the processes governing the flow has not been reached yet. In particular, it is still not completely clear whether, due to rarefaction effects, the barrel shock still protects the supersonic part of the flow from the invasion of background molecules, i.e.…”

“…It has been shown [5] that, because of rarefaction effects, the Navier-Stokes equations are not adequate for the description of this problem, and therefore, the continuum CFD (Computational Fluid Dynamics) approach fails in predicting the flow field in the expansion-shock region. A kinetic simulation model should be applied to correctly study the flow.…”

“…A kinetic simulation model should be applied to correctly study the flow. For this reason, in the past, DSMC (Direct Simulation Monte Carlo) has been used [5]. However, because DSMC computational expenses scale with Kn −4 , it was impossible to fulfill the DSMC requirements with respect to the size of gridcells and timesteps, expecially near the inlet, where the Knudsen number is quite low [5].…”