Uncertainty Quantification of Ultrasound Image Velocimetry for Liquid Metal Flow Mapping

Ultrasound image velocimetry (UIV) allows noninvasive flow imaging of opaque media with high spatial and temporal resolution, which is especially relevant for experimental research in magnetohydrodynamics (MHD). To extract quantitative flow data from lab-scale experiments in low melting alloys and interpret the results, the measurement uncertainty of a specific experiment has to be determined. In this article, we describe a novel, generic method for estimating the uncertainty of a specific experimental setup according to the guide to the expression of uncertainty in measurement (GUM). It is based on an uncertainty model of the UIV processing, which is calibrated using a flow reference in liquid metal. The proposed model uses a priori knowledge of an expected velocity gradient, a static calibration of the focus distortion, and the peak ratio of the correlation from the measurement data itself to yield the optimal parameterization of UIV and the velocity uncertainty for a specific experiment. This enables the use of the UIV method for quantitative flow imaging with an explicit uncertainty estimate in experiments where no reference flow is available. Building on this, we derive generic guidelines for an optimal parameterization of UIV to a specific experiment. The approach is demonstrated on a magnetically driven flow of gallium-indium-tin (GaInSn) alloy in a cuboid container. In conclusion, this work is a blueprint to obtain quantified planar vector flow maps with UIV in diverse MHD experiments; practical guidelines are derived and an uncertainty estimation procedure is elaborated.