Numerical study of flow physics and drag of spheres in unsteady motion

The drag properties of spheres in unsteady motion are studied numerically for the Reynolds number range from 20 to 170 and the Acceleration number range from-0.2 to 0.2. The unsteady laminar Navier-Stokes equations are solved using the finite volume method. The global moving mesh is used to deal with the unsteady relative motion between the sphere and its ambient air. It is found that, within the given Reynolds number range, the drag coefficient of spheres is closely related to the Acceleration number. For small Reynolds number, compared with the steady motion, accelerated spheres suffer larger drag coefficient, while the decelerated spheres suffer smaller drag. With the increasing Reynolds number, the difference between the unsteady drag and the steady drag gradually decreases. There is an obvious lagging effect in the unsteady motion with low Reynolds number. When a sphere accelerates from resting state to a nominal Reynolds number, the ambient airflow field structure around the sphere and the drag coefficient tend to the state of steady motion with smaller Reynolds number. When the sphere decelerates from a large velocity to a nominal Reynolds number, those parameters tend to the case of steady motion with larger Reynolds number. Finally, a new corrected formula of unsteady drag coefficient of spheres is proposed.