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GOVERNING EQUATIONS FOR ISOTHERMAL FLOW THROUGH WOVEN FIBER MATS BY EMPLOYING LOCAL VOLUME AVERAGING TECHNIQUE

Year 2011, Issue: 024, 91 - 106, 15.04.2011

Abstract

Accurate
mathematical modeling of resin flow in liquid composite molding (LCM) processes
is important for effective simulations of the mold-filling process. Recent
experiments indicate that the physics of resin flow in woven fiber mats is very
different from the flow in random fiber mats. In this study, the mathematically
rigorous volume averaging method is adapted to derive the averaged form of mass
and momentum balance equations for unsaturated flow in LCM. The two phases used
in the volume averaging method are the dense bundle of fibers called tows, and
the surrounding gap present in the woven fiber mats. Averaging the mass balance
equation yields a macroscopic equation of continuity which is similar to the
conventional continuity equation for a single-phase flow. Similar averaging of
the momentum balance equation is accomplished for the dual-scale porous medium. 

References

  • [1] C.D. Rudd, A.C. Long, K.N. Kendall and C.G.E. Mangin, Liquid molding technologies, Woodhead Publishing Ltd (1997).
  • [2] M.V. Bruschke and S.G. Advani, RTM filling simulation of complex three dimensional shell-like structures, SAMPE Q 23 (1) (1991), pp. 2–11.
  • [3] C.A. Fracchia, J. Castro and C.L. Tucker III, A finite element/control volume simulation of resin transfer molding, Proceedings of the American Society for Composites Fourth Technical Conference, Technomic, Lancaster, PA (1989), pp. 157–166.
  • [4] C.L. Tucker III and R.B. Dessenberger, Governing equations for flow and heat transfer in stationary fiber beds. In: S.G. Advani, Editor, Flow and rheology in polymer composites manufacturing, Elsevier, Amsterdam (1994), pp. 257–323.
  • [5] J. Bear and Y. Bachmat, Introduction to modeling of transport phenomena in porous media, Kluwer, Dordrecht (1990).
  • [6] S. Whitaker, The method of volume averaging, Kluwer, Dordrecht (1999).
  • [7] L. Trevino, K. Rupel, W.B. Young, M.J. Liou and L.J. Lee, Analysis of resin injection molding in molds with preplaced fiber mats. I. Permeability and compressibility measurements, Polym Compos 12 (1) (1991).
  • [8] C. Lekakou, M.A.K.B. Johari and M.G. Bader, Compressibility and flow permeability of two-dimensional woven reinforcements in the processing of composites, Polym Compos 17 (1996), pp. 666–672.
  • [9] Y.D. Parseval, K.M. Pillai and S.G. Advani, A simple model for the variation of permeability due to partial saturation in dual scale porous media, Transport Porous Media 27 (1997), pp. 243–264.
  • [10] Alakus B. Finite elemet fluid flow computations through porous media employing quasi-linear and non-linear viscoelastic models. PhD Thesis. University of Minnesota; 2001.
  • [11] Pillai KM, Advani SG. Modeling of void migration in resin transfer molding process. Proceedings of ASME Winter Meet, Atlanta, GA; September 1996.
  • [12] K.M. Pillai and S.G. Advani, A model for unsaturated flow in woven or stitched fiber mats during mold filling in resin transfer molding, J Compos Mater 32 (19) (1998), pp. 1753–1783.
  • [13] K.M. Pillai and S.G. Advani, Wicking across a fiber-bank, J Colloid Interface Sci 183 (1) (1996), pp. 100–110
  • [14] K.M. Pillai and S.G. Advani, Numerical simulation of unsaturated flow in woven or stitched fiber mats in resin transfer molding, Polym Compos 19 (1) (1998), pp. 71–80
  • [15] R.S. Parnas and F.R. Phelan, The effect of heterogeneous porous media on mold filling in resin transfer molding, SAMPE Q (1990).
  • [16] C. Binetruy, B. Hilaire and J. Pabiot, Tow impregnation model and void formation mechanisms during RTM, J Compos Mater 32 (3) (1998), pp. 223–245.
  • [17] J.C. Slattery, Single-phase flow through porous media, AIChE J 15 (6) (1969), pp. 866–872.
  • [18] W.G. Gray and P.C.Y. Lee, On the theorems for local volume averaging of multiphase systems, Int J Multiphase Flow 3 (1977), pp. 333–340.
  • [19] S. Whitaker, Flow in porous media. I. A theoretical derivation of Darcy's law, Transport Porous Media 1 (1986), pp. 3–25.
  • [20] M. Kaviany, Principles of heat transfer in porous media (2nd ed), Springer, New York (1995).
  • [21] K. O'Neill and G.F. Pinder, A derivation of equations for transport of liquid and heat in three dimensions in a fractured porous medium, Adv Water Resour 4 (1981), pp. 150–164.
  • [22] S.M. Hassanizadeh, Modeling species transport by concentrated brine in aggregated porous media, Transport Porous Media 3 (1988), pp. 299–318.

FİBERLİ GÖZENEKLİ BİR ORTAMDAKİ İZOTERMAL BİR AKIŞKANIN YEREL HACİMSEL ORTALAMA METODU KULLANILARAK HAREKET DENKLEMLERİNİN ELDE EDİLMESİ

Year 2011, Issue: 024, 91 - 106, 15.04.2011

Abstract

Sıvı kompozit kalıp işlemi 
sırasındaki resin akışının doğru bir matematiksel modelinin
oluşturulması, simülasyon ve kalıp doldurma işlemi için çok önemlidir. Bu
çalışmada, yerel hacimsel ortalama metodu detaylı olarak kullanılmak sureti ile
akış alanına ait  kütle ve momentum
denklemleri elde edildi. Oluşan matematiksel model  akışkan resine ait ortalama hız bileşenleri
ile basıncı verir. Benzer ortalama teknikleri ile, çift skalalı gözenekli
ortama ait  momentum balans deklemleri
elde edilebilir.

References

  • [1] C.D. Rudd, A.C. Long, K.N. Kendall and C.G.E. Mangin, Liquid molding technologies, Woodhead Publishing Ltd (1997).
  • [2] M.V. Bruschke and S.G. Advani, RTM filling simulation of complex three dimensional shell-like structures, SAMPE Q 23 (1) (1991), pp. 2–11.
  • [3] C.A. Fracchia, J. Castro and C.L. Tucker III, A finite element/control volume simulation of resin transfer molding, Proceedings of the American Society for Composites Fourth Technical Conference, Technomic, Lancaster, PA (1989), pp. 157–166.
  • [4] C.L. Tucker III and R.B. Dessenberger, Governing equations for flow and heat transfer in stationary fiber beds. In: S.G. Advani, Editor, Flow and rheology in polymer composites manufacturing, Elsevier, Amsterdam (1994), pp. 257–323.
  • [5] J. Bear and Y. Bachmat, Introduction to modeling of transport phenomena in porous media, Kluwer, Dordrecht (1990).
  • [6] S. Whitaker, The method of volume averaging, Kluwer, Dordrecht (1999).
  • [7] L. Trevino, K. Rupel, W.B. Young, M.J. Liou and L.J. Lee, Analysis of resin injection molding in molds with preplaced fiber mats. I. Permeability and compressibility measurements, Polym Compos 12 (1) (1991).
  • [8] C. Lekakou, M.A.K.B. Johari and M.G. Bader, Compressibility and flow permeability of two-dimensional woven reinforcements in the processing of composites, Polym Compos 17 (1996), pp. 666–672.
  • [9] Y.D. Parseval, K.M. Pillai and S.G. Advani, A simple model for the variation of permeability due to partial saturation in dual scale porous media, Transport Porous Media 27 (1997), pp. 243–264.
  • [10] Alakus B. Finite elemet fluid flow computations through porous media employing quasi-linear and non-linear viscoelastic models. PhD Thesis. University of Minnesota; 2001.
  • [11] Pillai KM, Advani SG. Modeling of void migration in resin transfer molding process. Proceedings of ASME Winter Meet, Atlanta, GA; September 1996.
  • [12] K.M. Pillai and S.G. Advani, A model for unsaturated flow in woven or stitched fiber mats during mold filling in resin transfer molding, J Compos Mater 32 (19) (1998), pp. 1753–1783.
  • [13] K.M. Pillai and S.G. Advani, Wicking across a fiber-bank, J Colloid Interface Sci 183 (1) (1996), pp. 100–110
  • [14] K.M. Pillai and S.G. Advani, Numerical simulation of unsaturated flow in woven or stitched fiber mats in resin transfer molding, Polym Compos 19 (1) (1998), pp. 71–80
  • [15] R.S. Parnas and F.R. Phelan, The effect of heterogeneous porous media on mold filling in resin transfer molding, SAMPE Q (1990).
  • [16] C. Binetruy, B. Hilaire and J. Pabiot, Tow impregnation model and void formation mechanisms during RTM, J Compos Mater 32 (3) (1998), pp. 223–245.
  • [17] J.C. Slattery, Single-phase flow through porous media, AIChE J 15 (6) (1969), pp. 866–872.
  • [18] W.G. Gray and P.C.Y. Lee, On the theorems for local volume averaging of multiphase systems, Int J Multiphase Flow 3 (1977), pp. 333–340.
  • [19] S. Whitaker, Flow in porous media. I. A theoretical derivation of Darcy's law, Transport Porous Media 1 (1986), pp. 3–25.
  • [20] M. Kaviany, Principles of heat transfer in porous media (2nd ed), Springer, New York (1995).
  • [21] K. O'Neill and G.F. Pinder, A derivation of equations for transport of liquid and heat in three dimensions in a fractured porous medium, Adv Water Resour 4 (1981), pp. 150–164.
  • [22] S.M. Hassanizadeh, Modeling species transport by concentrated brine in aggregated porous media, Transport Porous Media 3 (1988), pp. 299–318.
There are 22 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Bayram Alakuş This is me

Publication Date April 15, 2011
Published in Issue Year 2011 Issue: 024

Cite

APA Alakuş, B. (2011). GOVERNING EQUATIONS FOR ISOTHERMAL FLOW THROUGH WOVEN FIBER MATS BY EMPLOYING LOCAL VOLUME AVERAGING TECHNIQUE. Journal of Science and Technology of Dumlupınar University(024), 91-106.

HAZİRAN 2020'den itibaren Journal of Scientific Reports-A adı altında ingilizce olarak yayın hayatına devam edecektir.