Diapositivo 1

L. L. Ferrs1, J. M. Nbrega1 , F. T. Pinho 2, O. S.Carneiro11 IPC Institute for Polymers and Composites, University of Minho, Campus de Azurm, 4800-058 Guimares, Portugal2 University of Porto, Centro de Estudos de Fenmenos de Transporte, Faculdade de Engenharia, Rua Dr. Roberto Frias s/n, 4200-465 Porto, PortugalOn The Effect of THE Wall Slip BOUNDARY Condition

IPC - Institute for Polymers and CompositesUniversity of MinhoPortugalCFD Computational fluid dynamics (Cfd) extrusion Friction - slip Case study I 4:1 contractionExtrusionFriction - SlipCase Study I Case study II extrusion dieCase Study IICFD ExtrusionFriction - SlipCase Study ICase Study II

CFD ExtrusionFriction - SlipCase Study ICase Study II

Conservation of Mass:

Conservation of Momentum:Constitutive Equation (simplified PTT):Linear Exponential CFD ExtrusionFriction - SlipCase Study ICase Study IIEquations:

no-slip boundary condition

CFD ExtrusionFriction - SlipCase Study ICase Study II

CFD ExtrusionFriction - SlipCase Study ICase Study IIExperimentalnumerical

MA Alves,FT Pinho, PJ Oliveira. Viscoelastic flow in a 3D square/square contraction: visualizations and simulations. Journal of Rheology 52(6) (2008) 1347-1368CFD ExtrusionFriction - SlipCase Study ICase Study IInumerical

AM Afonso, PJ Oliveira, FT Pinho, MA Alves, Dynamics of high-Deborah-number entry flows - A numerical study. Journal of Fluid Mechanics 677 (2011) 277-304CFD ExtrusionFriction - SlipCase Study ICase Study IIband heatersscrewpolymerextrusion diecooling systemwatermeltCFD ExtrusionFriction - SlipCase Study ICase Study IIExtrusion:hopperscrew drivemotor

Extrusion dIE:CFD ExtrusionFriction - SlipCase Study ICase Study IIFriction: solidsCFD ExtrusionFriction - SlipCase Study ICase Study II

Friction: solidsCFD ExtrusionFriction - SlipCase Study ICase Study II13Friction: Fluids

CFD ExtrusionFriction - SlipCase Study ICase Study IIFriction: Fluids?solidliquidSurface roughnessMolecular interactionwettingShear ratepressureCFD ExtrusionFriction - SlipCase Study ICase Study II

CFD ExtrusionFriction - SlipCase Study ICase Study IIwaterViscoelastic fluid

slip velocityslip coefficienttangent stress vectorCFD ExtrusionFriction - SlipCase Study ICase Study IIConservation of Mass:

Conservation of Momentum:Constitutive Equation (simplified PTT):Equations:slip boundary conditionCFD ExtrusionFriction - SlipCase Study ICase Study IINoRemove the boundary velocity from the momentum equationCompute velocity at the Boundary

CFD ExtrusionFriction - SlipCase Study ICase Study II Case study I 4:1 contractionCFD ExtrusionFriction - SlipCase Study ICase Study IIA

CFD ExtrusionFriction - SlipCase Study ICase Study II21B

CFD ExtrusionFriction - SlipCase Study ICase Study II22Ba

CFD ExtrusionFriction - SlipCase Study ICase Study II23Bb

CFD ExtrusionFriction - SlipCase Study ICase Study II24Bc

CFD ExtrusionFriction - SlipCase Study ICase Study II25Bd

CFD ExtrusionFriction - SlipCase Study ICase Study II26C

CFD ExtrusionFriction - SlipCase Study ICase Study II27Ca

CFD ExtrusionFriction - SlipCase Study ICase Study II28Caa

CFD ExtrusionFriction - SlipCase Study ICase Study II29Cab

CFD ExtrusionFriction - SlipCase Study ICase Study II30Cac

CFD ExtrusionFriction - SlipCase Study ICase Study II31Cad

CFD ExtrusionFriction - SlipCase Study ICase Study II32Cb

CFD ExtrusionFriction - SlipCase Study ICase Study II33Cc

CFD ExtrusionFriction - SlipCase Study ICase Study II34Cd

CFD ExtrusionFriction - SlipCase Study ICase Study II35D

CFD ExtrusionFriction - SlipCase Study ICase Study II36Da

CFD ExtrusionFriction - SlipCase Study ICase Study II37Db

CFD ExtrusionFriction - SlipCase Study ICase Study II38Dc

CFD ExtrusionFriction - SlipCase Study ICase Study II39Dd

CFD ExtrusionFriction - SlipCase Study ICase Study II40E

CFD ExtrusionFriction - SlipCase Study ICase Study II41Ea

CFD ExtrusionFriction - SlipCase Study ICase Study II42Eb

CFD ExtrusionFriction - SlipCase Study ICase Study II43Ed

CFD ExtrusionFriction - SlipCase Study ICase Study II44F

CFD ExtrusionFriction - SlipCase Study ICase Study II45Fa

CFD ExtrusionFriction - SlipCase Study ICase Study II46Fb

CFD ExtrusionFriction - SlipCase Study ICase Study II47Fc

CFD ExtrusionFriction - SlipCase Study ICase Study II48Fd

CFD ExtrusionFriction - SlipCase Study ICase Study II49G

CFD ExtrusionFriction - SlipCase Study ICase Study II50H

CFD ExtrusionFriction - SlipCase Study ICase Study II51Ucenter/U2Ucenter= velocity along the center of the flow channelxyx/H

CFD ExtrusionFriction - SlipCase Study ICase Study II Case study II extrusion dieCFD ExtrusionFriction - SlipCase Study ICase Study II

CFD ExtrusionFriction - SlipCase Study ICase Study II

Pre-Processor

GeometryMesh

3D non-isothermal flow field calculation (FVM)VelocityPressureTemperatureTrial ParametersPerformance Evaluation

Modification of the controllable geometrical parameters until the optimum is reachedCFD ExtrusionFriction - SlipCase Study ICase Study IICFD ExtrusionFriction - SlipCase Study ICase Study II

CFD ExtrusionFriction - SlipCase Study ICase Study II

K=0

CFD ExtrusionFriction - SlipCase Study ICase Study II

K=0.25E-8

CFD ExtrusionFriction - SlipCase Study ICase Study II

K=0.25E-7

CFD ExtrusionFriction - SlipCase Study ICase Study II

K=1.0E-7

CFD ExtrusionFriction - SlipCase Study ICase Study II

K=0.25E-6

CFD ExtrusionFriction - SlipCase Study ICase Study II

K=1.0E-6The end