a Study of Three-Dimensional Natural Convection in High Pressure Mercury Lamps.

A three-dimensional numerical model utilizing curvilinear coordinates and an efficient solution method has been developed and used to investigate natural convection in horizontal, high-pressure mercury-vapor arcs confined in electroded, quartz arctubes. This investigation consists of two topics of critical importance to lamp design considerations, namely, a parametric study of the arctube design parameters and a study of arctube orientation with respect to gravity. First, a parametric study of the design parameters of the arctube, such as the mercury pressure, the curvature of the curved arctube, the arctube diameter, and etc. is performed. The objective is to investigate their effects on the temperature distribution of the arctube. Results show that the geometric design parameters can be ranked in the order of their significance: curvature of the arctube, electrode offset distance, arctube diameter, electrode insertion length. Secondly, based on the above result, a downward curved arctube with offset electrodes has been chosen to perform a further study which investigates the degree of uniformity of the wall temperature distribution, and the impact of arctube inclination angle with respect to gravity on the transport process and the resulting temperature distribution. For the horizontally mounted arctube, both the prediction and measurement show that the interactions of the curved high temperature core, resulting from the balance of the buoyancy and the electric field, and the bent arctube shape, gives the top wall temperature a double -peak distribution while the bottom wall temperature shows a single-peak distribution. The wall temperature distribution exhibits substantially sensitivity to the inclination angle, changing the top wall temperature from a symmetric double -peak profile for horizontal mounting to progressively more asymmetric single-peak profiles with increasing inclination angle. This change of characteristics in wall temperature distribution has important effects on the performance of the arctube. With regard to numerical algorithm, a new relaxation procedure has been developed to treat the exponential source term in the energy equation arising from the combined radiation and ohmic heating effects. Consequently, the number of iterations needed to obtain satisfactory results can be reduced by half.