Www.berndbaumann.de | Milan, October 2009 | page 1 Towards a Finite Element Calculation of...

www.berndbaumann.de | Milan, October 2009 | page 1

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!