/MONVOL/AIRBAG (Obsolete)
Block Format Keyword Describes the airbag monitored volume type.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MONVOL/AIRBAG/monvol_ID/unit_ID  
monvol_title  
surf_ID_{ex}  
Ascale_{t}  Ascale_{P}  Ascale_{S}  Ascale_{A}  Ascale_{D}  
$\mu $  P_{ext}  T_{0}  _{equi}  I_{ttf}  
${\gamma}_{i}$  cpa_{i}  cpb_{i}  cpc_{i} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

N_{jet} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

$\gamma $  cpa  cpb  cpc  
fct_ID_{mas}  I_{flow}  Fscale_{mas}  fct_ID_{T}  Fscale_{T}  sens_ID  
I_{jet}  node_ID_{1}  node_ID_{2}  node_ID_{3} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{Pt}  fct_ID_{P} $\theta $  fct_ID_{P} $\theta $  Fscale_{pt}  Fscale_{p} $\theta $  Fscale_{p} $\delta $ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

N_{vent} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

surf_ID_{v}  A_{vent}  B_{vent}  T_{stop}  
T_{vent}  $\text{\Delta}{P}_{def}$  $\text{\Delta t}{P}_{def}$  fct_ID_{V}  Fscale_{V}  I_{dtPdef}  
fct_ID_{t}  fct_ID_{P}  fct_ID_{A}  Fscale_{t}  Fscale_{P}  Fscale_{A}  
fct_ID_{t'}  fct_ID_{P'}  fct_ID_{A'}  Fscale_{t'}  Fscale_{P'}  Fscale_{A'} 
Definitions
Field  Contents  SI Unit Example 

monvol_ID  Monitored volume
identifier (Integer, maximum 10 digits) 

unit_ID  Unit Identifier (Integer, maximum 10 digits) 

monvol_title  Monitored volume
title (Character, maximum 100 characters) 

surf_ID_{ex}  External surface
identifier 1 (Integer) 

Ascale_{t}  Abscissa scale factor for
time based functions Default = 1.0 (Real) 
$\left[\text{s}\right]$ 
Ascale_{P}  Abscissa scale factor for
pressure based functions Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Ascale_{S}  Abscissa scale factor for
area based functions Default = 1.0 (Real) 
$\left[{\text{m}}^{2}\right]$ 
Ascale_{A}  Abscissa scale factor for
angle based functions Default = 1.0 (Real) 
$\left[\mathrm{deg}\right]$ 
Ascale_{D}  Abscissa scale factor for
distance based functions Default = 1.0 (Real) 
$\left[\text{m}\right]$ 
mat_ID  Initial gas material
identifier (/MAT/GAS) (Real) 

$\mu $  Volumetric
viscosity Default = 0.01 (Real) 

P_{ext}  External
pressure (Real) 
$\left[\text{Pa}\right]$ 
T_{0}  Initial
temperature. Default = 295 (Real) 
$\left[\text{K}\right]$ 
I_{equi}  Initial thermodynamic
equilibrium flag.
(Integer) 

I_{ttf}  Venting time shift flag.
Active only when injection sensor is specified.


${\gamma}_{i}$  Ratio of specific heats at
initial temperature ${\gamma}_{\text{i}}=\frac{{\text{cp}}_{\text{i}}}{{\text{cv}}_{\text{i}}}$ (Real) 

cpa_{i}  cpa
coefficient in the relation
cp_{i}(T) (Real) 
$\left[\frac{\text{J}}{\text{kg}\cdot \text{K}}\right]$ 
cpb_{i}  cpb
coefficient in the relation
cp_{i}(T) (Real) 
$\left[\frac{\text{J}}{\text{kg}\cdot {\text{K}}^{2}}\right]$ 
cpc_{i}  cpc
coefficient in the relation
cp_{i}(T) (Real) 
$\left[\frac{\text{J}}{\text{kg}\cdot {\text{K}}^{3}}\right]$ 
N_{jet}  Number of
injectors (Integer) 

$\gamma $  Ratio of specific heats $\gamma =\frac{{C}_{p}}{{C}_{v}}$ (Real) 

cpa  cpa
coefficient in the relation cp(T) (Real) 
$\left[\frac{\text{J}}{\text{kg}\cdot \text{K}}\right]$ 
cpb  cpa
coefficient in the relation cp(T) (Real) 
$\left[\frac{\text{J}}{\text{kg}\cdot {\text{K}}^{2}}\right]$ 
cpc  cpa
coefficient in the relation cp(T) (Real) 
$\left[\frac{\text{J}}{\text{kg}\cdot {\text{K}}^{3}}\right]$ 
surf_ID_{v}  Vent holes membrane
surface identifier (Integer) 

A_{vent}  If
surf_ID_{v} ≠
0: scale factor on surface Default = 1.0 If surf_ID_{v} = 0: surface of vent holes Default = 0.0 (Real) 
$\left[{\text{m}}^{2}\right]$ , if surf_ID_{V} = 0 
B_{vent}  If
surf_ID_{v} ≠
0: scale factor on impacted surface Default = 1.0 If surf_ID_{v} = 0: B_{vent} is reset to 0. Default = 0.0 (Real) 
$\left[{\text{m}}^{2}\right]$ , if surf_ID_{V} = 0 
T_{stop}  Stop time for
venting Default = 1E+30 (Real) 
$\left[\text{s}\right]$ 
T_{vent}  Start time for
venting Default = 0.0 (Real) 
$\left[\text{s}\right]$ 
$\text{\Delta}{P}_{def}$  Pressure difference to
open vent hole membrane (
$\text{\Delta}{P}_{def}$
=
P_{def}  P_{ext}) (Real) 
$\left[\text{Pa}\right]$ 
$\text{\Delta t}{P}_{def}$  Minimum duration pressure
exceeds P_{def} to
open vent hole membrane (Real) 
$\left[\text{s}\right]$ 
fct_ID_{V}  Outflow velocity function
identifier (Integer) 

Fscale_{V}  Scale factor on
fct_ID_{V} Default = 1.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
I_{dtPdef}  Time delay flag when
$\text{\Delta}{P}_{def}$
is reached:


fct_ID_{t}  Porosity versus time
function identifier (Integer) 

fct_ID_{P}  Porosity versus pressure
function identifier (Integer) 

fct_ID_{A}  Porosity versus area
function identifier (Integer) 

Fscale_{t}  Scale factor for
fct_ID_{t} Default = 1.0 (Real) 

Fscale_{P}  Scale factor for
fct_ID_{P} Default = 1.0 (Real) 

Fscale_{A}  Scale factor for
fct_ID_{A} Default = 1.0 (Real) 

fct_ID_{mas}  Mass of injected gas
versus time function identifier (Integer) 

I_{flow}  Mass versus time function
input type flag
(Integer) 

Fscale_{mas}  Mass function scale
factor Default = 1.0 (Real) 
$\left[\text{kg}\right]$ or $\left[\frac{\text{kg}}{\text{s}}\right]$ 
fct_ID_{T}  Temperature of injected
gas versus time function identifier (Integer) 

Fscale_{T}  Temperature function scale
factor Default = 1.0 (Real) 
$\left[\text{K}\right]$ 
sens_ID  Sensor
identifier. (Integer) 

I_{jet}  Jetting flag.
(Integer) 

node_ID_{1}, node_ID_{2}, node_ID_{3}  Node identifiers
N_{1},
N_{2}, and
N_{3} for jet shape
definition. (Integer) 

fct_ID_{Pt}  If
I_{jet} =
1: identifier of the function number defining
$\text{\Delta Pt}$
. (Integer) 

fct_ID_{P} $\theta $  If
I_{jet} =
1: identifier of the function number defining
$\text{\Delta P}\left(\theta \right)$
) (Integer) 

fct_ID_{P} $\delta $  If
I_{jet} =
1: identifier of the function number defining
$\text{\Delta P}\left(\delta \right)$
(Integer) 

Fscale_{Pt}  If
I_{jet} =
1: scale factor for
fct_ID_{Pt} Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{P} $\theta $  If
I_{jet} =
1: scale factor for
fct_ID_{P}
$\theta $
Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
Fscale_{P} $\delta $  If
I_{jet} =
1: scale factor for
fct_ID_{P}
$\delta $
Default = 1.0 (Real) 
$\left[\text{Pa}\right]$ 
N_{vent}  Number of vent
holes. (Integer) 

fct_ID_{t'}  Porosity versus time when
contact function identifier. (Integer) 

fct_ID_{P'}  Porosity versus pressure
when contact function identifier. (Integer) 

fct_ID_{A'}  Porosity versus impacted
surface function identifier. (Integer) 

Fscale_{t'}  Scale factor for
fct_ID_{t'} Default = 1.0 (Real) 

Fscale_{P'}  Scale factor for
fct_ID_{P'} Default = 1.0 (Real) 

Fscale_{A'}  Scale factor for
fct_ID_{A'} Default = 1.0 (Real) 
Comments
 surf_ID_{ex} must be defined using segments associated with 4nodes or 3nodes shell elements (possibly void elements).
 The volume must be closed and the normals must be oriented outwards.
 Abscissa scale factors
are used to transform abscissa units in airbag functions, for
example:
(1) $$\text{F}(\text{t}\prime )=\text{fct}\_\text{ID}\left(\frac{\text{t}}{{\text{Ascale}}_{\text{t}}}\right)$$Where, t is the time.
For example, if your input data is in [ms], but you need a data in [s], you could set Ascale to 0.001.(2) $$\text{F}(\text{p}\prime )=\text{fct}\_\text{ID}\left(\frac{\text{p}}{{\text{Ascale}}_{\text{p}}}\right)$$Where, p is the pressure.
 Initial pressure is set to P_{ext}.
 Initial thermodynamic
equilibrium is written at time zero
(I_{equi} =0)
or at beginning of jetting (I_{equi}
=1), based on the following equation with respect to the volume
at time zero, or the volume at beginning of jetting:
${\text{P}}_{\text{ext}}\text{V}=\text{R}\frac{{\text{M}}_{0}}{{\text{M}}_{\text{i}}}{\text{T}}_{0}$
where, M_{0} is the mass of gas initially filling the airbag, M_{i} is the molar mass of the gas initially filling the airbag, and R is the gas constant depending on the units system.
(3) $$R=8.314\frac{\text{J}}{\mathit{mole}\cdot K}$$  Ratio of specific heats
at constant pressure per mass unit
cp_{i} of the gas initially
filling the airbag is quadratic versus temperature:
(4) $${\text{cp}}_{\text{i}}(\text{T})=\text{cpa}+{\text{cpb}}_{\text{i}}*\text{T}+{\text{cpc}}_{\text{i}}*{\text{T}}^{2}$$  Gas constant at initial
temperature
$\gamma $
_{i} must be related to specific
heat per mass unit at initial temperature and molar mass of the gas initially
filling the airbag with respect to the following relation:
(5) $$\frac{(\gamma 1)}{{\gamma}_{\text{i}}}{\text{cp}}_{\text{i}}({\text{T}}_{\text{o}})=\frac{\text{R}}{{\text{M}}_{\text{i}}}$$Where, M_{i} is the molar mass of the gas initially filling the airbag, and R is the gas constant depending on the units system.(6) $$\text{R}=8.314\frac{\text{J}}{\text{mole}\cdot \text{K}}$$  The characteristics of the gas initially filling the airbag must be defined (no default) and must be equal for each communicating airbag.
 If $\gamma $ _{i} = 0, the characteristics of the gas initially filling the airbag are set to the characteristics of the gas provided by the first injector.
 Ratio of specific
heats at constant pressure per mass unit
cp_{i} of the gas is quadratic
with regard to the temperature:
(7) $$\text{cp}(\text{T})=\text{cpa}+\text{cpb}*\text{T}+\text{cpc}*{\text{T}}^{2}$$  Gas constant at
initial temperature
$\gamma $
must be related to specific heat per mass unit at initial
temperature and molar mass of the with respect to the following
relation:
(8) $$\frac{(\gamma 1)}{\gamma}\text{cp}({\text{T}}_{\text{o}})=\frac{\text{R}}{\text{M}}$$Where, M
 Molar mass of the gas
 R
 Gas constant depending on the units system
(9) $$\text{R}=8.314\frac{\text{J}}{\text{mole}\cdot \text{K}}$$  If jetting is used, an
additional $\text{\Delta}$
P_{jet} pressure is applied to
each element of the airbag:
(10) $$\Delta {\text{P}}_{\text{jet}}=\Delta \text{P}(\text{t})*\Delta \text{P}(\theta )*\Delta \text{P}(\delta )*\text{max}(\overrightarrow{n}*\overrightarrow{m},0)$$  With
$\overrightarrow{m}$
being the normalized vector between the
projection of the center of the element upon segment (node_ID_{1} and node_ID_{3}) and the center of
the element;
$\theta $
the angle between vectors
MN_{2} and
$\overrightarrow{m}$
(in degrees),
$\delta $
is the distance between the center of the element and
its projection upon segment (node_ID_{1} and node_ID_{3}).The projection of a point upon segment (node_ID_{1} and node_ID_{3}) is defined as the projection of the point in direction MN_{2} upon the line (node_ID_{1} and node_ID_{3}) if it lies inside the segment (node_ID_{1} and node_ID_{3}). If this is not the case, the projection of the point upon segment (node_ID_{1} and node_ID_{3}) is defined as the closest node node_ID_{1} or node_ID_{3}.
with M between N_{1} and N_{3}
 If node_ID_{3} = 0, node_ID_{3} is set to node_ID_{1} and the dihedral shape is reduced to a conical shape.
 If
fct_ID_{V} = 0:
isenthalpic outflow is assumed, else Chemkin model is used and outflow velocity
is:
(11) $$\nu ={\text{Fscale}}_{\text{V}}\ast \text{fct}\_{\text{ID}}_{\text{V}}\left(\text{P}{\text{P}}_{\mathrm{ext}}\right)$$ Isenthalpic model
Venting or the expulsion of gas from the volume, is assumed to be isenthalpic.
The flow is also assumed to be unshocked, coming from a large reservoir and through a small orifice with effective surface area, A.
Conservation of enthalpy leads to velocity, u, at the vent hole. The Bernouilli equation is then written as:
(monitored volume) $\frac{\gamma}{\gamma 1}\frac{\text{P}}{\rho}=\frac{\gamma}{\gamma 1}\frac{{\text{P}}_{\text{ext}}}{{\rho}_{\text{vent}}}+\frac{{\text{u}}^{2}}{2}$ (vent hole)
Applying the adiabatic conditions:
(monitored volume) $\frac{\text{P}}{{\rho}^{\gamma}}=\frac{{\text{P}}_{\text{ext}}}{{{\rho}_{\text{vent}}}^{\gamma}}$ (vent hole)
Where, P is the pressure of gas into the airbag and $\rho $ is the density of gas into the airbag.
Therefore, the exit velocity is given by:(12) $${\text{u}}^{2}=\frac{2\gamma}{\gamma 1}\frac{\text{P}}{\rho}\left(1{\left(\frac{{\text{P}}_{\text{ext}}}{\text{P}}\right)}^{\frac{\gamma 1}{\gamma}}\right)$$For supersonic flows the outlet velocity is determined as described in 10.4.4.1 of the Theory Manual.
The mass out flow rate is given by:(13) $${\dot{\text{m}}}_{\text{out}}={\rho}_{\text{vent}}*\text{vent}\_\text{holes}\_\text{surface}*\text{u}=\rho {\left(\frac{{\text{P}}_{\text{ext}}}{\text{P}}\right)}^{\frac{1}{\gamma}}*\text{vent}\_\text{holes}\_\text{surface}*\text{u}$$The energy flow rate is given by:(14) $${\dot{\text{E}}}_{\text{out}}={\dot{\text{m}}}_{\text{out}}\frac{\text{E}}{\rho \text{V}}={\left(\frac{{\text{P}}_{\text{ext}}}{\text{P}}\right)}^{\frac{1}{\gamma}}*\text{vent}\_\text{holes}\_\text{surface}*\text{u}\frac{\text{E}}{\text{V}}$$Where, V is the airbag volume and E is the internal energy of gas into the airbag.
 Chemkin model
(15) $${\dot{\text{m}}}_{\text{out}}=\text{vent}\text{}\_\text{}\text{holes}\text{}\_\text{}\text{surface}*{\text{Fscale}}_{\text{v}}*\text{fct}\text{}\_\text{}{\text{ID}}_{\text{v}}\left(\text{P}{\text{P}}_{\text{ext}}\right)*\rho $$Where, $\rho $ is the density of the gas within the airbag.
 Isenthalpic model
 Vent holes surface is
computed as follows:
(16) $$\begin{array}{ll}\text{vent}\_\text{holes}\_\text{surface}\hfill & {\text{=A}}_{\text{vent}}*{\text{A}}_{\text{non}\_\text{impacted}}*\text{fct}\_{\text{ID}}_{\text{t}}({\text{A}}_{\text{non}\_\text{impacted}}/{\text{A}}_{0})*\text{fct}\_{\text{ID}}_{\text{P}}(\text{P}{\text{P}}_{\text{ext}})\hfill \end{array}$$(17) $$\begin{array}{l}+{\text{B}}_{\text{vent}}*{\text{A}}_{\text{impacted}}*\text{fct}\_{\text{ID}}_{{\text{t}}^{\prime}}({\text{A}}_{\text{impacted}}/{\text{A}}_{0})*\text{fct}\_{\text{ID}}_{{\text{P}}^{\prime}}(\text{P}{\text{P}}_{\text{ext}})\hfill \end{array}$$with impacted surface:(18) $${\text{A}}_{\text{impacted}}=\sum _{\text{e}\in {\text{S}}_{\text{vent}}}\frac{{\text{n}}_{\text{c}}\left(\text{e}\right)}{\text{n}\left(\text{e}\right)}{\text{A}}_{\text{e}}$$and nonimpacted surface:(19) $${\text{A}}_{\text{non}\_\text{impacted}}=\sum _{\text{e}\in {\text{S}}_{\text{vent}}}\left(1\frac{{\text{n}}_{\text{c}}\left(\text{e}\right)}{\text{n}\left(\text{e}\right)}\right){\text{A}}_{\text{e}}$$Where for each element e of the vent holes surf_ID_{v}, n_{c}(e) means the number of impacted nodes among the n(e) nodes defining the element.
 Functions fct_ID_{t'} and fct_ID_{P'} are assumed to be equal to 1, if they are not specified (null identifier).
 Function fct_ID_{A'} is assumed as the fct_ID_{A'}(A) = A, if it is not specified.
 In order to use porosity during contact, flag I_{BAG} must be set to 1 in the interfaces concerned (Line 3 of interface Type 5 and Type 7). If not, the nodes impacted into the interface are not considered as impacted nodes in the previous formula for A_{impacted} and A_{non_impacted}.
 When defining venting,
there are some limitations concerning the definition of airbag surface and surface venting:
 The airbag external surface should be built only from shells and 3nodes shell elements.
 The airbag external surface can not be defined with option /SURF/SEG (or with option /SURF/SURF if a subsurface is defined with option /SURF/SEG).
 Same restriction applies to vent hole surface.
 Shells and 3nodes shell elements included in vent hole surface have to also be included in external surface.
 Vent hole membrane is deflated if T > T_{vent} or if the pressure exceeds P_{def} during more than $\text{\Delta t}{P}_{def}$ .