Bias Errors Induced By Gradients In Open Channel Flow Measurement

Particle tracking velocimetry(PTV) provides randomly spaced instantaneous velocity data, and average of these data over a finite sampling bin introduces bias errors due to the existence of velocity gradient, concentration gradient and velocity lag between liquid and solid phases. This thesis presents a systematic study of such bias errors in the measurement of open channel flow with typical velocity profiles(the log-law and the power-law) and concentration distribution(the Rouse equation). The magnitude of the bias errors in mean velocity and root mean square(RMS) velocity is illustrated through both analytical and numerical investigations.The presence of velocity gradient leads to an underestimation of mean velocity and an overestimation of RMS velocity in the sampling bin, irrespective of specific velocity profiles. The errors depend on the velocity profile, the size of sampling bin, and the vertical location of the sampling bin. Given a fixed vertical bin size, the bias error in the near-bed region exceeds that in the upper flow. The error magnitude for power-law is greater than that for the log-law. Experimental evidence from laboratory flumes and natural rivers shows that the bias error in mean velocity is negligibly small while the bias in RMS velocity cannot be neglected.The concentration gradient exacerbates the bias error in the measurement of the solid phase. The errors depend on the size of the sampling bin, the vertical location of measurement, the profile of velocity distribution, and the suspension index of the solid phase. Underestimation of mean velocity and overestimation of RMS velocity occur due to the presence of gradient in both velocity and concentration distributions. The magnitude of the overall bias error indicates a ‘turning point' at y/ h ?0.3-0.5.The traditional mixed-flow perspective yields an averaged velocity for the two phases, and this averaged velocity differs from the velocity of either phase. For typical bulk flow characteristics of sediment-laden flow, the averaged velocity for the mixed-flow approaches that of the solid phase when the concentration increases. Analytical and experimental results show that the RMS velocity for the mixed-flow can be either smaller or greater than that of the liquid phase. Treating sediment-laden flow as flow of a single liquid leads to arbitrary results in experimental measurements.