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

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

Excerpt from the Proceedings of the COMSOL Multiphysics User's Conference 2005 BostonThomas DreebenSimulation of heat and momentum flow in a quartz mercury-filledHID lamp in vertical operationAbstract FEMLAB is used to provide a benchmarksimulation for a classical problem in high-intensitydischarge lighting: the pure mercury-filled quartzHID (high-intensity discharge) lamp. A briefdescription of how an HID lamp works is provided.A steady 2-dimensional axi-symmetric formulationestimates the operating temperatures, electricalpotential, and gas velocities for an HID lamp runningin vertical orientation. Governing equations and theirapproximations are described: These include thecompressible continuity equation, the Elenbaas-Heller (heat balance) equation, the current continuityequation for electrical potential, and momentumequations in the radial and vertical directions. Lamppower of 175 W is imposed by adjusting theelectrode voltage so that the specified power isobtained. This uses the integration coupling variablefeature in FEMLAB, as the lamp power is a volumeintegratedquantity. Heat conduction through thequartz arc-tube wall is also included, with theexternal boundary condition governed by radiationfrom the exposed surface. The model providesestimates of the temperature profiles in the gas and inthe arc tube, electrical potential in the gas, andbuoyancy-driven velocity in the gas. Results give usa wealth of baseline information on a working HIDlamp.1 How a mercury HID lamp worksA typical mercury HID lamp 1 is comprised of 10 –50 mg of mercury enclosed in a transparent arc tube,usually made of quartz. The arc tube has a tungstenelectrode sealed in each end. A ballast supplieselectrical power to the electrodes in the form ofalternating current. This electrical power raises thetemperature of the mercury to the point that it turnscompletely into vapor. The current then ionizes thevapor in a path between the electrodes called the arc.In steady operation, the temperature in the arc istypically around 6000 K, and many mercury ionsthere are in excited states. A photon is emitted everytime an excited ion reduces its energy level to a lowerstate – this is how the lamp gives off light. Theelectrical power that is not converted to light is lost asheat, most of which conducts to the arc-tube wall andradiates from the outer surface according to theStefan-Boltzmann law.2 Problem formulationThe computational domain is a 2-d axisymmetricslice of an arc tube in vertical orientation as shown inFigure 1.Keywords FEMLAB 3.1 – HID lamp, buoyancy,natural convection, Elenbaas-Heller, compressibleT. DreebenOSRAM SYLVANIATel: 978-750-1688Fax: 978-750-1792E-mail: thomas.dreeben@sylvania.comFigure 1: HID lamp computational domain.Axisymmetric coordinates are normalized to thearc-tube inner radius.