In this paper, we build a model for calculating the drag coefficient and ultimate settling velocity of high-density and large-diameter solid particles in cylindrical pipes. The settling process of particles in a cylindrical pipe was recorded by using a high-speed camera. Based on the analysis of the experimental data, a gap area ratio was introduced into the model in order to predict the resistance coefficient and ultimate settling velocity of the particles settling in the open space, enabling the model to predict the resistance coefficient and ultimate settling velocity of spherical particles settling in cylindrical pipes. The values of the ultimate settling velocity and the drag coefficient that were obtained with the proposed formulas were validated using experimental data and computational fluid dynamics results. The model was found to be accurate and reliable.

A cylindrical rod placed at the leading edge of the S809 airfoil is used as an alternative for the conventional vortex generators. In this paper, extensive numerical investigations have been conducted on the effects of the rod on the static and dynamic stall performance of the S809 airfoil. The flows around the stationary and sinusoidally oscillating S809 airfoils at Re = 10⁶ are simulated by solving the unsteady two-dimensional Reynolds-averaged Navier–Stokes equations with the Shear Stress Transport k–ω model. For the stationary airfoil, the leading edge rod can effectively enhance the aerodynamic characteristics of the airfoil and delay the stall angle, with the maximum lift–drag ratio increased by 30.7%. For the airfoil undergoing deep dynamic stall, the rod shows the capacity of eliminating the dynamic stall vortex at the leading edge and suppressing the flow separation at the tailing edge. It also reduces the peak of the negative pitching moment and the hysteresis effects substantially, and eliminates the negative damping sub-loop of the moment coefficient. Moreover, the distance between the rod and the airfoil has a strong influence on the lift forces but little effect on drag and moment coefficients of airfoil under deep dynamic stall.