Ac modelling of D2 automotive HID lamps including plasma and electrodes

Abstract

The 35 W D2 automotive headlight lamp with an electrode gap of around 4 mm is a well known example of a short-arc high-intensity discharge (HID) lamp. It has a filling of xenon, mercury, and sodium/scandium iodide and is driven by a rectangular-wave current of 0.4 A, 400 Hz. Other fields of application of HID lamps are video projection (UHP), street and industrial lighting, floodlighting, etc. Due to their small size and short timescales, HID lamps are often experimentally difficult to investigate or even inaccessible. Thus modelling gets more and more important. The challenges in modelling such lamps are e.g. the important plasma–electrode interaction, the time dependence (electrodes change with 400 Hz from anode to cathode phase and vice versa in the case of D2 lamps), and the complex plasma composition (Xe, Hg, NaI, ScI3 in the case of D2 lamps). Additionally the electrodes might change their well-defined tip geometry during operation, causing substantial changes in electrode temperature or electrode fall voltages. This paper intends to address all these questions and compare results of numerical simulations with measurements of plasma and electrode temperatures. Special focus is directed towards the important electrode–plasma interaction, which, even after seven decades of HID lamps, has not been understood satisfactorily. The results presented in this paper are very important for a better understanding of dc and ac HID lamps including the treatment of complex plasma compositions, the choice of the work functions, and the effect of different electrode geometries. Furthermore the results of the numerical simulations will lead to improved or new HID lamps.

Numerical investigation of time-dependent electrode-plasma interaction in commercial HID lamps

“…All these features are included in the numerical simulations. The numerical results for plasma and electrodes agree well with experimental findings [2]. The equations are solved using the finite element method assuming rotational symmetry on a HP visualize j6000 workstation with two 64-bit PA-8600 processors.…”

“…even for time-dependent lamp currents (alternating current (ac) operation). The model uses a complete energy balance for plasma temperature (1) and electrode temperature (2), and electric current continuity (3). As a special feature, an additional differential equation (4) accounting for deviations from local thermal equilibrium (LTE) due to strong diffusion of electrons and ions close to the electrodes is used (due to large particle density gradients between hot plasma spot and "cold" near-electrode plasma, cf.…”

“…This visualizes the problems experimental setups would have in measuring the time dependent temperature fluctuation at the electrode tip (complicated even more by interfering radiation from the plasma, cf. [2]). …”

Understanding anode and cathode behaviour in high-pressure discharge lamps

“…The dimensions taken into account (one-, two-or three-dimensional models 2 ) and the geometry of the electrode tip also have a major influence on the type of arc attachment and the local temperature distribution at the electrode tips and in the hot plasma spots [11]. The self-adjustment of plasma and electrodes as described in [10] for different processes is disturbed by applying external laser heating of anode or cathode.…”

Arc Shape of High-Intensity Discharge Lamps: Simulation and Experiments

“…The second part q accounts for radiation losses and is included in the simulation via a temperature-dependent function. Therefore, all radiation processes (e.g., line radiation of Hg or atom bremsstrahlung) were determined separately and added afterwards [15]. The heat capacity c p of the plasma is approximately constant (114 W·m −1 ·K −1 ), whereas the mass density ρ is space dependent due to the compressibility of the fluid.…”