Bias Errors Induced by Concentration Gradient in Sediment-Laden Flow Measurement with PTV

Abstract

Sediment-laden flow measurement with Particle Tracking Velocimetry (PTV) introduces a series of finite-sized sampling bins along the vertical of the flow. Instantaneous velocities are collected at each bin and a significantly large sample is established to evaluate mean and root mean square (rms) velocities of the flow. Due to the presence of concentration gradient, the established sample for the solid phase involves more data from the lower part of the sampling bin than from the upper part. The concentration effect causes bias errors in the measured mean and rms velocities when velocity varies across the bin. These bias errors are analytically quantified in this study based on simplified linear velocity and concentration distributions. Typical bulk flow characteristics from sediment-laden flow measurements are used to demonstrate rough estimation of the error magnitude. Results indicate that the mean velocity is underestimated while the rms velocity is overestimated in the ensemble-averaged measurement. The extent of deviation is commensurate with the bin size and the rate of concentration gradient. Procedures are proposed to assist determining an appropriate sampling bin size in certain error limits.