# 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)
${A}_{eff}=\sum _{n}LC\cdot AC\cdot Are{a}_{n}$
Ileakage =2:(2)
${A}_{eff}=\sum _{n}\mathrm{LC}\left(t\right)\cdot \mathrm{AC}\left(P\right)\cdot Are{a}_{n}$
Ileakage =3:(3)
${A}_{eff}=\sum _{n}\mathrm{LC}\left(t\right)\cdot \mathrm{AC}\left(P-Pext\right)\cdot Are{a}_{n}$
Ileakage =4:(4)
${A}_{eff}=\sum _{n}\mathrm{LC}\left(Are{a}_{n}/Are{a}_{0}\right)\cdot \mathrm{AC}\left({P}_{ext}/P\right)\cdot Are{a}_{n}$
Ileakage =5:(5)
${A}_{eff}=\sum _{n}\frac{Are{a}_{0}}{{L}^{2}}\left[\left({C}_{1}\text{Δ}{P}^{{C}_{2}}-{C}_{3}\right){\left(L-R\right)}^{2}+{C}_{3}\left(L{\lambda }_{1}-R/\sqrt{{\lambda }_{2}}\right)\left(L{\lambda }_{2}-R/\sqrt{{\lambda }_{1}}\right)\right]\cdot \mathrm{sin}{\alpha }_{12}$

$\text{Δ}P=P/{P}_{ext}-1$

Where, ${\lambda }_{1}$ and ${\lambda }_{2}$ are the stretches in warp and weft directions and ${\alpha }_{12}$ is the angle between warp and weft directions.

Ileakage =6:(6)
${A}_{eff}=\sum _{n}Are{a}_{0}\left({X}_{0}+{X}_{1}{r}_{s}+{X}_{2}{r}_{p}+{X}_{3}{r}_{s}{r}_{p}\right)$

with ${r}_{s}=Are{a}_{n}/Are{a}_{0}$ and ${r}_{p}={P}_{ext}/P$ .

Parts with this material are considered porous, when referenced via a surface ID using the /MONVOL/FVMBAG1 surf_IDps 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 Iformps and has the following formulations:
• Iformps = 1 ${\stackrel{˙}{m}}_{\mathit{out}}={A}_{\mathit{eff}}\sqrt{2P\rho }{Q}^{\frac{1}{\gamma }}\sqrt{\frac{\gamma }{\gamma -1}\left[1-{Q}^{\frac{\gamma -1}{\gamma }}\right]}$ (Isentropic - Wang Nefske)
• Iformps = 2 ${\stackrel{˙}{m}}_{\mathit{out}}={A}_{\mathit{eff}}\rho v\left(P-{P}_{\mathit{ext}}\right)$

Where, v is the outflow gas velocity (Chemkin)

• Iformps = 3 ${\stackrel{˙}{m}}_{\mathit{out}}={A}_{\mathit{eff}}\sqrt{2\rho \left(P-{P}_{\mathit{ext}}\right)}$ (Graefe)
The Iformps =2 option is normally used to represent fabric porosity. The outflow gas velocity as function of airbag overpressure comes from test data.