Electrothermal instability in the seeded combustion gas boundary layer near cold electrodes

Abstract

A transition of discharge mode from diffuse to constricted or arc mode in the laminar boundary layer of the seeded combustion gas over a coid anode is analyzed by use of a linear stability theory on temperature and electrical fields. Cases of an externally applied eiectric field are investigated. For the basic steady distribution of unperturbed physical quantities in the boundary layer, an exact solution is used that is obtained as a result of analysis made around the anode by use of a three-fluid model. It is proven that when the parameter, expressed by the ratio of Joule heat to conductive heat of gas, exceeds a certain critical value, the diffuse mode discharge shows instability and that a transition of discharge mode to arc mode can occur as a result of electrotherma l instability for small perturbations of gas temperature, electron temperature, current density, and electron number density. This type of instability is tightly connected with the extremely low electrical conductivity region near the cold electrode and the lower wall temperature brings about this instability more easily. It is also proven from a study for three kinds of surface boundary conditions of different physical situations that the instability is controlled by use of electrodes of higher thermal conductivity but lower electrical conductivity.