Volumetric visualization of coherent structure in a low Reynolds number turbulent boundary layer

2. Acquisition and Visualization of the Volumetric Data Set

Experiments were conducted in the Princeton University Gas Dynamics Laboratory Water Channel Facility. It is a closed-loop, free-surface apparatus with a full-width flat plate positioned in the test section, as shown in Figure 4 . Flow visualization was accomplished using disodium fluorescein dye introduced from two spanwise dye slots, illuminated with an argon ion laser via a laser sheet scanning apparatus. The laser sheets were imaged with a high-speed analog video system, then digitized and reassembled into volumes for subsequent visualization and quantitative analysis. The experimental configuration for data acquisition is shown in Figure 5 . The freestream velocity was U_e = 229 mm/s and the boundary layer thickness at the upstream edge of the volume was = 26.9mm. The Reynolds number based on momentum thickness was = U_e / = 701, the friction velocity, = 11.1 mm/s, and the Kármán number ⁺ = / = 299. The useful portion of the interrogation volume measured: L_x / = 3.53, L_y / = 1.49, L_z / = 3.34 (in viscous units: L_x⁺ = 1054, L_y⁺ = 444, L_z⁺ = 999). For other experimental parameters, see the accompanying Table 1. The mean velocity profile was measured using a hydrogen bubble seeding technique. Wall normal bubble lines were written into the flow, recorded on standard video, and tracked from one frame to the next to generate instantaneous velocity profiles. 256 instantaneous profiles were then averaged to give the mean velocity profile shown in Figure 6 and Figure 7. See Delo (1996) for details of the approach, which was adapted from Lu and Smith (1985).

The two-point flow-tagging scheme developed by Goldstein (1991) was used in order to distinguish between fluid in the inner and outer portions of the boundary layer. The upstream dye slot, situated just behind the trip wire, was used to give a discernible background dye level to the turbulent fluid throughout the boundary layer. The dye was heavily concentrated (500 ppm by weight) to offset the effects of turbulent diffusion and the entrainment of un-dyed freestream fluid. The downstream dye slot was placed just upstream of the interrogation volume in order to brightly mark near-wall fluid. Because of the close proximity of the second slot, the dye released was less concentrated (250 ppm), while still being distinguishably brighter than the dye marking the outer layer fluid. The scalar released from the first dye slot was assumed to give a good indication of the large-scale structure in the boundary layer, particularly the turbulent-non-turbulent interface, and the scalar released from the second dye slot was tracked in order to investigate near-wall motions. The two dye slots were located 39 and 4.7 respectively upstream of the leading edge of the volume (see Goldstein and Smits (1994) and Delo (1996) for a discussion of Schmidt number effects on the two-point flow-tagging scheme).

The volume was interrogated using the laser sheet scanning apparatus shown in Figure 8 . A stack of twenty laser sheets was formed by sweeping a focused laser beam through the flow volume parallel to the flat plate (in x-z planes) at twenty y-locations. To sweep the beam, a helical array of 45 mirrors was fixed to twenty faceted faces of a rotating drum. The focused beam of a 5 Watt CW Argon Ion Laser (operating in single line mode, 501nm, 1.8 Watts nominal power) was directed parallel to the axis of the drum, and reflected off each mirror as the drum rotated. The rotation of the flat mirror face caused the reflected beam to sweep through an angle of 18 . The resulting laser sheet has uniform intensity, and its y-location (determined by the position of the mirror on the drum) was precisely repeatable. As the drum continued to turn, the beam reflected off the next mirror in the helix, forming another sheet at a different location. To minimize reflections from the flat plate, the bottom x-z laser sheet was set at y = 2mm; to facilitate the volumetric reconstructions, the sheets had uniform separation of 2mm in the y direction ( y / = 0.074, y⁺ = 22.2).

The scanner was driven by a stepper motor synchronized to the frame-rate signal from the analog video imager. The laser sheets were imaged from directly overhead with a Kodak/Spin Physics Ektapro 1000 High-speed Motion Analyzer. Images were acquired at 500 frame/s, yielding 25 full volumes per second. The rotation of the drum was such that the top slice of each volume was imaged first, the next lower slice 0.002s later, and so on. The elapsed time between subsequent volumes (0.04s) corresponded to approximately one third of a characteristic "eddy turnover time" ( t U_e / = 0.34; t ² / = 4.9). The time resolution was therefore adequate for the examination of large-scale coherent structures, and no interpolation in time was performed. Initially, one thousand sequential images of the data set were digitized and stored as computer files. These images constitute fifty volumes (timesteps 1-50), covering an elapsed time of 2.00s ( T U_e / = 17.0; T ² / = 246). Additional volumes from the complete data set have been digitized but will not be presented here (timesteps 51-1611, every tenth volume). The full data set spanned an elapsed time of 65 seconds ( T U_e / = 545; T ² / = 7880).

The component images of the stacks were digitized with 8-bit resolution using an Imaging Technologies Series 151 frame grabber controlled with Whyndham-Hannaway image processing software. The pixel resolution was 0.25mm (0.0093 ; 2.78 / ). After preliminary image processing to remove noise, a correction was made to account for convection during image stack acquisition. The slices were offset in the x-direction based on the mean convection velocity of the scalar field at each laser sheet height and the time delay during stack acquisition. This resulted in the skewed image stack shown in Figure 9 . The correction was performed to preserve the spatial orientation of the structures in the visualizations, particularly their inclination in the x-y plane.

The paired projections of the volumetric data used to create the stereoscopic visualizations were calculated with "3Dviewer5.4", a volume rendering program developed by Delo et al. (1994) for the creation of stereoscopic visualizations. The program generates true translucent volumetric views of an image stack using a ray-tracing method, utilizing a source-attenuation model (Beer's Law) to create a pair of monochrome projections of a stack of two-dimensional images. It includes a range of variable viewing parameters including: opacity, perspective, angle of orientation, projection plane location, viewing distance and binocular parallax angle. The projection plane was located so as to intersect the center of the image stack; the binocular parallax was fixed at 3 . The projections from the two viewpoints were calculated separately, then combined to form the anaglyph stereograms.

The construction of anaglyph stereograms from the paired projections was straightforward. The left and right eye views were converted to images in SGI (Silicon Graphics) grayscale format. A three-color RGB (Red-Green-Blue) image was then constructed from these two images: the left eye view was copied to the red band of the image, the right eye view was copied to the blue and green bands, resulting in a red/cyan anaglyph image. After the monochrome views were combined, the color stereograms were enhanced using a "gamma" histogram adjustment, an increase in color saturation and an image sharpening routine (unsharp masking). The enhancements were carried out using SGI image processing software. Initially, the processing routines were chosen simply to create more intelligible images. Interestingly, the perception of depth in the stereograms was increased by each step.

Abstract

1. Introduction

2. Acquisition and Visualization of the Volumetric Data Set

Next Section: 3. Results: Two- and Three-Dimensional Visualizations

4. Discussion

Acknowledgements

References