Stability of elliptical cylinders in two-dimensional channel flow.

Abstract

The flow around rigid cylinders of elliptical cross section placed transverse to Poiseuille flow between parallel plates was simulated to investigate issues related to the tumbling of red blood cells and other particles of moderate aspect ratio in the similar flow in a Field Flow Fractionation (FFF) channel. The torque and transverse force on the cylinder were calculated with the cylinder freely translating, but prevented from rotating, in the flow. The aspect ratios (long axis to short axis) of the elliptical cylinders were 2, 3, 4, and 5. The cylinder was placed transversely at locations of y0/H = 0.1, 0.2, 0.3, and 0.4, where y0 is the distance from the bottom of the channel and H is the height of the channel, and the orientation of the cylinder was varied from 0 to 10 deg with respect to the axis of the channel for a channel Reynolds number of 20. The results showed that equilibrium orientations (indicated by a zero net torque on the cylinder) were possible for high-aspect-ratio cylinders at transverse locations y0/H < 0.2. Otherwise, the net torque on the cylinder was positive, indicating that the cylinder would rotate. For cylinders with a stable orientation, however, a transverse lift forced existed up to about y0/H = 0.25. Thus, a cylinder of neutral or low buoyancy might be lifted with a stable orientation from an initial position near the wall until it reached y0/H < 0.2, whereupon it would begin to tumble or oscillate. The dependence of lift and torque on cylinder orientation suggested that neutral or low-buoyancy cylinders may oscillate in both transverse location and angular velocity. Cylinders more dense than the carrier fluid could be in equilibrium both in terms of orientation and transverse location if their sedimentation force matched their lift force for a location y0/H < 0.2.