Orientation, distribution, and deformation of inertial flexible fibers in turbulent channel flow

  • Diego Dotto
  • Cristian MarchioliEmail author
Original Paper


In this paper, we investigate the dynamics of flexible fibers in turbulent channel flow. Fibers are longer than the Kolmogorov length scale of the carrier flow, and their velocity relative to the surrounding fluid is non-negligible. Our aim is to examine the effect of local shear and turbulence anisotropy on the translational and rotational behavior of the fibers, considering different elongation (parameterized by the aspect ratio, \(\lambda \)) and inertia (parameterized by the Stokes number, St). To these aims, we use a Eulerian–Lagrangian approach based on direct numerical simulation of turbulence in the dilute regime. Fibers are modeled as chains of sub-Kolmogorov rods (referred to as elements hereinafter) connected through ball-and-socket joints that enable bending and twisting under the action of the local fluid velocity gradients. Velocity, orientation, and concentration statistics, extracted from simulations at shear Reynolds number \(Re_{\tau }=150\) (based on the channel half height), are presented to give insights into the complex fiber–turbulence interactions that arise when non-sphericity and deformability add to inertial bias. These statistical observables are examined at varying aspect ratios (namely \(\lambda _{r}=l_{r}/a=2\) and 5, with \(l_{r}\) the semi-length of each rod-like element r composing the fiber and a its cross-sectional radius) and varying fiber inertia (considering values of the element Stokes number, \(St_{r}=1\), 5, 30). To highlight the effect of flexibility, statistics are compared with those obtained for fibers of equal mass that translate and rotate as rigid bodies relative to the surrounding fluid. Flexible fibers exhibit a stronger tendency to accumulate in the very-near-wall region, where they appear to be trapped by the same inertia-driven mechanisms that govern the preferential concentration of spherical particles and rigid fibers in bounded flows. In such region, the bending of flexible fibers increases as inertia decreases, and fiber deformation appears to be controlled by mean shear and turbulent Reynolds stresses. Preferential segregation into low-speed streaks and preferential orientation in the mean flow direction is also observed.

List of symbols


Fiber radius

\(\bar{\bar{\mathbf {A}}}\)

Drag force resistance tensor


Drag coefficient


Equivalent fiber eccentricity

\(\mathbf {F}^{D}\)

Hydrodynamic drag force


Channel half height

\(\mathbf {H}^{D}\)

Hydrodynamic drag torque due to fluid velocity gradients

\(\bar{\bar{\mathbf {J}}}\)

Inertia tensor


Semi-length of one fiber element


End-to-end distance


Lenght of the entire fiber


Mass of the fiber

\(\mathcal {N}\)

Number of elements per fiber

\(\mathbf {o}\)

Orientation vector

\(\mathcal {P}\)


\(\mathbf {p}\)

Position vector


Reynolds number


Stokes number




Fiber-to-fluid density ratio

\(\mathbf {T}^{D}\)

Hydrodynamic drag torque due to the action of the fluid vorticity on the element

\(\mathbf {u}\)

Fluid velocity

\(\mathbf {v}\)

Fiber velocity


Streamwise direction

\(\mathbf {X}\)

Constraint force


Spanwise direction


Wall-normal direction

Greek letters

\(\alpha \)

Solid angle between neighboring fiber elements

\(\delta _\mathrm{VS}\)

Viscous sublayer thickness

\(\bar{\bar{\varvec{\delta }}}\)

Identity matrix

\(\varDelta t\)

Time step

\(\bar{\bar{\bar{\varvec{\epsilon }}}}\)

Levi-Civita tensor

\(\bar{\bar{\varvec{\gamma }}}\)

Fluid velocity gradient tensor

\(\lambda \)

Aspect ratio

\(\mu \)

Fluid dynamic viscosity

\(\rho \)

Fluid density

\(\nu \)

Fluid kinematic viscosity

\(\varvec{\omega }\)

Fiber angular velocity

\(\varvec{\Omega }\)

Fluid angular velocity


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Authors and Affiliations

  1. 1.Department of Engineering and ArchitectureUniversity of UdineUdineItaly
  2. 2.Department of Fluid MechanicsCISMUdineItaly

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