Numerical Modeling of Turbulent fibre Suspensions ...

Presented at The XVIth International Congress on Rheology, Lisbon, Portugal, 2012.

Numerical Modeling of Turbulent fibre Suspensions by LES Yousef kanani1; Mohammadali Masoudian2; Norouz Mohammad Nouri1 1

Applied Hydrodynamics Laboratory, Mechanical Engineering Department, Iran University of Science and Technology 2 Transport Phenomena Research Center, University of Porto, Portugal

MOTIVATION Polymer drag reduction was observed by Tom in 1946 when he was investigating the degradation of polymers in the turbulent flow. He noticed that with a constant pressure gradient the flow increases by increasing the amount of polymer in the flow. Indeed, Presence of polymers in the flow can reduce turbulent friction loses respect to solvent itself in a specific pressure gradient. This phenomenon is called “Tom’s effect”. Numerical simulation of drag-reduced flows is widely investigated. There are two major categories of polymers that can reduce drag in the turbulent flow: flexible and rigid polymers(fibres). Effect of fibres on the turbulent flow is less investigated regarding their lower drag reduction respect to the flexible polymers in a specified concentration. The polymer models more often implemented for the study of DR is the FENE-P and FENE models. A common method to account the effect of the fibres is supplementing the Navier-Stokes equations by the fibre stress tensor, which depends on the distribution function of fibre orientation angles. This function is computed in turbulent channel flow by solving the Fokker-Planck equation numerically. The flow around an individual fibre is governed by Stokes’ equations as the local flow around fibre is low Raynolds. In the previous researches, the hydrodynamic forces acting on the particle is calculated by solving Stokes’ equations considering fibres as a point that results in a fibre stress distribution. These methods have a high numerical costs.

OBJECTIVE In this work we propose that the drag reduction of fibre-induced flows is caused by changing in the vorticity distribution of flow. fibre is assumed to be ellipsoidal with large aspect ratio. Numerical modeling of fibres is done by applying a nonconstructive force field per each fibre on the fluid to generate the same vorticity as the presence of fibre in a stokes flow generates.

ASSUMPTIONS ‒fibres is modeled as ellipsoidal with large aspect ratio ‒Flow around fibres is considered as Stokes flow ‒Fibres are assumed to be uniformly distributed in the domain. ‒Fibre Orientations are predicted by provided statistics in previous researchs. ‒Fibre-fibre intractions are neglected. ‒Backgroud flow in absence of fibre is assumed to be uniform due to small lenght scale of fibres.

Numerical domain and fibres’ distribution

𝜕𝐮 1 2 𝛻. 𝐮 = 0 , + 𝐮. 𝛻 𝐮 = −𝛻𝑃 + 𝛻 𝐮 + 𝐅 𝜕𝑡 Re

GOVERNING EQUATIONS:

Non-Constructive Force field for modeling interaction of fibres with the turbulent flow

RESULTS No. of fibres 𝑹𝒆 0 500

5632 5632

𝑹𝒆𝝉

𝒇

359 348

8.12 × 10−3 7.64 × 10−3

𝒖𝝉

𝑼𝒄

0.996 18.18 0.966 18.24

𝑫𝑹

Friction factor is reduced in the presence of fibres

0% 6%

6% Drag reduction is observed

‒Upward shift in the logarithmic region (y+>30) of velocity profile in the wall units. ‒Velocity is increased in the buffer layer (5