Image processing

The image processing procedures that have been used for the PLIF images presented herein are described in the following sections. Raw images from the intensified CCD were stored as .spe files, a proprietary binary file format used by the Princeton Instruments WinView32 image acquisition software. These raw images were imported

into MATLAB, processed according to the procedures outlined below, and stored as images (.png or .bmp files) or movies (.avi files).

5.2.1.1 Background su btraction an d la ser sh eet correction

The intensity at a given pixel in a PLIF image may be due to fluorescence, elastic scattering of laser light (Rayleigh scattering, glints, reflections, etc.), room lights, camera offset, or dark current. Experimental controls are used to reduce unwanted sources of intensity; the camera is cooled to reduce dark current, unused windows are covered to block room lights, filters in front of the camera lens block most of the light at the frequency of the laser, etc. In order to remove the remaining contributions of all but fluorescence, a background image is subtracted. A background image is an image acquired at conditions nearly identical to run conditions but without nitric oxide present in the test region. This includes using the same laser operating conditions, camera gain and gate settings, as well as acquiring images at the same ambient pressure. In practice, the conditions may not be identical. In order to minimize the effect of shot-to-shot variations in background intensity, 100 single-shot background images were acquired for a several gain settings and test section pressures on each day of running. An averaged image was created for each set of 100 images, and this averaged image was then smoothed by a 7 pixels x 7 pixels rotationally symmetric Gaussian filter with a sigma (standard deviation) of 2 pixels in order to further reduce random noise. The raw images are smoothed by a similar but smaller 3 pixels x 3 pixels filter (with a sigma of 1 pixel) prior to background subtraction. The smaller filter is used on the single shot images to minimize the blurring of flow structures while still reducing the effects of random noise.

After a background image is subtracted from each smoothed PLIF image, significant left-to-right variations in intensity remain. These variations are due to the left-to-right variations in both the laser sheet intensity and laser wavelength. The intensity of the laser sheet has an approximately Gaussian spatial profile, so near the edges where the laser intensity is lower, the resulting fluorescence signal is also lower. Additionally, the spectral profile of the laser sheet varies spatially: the right side of the sheet is slightly red shifted relative to the central frequency, while the left side is slightly blue-shifted. This effect is created by a spectrally-dispersive Pellin-Broca prism just prior to the output of the WEX, used to separate the final UV beam from the other residual beams. These spectral shifts result in a decrease in the spectral overlap integral, g, between the laser and molecular absorption profile, with a corresponding decrease in fluorescence intensity on the left and right edges of the laser sheet. (See the section in Chapter 7 on Recommendations for Future Work for a suggestion on how to minimize this effect in future applications.)

To correct for these effects, the images are divided by a laser sheet profile. For some runs, a laser sheet profile was created for each single shot: a region of the image far from the jet was selected, and the average intensity along each column in this region was calculated. Enough nitric oxide mixed into the ambient gas to provide a low fluorescence signal in this region. Each column in the PLIF image was then divided by the average intensity of the corresponding column in the region far from the jet. This had the effect of increasing the intensity on the left and right edges of the images, where the laser sheet was less intense and typically slightly detuned from the center of the absorption spectral line, as explained above. While this shot-by-shot laser sheet correction was effective for

many runs, it was computationally intensive. Some runs lacked sufficient intensity far from the jet, and impinging cases (covered in the next chapter) often had flow extending toward the top of the image, so no region “far from the jet” existed. For these reasons, the image processing procedure was modified and a single, averaged laser profile was generated for each run. Each single-shot image was then corrected using the same laser sheet profile. This method was experimentally much easier to implement than a two- camera reference system that others have used in past work (see, for example, Palma

1999).

As final steps in the image processing procedure, images were sometimes cropped, a mask was applied to cover the nozzle hardware in order to eliminate any persistent glints or scattered light, a scale was applied to the sides and bottom of the images based upon the measured spatial resolution, and a false-color mapping was applied. In some of the earlier tests, the spatial resolution was determined by imaging a ruler in the same plane as the laser sheet. This process was improved in later tests. A dotcard was used in place of a ruler. Dotcards consisted of a rigid metal plates covered with a sheet of paper. The paper was white with black squares printed in a regular grid pattern. Spatial resolution was calculated by capturing images of a dotcard positioned in the same plane as the laser sheet. The optical access in these experiments permitted perpendicular viewing of the measurement plane and no significant perspective distortion was found in the images. For experimental configurations where optical access is more limited and perpendicular viewing is not possible, dotcard imaging makes it possible to correct for perspective distortion (and in the case of lower-quality camera lenses, for lens distortion) (Danehy et al. 2007).

5.2.1.2 Stan dard deviation im ages

After background subtraction and laser sheet correction, an average image was created from all the images from a given run (each run consisting of either 100 or 200 single-shot images). A standard deviation image was then created in the following manner. Each single shot image was subtracted from the averaged image. The images contained intensities spanning a large dynamic range, and so the difference in intensity was divided by the average intensity, resulting in a percentage difference, rather than an absolute difference. This “percentage difference” in intensity at each pixel was squared, and the squares were summed over all images in the run. Finally, the sum of the squares was divided by the number of images and the square root was taken. The resulting image provides a map of the flow, highlighting regions of large percentage variations in intensity. For an explanation of the features that can be identified in standard deviation images, as well as examples of standard deviation images, see section 5.2.2. In general, steady laminar flows will have relatively consistent shot-to-shot intensity at a given location in the flow, resulting in percentage standard deviations of less than about 30%. Unsteady flows, by contrast, will have regions where the intensity varies in each image, resulting in typical percentage standard deviations of between about 35% and 100%. A drawback of this technique is that it tends to more prominently highlight variations in regions where there are steep intensity gradients in the average image (e.g. along jet boundaries).

5.2.1.3 Volume Im aging

In addition to data taken along the flow centerline, volumetric imaging was performed for many of the test cases. To obtain these data, a series of 200 single-shot images was acquired as the laser sheet was swept spanwise through the flow, providing slices of the flow field. These slices allow the reconstruction of cross-sections of the flow in planes perpendicular to the jet axis, a technique which will be referred to as volume

imaging. Figures 5.1 and 5.2 display cross-sectional slices at six axial locations.

Figure 5.1: Six reconstructed slices and one single-shot centerline image. These images are from a supersonic nozzle run (Run 339) with JPR = 3.9 and Reexit = 4,303. White vertical lines through the reference image indicate the axial locations of each of the slices. The fourth and fifth slices show evidence of the cos(60) azimuthal instability mode, a feature not evident in the centerline image. Being able to capture symmetry-breaking flow features represents one of the advantages of volume-imaging.

The single-shot images acquired on the flow centerline during the spatial scan of the laser sheet provide a reference for the relative locations of these slices. In both of these

figures, the axial symmetry of the jet is seen to be breaking down as azimuthal cosine modes (described in more detail in section 5.5) become manifest. While the centerline image in Fig. 5.2 shows some evidence of this breakdown, no such evidence can be seen on the centerline in Fig. 5.1. This demonstrates one of the advantages of this technique, since it can reveal non-axisymmetric flow structures that may not be evident in centerline imaging.

Figure 5.2: Six reconstructed slices and one single-shot centerline image. These images are from a supersonic nozzle run (Run 342) with JPR = 2.1 and Reexit = 9,501. White vertical lines through the reference image indicate the axial locations of each of the slices. Note the growth of azimuthal instability modes stemming from the second flow maximum. The fact that the cross-sectional slices are constructed from ~200 single shots (which take 20 seconds to acquire) indicates that the breakdown mode shown here is relatively persistent and spatially stable.

Slices reconstructed from scans through unsteady flows could potentially be used to give an indication of the level of unsteadiness at a given axial location. For the relatively steady upstream slice location, the flow appears to be a smooth circle. As slices are

reconstructed further downstream, the circular outline of the flow becomes jagged, due to shot-to-shot variations in the position of the jet. Thus, a single slice image can provide a visual representation of the degree of flow unsteadiness. Volume imaging also represents a promising means of making PLIF measurements in flows where optical access constraint do not permit imaging in the most desirable measurement plane.