Airbag Fabric Porosity

Porosity of airbag material is modeled by the addition of a porosity card /LEAK/MAT to /MAT/LAW58 card.

Generic /TYPE7 and TYPE11 contacts between airbag and housing (kg, mm, ms)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/LAW58/1	
Altair test fabric law58
#        Init. dens.          Ref. dens.
                8E-7                   0
#                 E1                  B1                  E2                  B2                FLEX
               0.380                   0               0.380                   0                 1.0
#                 G0                  GT              AlphaT                                  Sensor
              0.0035              0.0055               7.175                                       1
#                 Df                  Ds               Gfrot                              ZeroStress
                   0                   0                   0                                       1
#       N1        N2                  S1                  S2
         1         1                   0                   0
#    Dir 1
       500                1.00
#    Dir 2
       501                1.00
#    Dir12
       502                1.00
#  FCT_ID4   FCT_ID5             Fscale4             Fscale5   FCT_ID6             Fscale6
       600       600                   1                   1       502                   1
/LEAK/MAT/1
Fabric
#    Ileak             AscaleT             AscaleP
         1
#                AC' fct_IDAC’
#                 LC                  AC
             1.0e-03             1.0e-03 
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

The /LEAK/MAT specifies how the effective porous area of a component having this material will vary as a function time or pressure. It is determined by the value of Ileakage.

Ileakage =1:(1)

A_{e f f} = \sum_{n} L C \cdot A C \cdot A r e a_{n}

Ileakage =2:(2)

A_{e f f} = \sum_{n} LC (t) \cdot AC (P) \cdot A r e a_{n}

Ileakage =3:(3)

A_{e f f} = \sum_{n} LC (t) \cdot AC (P - P e x t) \cdot A r e a_{n}

Ileakage =4:(4)

A_{e f f} = \sum_{n} LC (A r e a_{n} / A r e a_{0}) \cdot AC (P_{e x t} / P) \cdot A r e a_{n}

Ileakage =5:(5)

A_{e f f} = \sum_{n} \frac{A r e a_{0}}{L^{2}} [(C_{1} Δ P^{C_{2}} - C_{3}) {(L - R)}^{2} + C_{3} (L λ_{1} - R / \sqrt{λ_{2}}) (L λ_{2} - R / \sqrt{λ_{1}})] \cdot \sin α_{12}

$Δ P = P / P_{e x t} - 1$

Where, $λ_{1}$ and $λ_{2}$ are the stretches in warp and weft directions and $α_{12}$ is the angle between warp and weft directions.

Ileakage =6:(6)

A_{e f f} = \sum_{n} A r e a_{0} (X_{0} + X_{1} r_{s} + X_{2} r_{p} + X_{3} r_{s} r_{p})

with $r_{s} = A r e a_{n} / A r e a_{0}$ and $r_{p} = P_{e x t} / P$ .

Parts with this material are considered porous, when referenced via a surface ID using the /MONVOL/FVMBAG1 surf_ID_ps option.

Example of porosity definition in /MONVOL/FVMBAG1.

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MONVOL/FVMBAG1/1
DAB
#     Isur
         4
#             Scal_T              Scal_P              Scal_S              Scal_A              Scal_D
                   0                   0                   0                   0                   0
#   Mat_ID                            Mu                Pext                Tphi     Iequi        Ittf
         4                           0.1          0.00010135                   0         0           3
#     Njet
         1
#   Inj_ID   Isensor surf_IDinj     
        10         1           100
#    Nvent       Nps
         0         1
#Sur_id_ps  Iform_ps
         4         1
#             Tstart               Tstop               dPdef              DtPdef             ldtpdef   
….    
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

The mass flow though the porous material is defined using /MONVOL/FVMBAG1 Iform_ps and has the following formulations:

Iform_ps = 1 ${\dot{m}}_{out} = A_{eff} \sqrt{2 P ρ} Q^{\frac{1}{γ}} \sqrt{\frac{γ}{γ - 1} [1 - Q^{\frac{γ - 1}{γ}}]}$ (Isentropic - Wang Nefske)
Iform_ps = 2 ${\dot{m}}_{out} = A_{eff} ρ v (P - P_{ext})$
Where, v is the outflow gas velocity (Chemkin)
Iform_ps = 3 ${\dot{m}}_{out} = A_{eff} \sqrt{2 ρ (P - P_{ext})}$ (Graefe)

The Iform_ps =2 option is normally used to represent fabric porosity. The outflow gas velocity as function of airbag overpressure comes from test data.