Multiphysics Modeling in Discharge Lighting

By Thomas D. Dreeben, OSRAM SYLVANIA, BEVERLY, MASSACHUSETTS

The Jefferson Memorial is showcased with brilliance and energy efficiency using HID lamps from OSRAM SYLVANIA.

Modeling is being used extensively to reduce the amount of energy consumed by lighting. Worldwide, the energy consumption of lighting is approximately 2800 TWh, 20% of the global supply of electricity. At a conservative 10 cents per kWh, the cost of this energy is $280 billion per year. For the light-sources industry, gross annual income is approximately $25 billion, one order of magnitude smaller than the cost of energy used for lighting. As we pursue reduced energy consumption in all of our light-source technologies, we expect to offer global energy savings that repeatedly offsets the full cost of operating our industry.

High-Intensity Discharge Lamps

Research and development of highintensity discharge (HID) lamps is a key component of this effort. An HID lamp works by driving alternating current between two electrodes to establish an arc discharge through a gas. The gas is enclosed in a hermetically-sealed arc tube made of quartz or ceramic. A 175-W mercury-filled HID lamp is shown in Figure 1. Most of the light from a running HID lamp is emitted from the arc, which typically reaches temperatures of 5000-6000 K. HID lamps are commonly used to supply light in expansive spaces both indoor and outdoor, where they offer advantages in space efficiency and energy efficiency.

Figure 1. An HID lamp, with the arc tube and one of the two electrodes labeled.

Acoustic waves are generated in an HID lamp through systematic modulation of the current that powers the lamp at frequencies that correspond to standing sound waves. Although acoustic phenomena are known to cause unwanted effects in some circumstances¹, proper application of acoustics has been shown to enable a 50% increase in lamp efficiency over current HID technology². If such an improvement could penetrate the US market, a simple estimate offers potential energy savings of 50 TWH per year, equivalent to the total energy that was generated by wind power in the US in 2008.

Jo Olsen (left) and Thomas Dreeben, with OSRAM SYLVANIA (Beverly, MA) showcase their simulation results from their acoustic arc straightening study.

“Modeling is necessary because many of the key mechanisms are beyond the reach of experimental measurement techniques.”

Modeling for Lighting Research

In an engineering setting, modeling is often used as a time and cost-saving measure: By providing equivalent information to experiments, models can be used to reduce the number of prototypes that need to be built. In a research setting such as ours, the needs are somewhat different: The primary role of modeling is to help build the knowledge base. To that end we use modeling and experimental work in complementary roles: Experiments expose critical aspects of the problem that models cannot reach, and models expose critical aspects of the problem that experiments cannot reach. Where the two methods provide overlapping information, comparisons are made to build credibility and clarify the limits of the model’s application. Because we often use the model to provide information for which the experimental evidence is indirect, there is a stronger burden on the model to get the physics right.

Figure 2³. Comparison of a bowed arc with an acoustically straightened arc. Temperature (K) is shown in the color map and vectors represent streaming velocity. The arc is the region of temperature greater than 5000 K.

We use COMSOL® primarily for the flexibility that it offers. Because of the exploratory nature of our modeling, we routinely “user-define” the full set of governing equations and parameterize every coefficient and dimension. This requires considerable mathematical freedom, much more than the “user-defined functions” that most packages normally offer. The general and weak forms in COMSOL’s PDE mode, together with scripting through the MATLAB® interface, give us the flexibility that we need to grow our modeling into new areas of research.

Figure 3³. Arc curvature versus spectral power ratio (SPR), a measure of the amplitude of acoustic excitation. Curvature is normalized by the arc-tube inner radius.

Model Description³

Figure 4³. Pressure modes that are needed for arc straightening. The second azimuthal mode (a) initially causes streaming flows that lower the arc from its bowed position. The first radial mode (b) causes streaming flow that holds the arc close to the center.

Modeling of acoustics and its effect on HID lamp performance involves capturing the physics on two separate time scales. On the smaller scale of 10^-5 sec, compressible unsteady flow simulates instantaneous sound-wave propagation. On the longer time scale of 10^-2 sec, “streaming” flows are resolved, where streaming refers to flow that is time averaged over the acoustic scale4. This flow results from the convective terms in the governing equations and is responsible for all acoustic effects on HID-lamp performance. To capture the full physics on both time scales, the model formulation includes governing equations that conserve mass, momentum in two or three directions, energy, and electric current, all in a fully coupled, compressible, and unsteady formulation.

Arc Straightening in HID Lamps

Inspecting the arc of the HID lamp.

One of the key capabilities of acoustics is straightening a bowed arc in an HID lamp. Arc bowing occurs in a horizontally running lamp, where strong temperature and density gradients exist between the arc and the wall, and buoyancy forces act to move the arc up against the top wall. Simulated arc bowing and acoustic straightening is shown in an arctube cross section that is perpendicular to the arc in Figure 2.

Model output of the arc’s vertical location is compared with experimental results in Figure 3. The benefit of reproducing arc straightening on the computer is that we obtain access to detailed information about the structure of the sound waves that are needed to bring about arc straightening. Arc straightening occurs as a result of two different modes of pressure, the second azimuthal and the first radial, shown in Figure 4.

Through techniques such as arc straightening, acoustic excitation enables us to greatly enhance the efficiency of HID lamps, and save energy on a global scale. Modeling enables us to estimate and visualize the important aspects of acoustic enhancement in HID lamps that we need to understand, predict, and control. Modeling is necessary because many of the key mechanisms are beyond the reach of experimental measurement techniques. COMSOL gives us the mathematical flexibility that is needed to represent acoustics in HID lamps.

References

¹ R. Schafer and H. P. Stormberg, Investigations on the fundamental longitudinal acoustic resonance of high pressure discharge lamps, J. Appl. Phys., 53 (5), p. 3476-3480, 1982.

² K. Stockwald, H. Kaestle, and H. Weiss, Significant efficacy enhancement of low-wattage metal-halide HID lamp systems by acoustically induced convection configuration, ICOPS 2008: Proceedings of 35’th IEEE International Conference on Plasma Science, 2008.

³ J. Olsen and T. D. Dreeben, “Experimental and Simulated Straightening of Metal Halide Arcs Using Power Modulation”, IEEE Transactions, submitted.

⁴ Lord Rayleigh, On the Circulation of Air observed in Kundt’s Tubes, and on some Allied Acoustical Problems, Transactions of the Royal Society of London, 175 (1), 1883.