Simultaneous measurement of surface topography and subsurface velocity field in free-surface turbulent flow

TL;DR

This work presents a method to measure free-surface topography and subsurface velocity simultaneously by combining fringe projection profilometry (FPP) with particle image velocimetry (PIV) in fluorescein-dyed water. Fluorescein makes the surface opaque to the projected fringe light while remaining transparent to the PIV laser, enabling coincident measurements with optical filtering to minimize cross-talk. The authors validate FPP against a point-LIF reference and demonstrate the approach in two applications: vortex wake behind a cylinder interacting with surface waves and droplet impact on a free surface, achieving about 20 µm mean absolute error at higher dye concentrations. The method offers a practical, scalable tool for high-resolution, multi-physics measurements of surface-turbulence interactions with potential for broad use in experiments and numerical validation.

Abstract

This work presents a novel combination of two well-established techniques: particle image velocimetry (PIV) and fringe projection profilometry (FPP). Despite seemingly conflicting requirements -- PIV requires a transparent fluid, while FPP requires an opaque surface to project onto -- both requirements are met by adding fluorescein disodium salt, a fluorescent dye, to the water. This dye strongly absorbs the blue light projected onto the surface for FPP while interacting weakly with the green laser light used for PIV, achieving simultaneous opacity and transparency depending on colour. However, this approach presents several challenges, which we are able to solve with a combination of optical filters on the projector and cameras. A series of validation experiments were performed to assess the accuracy of surface elevation measurements at various dye concentrations. The technique was then demonstrated for the case of a vortex street generated by a cylinder interacting with surface waves. Our results show that a dye concentration of 12\,mg/L, although insufficient to make the water opaque to the projected light, yields a mean absolute error in surface elevation of only 20 micrometres.

Figures (13)

• Figure 1: Excitation and emission spectra of fluorescein overlaid with the spectra of the bandpass filters used in this study. Light from the projector is filtered with a $20$ nm wide filter at $490$ nm (cyan), a long-pass filter at 510 nm (orange) is placed on the profilometry camera lens and fluorescence noise is reduced with a $4$ nm wide bandpass filter (green) centred at $532$ nm on the PIV camera.
• Figure 2: Schematic of the experimental setup. The laser pointer and LIF camera were only present for the validation experiments.
• Figure 3: Optical challenges associated with this experimental approach. (a) PIV image showing noise which stems from the absorption of laser light at 532 nm by fluorescein. (b) PIV image taken under the same conditions as (a), but with an ultranarrow bandpass filter with a full-width half-maximum of 4 nm which removes most of the noise. (c) Profilometry image of the fringe pattern shows specular reflections from the water surface which saturates parts of the camera sensor. (d) Profilometry image with the addition of a long-pass filter at 510 nm to the camera, eliminating the specular reflections.
• Figure 4: (a) Profilometry image taken from above the water surface showing reflection of light from the ultranarrow bandpass filter on the PIV camera below the surface. (b) PIV image showing cut-off of light when using a wide-angle lens with the ultranarrow filter.
• Figure 5: Representative side-view image from the point-LIF camera showing the air-water interface. A vertical laser beam illuminates the water column from above, exciting the fluorescent dye along its path. The detected air-water interface is overlaid as a black line with red markers.