Skip to main content
SpringerLink
Log in

An Air Permeability Study of Anisotropic Glass Wool Fibrous Products

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

This article reports an experimental study of the permeability of fibrous porous media based on air flow. Two glass wools have been analyzed in three different flow directions to evaluate their anisotropic structure. The usual flow theories such as Darcy’s law, valid for granular materials, have been shown to apply also to these fibrous media which is a more complex structure (fiber arrangement, high porous media,…). The intrinsic permeabilities and the anisotropic factors have been determined from an air permeability measurement based on a standard test for industrial fabrics. The experimental results have been compared to different models, showing the limits of some simplistic models when applied to our highly porous structures. One model, Kyan’s model based on the flow around submerged objects, was, however, found to agree with our experimental data. This study also demonstrates the interesting use of an experimental technique, which is air permeability measurement (water permeability is not adapted), in the investigation of flow phenomena in a fibrous medium.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

A :

Cross-sectional area (m2)

AF:

Anisotropic factor

A 0 :

Specific surface area (m−1)

D e :

Equivalent diameter (m)

D f :

Average fiber diameter (m)

d h :

Hydraulic diameter (m)

f fk :

Kinetic friction factor

f p :

The friction factor

E :

The elastic modulus of the glass fiber

G :

Acceleration due to gravity (9.81 m s−2)

k :

Intrinsic permeability (m2)

K :

Darcian permeability

k A :

Air permeability (m s−1)

K k :

Kozeny constant

K n :

Knudsen number

k 0 :

Shape parameter

K sat :

The conventional saturated

L :

Length (m)

L t :

Length of the straight line (m)

L e :

Effective length (m)

n :

Space between parallel fibers

N e :

Effective pore number

N d :

Fiber deflection number

N Re :

Reynolds number

q :

Volumetric flow rate of fluid (m3 s−1)

Re f :

Reynolds number of the fiber

R f :

Fiber radius (m)

R v :

Hydrodynamic radius (m)

R L :

Laplace radius (m)

R W :

Washburn radius (m)

S :

Solid surface area (m2)

U D :

Filtration or filter velocity (m s−1)

α :

Angle of inclination between two adjacent inclined fibers (\({\circ}\))

\({\varepsilon}\) :

Total porosity

\({\varepsilon_{\rm e}}\) :

Effective porosity

ρ :

Density (kg m−3) of the fluid

λ air :

Mean free path of an air molecule (m)

μ :

Dynamic viscosity (Pa s)

\({\phi}\) :

Solid volume (\({=1-\varepsilon}\))

τ :

Tortuosity

ΔP :

Hydrostatic pressure difference (Pa)

ΔP flow :

Pressure drop due to viscous flow losses (Pa)

ΔP formdrag :

Pressure drop caused by form drag (Pa)

ΔP deflection :

Pressure drop due to deflection of fibers (Pa)

References

  • Achchaq, F., Beji, H., Gassita, S., Marmoret, L.: Comportement hydrique d’un isolant fibreux, juillet, 8ème congrès de mécanique du 17–20 avril, El Jadida Maroc (2007)

  • Achchaq F., Djellab K., Beji H., Marmoret L.: Hydric, morphological and thermo-physical characterization of glass wools: from macroscopic to microscopic approach. Constr. Build. Mater. 23, 3214–3219 (2009)

    Article  Google Scholar 

  • Bear J.: Dynamics of Fluids in Porous Media. Dover, New York (1972)

    Google Scholar 

  • Bergonnier S., Hild F., Rieunier J.B., Roux S.: Strain heterogeneities and local anisotropy in crimped glass wool. J. Mater. Sci. 40, 5949–5954 (2005)

    Article  Google Scholar 

  • Carman P.C.: The determination of the specific surface area of powder I. J. Soc. Chem. Ind. 57, 225–234 (1937)

    Google Scholar 

  • Davies C.N.: The separation of airborne dust and particles. Proc Inst. Mech. Engng. 1, 185 (1952)

    Google Scholar 

  • Drummond J.E, Tahir M.I: Laminar viscous flow through regular arrays of parallel solid cylinders. Int. J. Multiphase Flow 10, 515–539 (1984)

    Article  Google Scholar 

  • Dullien F.A.: Porous Media, Fluid Transport and Pore Structure. Academic press, New York (1992)

    Google Scholar 

  • Happel J.: Viscous flow relative to arrays of cylinders. AIChE J. 5, 174–177 (1959)

    Article  Google Scholar 

  • Happel J., Brenner H.: Low Reynolds Number Hydrodynamics. Martinus Nijhoff Publishers, Norwell, MA (1986)

    Google Scholar 

  • Hasimoto H.: On the periodic fundamental solutions of the stokes equations and their applications to viscous flow pas a cubic array of spheres. J. Fluid Mech. 5, 317–328 (1959)

    Article  Google Scholar 

  • Ingmanson W.L., Andrews B.D., Johnson R.C.: Internal pressure distributions in compressible mats under fluid stress. Tappi 42, 840–849 (1959)

    Google Scholar 

  • Jackson G.W., James D.F.: The permeability of fibrous porous media. Canad. J. Chem. Eng. 64, 364–374 (1986)

    Article  Google Scholar 

  • Kaviani M.: Principles of Heat Transfer in Porous Media, 2nd ed. Springer, New York (1995)

    Book  Google Scholar 

  • Kołodziej J.A: Filtration resistance of a system of parallel cylinders at transverse creeping flow. J. Theor. Appl. Mech. 24, 537–549 (1986)

    Google Scholar 

  • Kołodziej J.A., Cielak R.D., Konczak Z.: Permeability tensor for heterogeneous porous medium of fibre type. Transp. Porous Media 32, 1–19 (1998)

    Article  Google Scholar 

  • Koponen A., Kataja M., Timonen J.: Permeability and effective porosity of porous media. Phys. Rev. E 56(3), 3319–3325 (1997)

    Article  Google Scholar 

  • Kuwabara S.: The force experienced by randomly distributed parallel circular cylinders or spheres in a viscous flow at small Reynolds numbers. J. Phys. Soc. Jpn. 14, 527–532 (1959)

    Article  Google Scholar 

  • Kyan C.P., Wasan D.T., Kintner R.C.: Flow of single phase fluids through fibrous beds. Ind. Eng. Chem. Fundam. 9, 4 (1970)

    Article  Google Scholar 

  • Langlais, C., Klarsfeld, S.: Transfert de chaleur à à travers les isolants fibreux en relation avec leur morphologie. Journée d’études du GUT sur le transfert de chaleur dans les isolants fibreux, 6 mars (1985)

  • Marmoret L., Beji H., Perwuelz A.: Determination of the pore sizes and their influence on the dynamics of imbibition into thermal insulating glass wool. Defect Diffus. Forum (DDF) 312-315, 812–817 (2011)

    Article  Google Scholar 

  • Mauret E., Renaud M.: Transport phenomena in multi-particle systems. Part I: limits of applicability of capillary model in high voidage beds—application to fixed beds of fibers and fluidized beds of spheres. Chem. Eng. Sci. 52(N 11), 1807–1817 (1997)

    Article  Google Scholar 

  • Nilsson L., Strenström S.: A study of the permeability of pulp and paper. Int. J. Multiphase Flow 23(1), 131–153 (1997)

    Article  Google Scholar 

  • Rahli O., Tadrist L., Miscevic M.: Experimental analysis of fibrous porous media permeability. AIChE J. 42, 3547–3549 (1996)

    Article  Google Scholar 

  • Rahli O., Tadrist L., Miscevic M., Santini R.: Fluid flow through randomly packed monodisperse fibers: the Kozeny–Carman parameter analysis. J. Fluids Eng. 119, 188–192 (1997)

    Article  Google Scholar 

  • Rodriguez E., Giacomelli F., Vazquez A.: Permeability–porosity relationship in RTM for different fiberglass and natural reinforcements. J. Compos. Mater. 38, 259–268 (2004)

    Article  Google Scholar 

  • Rumps H., Gupte A.: R Chem. Ing. Tech. 43, 367 (1971)

    Article  Google Scholar 

  • Sadiq T.A.K., Advani S.G, Parnas R.S: Experimental investigation of transverse flow through aligned cylinders. Int. J. Multiphase Flow 21, 755–774 (1995)

    Article  Google Scholar 

  • Sangani, A.S, Acrivos, A.: Slow flow through a periodic array of spheres. Int. J. Multiphase Flow 8, 193–206 and 343–360 (1982)

    Google Scholar 

  • Scheidegger A.: The Physics of Flow Through Porous Media. Macmillan, New York (1957)

    Google Scholar 

  • Shih C.H, Lee J.: Effect of fiber architecture on permeability in liquid composite molding. Polym. Compos. 19, 629–639 (1998)

    Article  Google Scholar 

  • Sparrow E.M., Loeffler A.M: Longitudinal laminar flow between cylinders arranged in regular array. AIChE J. 5, 325–330 (1959)

    Article  Google Scholar 

  • Sullivan R.R.: Specific surface measurements on compact bundles of parallel fibres. J. Appl. Phys. 13, 725–730 (1942)

    Article  Google Scholar 

  • Westhuizen J.V., Prieur Du Plessis J.: An attempt to quantify fibre bed permeability utilizing the phase average Navier–Stokes equation. Composites Part A 27, 263–269 (1996)

    Article  Google Scholar 

  • Wu Y.S., Pruess K., Persoff P.: Gas flow in porous media with Klinkenberg’s effect. Transp. Porous media 32, 117–137 (1998)

    Article  Google Scholar 

  • Xu P., Yu B.: Developing a new form of permeability and Kozeny Carman constant for homogeous porous media by means of fractal geometry. Adv. Water Resour. 31, 4–81 (2008)

    Article  Google Scholar 

  • Young W.B., Wu S.F.: Permeability measurement of bidirectional woven glass fibres. J. Reinf. Plast. Compos. 21, 755–774 (1995)

    Google Scholar 

  • Zhong W.H., Currie I.G., James D.F.: Creeping flow through a model fibrous porous medium. Exp. Fluids 40, 119–126 (2006)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Laboratoire des Technologies Innovantes, Equipe Phénomènes de Transfert et Construction Durable, Université de Picardie Jules Verne, IUT Génie Civil, Avenue des facultés, Le Bailly, 80025, Amiens, France

    L. Marmoret

  2. Univ Lille Nord de France, 59000, Lille, France

    M. Lewandowski & A. Perwuelz

  3. ENSAIT, GEMTEX, 59100, Roubaix, France

    M. Lewandowski & A. Perwuelz

Authors
  1. L. Marmoret
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Lewandowski
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Perwuelz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to L. Marmoret.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marmoret, L., Lewandowski, M. & Perwuelz, A. An Air Permeability Study of Anisotropic Glass Wool Fibrous Products. Transp Porous Med 93, 79–97 (2012). https://doi.org/10.1007/s11242-012-9945-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-012-9945-8

Keywords

Search

Navigation