An Improved Model for Predicting the Drag Coefficient and Terminal Settling Velocity of Natural Sands in Newtonian Fluid

The drag coefficient C-D plays an important role in studying the interaction forces between individual particles and fluid. Due to the irregular particle shape of natural sands, studying the sedimentation characteristics and drag coefficient model of irregular particles is of great significance in explaining natural phenomena, predicting the sedimentation process, and calculating the interphase forces between individual particles and fluid. In this paper, firstly, an experimental system for measuring the settling velocity was built, the settling velocity of 67 tests of spheres with different particle Reynolds number Re-s in the Newtonian fluid were obtained, and the C-D-Re-s correlation of sphere settling in the Newtonian fluid was established. The proposed C-D-Re-s correlation was in good agreement with the existing classical C-D-Re-s correlations, which proves the reliability of the experimental system and data processing method. Existing literature shows that the previous models are only suitable for irregular-shaped particles with three-dimensional shape-described parameters. However, the three-dimensional shape information of sand particles can only be obtained through accurate laboratory measurements, and it is often impossible to calculate accurately. By introducing the two-dimensional shape-described parameter (circularity c), using image analysis technology, the two-dimensional shape information of natural sands was obtained. The settling velocity of 221 tests of natural sands in the Newtonian fluid was obtained experimentally. It is found that the sand particles' drag force exerted by the fluid is more significant than its equivalent sphere. With the increase in the particle Reynolds number, the shape irregularity's influence on sand particle drag coefficient is more significant, and the C-D-Re-s correlation of natural sand was proposed by fitting. The established C-D-Re-s correlation has good prediction accuracy and can better predict the drag coefficient and terminal settling velocity of natural sand with irregular shapes.