Development of a Robust 3-D Model for HID Lamps and Comparison of Predicted and Measured Electrode Temperatures

Abstract

A 3-D numerical model is developed for predicting properties of high-intensity-discharge (HID) lamps. The developed model is based on the powerful and globally suitable, irrespective of optical thickness, discrete ordinates (DO) method for evaluating radiation transfer and predicting the properties of all sections of an HID lamp between two power-supply ends (viz., plasma, electrodes, glass bulb, stem, and lamp house) as a single entity. A test lamp is studied using this model, and the theoretically predicted electrode temperatures are compared with the experimentally measured values for realizing the model performance. The horizontally oriented lamp is operated at a discharge pressure of 2.5 MPa and a direct current (dc) of 2.69 A. In the plasma or gas-filled region, the developed 3-D model solves the complete set of magnetohydrodynamics: transport equations of mass, momentum, and energy along with the vector potential form of Maxwell's equations to account for the electromagnetic effects, and in the solid regions, it solves the energy balance equation with or without radiation transfer. Radiation transfer equation is solved using the DO method by dividing the electromagnetic spectrum into several gray bands. The model has been applied for calculating the properties of the test lamp. Calculations have been done for the electrodes and gas-filled or discharge region, but it is useful for the whole lamp. Output results give clear picture of distributions for temperature, velocity, electromagnetic fields, and radiation. Temperature of plasma near the cathode tip has been found as the maximum of 13 000 K, and it is about 8300 K near the anode tip. For an input power of 145 W, 67% has been dissipated in the bulk plasma as Joule heating, and the rest has been lost in the near-electrode regions or sheaths. The lamp converts 54% of the total input into radiation energy. Electrodes' surface temperatures have been measured experimentally using a two-color radiation thermometer. Comparison of experimentally measured temperature and theoretically predicted temperature is found to agree convincingly (within 8%)