A new dynamic masking technique for time resolved PIV analysis

The coating consists of a dispersion of commercially available fluorescent powder (fluorescein (Taniguchi and Lindsey 2018; Taniguchi et al. 2018)) in a structural matrix. In case of rigid objects, the matrix can be a polyester/epoxy (based on the chemical compatibility with the object material) transparent resin. In case of deformable objects, the matrix can be made of transparent silicone rubber. The fluorescent-coated object needs to be illuminated for a sufficiently long time prior to the experiment in order for it to constantly emit light during the run. We found that a 20 s long exposure to a 4W LED source (visible in Fig. 2) is largely sufficient to provide consistent fluorescence emission for the short duration of our experimental run (few seconds).

Given the substantial difference between the object and the particles size in our experiment, identification of the former is straightforward. Figure 3 shows a superimposition of both the seeding particles and the object shapes at three different times (coloring refers to different instants).

Instead, when such size-based classification is not feasible, separation of wavelengths of particles and object needs to be sought: such separation can be achieved either by choosing a fluorescent coating emitting at a markedly different wavelength from the light scattered by the seeding particles, or exploiting fluorescent particles emitting in a band far from the one of the laser (Pedocchi et al. 2008). In both cases, either channel isolation of a color image acquisition or ad-hoc filtering of a multicamera setup, can greatly facilitate object identification. In our case, there is no need to achieve such wavelength separation: indeed, the peak of the emission spectrum of the fluorescent coating is at 540 nm (Taniguchi and Lindsey 2018; Taniguchi et al. 2018), very close to the 532 nm one of the employed laser.

The developed algorithm for DM is an open-source freeware GUI-based tool (Prestininzi and Lombardi 2021) conceived to work in conjunction with the free PIV analysis package PIVlab (Thielicke 2020; Thielicke and Stamhuis 2014). It consists of the sequential run of three phases (referred to as a–b–c in Fig. 1): the first one (a) is aimed at locating the laser position in the scene (i.e., calculates the coordinates of the source of light hitting the obstacles); the second one (b) tracks the objects position and calculates the shaded areas for each frame; the third one (c) merges the tracked objects areas with the shaded ones into a single mask for the PIV algorithm.

More details for each phase follow: In case of multiple laser sources, the RC algorithm needs to be applied to each of them, and the union of the shaded areas is taken. A pseudocode of the raycasting procedure is reported in Alg. 1.

We designed the PIV setup and developed the present DM technique, in order to analyze the performance of vibration inducers (VIs) (Curatolo et al. 2019, 2020). The latter are winglets able to induce regular and wide oscillations of a cantilever placed counterflow in a non-pulsating fluid flow. Such VIs are mounted at the tip of the cantilever (see Fig.  2) and feature two concave wings able to generate lift towards the neutral configuration of the cantilever at any point of the oscillating motion.

The VIs are envisaged to enhance mechanical energy extraction from stationary fluid flows by means of piezoelectric patches mounted on the surface of the cantilever. The whole lateral edge of the wing, highlighted in Fig. 2, is coated with fluorescent paint according to the specifications described in Sect. 2.1. The experiments are carried out in the free surface channel of the Hydraulics Laboratory of the Engineering Department of Roma Tre University. The 10.8 cm long cantilever is placed at the centerline of the channel, oriented upstream, and oscillates in the vertical-longitudinal plane. A ceramic perovskite (PZT) piezoelectric patch (7 \(\times \) 3 cm) made by Physik Instrumente (PI) is attached to the upper surface of the cantilever. It provides an AC electrical voltage difference consequent to its deformation under flow induced oscillations. The 2D velocity field in the vertical midplane of the left wing of the VI has been obtained by means of a homemade underwater PIV equipment.¹ A continuous wave, low cost, low power (150 mW), green (532 nm) laser beam is spread into a 2 mm thick fanned sheet of \(120^\circ \) intersecting one wing of the VI at half span as shown in Fig. 2. The water is seeded with polyamide particles with a mean diameter of 100 \(\upmu \)m and a density of 1016 Kg/m\(^3\). The laser source is placed 15 cm above (roughly 4 cm below the free surface) and 5 cm downstream of the VI, inclined \(5^\circ \) upstream. The above setup is conceived to investigate mainly the wake of the wing. The upstream face of the wing and part of the downstream one are not directly hit by the laser sheet. A high speed commercial camera (Sony RX100 M5) shooting perpendicularly to the laser sheet is used to acquire a movie. The latter is recorded in high frame rate mode at 500 fps with a frame size of 1920 \(\times \) 1080 px, later cropped to a smaller 655 \(\times \) 850 px ROI to be analyzed during the image analysis. A time-resolved, freeware, open source, PIV analysis tool for MatLab is used (Thielicke and Stamhuis 2014). This tool employs a multipass direct Fourier transform correlation with interrogation area (IA) deformation (in our case 64 \(\times \) 64, 32 \(\times \) 32, and 26 \(\times \) 26). At each pass, the overlapping of 50% between adjacent IA is allowed in order to obtain additional displacement information at the borders and corners of each IA. After the first pass, particles displacement information is interpolated to derive the displacement of every pixel of the IA, which is deformed accordingly.

The seeding particles number density is about 5 per IA at the first pass; according to Keane and Adrian (1992), such density value ensures a 95% valid detection probability. IAs are sized in order to ensure a sufficient permanence of particle within frame couples. The analyzed flow dynamics is characterized by flow velocities ranging between 0.4 and 0.7 m/s. Therefore, the particles appear in the third pass IA for roughly 3-4 frames, which is larger than the recommended minimum value of 2 frames (Keane and Adrian 1992).

The accuracy of the employed PIV algorithm has been previously exstensively assessed in literature (e.g., Guérin et al. (2020), Vennemann and Rösgen (2020), Mohammadshahi et al. (2020), Narayan et al. (2020)). However, in order to ensure the physical consistency of our PIV measurements, two benchmark cases are here presented.

The first one compares the vertical profile of longitudinal flow velocity measured by means of the same PIV setup described in Sect. 3.1 in the experimental channel with an analytical reference solution. The latter has been calibrated through PTV (particle tracking velocimetry) measurements carried out by means of floating tracers. The analytical velocity profile is described by Eq. 1 (Keulegan 1938).where u is the horizontal flow velocity component, z is the vertical coordinate, \(\delta \) the bed roughness and \(v^*\) the friction velocity assumed to be given by a uniform flow formula, namely \(u^*=U/C\); U is the depth averaged flow velocity, and C is a friction coefficient given by \(C=5.75 \, \log {\left( 13.3 \, f \, R/\delta \right) }\), \(R=0.2\) m being the hydraulic radius and \(f=0.92\) the shape factor for finite width channels. Figure 4 shows the comparison between the analytical profile and the PIV measurements resulting from averaging the instantaneous values over a 4 s time window. Local fluctuations are found to evolve on time scales of roughly 0.5 s. Best fit of the PTV results yields a value of \(\delta =1\) cm for the bed roughness, the only free parameter in Eq. 1, compatible with the actual condition of the experimental channel bed surface. The analytical value of flow velocity at the location of the resting configuration of the VI is indicated in figure by a black cross. The comparison shows a remarkable agreement, thus proving that the combination of experimental setup and PIV algorithm can be considered reliable for the analyzed setup.

The second benchmark compares the amount of reattached flow over the back surface of the VI. Indeed, given the high camber of these devices, the flow detaches from the downstream surface and eventually reattaches. The amount of surface exhibiting attached flow is found (Curatolo et al. 2020) to be correlated with the efficiency of the VI in exciting the piezoelectric patch (i.e., efficiency is higher if larger and faster oscillations are induced). Here, we compare the length of the reattached flow at top dead point of the oscillation as measured through the PIV analysis, with the one predicted by a CFD (computational fluid dynamics) commercial code FLOW-3D® (Flow Science 2019), solving RANS (Reynolds-averaged Navier–Stokes) equations coupled with a k-\(\epsilon \) turbulence closure on a structured grid (1 mm spacing is chosen for our simulations). The flow on the downstream side detaches and reattaches at several locations for such high camber VI. The quantity compared in this benchmark is the length of the arc between the leading edge of the VI and the closest location of flow reattachment. With reference to Fig. 5, the length of the arc predicted by the CFD model is just 10% higher than the measured one. The PIV analysis, employing the DM technique presented in this work, is then demonstrated to provide physically sound measurements. A detailed analysis of the fluid mechanics of the wake and its correlation with the overall efficiency of the VI are currently ongoing and will be the object of future works.

With reference to Fig. 6, we compare the results of the three approaches in terms of instantaneous flow velocity field. The chosen instant corresponds to the top dead point of the oscillation.

The proposed DM (panel a of Fig. 6) yields a smooth flow field, which reveals coherent swirling structures in the wake.

The NM approach (panel b1 of Fig. 6) also correctly predicts the vortex structures in the wake, but yields largely inaccurate values in the shaded area. It is also evident that an a posteriori filtering of the obtained flow field is not feasible since no reasonable criterion can be inferred from the comparison. Indeed, the flow velocity has a “reasonable” magnitude also at locations where the largest errors are produced as can be observed in panel c1 of Fig. 6, where differences between the velocity fields obtained by DM and NM approaches are shown. Moreover, no filtering criterion can be formulated even assuming a plausible flow direction, since the highly unstable swirling motions, which develop in the wake, happen to move close to such locations. Even if the modeler was aware of such inaccuracies, the NM approach would yield a “reasonable” but still largely inaccurate flow field at the inner chord of the wing and just below it. Such behavior could be highly misleading.

Panel b2 of Fig. 6 shows the flow velocity field obtained with the SM approach, while panel c2 shows the differences between the results obtained with SM and DM approaches. The SM approach clearly shows an overall better accuracy compared to the NM counterpart, but this is due to the fact that the location of the laser source is such that the shaded area does not move much during the oscillation (see Fig. 3 for a visual inspection of the maximum displacement experienced by the VI during one oscillation); in other words, for the analyzed case, the choice of the neutral configuration to draw the static mask is sufficient to obtain an error lower than the NM approach. We would like to highlight that the superiority of the SM over the NM cannot be generalized, since any experimental setup encompassing larger object displacements would result in the NM to be consistently more accurate.

Although Fig. 6 exhaustively demonstrates the differences yielded by the analyzed approaches, in order to provide a more quantitative assessment of the results, frequency distributions of the errors have been computed. Inspection of such distributions in Fig. 7 confirms that the SM approach yields better overall predictions than NM, the SM distributions being more peaked. Nonetheless, the SM still produces spikes of abnormal intensity. Such values, represented by the tails of the distributions, are connected to an overestimation (left tail) and an underestimation (right tail) of the extent of the static mask. The magnitudes of the frequencies, however, rule out the applicability of both SM and NM for the considered case, making the resort to DM mandatory.