Self-Consistent Model of HID Lamp for Design Applications

This paper describes a robust and self-consistent high-intensity-discharge (HID)-lamp model implemented on a vendor-supplied computational platform. The model includes a one-dimensional representation of the sheath in the near-cathode region, which allows one to join solutions in the plasma and in the cathode body and thus to self-consistently determine the cathode fall and temperature and current density distribution along cathode's surface. The model has the capability to predict direct-current-operated-lamp properties from the first physical principles without relying on the experimental information (except the confirmation purpose of the predicted results). The P-1 method is used to model radiation transfer, where the mean absorption coefficient for spectral bands is being used to calculate the mean incident radiation for each band. In the scheme developed, the lamp body is divided into a number of domains that are coupled through boundary conditions (for example, boundary conditions for energy and current continuity equations in the plasma depend on the solutions of the cathode and anode models). The complete global solution is obtained iteratively. Properties of interest of the cathode body, the adjacent sheath, the gas-filled region, and the anode body are computed for a typical HID lamp. Results are presented for a discharge medium consisting of an argon-mercury mixture at an operating pressure of 0.11 MPa. The lamp current is 10 A. The predicted maximum temperature and plasma velocity are 10 700 K and 8 m/s, respectively, for this particular lamp. Adequate accuracy (experimental validation) occurs under the following operating conditions: a dc current between a few amperes and a few tens of amperes flows in a discharge medium with a pressure from one to a few tens of atmospheres