On corona-induced gas motion and heating I: Field equations, modelling and vortex formation

Corona discharges generate ionic currents that flow from the glow into the inter-electrode space. These spatial currents force the gas through which they travel into motion, as the collisions between the ions and the neutral gas molecules transfer momentum and the energy of the electric field driving the ions to the gas. The transfer of momentum causes the gas to accelerate in the direction of the electric field; and the energy transfer results in gas heating and buoyancy forces. The governing field equations for the phenomenon are reviewed which describe the variations in gas temperature, velocity, density and pressure in terms of the rates of ionic momentum and electrical energy transfer. Boundary conditions are also considered with small-scale negative point–plane DC discharges in air in mind, and the order of magnitude of the terms in the equations is assessed for such situations. In this first paper of a two-part study, numerical solutions are not sought, but the situation is modelled using the known experimental facts for these discharges. The gas flow is shown to be dominated by the momentum transfer terms rather than the buoyancy terms, and resembles an entrained jet passing down the shank of the point electrode before leaving the tip and impinging on the plane. Transition from the Trichel pulse regime to the continuous glow with the central-channel heating that precedes breakdown is considered using vortex formation and shedding from the point electrode. Theoretical temperature predictions are in accord with experimental measurements. Previously discovered empirical laws describing the transition are discussed and it is shown that these may be explained by the transition of the flow to turbulence at a critical Reynolds number.