Simulation of heat and momentum flow in a quartz mercury ... - Comsol

Excerpt from the Proceedings of the COMSOL Multiphysics User's Conference 2005 BostonFigure 4: Temperature profile versus normalizedlamp radius, halfway between the electrodes.Figure 6: Electrical potential (Voltage) throughoutthe lamp.The predicted voltage across the electrodes of 106.5V is lower than the real lamp voltage by 20%, due tothe model’s neglect of electrode plasma effects andtheir associated cathode fall. The slight verticalasymmetry in potential is an indirect result of theconvection: Convection causes a slight verticalasymmetry in the temperature profile of Figure 3.This influences the electrical potential through theappearance of electrical conductivity σ in Eq. (6).A pressure map, referenced to zero at the lowerelectrode tip, is shown in Figure 7.Figure 5: Vertical velocity profile versusnormalized lamp radius, halfway between theelectrodes.Historically, measurement of temperature profiles inmercury lamps show that the profiles such as Figure4 are generally accurate to within 5 or 10%. Thereare no direct measurements of gas velocity profiles,so Figure 5 gives us an approximation that would beunavailable without modeling: The maximumvelocity for a lamp of these dimensions is of order 10– 20 cm /sec. Note that the velocity upward in thecenter greatly exceeds the velocity downward nearthe walls. This is partly because the gas in the centeris much less dense, and partly because the gas in thecenter occupies less volume than the gas near thewall due to the axisymmetry of the arc tube.The electrical potential is shown in Figure 6.Figure 7: Pressure referenced to zero at the lowerelectrode tipThis characterizes the scale of the buoyancy forcesand shows that the pressure difference required tosupport the weight of the gas is about 2 Pa.ConclusionFinite-element analysis using FEMLAB is anefficient method for obtaining baseline informationon the working of a mercury-filled HID lamp.