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Towards a Finite Element Calculationof Acoustical Amplitudes in HID Lamps
Bernd Baumann1, Marcus Wolff1, John Hirsch2, Piet Antonis2,Sounil Bhosle3 and Ricardo Valdivia Barrientos4
1) Hamburg University of Applied Sciences, Germany2) Philips Lighting, Eindhoven, The Netherlands3) Université de Toulouse and CNRS LAPLACE, Toulouse, France4) National Institute of Nuclear Research, Salazar, Ocoyoacac, Mexico
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Energy Consumption
Industrial production Transportation Heating and cooling Lighting …
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High Intensity Discharge (HID) Lamp
Arc tube / burner– Wall: Quartz or ceramics– Filling: Mercury– Additives: Metal halides etc
Electrodes– Tungsten
Discharge arc– Temperature: ca. 5000 – 6000 K– Light source
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AC Operation
Advantages:– Avoids demixing– Avoids electrode errosion
Disadvantages:– Flickering– Reduction of lamp‘s lifetime– Lamp destruction
Counteraction:– Electronical measures– Lamp design
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Objective and Scope of Paper
Numerical calculation of acoustic amplitudesin HID lamps
Simplifications:– No inclusion of plasma dynamics– Simplified geometry– 2 dimensional axisymmetric FE model– Simplified model for power input
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Temperature Profile
(Sutherland’s law)
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Inhomogenous Helmholtz Equation
Power density
Ideal gas law
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Solution
Eigenmodes
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Amplitudes
Loss factor
Excitation amplitude:
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Surface Loss: Shear Stress
ceramics
fluid
Prandtl‘s boundary layer
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Surface Loss: Thermal Conduction
region of transistion
adiabatic region
isothermal regionceramics: Isothermal region ???
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Surface Loss: Thermal Conduction
Metallic wall:
Ceramic wall:
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Volume Loss: Thermal Conduction
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Volume Loss: Shear Stress
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Volume Loss: Shear Stress
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Volume Loss
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Volume Loss
Critical damping:
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Gaussian Power Density
Measuring points
Cylinder axis
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Response Function and Excitation Amplitude
All large amplitudescorrespond to radial modes!
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Radial Modes
Power density
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Nonradial Modes
Power density
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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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Molto grazie!