The Forming and Densification of Fibre Mats in

Twin-Wire Formers: Modelling

Vinicius Lobosco, Bo Norman & Sören Östlund

Outline

● Background on forming● Model● Results● Conclusion● Future Work

A. Flaks

Schematic Papermachine

● Blades improve formation● Mats start on the roll

A Modern Forming Section

Norman & Fellers

Dewatering Mechanisms

ThickeningFiltration

Parker, 1972

Outline

● Background on forming● Model● Results● Conclusion● Future Work

Present Available Models● Incompressible

– Zhao & Kerekes– Roshanzamir et al.– Holmqvist

● Elastic– Martinez– Zahrai et al.

Experimental Material Behaviour

● Vomhoff & Schmidt– Permanent

deformation– Hysteresis

Mathematical Model

● Balance Equations:– Mass;– Momentum

● Transfer Equations● Constitutive Equations

Assumptions

● Continuum● Intertial effect neglected● Wire gives no resistance● Symmetry● Darcyan flow● No interface resistance

Mathematical Model 2

● Convective-diffusive time-dependent equation● Finite Element Method (FEM)

Variation = Convection + Diffusion

Outline

● Background on forming● Model● Results● Conclusion● Future Work

Results 1

● Filtration● Dryness● Unbeaten

Kraft pulp – CSF 718

● 10 kPa – 20 ms

Results 2● Dryness● Beaten kraft

pulp CSF 598● 10 kPa – 20 ms

Results 3● Thickning● Blade forming ● Three

haversinus pulses 15 kPa 2 ms with 2 ms interval

Results 4● Contours of

Structural stress

Results 5

● Material response from the different elements and the experimental data (Vomhoff & Schmidt)

Results 6

● Diminishing returns● Average solids

content vs. applied stress

● No improvement after 15 kPa

Ave

rage

fin

al s

olid

s co

nten

t

Conclusions

● Demonstrates considerable dryness gradient effects.

● Demontrates dryness relaxation effects.● Needs more data on unloading of webs.● Available to the industry.● Will be of large interest in modelling of twin-wire

roll and blade forming.

Future Work● Numerical

– Streamline diffusion– Moving Finite Elements (Yi Liu – C4)

● Physical Model– Hysteresis operator– Wire and interface resistance

● Generalisation– Couple with Holmqvist's blade pressure model

● Validate– Filtration and papermachine (e.g. Euro-FEX)

Acknowledgements

● CPDC for the funds that made this project possible

● Hannes Vomhoff for making his experimental data available.

● Raul Tempone (NADA – KTH) for the support regarding the numerical method