Uncertainty quantification of three-dimensional velocimetry techniques for small measurement depths

In this paper, the multi-camera techniques tomographic PTV and 3D-PTV as well as the single-camera defocusing PTV approach are assessed for flow measurements with a small measurement depth in conjunction with a high resolution along the optical axis. This includes the measurement of flows with strong velocity gradients in z direction and flow features, which have smaller scales than the actual light sheet thickness. Furthermore, in fields like turbomachinery, the measurement of flows in domains with small depth dimensions is of great interest. Typically, these domains have dimensions on the order of 100 mm in z direction and of 101 mm in x and y direction. For small domain depths, employing a 3D flow velocimetry technique is inevitable, since the measurement depths lie in the range of the light sheet thickness. To resolve strong velocity gradients and small-scale flow features along the z axis, the accuracy and spatial resolution of the 3D technique are very important. For the comparison of the different measurement methods, a planar Poiseuille flow is investigated. Quantitative uncertainty analyses reveal the excellent suitability of all three methods for the measurement of flows in domains with small measurement depths. Naturally, the multi-camera approaches tomographic PTV and 3D-PTV yield lower uncertainties, since they image the measurement volume from different angles. Other criteria, such as optical access requirements, hardware costs, and setup complexity, clearly favor defocusing PTV over the more complex multi-camera techniques.