CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 1 CFD Modelling of the Flow Inside an LC Refiner Dariusz Asendrych, Grzegorz Kondora Częstochowa Univ. of Technology, Poland A joint meeting COST Action FP1005 Fibre suspension flow modelling - a key for innovation & competitiveness in the pulp & paper industry ERCOFTAC SIG 43 Fibre suspension flows

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 2  Introduction / Motivation  Numerical model  Simplified / full geometry  Boundary conditions  Governing equations  Results  Simplified geometry - Diverging grooves  Full geometry - General flow pattern  Summary / Perspectives Outline

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 3 plate disc refiner Geometry – assumptions simplified neglected housing  axisymmetric outlet (instead of point outlet) neglected axial part of inlet, radial inlet applied periodicity of discs geometry - single- segment (30 degrees of angular extent - 1/12) full 12 segments housing single-pipe outlet typical refiner filling LC refiner

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 4  simplified filling  inlet - VELOCITY INLET  outlet - PRESSURE OUTLET  PERIODIC B.C.  INTERFACE for sliding meshes geometry and mesh - GAMBIT mesh: 6 / 24 mln cells FLUENT 6.3 / 13 Boundary conditions

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 5 pulp suspension treated as a single-phase continuum (N-S, continuity) flow character assumed to be laminar (confirmed by simulation results) pulp modelled as either Newtonian or non-Newtonian fluid fibre-fibre and fibre-wall interactions are neglected - main goal was to analyze the LC refining hydraulics or Governing equations where - rate of deformation tensor

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 6 softwood pulp, C m = 4%, fibre lenght = 1400 μm, diameter = 26 μm ln(l/d) = 3,986ln(μ r ) = 5,91 μ r = 370 μ pulp = μ r · μ water = 370 · 0, = 0,371 Pa ·s Newtonian fluid - constant apparent viscosity Pulp material properties source:Radoslavova, Silvy, Roux, 1996,,TAPPI Papermakers Conf., Philadelphia

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 7 reverse flows in stator disc  enhanced internal circulation General flow pattern

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 8 α div = 0.0 deg α div = 0.25 deg α div = 0.50 deg Diverging grooves

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 9 intensification of reverse flow Diverging grooves

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 10 Diverging grooves

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 11 mass flux exiting stator grows power consumption decreases Diverging grooves

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 12 Full refiner simulation

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 13 housing includedhousing included pipe outletpipe outlet 12 segments12 segments collector outlet pipe inlet outlet Full refiner geometry model

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 14 Velocity magnitude rotor stator

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 15 Pressure distribution p [bar] rotor stator

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 16 Pressure distribution p [bar] r* [-] p [bar] r* 0 1

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 17 Pressure distribution p [bar] gap

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 18 LC refiner flow model - Fox et al. Fox, T.S., Brodkey, R.S. Nissan, A.H., 1979, TAPPI J., 62 (3)

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 19 Pressure distribution - CFD vs Fox et al [bar] exit region

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 20 Mass flux at filling outlet

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 21 Mass flux at filling outlet full refiner single-segment refiner

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 22 Flow reversals in stator full refiner

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 23 Simplified geometry model qualitative agreement with experimental observation - adequate numerical model divergent grooves:  modify pressure distribution and enhance flow reversals  no energy penalty - improved flow quality Summary / Perspectives Full geometry model circulation / exit regions - analogy to Fox et al. existence of the backflows in the stator mass flow rate distributions stongly non-uniform and rotor position dependent General no fibres included... CFD can really help - useful tool in process optimisation time consuming simulations ongoing simulations / data processing for varying conditions

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 24 Thank You for Your Attention

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 25 Re is low enough to justify the assumption about laminar flow character gap groove Reynolds number - Laminar vs Turbulent

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 26 Investigated parameters: succesive ratio interval count at the cross-section interval count along the groove Grid tests

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 27 simulation literature velocity vectors axial velocity [Lumiainen] - LDA [Fox et al.] refiner grooves occupied by spiral vortices tertiary flows (momentum exchange between discs) good qualitative agreement CFD vs experiment

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 28 source [Ventura et al.]  II - 2 nd invariant o D D - deformation rate tensor non-Newtonian pulp model refining regime istan Pulp material properties

CFD Modelling of the Flow Inside an LC Refiner COST FP1005 / SIG 43 meeting, X.2012, Trondheim 29 Solution monitoring progressing solution (time step No) mass flux at selected groove outlet