The following research focuses on the analytical and numerical study of an arcjet constrictor. In order to perform these analyses, a geometric design of the constrictor was proposed. The analytical study considers mathematical models proposed by Stine and Watson, related to the properties of air propellants, such as the specific enthalpy, electric conductivity, thermal conductivity, and specific heat. The numerical study considered the equations for mass, momentum, energy, and electricity that describe the interaction between the electric arc and the fluid flow. These equations were solved in ANSYS FLUENT software, in which the $\kappa$-$ϵ$ turbulence and the magnetohydrodynamic (MHD) models were used. The external routines, including user-defined functions, user-defined scalars, and user-defined memory were implemented in C++ language for source terms and linked to ANSYS FLUENT. The velocity profiles were obtained analytically for the electric arc temperatures of 9000 K, 10,000 K, and 11,000 K with peak magnitudes of 2960 m/s, 3350 m/s, and 3100 m/s, respectively, at the outlet of the constrictor. It was observed from the numerical results that the velocity magnitude of the air-based plasma inside the constrictor increases as the temperature of the electric arc rises up to 10,000 K However, above 10,000 K, the velocity magnitude decreases because at this temperature level, the air particles become completely ionized, and the specific heat of the air-based plasma decreases. The numerical simulation produced velocity profile magnitudes at two different electric arc temperatures (9000 K and 10,000 K) with peak magnitudes of 2400 m/s and 2900 m/s, respectively, at the outlet of the constrictor. The numerical and analytical results were very close with an error of 16.327%.

The following research focuses on the study of the behavior of air plasma developed inside a 200 kW arc-jet constrictor. The scope of the analysis performed in the present document is focused specifically on the velocity fields and their characteristics inside the constrictor domain. Among them, the velocity magnitude, the distribution of the radial profiles at different stations along the length of the constrictor, and the axial velocity profile distribution. The analytical study considers mathematical models, which include air properties like specific heat, thermal conductivity, electric conductivity and enthalpy. The axial enthalpy distribution is shown at different radii of the constrictor in order to explain the presence of the velocity fields inside the control volume of interest. In the present work, it was found that the magnitude of the air plasma velocity fields increases due to the contact with the electric arc along the constrictor, reaching maximum velocity values of 5000 m/s at 10,000 K in the center of the constrictor and gradually decreasing when the constrictor radius approaches the wall. These findings provide insight into performance aspects of an arc jet constrictor using atmospheric air as a propellant. A key limitation of the present study stems from the initial assumptions and restrictions detailed in the Materials and Methods section. These constraints inherently alter several plasma flow parameters, namely the Lorentz force, the radial variation of the electric potential, etc.