Restrike model for an MHD solver: application to plasma assisted supersonic combustion in scramjet
Creators: name:  A. BOURLET 
name:   J. LABAUNE 
name:   F. THOLIN 
name:   A. VINCENT-RANDONNIER 
name:   F. PECHEREAU 
name:   C. LAUX 
Publisher: name: Proceedings of  the 9th European Conference for Aerospace Sciences. Lille, France, 27 June - 1 July, 2022
Year: 2022
Subjects: FLIGHT PHYSICS
PLASMA FLOWS
ENERGY DEPOSITION

description: Over the last decades, many Plasma-Assisted Combustion (PAC) experiments in scramjet have demonstrated positive effects on supersonic combustion, such as increased pressure in the chamber or the flame stabilization inside the combustion chamber. Understanding these effects could lead to a breakthrough in scramjet technology, allowing an extension of the flight envelope of the current scramjet-powered aircraft. Only a few numerical studies have been reported in the literature since the modeling of plasma discharges requires taking into account many physical processes and a wide range of space and time scales for the flow and the plasma that can barely be addressed for the simulation of a complete combustion chamber. A promising yet straightforward technology relies on DC electric arc discharges, with currents in the range of a few amperes that generate a plasma channel of a few thousand Kelvin in interaction with the flow. Magnetohydrodynamic (MHD) can adequately solve the two-way coupling between the plasma and the fluid: the electric arc may influence the flow-field via Joule heating, and the flow may stretch the arc column over long distances. However, experiments have revealed the existence of a limiting-size process. Indeed, as the arc grows, voltage increases between the two feet of the arc. Consequently, the electric field is magnified up to the breakdown value (35 kV/cm in air), which allows a streamer breakdown and possibly an arc transition between two arcs branches, as shown in figure 1. The new arc acts as a shortcut for the most extended part of the old arc, leading to its blowout. This electrical breakdown, called \"restrike\" or \"back-breakdown\" in the literature, is fundamentally a non-equilibrium and non-neutral discharge. Because MHD assumes the quasi-neutrality and the local thermodynamic equilibrium of the plasma, this breakdown phenomenon cannot be simulated consistently. Therefore, adding a restrike model to the MHD approach is necessary to simulate the proper DC arc dynamics. Restrike models have already been developed for subsonic flows in DC-plasma torches, where the breakdown occurs between an electrode and the electrical arc. In the current work, we present an extended model suitable for supersonic flows and allowing a restrike between the arc\'s branches. In this two-step model, a first algorithm identifies the high-field regions likely to trigger ionization reactions where a streamer is assumed to appear, then it computes its trajectory, assuming the streamer follows the electric field line. Then, a second algorithm adds a plasma channel with a typical streamer radius and electrical conductivity along the field line. The added plasma acts like a branch circuit, collecting a fraction of the current and heated by Joule\'s effect. The streamer\'s modeled channel evolves to an arc channel if sufficiently high heating. Our model had been validated on 2D simulations of gliding arcs. In the current work, we present the validation of the model on 3D numerical simulations of a combustion chamber. The simulation is a reproduction of supersonic plasma-assisted combustion experiments done at ONERA\'s LAERTE facility, using a plasma module integrated in a hydrogen injector, as shown in figure 2.