16.522, Space Propulsion Prof.Manuel Martinez-Sanchez Lecture 11-12: SIMPLIFIED ANALYSIS OF ARCJET OPERATION 1. IntroductionThese notes aim at providing order-of-magnitude results and at illuminating the mechanisms involved. Numerical precision will be sacrificed in the interest of physical clarity. We look first at the arc in a cooled constrictor, with no flow, expand the analysis to the case with flow, and then use the results to extract performance parameters for arcjets. 2. Basic Physical AssumptionsThe gas conductivity model will be of the form σ=oa T−Te()⎧ ⎨ ⎩ T<Te()T>Te()Te≈6000−7000K()a≈0.8Si/m/K()(1) The termal conductivity k of the gas will be modelled as a constant (with possibly a different value outside the arc). This is a fairly drastic simplification, since in H2and N2k(T) exhibits very large peaks in the dissociation range (2000-5000K) and in the ionization range (12000-16000K). Because k always multiplies a temperature gradient, the combination dis relevant, and so the proper choice of ΦT( )=kdTk to be used is the averaged value k =1T2−T1kdTT1T2∫(2) over the range of temperatures intended. The arc gas is modelled as ideal, even though its molecular mass shifts strongly and its enthalpy increases rapidly in the dissociation and ionization ranges. In particular, cp=∂h∂T⎛ ⎝ ⎞ ⎠ phas strong peaks, similar to those of k(T), and, once again, we should use temperature-averaged values for it. The arc is assumed quasi-cylindrical, with axial symmetry and with gradients which are much stronger in the radial than in the axial direction (similar to boundary layers). The flow region comprises three sub-domains: (a) The arc itself, for r, corresponding to <Rax( )T>Te. This is the only part carrying current. (b) The outer gas, not ionized and with T<Te. 16.522, Space Propulsion Lecture 11-12 Prof. Manuel Martinez-Sanchez Page 1 of 18
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