COUPLED MECHANICAL AND

HEAT AND MASS TRANSFER NUMERICAL MODEL

FOR MDF HOT PRESSING PROCESS

Zanin

Kavazovi

Ph.D. Jean DeteixProf. Alain CloutierProf. Andr

Fortin

Physics involved:

Heat & Mass Transfer

Mechanical Compression of the Mat

Resin Polymerization

OUTLINE

Heat &

Mass Transfer Model

Mechanical

Model

Their Coupling & FEM & 3D Moving Domain

Numerical Results (Graphs & Movies)

Conclusions & Perspectives

Heat & Mass TransferSome

of the Literature:

Humphrey & Bolton (1982, 1989a,b,c,d)

Thmen & Humphrey et al. (2000, 2003,2006, 2008)

Zombori et al. (2001,2003,2004)

Dai et al . (2001,2004,2005,2006)

Carvalho & Costa et al. (2001,2003,2006)

Pereira et al. (2006)

Nigro & Storti (2006)

Conservation Principles:

Mass of AIR

Mass of Water Vapor

Energy

Sorption Model (EMC-RH-T)(Malmquist; Vidal&Cloutier 2005)

Resin Curing Kinetics (Xing&Riedl 2004)

Porosit (Belley 2009) Local Thermodynamic

Equilibrium

Heat & Mass Transfer ModelAIR

VAPOR

ENERGY

( ) 0

Molecular DiffusionBulk Flow

a a aa

D MP PDt RT

p effK D

( ) ( )

Evaporation Rate

v v vv OD

D M D MP PDt RT Dt

p effK D

fg( )

OD Mat a a v v

a a v v

a a v va v

r bw v OD

D DC T C T C TDt Dt

TT C C P

C M C MP PR R

D MQ H C C TDt

T p

eff eff

K K

D D

Heat & Mass Transfer Model Solution Strategy

The 3 conservation equations: form a coupled system

of 3 PDEs

are expressed in terms of 3 state variables (Pa , Pv , T)

3D Moving Domain

Space Discretization : Finite

Element

Method

Time Discretization : Implicit Second Order Backward scheme

Time Step of 0.5 s

was used

The 3 coupled equations

were

solved

simultaneously

as a system

Newtons method

was employed

All material properties were updated after each nonlinear iteration

Mechanical Model Ageing Linear Elastic Model Composite Constitutive Law

(Bazant 1979, 1993; Dubois 2005)

Quasi-static Incremental Formulation

: 0

: : 0

(Hardening, Tangent Law)

(Softening, Hooke's Law)

D DEED Dt Dt

D DE DEDt EDt Dt Dt

( )Nd iv d iv 0 0 00; 0; 0U

12

TU U U

1 : :N NE E

1

1

1

1

N NN N

N N

N N

U U U

E E E

Heat & Mass Coupled with

Mechanics

Beginning of a Time Step

Heat & Mass model is solved first

Pa, Pv, T, M, and Degree of Resin Cure are calculated Update of Mechanical Properties Displacement Increment is imposed at the top surface

Mechanical

model is solved is calculated Update of the Mesh, Element Sizes and the Mat Density Update of Heat

& Mass

transfer Material Properties

End of a Time Step

U

3D Moving Domain & Temperature

Comparison Lab - Numerical 3D: Temperature

ERROR LESS than 10%

Comparison Lab - Numerical 3D: Gas Pressure

STD DEV/MEAN = 6%ERROR LESS than 15%

Numerical Results: Predicted Oven-dry Density Profile

TEMPERATURE

MOISTURE CONTENT

Partial VAPOR PRESSURE

Conclusions & PerspectivesCoupling

of Mechanical and Heat & Mass

Transfer Models gives good and consistent resultsFEM & Implicit Time Scheme allow the use of

larger time steps

(lower computational cost)In the future:Consider a Viscoelastic

Mechanical Model

Take into account Press Opening

(Venting)Introduce a Plastic Component into the ModelLarge Deformations

Dpartement

de mathmatiques

et de statistique

Programmes de fermeture en rserve

7 diffrents programmes de fermeture de presse

Calculs effectus sur plusieurs maillages:16x16; 32x16; 32x32; 48x32; 64x32; 128x64;

Programmes de fermeture

Programmes de fermeture

Slide Number 1Slide Number 2OUTLINEHeat & Mass TransferHeat & Mass Transfer ModelHeat & Mass Transfer ModelSolution StrategyMechanical ModelHeat & Mass Coupled with Mechanics3D Moving Domain & TemperatureComparison Lab - Numerical 3D: TemperatureComparison Lab - Numerical 3D: Gas PressureNumerical Results: Predicted Oven-dry Density ProfileTEMPERATUREMOISTURE CONTENTPartial VAPOR PRESSUREConclusions & PerspectivesSlide Number 17Programmes de fermetureen rserveProgrammes de fermetureProgrammes de fermeture