Effect of Rotary Inertia on the Orientational Behavior of Dilute Brownian and Non-Brownian Fiber Suspensions

Abstract

The orientational behavior of a dilute suspension of slender Brownian and non-Brownian fibers with rotary inertia in simple shear and turbulent channel flows is numerically investigated. The translational inertia of fibers is neglected. The equations describing the evolution of fibers orientation are integrated along the Lagrangian paths of the fluid elements. The fully developed turbulent channel flow at Re _τ = 180 is provided by a direct numerical simulation (DNS). The coupling between the flow field and the fiber dynamics is one way. The Brownian motion is modeled by a stochastic Wiener process. The results are compared with those of inertia-free particles. In simple shear flow, the inertial non-Brownian fibers align slower than the inertia-free fibers to the shear direction while they tend to the same steady state orientation. For Brownian fibers, the steady state orientation of inertial and inertia-free fibers differ. In turbulent channel flow, the second moment of the orientation distribution function shows an oscillatory behavior at high values of inertia for non-Brownian fibers while the oscillations disappear at lower inertia. For Brownian fibers, the oscillations are weaker due to the damping effect of the Brownian diffusivity.

Keywords:

• Brownian motion
• dilute suspensions
• inertial effect
• slender fibers
• turbulent flow