(Color online) A modern HID lamp. Photograph by M. Foote, OSRAM SYLVANIA.
Experiment of Olsen: Effect of acoustic excitation and streaming on the arc of a horizontally running HID lamp. Without excitation, steady buoyant flow causes the arc to bow upward (top snapshot). With excitation, the arc oscillates vertically over an 80–100 ms timescale, causing flicker.
(Color) Acoustics-free condition, without gravity (left) and with gravity (right). Temperature (K) is shown for both cases. For the case with gravity, gas-velocity vectors for a bowed arc driven by steady, buoyant convection. The maximum vertical velocity given by the model is 8 cm/s and occurs just above the center of the lamp, inside the arc.
(Color) Simulation output: Propagation of sound waves in the second-azimuthal mode with temperature (K) shown in the colormap. Spatial maps of temperature and pressure are shown at three different times. This progression occurs 1.2 ms after the acoustics-free initial condition shown on the right side of Figure 3.
(Color) Simulation output: Snapshots of arc flicker at 161, 204, and 208 ms with a color map of temperature (K). Arrows are streaming velocities as defined by Eq. (1), time-averaged over four cycles, and normalized to the same scale in which the strongest motion at 204 ms has a velocity magnitude of 0.94 m/s.
(Color) A wall-bounded domain for classical steady-streaming analysis, representing one-half wavelength (a). The portion of the HID lamp domain (just against the inner wall on the lower right) which lends itself to classical streaming analysis (b). The color map is pressure in the second-azimuthal mode, with an antinode at each side of the section. The section is flattened out and cast analytically as the domain of (a).
(Color online) Simulation output at 15.8 ms. Instantaneous velocity (a) and pressure (b) outside the boundary layer, along the section shown in Figure 6(b). This section is located 0.375 mm from the wall, well outside the boundary layer. The horizontal axis is the arc length along the inner arc-tube wall. Times shown in the legend follow the profiles through a single acoustic cycle.
(Color online) Streaming velocity just outside the boundary layer along the section in Figure 6(b): Output from the simulation (blue) compared with Eq. (25) (green) at 15.8 ms. Simulation output is the time average of profiles shown in Figure 7(a) over four cycles.
Streaming velocity in the free stream: (a) classical [Eq. (25)] versus (b) dynamically driven [Eq. (34)] analysis. Note that the vertical axis in (a) is cast in terms of the Strouhal number St.
(Color) 2D simulation results: Dynamically driven streaming flow using Eq. (1), parallel to the wall at the free-stream boundary. A progression through time is shown, together with the steady analytical solution, Eq. (34).
(Color) Simulation results: Initial condition for the longitudinal case. Temperature (K) together with velocity vectors driven by steady, buoyant convection. The temperature scale is higher here than in the azimuthal case shown in Figure 3 because it includes the near-electrode region.
(Color) Simulation output: Progression of sound waves in the second longitudinal mode with temperature (K) shown in the color map, beginning at an arbitrary time during steady streaming. Spatial maps of temperature and pressure are shown at three different times.
(Color) Arc constriction and associated streaming flows for a vertically running lamp with the 2L mode excited, (a) simulation and (b) experiment of Stockwald et al. 14
Domains of applicability of the dynamically driven and classical analysis in a vertically running HID lamp with the second-longitudinal (2L) mode.
(Color online) Simulation output: Instantaneous velocity (a) and pressure (b) through the middle of the arc in the lower half of the lamp. Times shown in the legend follow the profiles through a single acoustic cycle, taken where the velocities and pressure are most extreme, and also most centered.
(Color online) Simulation output: Instantaneous velocity (a) and pressure (b) outside the boundary layer, along a vertical line 0.3 mm from the wall in the lower half of the arc tube. Times shown in the legend follow the profiles through a single acoustic cycle.
(Color online) Simulation results: Vertical streaming velocity in the domains of Figure 14 compared with the dynamically driven analysis in the arc (a) and the classical analysis close to the wall (b). Along the arc in (a), simulation results give Rz that reaches 20 at the streaming velocity peaks.
Summary of streaming implications of three different calculations.
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