Flow field measurements are important for a wide range of practical applications from aeronautical and aerospace engineering to bio-fluid studies. For two-dimensional (2D) velocity measurements, early optical studies exploited particle streak concepts [1], where particles were illuminated by a continuous light source, and their trajectories recorded on films by a camera with a fixed exposure time. The negatives were projected onto a digital pad, and the extremities of the streaks marked manually and then converted to velocity vectors. A piece of neutral density filter attached to the optical chopper on the illumination path could be used to bring asymmetry in the light pulse profile thereby lifting the directional ambiguity [2]. From the 90s, particle image velocimetry (PIV) rapidly developed in flow laboratories aided by technological advances. In PIV, tracer particles are dispersed in the flow and illuminated by two consecutive laser pulses separated by a set time delay. Images of the particles during each laser pulse are recorded on a single camera, and the velocity field is resolved by cross correlating those two images. The availability of practical high-power pulsed lasers and frame-transfer CCD cameras meant that the displacement of small particles could be tracked in separate frames, and computer hardware allowed the vector processing to be automatized, practically superseding streak velocimetry. As a window-based technique, PIV has an intrinsic limitation on spatial resolution due to the size of the interrogation region. In cases where a large velocity change over a small length scale needs to be resolved, e.g., boundary layer measurements, PTV is often applied instead [3], for which the hardware is the same, but the displacement of individual particles is processed instead of cross correlation. However, pairing of the particles between the two images is necessary, and, for this, various particle searching algorithms have been developed, which become increasingly complex and computationally expensive with the number density of particles.

Traditional PIV and particle tracking velocimetry (PTV) imaging are most often performed using Mie scattering from tracer particles/droplets being illuminated by a frequency doubled Nd:YAG laser. However, in some circumstances, photoluminescent tracers, for which emission is wavelength-shifted with regards to illumination, are used to effectively reject unwanted laser light reflection, e.g., from solid surfaces or gas–liquid interfaces, with spectral filters. This can be for the purpose of separating different phases in a multiphase flow [4], to avoid near-wall laser flare [5], and in µ-PIV experiments, where surfaces are always found near the measurement region [6]. Most often, the particles are encapsulated metal ligand complex, e.g., Rhodamine B, with short luminescence decay times on the order of nanoseconds, such that sharp light spots are formed independently of camera exposure. Particles with longer decay times, either inorganic phosphor or encapsulated lanthanide chelates, were also used for PIV by acquiring two time-separated images of the particles during a single luminescence decay [7,8], thereby avoiding the use of two laser pulses. However, to our knowledge, luminescence decay dynamics have never been exploited in the form of individual particle streaks, as is proposed in this paper. A recent study [9] exploited the emission color specific decay dynamics of upconversion particles to measure the ensemble velocity of nanoparticles in a microchannel. The luminescence emission from nanoparticle suspensions downstream of a continuous wave laser beam was imaged by two cameras, and the distance between the maxima was directly related to the fluid velocity. Although only an ensemble velocity was resolved, this work shed light on the concept that flow velocity can be measured from the signature left by a moving luminescent light source with known decay characteristics.

In this Letter, we present a new concept of particle streak velocimetry (PSV) based on the luminescence decay of individual phosphor particles following pulsed excitation. Unlike conventional PSV where streaks are formed due to continuous illumination, here phosphor particles are excited by a single-pulse UV laser, and, as a consequence of the persistence of phosphorescence, light streaks marking the trajectory of individual particles are captured on a single camera image. The local velocity in the flow is then extracted by fitting the intensity distribution of each streak.

A tin-doped phosphor ${({\rm{Sr,Mg}})_3}{({{\rm{PO}}_4})_2}:{\rm{S}}{{\rm{n}}^{2 +}}$ was used as the flow tracer. Its physical and optical properties have been characterized in [10] for use as a thermographic phosphor in gas flows. For gas flows, 90% of the particles (by number) fell below 2 µm, which match the typical size range of the PIV tracer. It shows a broad orange emission with a high brightness level when compared with other frequently used thermographic phosphors. The $1/e$ decay time measured in bulk powder form was 26.3 µs using a mono-exponential decay model and was found to be insensitive to temperature increases between 300–500 K [10]. To confirm that the state of the powder does not affect the decay time, in-situ measurements of the decay time were performed here in the seeded jet flow, which yielded a similar value (26.8 µs). The decay time was found to change by less than 5% over laser fluences from 10 to $120\;{\rm{mJ}}/{\rm{cm}}^2$ such that the streak intensity distribution is insensitive to local laser fluence.

Figure 1(a) illustrates the optical setup for the PSV diagnostic. The 266 nm output of a frequency quadrupled single-pulse Nd:YAG laser (Quanta-Ray LAB-150) was used to excite the tin-doped phosphor particles. PIV lasers with 532 nm output can also be used to produce a UV excitation beam by adding a non-linear crystal. The beam was formed into a 200 µm thin light sheet at the test field using three cylindrical lenses. The laser fluence was set just below the saturation limit of the phosphor at roughly $100\;{\rm{mJ}}/{\rm{cm}}^2$, requiring a pulse energy of 10 mJ, which can be achieved by frequency doubling 100 mJ of 532 nm output. The phosphorescence streaks were imaged by a 16 bit scientific CMOS camera equipped with a Tamron 60 mm $f/2$ macro lens. The projected spatial resolution in the object space was 10.2 µm/pixel. A 645 nm long-pass colored glass filter was used on the PSV camera to block Mie scattering from the 532 nm laser used for simultaneous PIV/PTV validation. For PSV alone, the filter can be removed to maximize the phosphorescence signal intensity since the 266 nm Mie scattered light is absorbed by the borosilicate glass of regular camera lenses.

 

Fig. 1. (a) Schematic of the PSV optical setup; (b) example of phosphor streaks recorded at different flow velocities.

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Fig. 2. Particle streak segmentation: (a) raw image, (b) object detection and binarization, (c) skeleton line detection, (d) determination of rectangular envelope for each particle streak, (e) 2D fitting to segmented streak, and (f) synthetic particle streak.

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To validate this PSV concept, conventional (Mie-scattering-based) PIV/PTVs were performed simultaneously. The output beam of a 532 nm double-pulse Nd:YAG laser (Litron NanoPIV) was expanded into a 0.5 mm thick laser sheet. The pulse interval was optimized for each case according to the bulk velocity, ensuring a 3–5 pixel particle displacement. The green light sheet was made thicker than that of UV to minimize the loss of pairs due to out-of-plane motion in PIV/PTV, while, for PSV, particles moving out of plane keep emitting light, so that their motion could still be tracked, avoiding sampling bias. UV and green beams were combined using a dichroic mirror. Mie scattering particle images were captured by a sCMOS camera equipped with a Nikon 60 mm $f/8$ micro lens and $532 \pm 5\;{\rm{nm}}$ interference filter. The projected spatial resolution was 16.2 µm/pixel. A 45:55 (R:T) pellicle beam splitter was used to image the particle field onto both sensor arrays from the same viewing direction.

Figure 1(b) presents example phosphor streaks acquired at different flow velocities. At the lowest velocity (0.4 m/s), the particle image is Gaussian like, with a short tail pointing in the downstream flow direction. The light spot is gradually elongated into a streak as the velocity increases, with the decay rate of the intensity profile in the flow direction showing an inverse dependence with velocity. Components of velocity are extracted using a 2D fit with an in-house Matlab program, where individual particle streaks are first identified and segmented from the raw image. This is illustrated in Fig. 2: an object detection function was applied to mark the area of each particle streak; the image was then binarized [Fig. 2(b)], and a skeleton line detection function was applied to the binarized image [Fig. 2(c)]; each skeleton line was used to derive the four coordinates of the rectangle that envelopes the corresponding particle streak. The width of the rectangle was set to 15 pixels, roughly three times the thickness of the streak. Finally, all of the pixels within this envelope were extracted from the raw image and stored as one particle streak [Fig. 2(d)]. Streaks with a peak intensity lower than 50 counts (equivalent to a signal to noise ratio or ${\rm{SNR}} \lt {{5}}$) were abandoned, e.g.,  the two faintly noticeable streaks on the bottom right of Fig. 2(a).

The $x$ and $y$ components of velocity are extracted by applying a 2D least square fit to each streak against its analytical expression [Fig. 2(e)]. Assuming the emission intensity of a phosphorescence light spot follows a mono-exponential decay and the particle moves at a velocity (${v_x}$, ${v_y}$), the instantaneous intensity profile of a moving particle image at time $t$ reads as

The above function contains six parameters $({I_0},{x_0},{y_0},\sigma ,{v_x},{v_y})$, including two velocity components. Local background signals, such as those from wall reflections or stray light, could be estimated from the intensity probability density function in each window, as a streak generally occupies less than 1/3 of the area. The intensity with the highest probability density was subtracted to the whole window before fitting.

For PIV, a multi-pass cross correlation with a final window size of $32 \times 32$ pixels and a 50% overlap ratio was applied, resulting in a vector spacing of 3.85 vectors/mm. For PTV, a coarse $128 \times 128$ pixels cross correlation was performed first in order to find the particle searching direction. After matching each particle image pair, a Gaussian estimator was used to locate the particle position on each frame and thus calculate the displacement.

The novel PSV approach was first validated in a free jet against simultaneous PTV and PIV and then applied to measure a canonical boundary layer flow. A sparse seeding case (1.1 particles per ${\rm{mm}}^2$ or ${{1}}{{{0}}^{- 4}}$ particles per pixel) was first studied in a 10 mm inner diameter air jet, where PSV could be validated with PTV on an individual vector basis. Examples of instantaneous raw PTV and PSV images and the resulting vector fields are shown in Fig. 3, where PTV and PSV vectors were slightly offset from each other for clearer display, and only vectors identified by both diagnostics are included for comparison. For most vectors, the direction and magnitude of both match very well. Velocity statistics were accumulated over 600 single shots for PSV and PTV in a ${{1}}\;{\rm{mm}} \times {{1}}\;{\rm{mm}}$ area in the jet core, $h = {{2}}\;{\rm{mm}}$ above the nozzle. The mean axial velocity was 3.7 m/s for both, and the root mean square (RMS) was 0.33 and 0.38 m/s for PSV and PTV, respectively. This indicates that PSV can achieve a similar level of random measurement uncertainty to Mie-scattering-based PTV. To examine the impact of particle brightness on the velocity determination, a linear fit was applied to the data from the jet core in the velocity ${I_0}$ space. It indicated a change in velocity of less than 8% for a 70-fold increase in ${I_0}$, showing the robustness of the fitting approach to varying SNR levels.

 

Fig. 3. (a) Raw PTV image (first frame), (b) PSV image taken simultaneously at the same area, and (c) a comparison between PSV (left) and PTV (right) vectors.

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Measurements were also performed at higher particle concentrations and over a range of jet velocities. Figure 4(a) shows an instantaneous PSV velocity field for a particle density of 7.0 particles per ${\rm{mm}}^2$ or ${{1}}{{{0}}^{- 3}}$ particles per pixel. The average inter-vector spacing is 32 pixels or 320 µm. Figure 4(b) is an accumulated velocity field consisting of 58,000 velocity vectors.

 

Fig. 4. (a) Instantaneous and (b) accumulated PSV velocity fields; (c) mean axial velocity profiles ($h \lt 5 {\rm{mm}}$); (d) ensemble average velocities in square region of (b).

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PIV was performed for validation since the particle number density was too high for PTV, with the basic particle matching procedure applied above. Figure 4(c) presents a comparison between the mean axial velocity profiles ($h \lt 5 {\rm{mm}}$) obtained by both methods averaged over 300 images. The velocity RMS is plotted as error bars for PSV or shaded area for PIV. The velocity profiles obtained by both methods show excellent agreement. Unlike the low seeding density case where the RMS of both PSV and PTV was slightly below 10%, the PIV RMS for a similar jet is much smaller (1%). This is partly attributed to the fact that both PSV and PTV track individual particles, whilst PIV calculates the ensemble average velocity over 10–15 particles within each interrogation window, hence with lower variations.

To establish the effective dynamic range of PSV using this phosphor, Fig. 4(d) compares PIV and PSV results in the square region marked in Fig. 4(b) for a wide range of jet velocities. Beyond 7 m/s, PSV measurements are found to be biased towards lower values. Long streaks such as those shown in the highest velocity example of Fig. 1(b) have relatively lower SNRs, as the photons emitted by a single particle are distributed over a larger area. This imposes an upper limit on the detectable velocity, which is specific to phosphor material. Below 0.5 m/s, the velocity was also found to be biased. At such low velocities, the accuracy of PSV is limited by the spatial resolution of the imaging system, and slower flows should be resolved with phosphors with a longer decay time. As phosphor materials may have decay times ranging from below a microsecond (${\rm{BaMgA}}{{\rm{l}}_{10}}{{\rm{O}}_{17}}:{\rm{E}}{{\rm{u}}^{2 +}}$) to over several milliseconds (${\rm{M}}{{\rm{g}}_4}{\rm{FGe}}{{\rm{O}}_6}:{\rm{M}}{{\rm{n}}^{4 +}}$), PSV has a wide application potential from micro-fluidics to high-speed flows. Considering another phosphor particle material with a lifetime $\tau$ and a similar brightness level, the velocity range can be estimated by multiplying the current velocity range by the ratio $\tau /{\tau _{{\rm{ref}}}}$, where ${\tau _{{\rm{ref}}}}$ is 26.8 µs. Furthermore, some phosphors present multiple emission bands with different decay times, e.g., ${{\rm{Y}}_2}{{\rm{O}}_2}{\rm{S}}:{\rm{T}}{{\rm{b}}^{3 +}}$, which can be used to broaden the velocity range.

Finally, the novel PSV technique was applied to near-wall measurements in a laminar boundary layer over a flat plate. A 5 mm thick stainless steel plate (painted mat black) with a sharp leading edge was fixed vertically above the air jet. The horizontal light sheet was redirected vertically and parallel to the wall using a periscope. The beamsplitter was removed for this near-wall demonstration, which allowed a shorter camera object distance and thus a higher pixel resolution of 7.2 µm/pixel.

Figure 5(a) shows an example of a raw PSV image where the wall is positioned at $x = 0 \;{\rm{mm}}$, with the leading edge at $y = 0 \;{\rm{mm}}$. The interfering near-wall signal remains limited to the emission from deposited particles and scattering of that light by near-wall particles thanks to the red-shift of luminescence. To avoid considering deposited particles, streaks with initial particle centers within the first two pixels (14 µm) from the wall were filtered off. Figure 5(b) presents the PSV velocity field accumulated over 300 single shots. As shown, the viscous boundary layer, which is as thin as 300 µm, is clearly resolved. With PIV, a $32 \times 32$ interrogation area would result in a resolution of 200 µm, significantly under-resolving the sharp velocity gradient within the boundary layer. Similar to PTV, PSV can achieve a subpixel accuracy in locating the initial position $({x_0},{y_0})$ of a particle, where Fig. 5(c) shows an example streak obtaining only 4.2 pixels (about 30 µm) from the surface of the plate. Figure 5(d) presents a comparison between the mean PSV velocity profiles extracted at axial positions $y = 4$ and $y = 7 \;{\rm{mm}}$ from the leading edge and the theoretical Blasius solution. This excellent agreement demonstrates that the new PSV technique can provide accurate and very high-resolution measurements, even in optically challenging configurations such as near walls.

 

Fig. 5. (a) Raw PSV image taken near wall; (b) the accumulated velocity field; (c) an example particle streak recorded near the surface; and (d) a comparison between the PSV result and the Blasius solution.

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In summary, a novel concept for high-resolution velocimetry based on the streaks of individual luminescent particles excited by a UV light sheet was presented. The local flow velocity is determined from a 2D least square fit to each streak, which describes the intensity distribution of a moving decaying point light source. The proposed technique was validated in an air jet by comparing it with conventional particle velocimetry using Mie scattering. Excellent agreement was found between PSV and PTV derived vectors. For the phosphor used, ${({\rm{Sr,Mg}})_3}{({{\rm{PO}}_4})_2}:{\rm{S}}{{\rm{n}}^{2 +}}$, the velocity dynamic range of this PSV approach was found to be about 0.5–7 m/s, which was limited by the SNR on the high end and the pixel resolution on the low end. Finally, this technique was applied to measure the velocity field in a 200 µm thick laminar boundary layer, which matched well with the Blasius solution, showcasing the utility of a high spatial resolution and the mitigation of wall reflections. This new single-laser, single-exposure concept is therefore a useful addition to the portfolio of high-resolution flow measurement techniques, drawing on the advantages of the different approaches. As in PTV and PIV, high signal levels are afforded by pulsed lasers; as in streak velocimetry, particle searching is not necessary, and a single exposure is needed, which can be captured by low noise cameras. In addition, the intrinsic color-shift of phosphors is critical near a wall or interface. Future work will focus on implementing simultaneous temperature measurements using two color detection of the streaks to utilize the temperature dependence of the emission spectrum in the range of 200 to 800 K. Investigations of the impact of significant (${\sim}40\%$) out-of-plane motion in the streak description and the extension of the concept to three-dimensional streak reconstructions are also envisaged.