FLUID MECHANICS IN HEADBOXES M. Shariati, E. Bibeau, M.Salc...

**1. **FLUID MECHANICS IN HEADBOXESM. Shariati, E. Bibeau, M.Salcudean and I. Gartshore

**2. **PRESENTATION Mathematical modelling in the pulp and paper industry
Why we model headboxes
How we model headboxes
Examples
flow in the header, tubes and slice
Conclusions and future

**3. **PROCESS MODELLING GROUP

**5. **PROCESS MODELLING

**6. **STAGES OF ANALYSIS

**8. **HEADBOXES Paper quality depends on the flow and fluid/fiber interaction in the headbox
Flow at the exit of the slice needs to be uniform
goal can be achieved only by knowing and controlling the flow upstream
Desirable paper properties impose certain requirements of fiber orientation which depends on the flow and turbulence characteristics

**9. **HOW WE MODEL HEADBOXES Developed a model for the flow through the headbox including the header, individual tubes and slice
Developed a fiber motion model, which allows to compute the motion of the fiber in the fluid
Couple the fiber motion model with the fluid dynamics model
Compute the fiber motion in the fluid for a large number of fibers and obtain information on fiber orientation through the slice
Water model experiments to validate the above

**10. **NUMERICAL CFD CODE Code developed at the University of British Columbia
Generalized curvilinear system
Finite volume method
Block structured
Second order accurate for cross derivative terms
Steady and transient
Partial multigrid capability

**11. **HEADBOX WISH LIST Select sheet properties
Improve control of fiber distribution
Control MD/CD ratios
Prevent non-uniformities (basis weight, fibre orientation)
Control fiber distribution

**12. **HEADBOX REQUIREMENTS Supply to sheet forming section
Well dispersed stock
Constant percentage of fibers
Prevent formation of flocs
Remove flow non-uniformities
Create high-intensity turbulence

**13. **MODEL DELIVERABLES Manufacturers and Pulp Mills
Evaluate new headbox designs
Compare headbox designs
Trouble-shoot existing headboxes
Predict influence of control devices
Evaluate proposed retrofits and design changes
Help correlate sheet properties to headbox behavior

**14. **GENERIC HEADBOX MODELLED

**15. **EFFECT OF FLOW RECIRCULATION

**17. **TYPICAL TUBE Velocity Vectors
Pressure contours

**18. **TUBE FLOW ENTRANCE EFFECT Green
Flow turns before entering tubes
Red
Flow enters straight
Affects
Flow profile into slice
Fibre distribution and orientation

**19. **CONVERGINGSECTION Velocityvectors
3 slices in CD direction

**20. **CONVERGING SECTION Velocity vectors
Contours in machine Direction (MD)

**25. **EXPERIMENTAL METHOD

**26. **MD VELOCITY

**28. **Velocity at the exit plane V, W/Uinlet and Uinlet= 1.22 m/s

**29. **CD VELOCITY (m/s)

**30. **Symmetry Plane Velocity Fluctuations (RMS/RMS at inlet)

**31. **TURBULENCE INTENSITY (RMS/MD VELOCITY) SYMMETRY PLANE

**32. **TURBULENCE KINETIC ENERGY

**33. **EFFECT OF SHAPE

**36. **FIBER MOTION Fiber is modeled as chains of spheroids
Model can deal with the wall automatically for different geometry

**37. **EXPERIMENTAL SETUP

**38. **FIBER MOTION RESULTS Fiber orientation mid channel at x = 12.2 cm

**39. **FIBER MOTION RESULTS Fiber orientation mid channel at x = 19.2 cm

**40. **FIBER MOTION RESULTS Fiber orientation mid channel at x = 26.2 cm

**41. **RESULTS HIGHLIGHTS There exists obvious difference between the results from the experiments and simulations
Cause for this phenomenon maybe the fact that in our fiber simulation, only the effects of the mean flow properties are considered
As a result, the turbulence effect on the fiber orientation should not be neglected

**42. **RESULTS OVERVIEW Simulation results from the mean flow field show fiber orientation has little relation with
the mean flow velocity
the channel length
the fiber aspect ratio in the interested range
Fiber orientation increases with the increment of the contraction ratio of the channel

**43. **CONCLUSIONS Designing of the header is critical to obtain flow uniformity in the slice
Level of turbulence induced by the tubes is very important for the exit flow characteristics
Secondary flows induced by turbulence anisotropy are negligible
Main flow is well predicted by the standard K-e equations
Turbulence characteristics are not well predicted by the standard K-e model
The fiber is significantly aligned by the contraction in the slice. However the turbulence induced fiber randomness is very essential

**44. **FUTURE WORK Turbulence modeling needs to be improved. Large eddy simulation is currently under development
Fiber/ fiber interaction will have to be introduced in the fiber model and will be introduced in the model in the future
Turbulence effect on the fiber has to be accounted for. The model is being currently developed.
The fiber orientation in the slice has to be modelled again with the above mentioned improvements
Current model allows for assessing headboxes and can be used as a design assessment and optimization tool
Development currently under way will allow for realistic assessment of fiber orientation at the exit of the slice