Chirality-dependent forces in simple shear flow for helix aligned with streamlines

We consider the chiral properties for a helix in uniform shear flow. We decompose the helical structure into arrays of [Formula: see text] closely packed beads with radius [Formula: see text]. In low Reynolds number regime, the chirality-specific lift forces in the vorticity direction experienced by helices are given by a set of helix geometry parameters: helix radius [Formula: see text], pitch length [Formula: see text], number of turns [Formula: see text] and helix phase angle [Formula: see text]. The analytical formula of the force is firstly given. The chirality-specific forces are the physical reasons for the chiral separation of helices in shear flow. Our results provide new insights into the separations of all kinds of chiral objects.

Lift on a steady 2-D symmetric airfoil in viscous uniform shear flow

We present an investigation into the influence of upstream shear on the viscous flow around a steady two-dimensional (2-D) symmetric airfoil at zero angle of attack, and the corresponding loads. In this computational study, we consider the NACA 0012 airfoil at a chord Reynolds number $1.2\times 10^{4}$ in an approach flow with uniform positive shear with non-dimensional shear rate varying in the range 0.0–1.0. Results show that the lift force is negative, in the opposite direction to the prediction from Tsien’s inviscid theory for lift generation in the presence of positive shear. A hypothesis is presented to explain the observed sign of the lift force on the basis of the asymmetry in boundary layer development on the upper and lower surfaces of the airfoil, which creates an effective airfoil shape with negative camber. The resulting scaling of the viscous effect with shear rate and Reynolds number is provided. The location of the leading edge stagnation point moves increasingly farther back along the airfoil’s upper surface with increased shear rate, a behaviour consistent with a negatively cambered airfoil. Furthermore, the symmetry in the location of the boundary layer separation point on the airfoil’s upper and lower surfaces in uniform flow is broken under the imposed shear, and the wake vortical structures exhibit more asymmetry with increasing shear rate.