Effects of plasma rotation and magnetic fields on convection flows in the horizontal burning high intensity discharge lamps

Li, Y.M.

Convection is critical in shaping the plasma temperature profiles, species segregation, arctube temperature distributions, plasma stability and a whole range of phenomena of importance to the high intensity discharge (HID) lamp performance and maintenance.

A 2D local thermodynamic equilibrium (LTE) arc plasma model is developed using FEMLAB. The model can be described by the energy balance equations for both arc plasma and arc-tube, and the compressible Navier-Stokes equations for low speed non-isothermal flow, and the current continuity equation for the plasma electric field determination.

Such a 2D model is appropriate to the positive column plasma with axial uniformity and only mercury plasma is used in the computation. In the absence of external applied magnetic field, the arc plasma bowing due to gravity driven natural convection can be demonstrated. The effect of uniform applied magnetic field and non-uniform field due to a line current (from the lead wire that powered the lamp) are added to the model. The Lorentz force due to applied magnetic field can counteract the buoyance force and reduce the arc bowing. The magnetic fields required to center the arc are determined. The net buoyance forces due to gravity are calculated for various lamp parameters and agreed well with the experimental measurements. The plasma rotation can be induced by arc-tube rotation. The plasma rotation is modelled by introducing the slip velocity boundary condition at the plasma arc-tube interface. At lower slip velocities, the hot plasma convective flow pattern is perturbed and moved sideway. At a critical slip velocity the plasma flow transits abruptly to nearly “centered” rotational flow. In a range of slip velocities, multiple steady state solutions are found.

Using the FEMLAB parametric solver, the solution branch obtained by increasing slip velocity, differs with the branch obtained by decreasing the slip velocity and the system clearly exhibits hysteresis behaviour. Different thermal energy balance models for the arc-tube are attempted.

For the fast rotating arc-tube, a simple single averaged temperature model based on total heat flux from the plasma balanced by overall thermal radiative cooling is also constructed. The multiple steady state and hysteresis behaviour is found to be robust and not affected by thermal models of the arc-tube. The effect of plasma rotation is explored with different lamp parameters.