Swirl Arc: A Model for Swirling, Turbulent, Radiative Arc Heater Flowfields

A model for swirling, turbulent, radiative arc heater flowfields, typical of those used for ablative testing of materials, is developed. Included in the model are provisions for secondary gas injection with swirl. The model is based on: swirl number less than unity, i.e., no reverse flow in the constrictor; a Prandtl mixing length turbulence formulation; and a gray gas radiation formulation so that absorption near the wall can be included. The resulting time-averaged conservation equations are then solved numerically using a finite-difference technique. The code results predict swirl decay and its influence on arc stability, the global performance parameters such as voltage, bulk enthalpy, and heat flux, and the enthalpy and velocity flowfields. Stability parameters are outlined and included in the arc heated flowfield model. These parameters are the electrical resistance between centerline and wall and the balance between the destabilizing arc column kink forces (expression given) and the swirl stabilizing pressure forces. The resulting flowf ield model is used to predict the characteristics of a high-pressure (10-MPa inlet chamber pressure) air arc heater. Progressing axially, i.e., in the direction of the gas gaining energy, these results indicate that: 1) the central enthalpy peak decreases; 2) the swirl flowfield and resultant stabilizing radial force decay rapidly until augmented by secondary wall injection; 3) the radial pressure differential is small, AP/P<1; 4) the radiative heat flux is constant while the turbulent heat flux increases; 5) the arc radius increases; 6) the electrical resistance from center to wall decreases exponentially; and 7) the stability radius (the equilibrium radius for stabilizing-destabilizing forces) increases until secondary injection occurs. Nomenclature A = cross-sectional area of constrictor, m2 B = Planck function E = voltage gradient, V/m F = magnetic force, N/m3 h = enthalpy, J/kg / = current, A; radiant intensity, W/m2