Three-Dimensional Modeling of an HID Lamp Operated by a Direct Current

Summary form only given. Numerical modeling can be used to shorten the development cycle for high intensity discharge (HID) lamps. 2-dimensional modeling has been the preferred choice for most designers given that 2D simulation run-times are reasonable. The 2-D axisymmetric MHD (magnetohydrodynamics) model, as reported by Paul et al., predicts most physical phenomena of an HID lamp, regardless of operating power, as long as the lamp geometry and operating characteristics imply axial symmetry. Operation of a horizontally-placed lamp leads to a significant departure from axial symmetry; hence 2D modeling is of little practical use. Consequently, a 3D model is required under these circumstances. In this paper, we report a 3-dimensional model that solves the complete set of MHD equations, including species diffusion. The calculation of electric and magnetic fields is done by solving the Laplace and vector potential equations respectively. The P-1 radiation method is used to calculate the radiative power. A commercial software package, Fluent, is used as the computational platform. The majority of the physical models are solved through customized modules. As is the case for the 2-D model, the lamp is divided into sections and each section is modeled separately. The conserved solution for the complete system is obtained through a back and forth iterative scheme. For illustration purposes, we have chosen an ellipsoid lamp with a 5-mm interelectrode gap. Solutions have been done for the electrodes, including the cathode sheath, and the discharge domain. Modeling of cathode and its sheath is exactly the same as reported in [K.C. Paul et al., 31^st International Conference on Plasma Science, p. 248 (2004)]. The solution of the thoriated-tungsten cathode and tungsten anode has produced the temperature and/or current density boundary profiles at the associate boundaries, used for the plasma calculation. The discharge medium is a mixture of mercury and argon with an o- erating pressure of 0.11 MPa. The lamp is supplied by a direct current of 20 A. Calculations within the discharge region show a maximum plasma temperature of 11350 K and a maximum gas velocity of 6.4 m/s, near the cathode tip. The potential drop (arc + sheath) across the electrodes is shown to be 28.8 V (16.8 + 12). As expected, the temperature and radiation energy at the upper cross-section of the lamp are higher