1. March 12th, 2001 Cincinnati, OH FLUID MECHANICS IN HEADBOXES M. Shariati, E. Bibeau, M.Salcudean and I. Gartshore CFD Modelling Group Department of Mechanical Engineering University of British Columbia Process Simulations Limited

2. PRESENTATION lMathematical modelling in the pulp and paper industry lWhy we model headboxes lHow we model headboxes lExamples - flow in the header, tubes and slice lConclusions and future

3. PROCESS MODELLING GROUP

4. UBC-PSL TECHNOLOGY APPLICATION Other Institutions Government Industry License agreement Service agreements Consulting agreements Custom agreements License agreements

5. PROCESS MODELLING

6. STAGES OF ANALYSIS INPROGRESSINDUSTRIALAPPLICATIONPROCESSSIMULATORS Literature review Mill interaction Industrial innovators Process knowledge Commitment of industry Physical model Numerical model Model development Model validation Industrial testing Industrial application Parametric studies Solve problems Model proposed retrofits Improve operations Reduce costs Envelope calculations Interpolation Operational simulator Training& safety Interacts with control system Technology transfer INITIALSTAGE

7. MODELLING EXAMPLES Computer Jet engines Weather Automotive Harrier jet

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

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

10. NUMERICAL CFD CODE lCode developed at the University of British Columbia lGeneralized curvilinear system lFinite volume method lBlock structured lSecond order accurate for cross derivative terms lSteady and transient lPartial multigrid capability

11. HEADBOX WISH LIST lSelect sheet properties lImprove control of fiber distribution lControl MD/CD ratios lPrevent non-uniformities (basis weight, fibre orientation) lControl fiber distribution lFlow Field (velocity, stresses, vorticity) lFluid-fibre interaction

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

13. MODEL DELIVERABLES lManufacturers and Pulp Mills lEvaluate new headbox designs lCompare headbox designs lTrouble-shoot existing headboxes lPredict influence of control devices lEvaluate proposed retrofits and design changes lHelp correlate sheet properties to headbox behavior

14. GENERIC HEADBOX MODELLED

15. EFFECT OF FLOW RECIRCULATION

16. VELOCITY IN CD DIRECTION

17. TYPICAL TUBE lVelocity Vectors lPressure contours

18. TUBE FLOW ENTRANCE EFFECT lGreen - Flow turns before entering tubes lRed - Flow enters straight lAffects - Flow profile into slice - Fibre distribution and orientation

19. CONVERGING SECTION lVelocity vectors l3 slices in CD direction

20. CONVERGING SECTION lVelocity vectors lContours in machine Direction (MD)

21. VELOCITY IN CD DIRECTION

22. VELOCITY IN MD DIRECTION

23. KINETIC ENERGY IN CONVERGING SECTION

24. LENGTH SCALE

25. EXPERIMENTAL METHOD

26. MD VELOCITY U

27. CD VELOCITY

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

29. CD VELOCITY (m/s) K-eRSM

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

34. KINETIC ENERGY

35. SIMULATION OF CONVERGING SECTION WITH TUBE BANKS

36. FIBER MOTION lFiber is modeled as chains of spheroids lModel can deal with the wall automatically for different geometry 2 3 N-1 1 N Ball and Socket Joints

37. EXPERIMENTAL SETUP

38. FIBER MOTION RESULTS lFiber orientation mid channel at x = 12.2 cm Edge view Side view

39. FIBER MOTION RESULTS lFiber orientation mid channel at x = 19.2 cm Edge view Side view

40. FIBER MOTION RESULTS lFiber orientation mid channel at x = 26.2 cm Edge view Side view

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

42. RESULTS OVERVIEW lSimulation 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 lFiber orientation increases with the increment of the contraction ratio of the channel

43. CONCLUSIONS lDesigning of the header is critical to obtain flow uniformity in the slice lLevel of turbulence induced by the tubes is very important for the exit flow characteristics lSecondary flows induced by turbulence anisotropy are negligible lMain flow is well predicted by the standard K-e equations lTurbulence characteristics are not well predicted by the standard K-e model lThe fiber is significantly aligned by the contraction in the slice. However the turbulence induced fiber randomness is very essential

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