4. Constricted Arc in a Parallel Flow This is the desired configuration for an arcjet (Fig. 4 ). Here, the heat which arrives through internal conduction at the arc periphery is removed by convection in the outer flow. The gas which comes into contact with the arc is heated as it moves axially and some of it reaches the ionization threshold Te and becomes part of the arc itself. This means the arc grows with distance, just as the thermal boundary layer adjacent to a heated surface does Swirling Propellant Flow Arc Column Anodic Arc Root Cathode Cathodic Arc Root Constricted Arc in Arcjet Fig. 4. Constricted Arc in Arcjet Let cpu), be the axial mass flux at the arc's edge(r=Ra). The amount of" new arc flow in a distance dx is then (ou) 2mR dr dx. The energy absorbed in heating this gas from Tout( the buffer gas temperature)to Te must be supplied by the arc power dissipation. Using(7), we then have (o)2c2(T-Tm)=4(T-7) (16) In order to estimate ou), we now make the further assumption that the quantity puis independent of r at a given x. This is motivated by the observation that in a parallel 16.522, Space Propulsion Lecture 11-124. Constricted Arc in a Parallel Flow This is the desired configuration for an arcjet (Fig. 4). Here, the heat which arrives through internal conduction at the arc periphery is removed by convection in the outer flow. The gas which comes into contact with the arc is heated as it moves axially, and some of it reaches the ionization threshold Te and becomes part of the arc itself. This means the arc grows with distance, just as the thermal boundary layer adjacent to a heated surface does. Fig. 4. Constricted Arc in Arcjet Let (ρu)e be the axial mass flux at the arc’s edge (r=Ra). The amount of “new” arc flow in a distance dx is then ( ) ρu e 2πRa dRa dx dx . The energy absorbed in heating this gas from Tout (the buffer gas temperature) to Te must be supplied by the arc power dissipation. Using (7), we then have ( ) ρu e 2πRa dRa dx cp Te − Tout ( )= 4πkc Tc − Te ( ) (16) In order to estimate (ρu)e , we now make the further assumption that the quantity ρu 2 is independent of r at a given x. This is motivated by the observation that in a parallel, 16.522, Space Propulsion Lecture 11-12 Prof. Manuel Martinez-Sanchez Page 8 of 18