20 kHz toluene planar laser-induced fluorescence imaging of a jet in nearly sonic crossflow

Abstract

This manuscript describes continuous, high-repetition-rate (20 kHz) toluene planar laser-induced fluorescence (PLIF) imaging in an expansion tube impulse flow facility. Cinematographic image sequences are acquired that visualize an underexpanded jet of hydrogen in Mach 0.9 crossflow, a practical flow configuration relevant to aerospace propulsion systems. The freestream gas is nitrogen seeded with toluene; toluene broadly absorbs and fluoresces in the ultraviolet, and the relatively high quantum yield of toluene produces large signals and high signal-to-noise ratios. Toluene is excited using a commercially available, frequency-quadrupled (266 nm), high-repetition-rate (20 kHz), pulsed (0.8–0.9 mJ per pulse), diode-pumped solid-state Nd:YAG laser, and fluorescence is imaged with a high-repetition-rate intensifier and CMOS camera. The resulting PLIF movie and image sequences are presented, visualizing the jet start-up process and the dynamics of the jet in crossflow; the freestream duration and a measure of freestream momentum flux steadiness are also inferred. This work demonstrates progress toward continuous PLIF imaging of practical flow systems in impulse facilities at kHz acquisition rates using practical, turn-key, high-speed laser and imaging systems.

Appendix: Phosphor decay correction

Image intensifiers operated at high acquisition rates that have a relatively slow decaying phosphor can suffer from significant amounts residual or ‘ghost’ signal, where signal from a previous frame is observed on the current frame. The intensifier used in this work is a P46 phosphor (green), which is available in two variants, a ‘fast’ and ‘slow’ type; a slow P46 is used in this work. The slow P46 has about 6.5 % residual signal on the first subsequent image at 50 kHz acquisition rate, whereas the fast P46 phosphor has well under 0.2 % residual signal at 50 kHz; however, the slow phosphor is about twice as sensitive as the fast phosphor (measured in number of green photons out per incident photoelectron). Hoess and Fleder [35] discuss ghost signal and its removal as well as quantify the decays of a P46 phosphor and a blue P47 phosphor.

To correct for the phosphor decay, we first measure the residual signal by imaging a uniform tracer field in a static cell. Using a BNC Model 555 delay and pulse generator, the camera is clocked as normal, and a single laser pulse is fired every 20 images while the camera continuously acquires its set acquisition rate. The average signal in each image is taken in a 10 × 10 pixel square within this image.

Traces of the residual signal decay are presented in Fig. 6 for different gains and acquisition rates, including the specific settings used in this work (20 kHz acquisition with a gain setting of 47); this curve is a discrete function and referred to as $\zeta (i).$ To correct for the decay, the decay per image must be known, and so for a quantitative LIF measurement, this decay should be characterized for the specific settings used in an experiment.

Fig. 6

Signal decay for 20 images at gains of 45, 50, 60 at 15 kHz and gain of 47 at 20 kHz

The residual signal is corrected by subtracting the residual signal from all $n$ relevant previous images from the current image. This correction method is a walk-forward process. A spinning and fluorescing oval illustrates the walk-forward process (Fig. 7). The first row of Fig. 7 shows how a single image will decay over subsequent frames; the second row shows the acquisition of three subsequent images $I_i$ of a spinning oval; the third row displays the corrected images $I^*_i$ and the corresponding expressions for those images.

Fig. 7

An imaginary fluorescing and spinning oval illustrates the need for a ‘walk-forward’ correction technique; a correct version of the third image cannot be computed from a linear combination of the first two images

In the second row of Fig. 7, the first image contains no residual signal, the second contains residual signal from the first image, and the third contains residual signal from the second and first images. In order to correct the third image, the original, uncontaminated first and second images must be subtracted. No scalar multiple of only the second image will adequately correct the third image because the residual signal of the first and second image is present in different relative proportions in the third image than in the second image. The ‘fresh’ fluorescence signal must be subtracted from subsequent images because each newly acquired image decays independently of previously acquired images. Therefore, corrected versions of the first and second images must be used to correct the third image. The decaying signal is proportional to the actual fluorescence signal collected by the imaging system, and corrections for laser-sheet spatial variation and shot-to-shot laser energy variation must be made after applying the phosphor decay correction.

In practice, to correct a set of acquired images, first, $n$ artificial dark images are appended to the front of the dataset. Then, the $\zeta _i$-weighted sum of the first $n$ images (which are all dark images and contain zero signal) is subtracted from the first image, referred to as $I_1;$ this operation will have no change on the first image because there is no residual signal in that image—it is the first image. This corrected first image is stored in a separate array as corrected image $I^*_1.$ Then, from the second image $I_2,$ the corrected first image $I^*_1,$ weighted by the first value in the residual signal decay $\zeta _1,$ is subtracted; this corrected second image is stored as a corrected image $I^*_2.$ For the third image $I_3,$ the $\zeta _i$-weighted sum of the corrected first and second images is subtracted from the uncorrected third image. This process walks forward through the dataset until all images are corrected.

Using this correction routine, we present uncorrected and corrected signal traces for two sequences of images: In Fig. 8a, a single laser pulse is fired, and the decaying phosphor signal is corrected; in Fig. 8b, the laser is fired every 3 images. In both cases, the residual signal is corrected to within 2 % of zero (relative to the peak signal level). In Fig.  8b, we see the slow rise of the uncorrected signals due to the accumulation of residual signal. This residual signals can grow to be roughly 10 % of the maximum signal in the image, and so this contamination gone uncorrected could significantly affect one's results.

Fig. 8

a Raw signal (red stars) and phosphor decay-corrected (blue circles) for a single image and b for divide-by-3 acquisition