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.

中文翻译：

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PTV含沙流量测量中浓度梯度引起的偏差误差

利用粒子跟踪测速（PTV）进行含沙流量测量，沿流量垂直方向引入了一系列有限大小的采样箱。在每个分箱处收集瞬时速度，并建立相当大的样本以评估流量的均方根和均方根（rms）速度。由于存在浓度梯度，因此固相的已建立样品所涉及的数据来自采样箱下部的数据要多于来自上部的数据。当整个仓中的速度变化时，浓度效应会导致测量的平均值和均方根速度产生偏差误差。这些偏差误差在本研究中基于简化的线速度和浓度分布进行了分析量化。来自载有泥沙的流量测量的典型总体流量特性用于证明误差幅度的粗略估计。结果表明，在整体平均测量中，平均速度被低估，而均方根速度被高估。偏差的程度与容器的大小和浓度梯度的速率相对应。提出了一些程序来帮助确定在某些误差范围内的适当采样箱大小。