Experimental study of oblique particle clouds in water

Laboratory experiments were conducted to investigate the dynamics of oblique particle cloud in stagnant water. Previous laboratory studies on vertically downward particle clouds indicated the importance of nozzle diameter do and mass of sand particles in form of an aspect ratio of Lo/do where Lo is the length of occupied sand particle in a pipe. In addition, particle size plays an important role in mixing capability of particle clouds. 30 laboratory experiments were carried out to consider the effects of Lo/do, particle size D50, angle of release θ, and release height H. In order to generalize the outcome of the present study, both particle size and release height were normalized to form Stokes number St and release number η. Three classes of particle size were identified for 0 < St < 1 and a relatively wide range of aspect ratio 0.8 ≤ Lo/do ≤ 40.1 was formed by changing the mass of sand particles. To consider the effects of release angle and release height, four release angles of θ = 15°, 30°, 45°, and 60° were chosen and three release numbers of η = 8.5, 13.2, and 17 were selected. Trajectories of particle clouds were identified based on the position of cloud front. Empirical formulations were developed to model the path of the frontal head of oblique particle clouds. Using a theoretical approach, the location of particle fall out was estimated within ± 10% accuracy. Variations of the frontal velocity of particle clouds in vertical direction were investigated and an empirical equation was proposed based on dimensional analysis to predict the frontal velocity at different initial conditions. Mixing efficiency of particle clouds was characterized by entrainment coefficient αe. The entrainment coefficients of particle clouds were computed using the theoretical entrainment hypothesis. It was found that the Stokes number can significantly alter the mixing capability of particle clouds. The influence of controlling parameters on particle−particle interactions can be studied by estimating the drag reduction due to particle grouping effects. The averaged drag coefficients Cd of particle clouds were calculated from momentum equation and a semi-empirical model was proposed to estimate the drag reduction of particle clouds. Significant drag reduction occurred in particle clouds in comparison with individual particles.