# AIRBAG1

Uniform pressure is assumed inside the volume. Perfect gas law and adiabatic conditions are assumed. Injected mass (or mass flow rate) and temperature are defined as a time function using the injector property. A sensor can define the inflator starting time.

## Numerical Damping

Viscosity, $\mu $ can be used to reduce numerical oscillations.

If $\mu $ =1, a critical damping (shell mass and volume stiffness) is used. A viscous pressure, $q$ is computed as:

$q=-\frac{\mu}{A}\sqrt{\frac{PA\rho t}{V}}\frac{dV}{dt}$ if $\frac{dV}{dt}<0$

$q=0$ if $\frac{dV}{dt}>0$

- $t$
- Fabric thickness
- $\rho $
- Density of the fabric
- $A$
- Bag surface

## Initial Conditions

To avoid initial disequilibrium and mathematical discontinuity for zero mass or zero volume, the
following initial conditions are set at time zero (`I`_{equil} =0) or at the beginning of jetting (if `I`_{equil} =1).

- ${P}_{ext}={P}_{ini}$ external pressure
- ${T}_{0}={T}_{ini}$ initial temperature (295K by default)
- If the initial volume is less than ${10}^{-4}{A}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ , a constant small volume is added to obtain an initial volume: ${V}_{ini}={10}^{-4}{A}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
- Initial mass, energy and density are defined from the above values.

There is no need to define an injected mass at time zero.

## Gases Definition

- Initial and injected gas is defined with /MAT/GAS. Four types
of gas (MASS, MOLE, PREDEF, or CSTA) could be defined. Then the specific
capacity per unit mass at constant pressure for the gas is:
- MASS type
(2) $${C}_{p}=\left({C}_{pa}+{C}_{pb}\text{\hspace{0.17em}}T+{C}_{pc}\text{\hspace{0.17em}}{T}^{2}+{C}_{pd}\text{\hspace{0.17em}}{T}^{3}+\frac{{C}_{pe}}{{T}^{2}}+{C}_{pf}\text{\hspace{0.17em}}{T}^{4}\right)$$ - MOLE type
(3) $${C}_{p}=\frac{1}{MW}\left({C}_{pa}+{C}_{pb}\text{\hspace{0.17em}}T+{C}_{pc}\text{\hspace{0.17em}}{T}^{2}+{C}_{pd}\text{\hspace{0.17em}}{T}^{3}+\frac{{C}_{pe}}{{T}^{2}}\right)$$Where, $MW$ is the molecular weight of the gas.

- CSTA type
User input ${C}_{p}$ and ${C}_{V}$ with the unit of $\left[\frac{J}{kgK}\right]$ .

- PREDEF type
About 14 commonly used gases (N2, O2, Air, etc) predefined in Radioss.

- MASS type
- Injected gas
`N`_{jet}defines the number of injectors by monitored volume. The material of the injected gas is defined with /MAT/GAS. The injector properties (/PROP/INJECT1 or /PROP/INJECT2) define the injected mass curve defined`fct_ID`_{M}and injected temperature curve defined`fct_ID`_{T}.Injected mass curve and injection temperature can be obtained:- From the airbag manufacturer
- From a tank test

`sens_ID`is the sensor number to start injection. - Jetting effect
`I`_{jet}is used only for /MONVOL/AIRBAG1 or /MONVOL/COMMU1If`I`_{jet}≠ 0, the jetting effect is modeled as an overpressure $\text{\Delta}{P}_{jet}$ applied to elements of the bag.(4) $$\text{\Delta}{P}_{jet}=\text{\Delta}\mathrm{P}\left(t\right)\cdot \text{\Delta}\mathrm{P}\left(\theta \right)\cdot \text{\Delta}\mathrm{P}\left(\delta \right)\cdot \mathrm{max}\left(n\xb7m,0\right)$$N

_{1}, N_{2}, and N_{3}are defined based on the injector geometry (refer to the Radioss Starter Input Manual)$\text{\Delta}\mathrm{P}\left(t\right),\text{\Delta}\mathrm{P}\left(\theta \right),\text{\Delta}\mathrm{P}\left(\delta \right)$ are empirical functions provided by the user via $fct\_I{D}_{Pt}$ , $fct\_I{D}_{P\theta}$ , and $fct\_I{D}_{P\delta}$

## Vent Hole Definition

`N`_{vent} defines the number of vent
holes used.

$surf\_I{D}_{v}$ is the surface identifier defining the vent hole

`A`_{vent} is the vent area (if
$surf\_I{D}_{v}=0$
) or a scale factor (
$surf\_I{D}_{v}$
≠ 0)

`B`_{vent} = 0 (if
$surf\_I{D}_{v}=0$
) or a scale factor on the impacted surface (
$surf\_I{D}_{v}$
≠ 0)

`T`_{stop} is a stop time for venting

`T`_{start} is the time at which leakage starts

$\text{\Delta}{P}_{def}$ is the relative vent deflation pressure

$\text{\Delta}t{P}_{def}$ is the time duration during which $\text{\Delta}P>\text{\Delta}{P}_{def}$

`I`

_{form}=2)

Where, $Fscal{e}_{v}$ is the scale factor of the function $fct\_I{D}_{v}$ .

from $P{V}^{\left(i\right)}={n}^{\left(i\right)}RT$ and $PV=\left[{\displaystyle \sum _{i}{n}^{\left(i\right)}}\right]RT$ .

## Porosity

- ${\mathrm{C}}_{ps}(t)$
- Function of
`fct_ID`_{cps} - ${\mathrm{Area}}_{ps}(P-{P}_{ext})$
- Function of
`fct_ID`_{aps}

It is also possible to define closure of the porous surface when contacts occurs by
defining the interface option `I`_{bag}=1.