Lift and drag forces on an isolated cubic particle in pipe flow

In this paper, the critical instantaneous lift force required to move an initially stationary magnetic cube from the wall of a cylindrical pipe was examined using a novel method in which an electromagnet was employed. The electromagnet was used to control the contact force between the magnetic particle and the pipe wall by, in effect, varying the effective particle density from 1000 kg m−3 to more than 12,000 kg m−3. This control over the effective particle density provided a simple and non-intrusive technique of determining the critical lift force acting on the cubic particle for a broad range of fluid velocities. The cubic particle was chosen to be greater in size than the depth of the von Kármán [von Kármán T., 1930. Mechanische ahnlichkeit und turbulenz. Math. Phys. Klasse5, 58–76] viscous sub-layer for the range of fluid velocities examined. Critical instantaneous lift forces deduced from the experimental data resulted in an average lift coefficient, CL, of 3 for pipe Reynolds numbers of Re < 20,000. A wall-corrected drag coefficient, CDw, of CDw = 114 Rep−0.8 CD for 100 < Rep < 1000 was used to calculate the critical lift force, where Rep is the particle Reynolds number and CD the drag coefficient. The wall-corrected drag coefficient correlation given above was determined in separate experiments in which the horizontal displacement of the cube, after its sudden release from the soffit of the pipe, was recorded. The release was achieved by firstly holding the particle in position using a magnet and then rapidly removing the magnet. This paper appears to be the first to non-intrusively evaluate the critical instantaneous lift force acting on a specific cubic particle at the pipe wall over a broad range of superficial fluid velocities.