Orientation and distribution of highly elongated and inertial fibres in turbulent flow: a comparison of experimental and numerical data Stella Dearing, Cristian Marchioli, Alfredo Soldati Dipartimento di Energetica e Macchine, Università di Udine, Italy 1 12th Workshop on two phase flow predictions, Halle-Wittenberg, Germany, March 2010.

Motivating factors for work “State of art” – DNS* Objectives Methodology Number density & mean orientations Summary MotivationMethodology Results Summary Contents DNSObjectives 2 *Marchioli C., Fantoni M. & Soldati A., Orientation, distribution, and deposition of elongated, inertial fibres in turbulent channel flow, Phys. Fluids, 22,(2010).

Fibres as an alternative to polymers as a drag reducing additives Examples include the TAPs, medical application, firehouse Fibres provide more modest reductions but improved shear degradation and filterability Introduction Pulp and paper processing Controlling rheological behaviour and fibre orientation distribution crucial to optimise operations Furniture Industry Pneumatic transport of fibres 3

DNS simulations – incompressible turbulent channel flow drive by streamwise pressure gradient Solved using a pseudo-spectral method: 128x128x129 modes in Fourier-Chebyshev space. (x, y, z- respectively ) Periodic boundary conditions in x & y No slip condition at the wall: turbulent boundary. Equations of continuity & Navier-Stokes: DNS – “State of Art”: methodology 4

Langrangian particle tracking. Each particle path, resulting from the forces acting on it by the turbulent flow, is calculated for each time step. 200,000 particles are tracked: initial position and orientation of particles are random; Initial particle velocity = to fluid 3 frames of reference (for orientations) Eulerian inertial frame of reference, x,y,z A Lagrangian fibre frame of reference: x’, y’, z’, attached to the fibre with origin at the fibre center of mass; A co-moving frame of reference, x’’, y’’, z’’ attached to the fibre with origin at the fibre center of mass and axes parallel to the inertial frame. Euler’s angles: φ,ψ,θ Euler angles : e 0, e 1, e 2, e 3 Rotation matrix :, … DNS – “State of Art”: orientation behaviour 5

Translational motion is strongly dependent on hydrodynamic drag Newton’s law : Hydrodynamic drag (Brenner) ( particle reference system ) In channel reference frame: Resistance tensor Coupling of translational motion and rotational motion ( particle trajectory ) ( assume other forces are negligible ) DNS – “State of Art” 6

Relative density : Particle and flow parameters: DNS – “State of Art” Aspect Ratio: 7

“State of the art”: macroscopic fibre motion 8 y z

9 y x

“State of the art”: Concentration data 10  Instantaneous concentration profiles computed as volumetric fiber number density  Near wall peak - behaviour of fibre build up is complex and largely dependent on wall normal fibre translational velocity  Decrease of concentration at z+ approximately 1- after which point λ has little or no effect on concentration profiles

State of the art: mean orientations Figure 16 λ=1.001 λ=3 λ=10 λ=50 11 Fibres tend to align in the streamwise direction Preferential orientation increases with aspect ratio and decreases with inertia b Up Spherical particles have no preferential alignment Fibres align in regions of high shear In regions of small velocity gradients: random orientations

Objectives One way coupling Inertia is concentrated in fibre centre of mass (CoM) Rotation is computed according to shear in CoM Dilute Numerical models Macroscopic fibres Fibres may affect flow Fibres may interact (increased local concentration) Very limited literature available* Real world 12 *Bernstein, O., Shapiro, M. Direct determination of the orientation distribution function of cylindrical particles immersed in laminar and turbulent shear flows. Journal of Aerosol Science,25, , (1994) Complete existing literature Justify DNS assumptions Objectives

Experimental Set-Up : Imaging for visualisations Figure (a) Laser Camera z x Mirror Flow Direction x z System details: PCO sensicam 1280 x1024 ND Yag laser 1000mJ Figure (b) 13 A Pipe length – 30m; Pipe diameter- 0.1m; Max Re ͠͠ 3 00,000

Experimental set-up: Fibres Uniform vs non uniform size distribution Synthetic plastic fibres (nylon) Shredded wood fibres

Experimental set-up: Fibres Cumulative frequency % Frequency % Most probable length Spurious Fibre diameter

Experimental set-up :Fibre and flow parameters [2] Flow Velocity, m/sReτ+τ+ Re τ Fibre typeSpecific Gravity Fibre length, microns Fibre diameter, (microns) Aspect ratio (λ) Mass fraction, % wppmConcentration parameter nb 3 Nylon Dilute suspensions: based on concentration parameter nb 3 << 1 16

Phase discrimination: fibre identification Pre-processing Object identification Discriminate objects based on length and aspect ratio Fitting object to an ellipse using least squares method Adjust intensity Dilate Remove noise Erode back to normal size Figure (b) Figure 6 Figure (a) 17

Phase discrimination: orientation calculations Special formulation of a general conic Least square fit to data point (centre locations of pixels that make up object): Fit an ellipse to fibre using least square fitting algorithm 18

Phase discrimination: statistics Mean orientations Normalised number density i 19

Results: Normalised mean number density Lower fibre mass fraction 20 Higher fibre mass fraction

Results: Normalised mean number density (a) (b) (c) (d) Re Re Re Re

Results: Mean orientations 22 Lower fibre mass fractionHigher fibre mass fraction

Results: Mean orientations (a) (b) (c) (d) 23 Re Re Re Re

Artificial Images of fibres Figure (b) 24

Discussion, Conclusions, Future Work Good agreement with mean statistics from DNS data Differences can be accounted for due to projection of a 3D body onto a 2D plane: We plan to calculate mean statistics using “phase discrimination” DNS slices Validate using 3D model Fibre velocities using PTV Validation in process of calculation of phase velocity Measurements of suspension viscosity 25

Thank you for your attention. Comments, suggestions and questions welcome! 26