Computational Investigation of the Flow Structure and Drag Characteristics of Spheres in Accelerated Motion

The unsteady motion of spheres is important for applications such as falling drops and fuel particle acceleration in nozzles. This study investigates the accelerated spheres’ drag for the acceleration number -0.2 to 0.2 and the Reynolds number 20-170. Unsteady laminar Navier-Stokes equations have been solved using the finite-volume approach, dynamic structured grid, and a second-order semi-implicit pressure-based method. The steady drag coefficient range is 2.7- 0.9 for the specified Reynolds range. For the accelerating sphere, Cd values are larger than the steady-state value (For Re = 20, Cd is 6.1 for a = 125 m/s2 and 3.7 for 32 m/s2). By increasing Re, Cd decreases gradually and then tends to the steady-state value. For deceleration, Cd is smaller than the steady-state value (for Re = 20, Cd is -2.5 for a = -125 m/s2 and 1.3 for -32 m/s2). By increasing Re, Cd increases firstly, then decreases, and finally tends to the steady-state value. The larger the magnitude of acceleration, the farther away the unsteady drag curve is from the steady-state curve. When the sphere is accelerated from rest, the flowfield and the drag tend to the state of steady motion with small Reynolds. For deceleration, they tend to the state of steady motion with a large Reynolds. A new equation is proposed providing a simple accurate method for estimating the spheres’ unsteady drag coefficients.