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| Milan, October 2009 | page 1 Towards a Finite Element Calculation of Acoustical Amplitudes in HID Lamps Bernd Baumann 1, Marcus Wolff 1, John Hirsch 2, Piet Antonis 2, Sounil Bhosle 3 and Ricardo Valdivia Barrientos 4 1) Hamburg University of Applied Sciences, Germany 2) Philips Lighting, Eindhoven, The Netherlands 3) Université de Toulouse and CNRS LAPLACE, Toulouse, France 4) National Institute of Nuclear Research, Salazar, Ocoyoacac, Mexico

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| Milan, October 2009 | page 2 Energy Consumption Industrial production Transportation Heating and cooling Lighting …

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| Milan, October 2009 | page 3 High Intensity Discharge (HID) Lamp Arc tube / burner –Wall: Quartz or ceramics –Filling: Mercury –Additives: Metal halides etc Electrodes –Tungsten Discharge arc –Temperature: ca – 6000 K –Light source

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| Milan, October 2009 | page 4 AC Operation Advantages: –Avoids demixing –Avoids electrode errosion Disadvantages: –Flickering –Reduction of lamps lifetime –Lamp destruction Counteraction: –Electronical measures –Lamp design

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| Milan, October 2009 | page 5 Objective and Scope of Paper Numerical calculation of acoustic amplitudes in HID lamps Simplifications: –No inclusion of plasma dynamics –Simplified geometry –2 dimensional axisymmetric FE model –Simplified model for power input

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| Milan, October 2009 | page 6 Temperature Profile (Sutherlands law)

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| Milan, October 2009 | page 7 Inhomogenous Helmholtz Equation Power density Ideal gas law

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| Milan, October 2009 | page 8 Solution Eigenmodes

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| Milan, October 2009 | page 9 Amplitudes Loss factor Excitation amplitude:

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| Milan, October 2009 | page 10 Surface Loss: Shear Stress ceramics fluid Prandtls boundary layer

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| Milan, October 2009 | page 11 Surface Loss: Thermal Conduction region of transistion adiabatic region isothermal region ceramics: Isothermal region ???

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| Milan, October 2009 | page 12 Surface Loss: Thermal Conduction Metallic wall: Ceramic wall:

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| Milan, October 2009 | page 13 Volume Loss: Thermal Conduction

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| Milan, October 2009 | page 14 Volume Loss: Shear Stress

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| Milan, October 2009 | page 15 Volume Loss: Shear Stress

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| Milan, October 2009 | page 16 Volume Loss

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| Milan, October 2009 | page 17 Volume Loss Critical damping:

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| Milan, October 2009 | page 18 Gaussian Power Density Measuring points Cylinder axis

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| Milan, October 2009 | page 19 Response Function and Excitation Amplitude All large amplitudes correspond to radial modes!

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| Milan, October 2009 | page 20 Radial Modes Power density

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| Milan, October 2009 | page 21 Nonradial Modes Power density

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| Milan, October 2009 | page 22 Summary and Conclusions Simplified model for calculation of acoustical resonances in HID lamps Consistent results obtained Next steps –Inclusion of plasma dynamics –Extension to 3d model –Optimization of burner geometry

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| Milan, October 2009 | page 23 Molto grazie!

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