Error analysis of 3D-PTV through unsteady interfaces

Abstract

The feasibility of stereoscopic measurements through an unsteady optical interface is investigated. Position errors produced by a wavy optical surface are determined analytically, as are the optimal viewing angles of the cameras to minimize such errors. Two methods of measuring the resulting velocity errors are proposed. These methods are applied to 3D particle tracking velocimetry (3D-PTV) data obtained through the free surface of a water flow within a cavity adjacent to a shallow channel. The experiments were performed using two sets of conditions, one having no strong surface perturbations, and the other exhibiting surface gravity waves. In the latter case, the amplitude of the gravity waves was 6% of the water depth, resulting in water surface inclinations of about 0.2 • . (The water depth is used herein as a relevant length scale because the measurements are performed in the entire water column. In a more general case, the relevant scale the maximum distance from the interface to the measurement plane, H, which here is the same as the water depth.) It was found that the contribution of the waves to the overall measurement error is low. The absolute position errors of the system were moderate (1.2% of H). However, given that the velocity is calculated from the relative displacement of a particle between two frames, the errors in the measured water velocities were reasonably small because the error in the velocity is the relative position error over the average displacement distance. The relative position error was measured to be 0.04% of H, resulting in small velocity errors of 0.3% of the free-stream velocity (equivalent to 1.1% of the average velocity in the domain). It is concluded that even though the absolute positions to which the velocity vectors are assigned is distorted by the unsteady interface, the magnitude of the velocity vectors themselves remains accurate as long as the waves are slowly varying (have low curvature). The stronger the disturbances on the interface are (high amplitude, short wave length), the smaller is the distance from the interface at which the measurements can be performed.

High-resolution single-camera photogrammetry: incorporation of refraction at a fluid interface

“…Meaning that an error of 1 mm in the position of the interface results in an error of less than half of that in the measurement. This effect of the error in the location of the interface on the accuracy of the measurement depends on the total depth (as also found by Akutina et al 2018, for 3D particle tracking velocimetry through an interface) and the angle of the projector. A uniform error in the water height results in a tilt in the reconstruction.…”

“…Recent studies have used photogrammetry to measure changes in the morphology of a sediment bed inside a flume (Butler et al 2002;Stancanelli et al 2011). However, measuring through the water interface is a common problem, which depends on the amplitude of the disturbances and on the distance from the measurement plane to the interface (as discussed by Akutina et al 2018, for particle tracking velocimetry measurements through a free surface ). Dynamic measurements were obtained by Baglio et al (2001) but did not account for distortions produced by the lens or effects due to refraction.…”

Capturing the Motion of the Free Surface of a Fluid Stored within a Floating Structure

“…Comparable big motion of the free surface in sloshing tanks leads to a high rate of mixing, which makes it harder to maintain the particle distribution. Akutina et al [45] capture the movement of neutrally buoyant particles and address the problem of the measurement validation as well as reduce the influence of optical distortion.…”

Accuracy Analysis of Measuring X-Y-Z Coordinates with Regard to the Investigation of the Tombolo Effect

“…where the standard deviation in the X, Y, and Z directions is σ x , σ y , and σ z , respectively. The same assumptions were used in [24] to assess the error of velocity of a point moving in space as well as in [7] to estimate the snow volume.…”