Introduction:
The velocity distribution in sediment-laden flows is an important and fundamental parameter for calculating the rate of suspended sediment transport. Previous studies have shown that suspended sediments significantly alter the velocity distribution in open channel flows and river systems. Suspended sediments tend to reduce the shear rate near the bed. This occurs because a part of the energy from the flow turbulence is spent on keeping sediment-laden particles in suspension, reducing the energy available for momentum transfer near the boundary. Also, the presence of suspended sediments suppresses the flow turbulence. Therefore, the velocity gradient near the bed shrinks. Consequently, ignoring the presence of these particles in the flow can cause significant errors in the estimation of parameters such as flow discharge and sediment discharge in rivers. Despite efforts to develop relationships for estimating the velocity distribution in sediment-laden flows, the estimation of the parameter is associated with a significant error, and it is essential to use a reliable method that is capable of accurately predicting the velocity distribution while considering the effects of suspended sediments. For this reason, the use of numerical models is a great help to researchers studying the mechanism of suspended sediment transport.
 
Materials and Methods:
In order to validate and calibrate the results of the numerical model, two laboratory data sets covering a wide range of hydraulic conditions were utilized. The first set of data was from the experiments by Einstein and Chien (1955) which were conducted in a flume 0.307 m wide, 0.357 m high, and 120 m long. These tests were performed on smooth and rough beds with slopes of 0.00185 and 0.0025. Sediment particles with diameters of 1.3, 0.94, and 0.274 mm were used. Sediment concentrations were determined by collecting point samples from the flow using a tube. At each sampling point, three to 15 samples with a volume of one liter were taken. About 16 data sets was chosen from the first set of experiments. The second set of data originated from the experiments of Vanoni (1946) conducted in a rotating flume with 0.305 m deep, 0.845 m wide, and 18.3 m long. The number of measurement points varied from 7 to 17, covering 2% of the flow depth. The flow rate varied from 28.3 to 155.7 L/s. The bottom of the flume was covered with sand particles with an average diameter of 0.47 mm and 0.88 mm. In the current study, Flow-3D software was used as a numerical simulation tool. Flow-3D software is a comprehensive software package in the field of computational fluid dynamics. This software package uses advanced numerical techniques to solve three-dimensional equations of fluid motion for multiphase problems.
 
Results and discussions:
By examining the experimental data of relative velocity (u/u*) versus relative depth (y/h) at different sediment concentrations on a semi-logarithmic scale, it was observed that the presence of suspended sediments in the flow caused a deviation from the logarithmic distribution observed in the experimental data. The amount of change in the inner region was greater than that in the outer region. After running the numerical model with different mesh sizes, a mesh size of 10 mm was selected as the optimal mesh size for running the numerical model in this study. The K-ε model was selected as the turbulence model for the present study. After ensuring the performance of the FLOW-3D numerical model in estimating the velocity distribution of sediment-laden flows, the effect of parameters such as bed roughness, suspended sediment diameter, and initial flow concentration on the velocity distribution was investigated. The purpose of this section is to simulate conditions that cannot be achieved in the laboratory, and the use of a numerical model provides valuable insights into the sediment-laden flow pattern.
 
Conclusions:
The results showed that the FLOW-3D numerical model demonstrated acceptable accuracy in estimating velocity values at different depths. The average error rate of the numerical model in estimating velocity distribution values was 12.6% for Vanoni data and 75.3% for Einstein and Shen data. In general, it can be said that the numerical model overestimates velocity values at shallow depths (inner region of velocity distribution) and underestimates them at greater depths (outer region) compared with the measured values. These results indicate that using the FLOW-3D numerical model provides a more accurate estimation of velocity in sediment-laden flow than employing empirical relations.