Journal of Materials Science

, Volume 41, Issue 23, pp 7989–8000 | Cite as

Lattice Boltzmann method based computation of the permeability of the orthogonal plain-weave fabric preforms

  • M. GrujicicEmail author
  • K.M. Chittajallu
  • Shawn Walsh


Changes in the permeability tensor of fabric preforms caused by various modes of fabric distortion and fabric-layers shifting and compacting is one of the key factors controlling resin flow during the infiltration stage of the common polymer-matrix composite liquid-molding processes. While direct measurements of the fabric permeability tensor generally yield the most reliable results, a large number of fabric architectures used and numerous deformation and layers rearrangement modes necessitates the development and the use of computational models for prediction of the preform permeability tensor. The Lattice Boltzmann method is used in the present work to study the effect of the mold walls, the compaction pressure, the fabric-tows shearing and the fabric-layers shifting on the permeability tensor of preforms based on orthogonal balanced plain-weave fabrics. The model predictions are compared with their respective experimental counterparts available in the literature and a reasonably good agreement is found between the corresponding sets of results.


Lattice Boltzmann Method Fiber Volume Fraction Effective Permeability Permeability Tensor Particle Distribution Function 



Particle distribution function


Fiber volume fraction


Fabric thickness (m)


Relative dimensionless shift of the adjacent fabric layers


Permeability tensor of the fabric (m2)


In-plane quarter cell dimension (m)


Pressure (Pa)


Shear angle (deg.)


Fiber radius (m)


Relative shift of the adjacent fabric layers (m)


Particle velocity component


Fluid point density (particles/lattice point)


Collision operator


Time (s)


Time relaxation parameter


Velocity component weighting factor


Fluid nodal velocity (lattice parameters/time increment)


Fluid kinematic viscosity (m2/s)


Nodal position vector



Quantity associated with the bottom surface of the fabric


Quantity associated with the top surface of the fabric



Quantity associated with the bottom channel


Equilibrium quantity


Quantity associated with the fabric


Quantity associated with the top channel



The material presented in this paper is based on work supported by the U.S. Army Grant Number DAAD19-01-1-0661. The authors are indebted to Drs. Walter Roy, Fred Stanton, William DeRosset and Dennis Helfritch of ARL for the support and a continuing interest in the present work. The authors also acknowledge the support of the Office of High Performance Computing Facilities at Clemson University.


  1. 1.
    Lee LJ (1997) In: Gutowski TG (eds) Advanced composites manufacturing. John Wiley & Sons, New York, pp. 393–456Google Scholar
  2. 2.
    Lam RC, Kardos JL (1988) In: Proc Third Tech Conf. American Society for CompositesGoogle Scholar
  3. 3.
    Gutowski TG (1985) in SAMPE Quart 4Google Scholar
  4. 4.
    Gebart BR (1992) J Compos Mater 26:1100CrossRefGoogle Scholar
  5. 5.
    Ranganathan S, Phelan F, Advani SG (1996) Polym Compos 17:222CrossRefGoogle Scholar
  6. 6.
    Ranganathan S, Wise GM, Phelan FR, Parnas RS, Advani SG (1994) A numerical and experimental study of the permeability of fiber preforms. In: Proc Tenth ASM/ESD Advanced Composites Conf, OctGoogle Scholar
  7. 7.
    Grujicic M, Chittajallu KM, Walsh S, Grujicic M (2003) Effect of shear, compaction and nesting on permeability of the orthogonal plain-weave fabric preforms. Applied Surface Science, submitted for publication, OctGoogle Scholar
  8. 8.
    Martys N, Chen H (1996) Phys Rev 53:743Google Scholar
  9. 9.
    Kandhai D, Vidal DJE, Hoekstra AG, Hoefsloot H, Iedema P, Sloot PMA (1998) Intl J Modern Phys C 9:1123CrossRefGoogle Scholar
  10. 10.
    Spaid MAA, Phelan FR (1997) Phys Fluids 9:2468CrossRefGoogle Scholar
  11. 11.
    Chen S, Doolen GD (1998) Annu Rev Fluid Mech 30:329CrossRefGoogle Scholar
  12. 12.
    Dungan FD, Senoguz MT, Sastry AM, Faillaci DA (2001) J Compos Mater 35:1250Google Scholar
  13. 13.
    Ito M, Chou TW (1998) J Compos Mater 32:2CrossRefGoogle Scholar
  14. 14.
    Pearce N, Summerscales J (1995) Compos Manuf 6:15CrossRefGoogle Scholar
  15. 15.
    Saunders RA, Lekakou C, Bader MG (1998) Compos Part A 29A:443CrossRefGoogle Scholar
  16. 16.
    Hu J, Newton A (1997) J Text Inst Part I 88:242CrossRefGoogle Scholar
  17. 17.
    Chen B, Chou TW (1999) Compos Sci Technol 59:1519CrossRefGoogle Scholar
  18. 18.
    Chen B, Chou TW (2000) Compos Sci Technol 60:2223CrossRefGoogle Scholar
  19. 19.
    Chen B, Lang EJ, Chou TW (2001) Mater Sci Eng A317:188CrossRefGoogle Scholar
  20. 20.
    Bhatnager PL, Gross EP, Krook M (1954) Phys Rev 94:511CrossRefGoogle Scholar
  21. 21.
    Chen H, Chen S, Mathaeus WH (1992) Phys Rev A 45:5339CrossRefGoogle Scholar
  22. 22.
    Stockman HW (1999) Sandai Report, Sand99-0162Google Scholar
  23. 23.
    Dungan FD, Senoguz MT, Sastry AM, Faillaci DA (2001) J Compos Mater 35:1250Google Scholar
  24. 24.
    Dungan FD, Senoguz MT, Sastry AM, Faillaci DA (1999) J Reinforced Plastics Compos 18:472CrossRefGoogle Scholar
  25. 25.
    Sozer EM, Chen B, Graham PJ, Bickerton S, Chou TW, Advani SG (1999) Proceedings of the fifth international conference on flow processes in composite materials, Plymouth, UK, 12–14 July, pp 25–36Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringClemson UniversityClemsonUSA
  2. 2.Army Research Laboratory—WMRD AMSRL-WM-MDAberdeenUSA

Personalised recommendations