/MONVOL/FVMBAG2
Block Format Keyword Describes Finite Volume Method Airbag, which has simplified input, similar to /MONVOL/FVMBAG1.
 Gas materials are specified in separate /MAT/GAS cards.
 Composition of injected gas mixture and injector properties are specified in separate /PROP/INJECT1 or /PROP/INJECT2 cards.
Format
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

/MONVOL/FVMBAG2/monvol_ID/unit_ID  
monvol_title  
surf_ID_{ex}  surf_ID_{in}  H_{conv}  
mat_ID  P_{ext}  T_{0}  I_{ttf} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

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

inject_ID  sens_ID  surf_ID_{inj} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

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

surf_ID_{v}  I_{form}  A_{vent}  B_{vent}  vent_title  
T_{start}  T_{stop}  $\text{\Delta}{P}_{def}$  $\text{\Delta}t{P}_{def}$  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'} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_{v}  Fscale_{v} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

surf_ID_{ps}  Iform_{ps}  Iblockage  surface_title  
T_{start}  T_{stop}  $\text{\Delta}{P}_{def}$  $\text{\Delta}t{P}_{def}$ 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

fct_ID_ps_{V}  Fscale_ps_{V} 
(1)  (2)  (3)  (4)  (5)  (6)  (7)  (8)  (9)  (10) 

C_{gmerg}  T_{switch}  I_{switch}  P_{switch}  
$\text{\Delta}{T}_{sca}$  $\text{\Delta}{T}_{\mathrm{min}}$ 
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
2 (Integer) 

surf_ID_{in}  Internal surface
identifier. (Integer) 

H_{conv}  Heat transfer coefficient.
17 (Real) 
$\left[\frac{\text{W}}{{\text{m}}^{\text{2}}\text{K}}\right]$ 
mat_ID  Initial gas material
identifier. (Integer) 

P_{ext}  External
pressure. (Real) 
$\left[\text{Pa}\right]$ 
T_{0}  Initial
temperature. Default = 295K (Real) 
$\left[\text{K}\right]$ 
I_{ttf}  Time shift flag. Active
only when at least one injection sensor is specified. Determines
time shift for venting and porosity options when injection
starts at a Time to Fire specified in a sensor.
(Integer) 

N_{jet}  Number of
injectors. (Integer) 

inject_ID  Injector property
identifier. (Integer) 

sens_ID  Sensor
identifier. (Integer) 

surf_ID_{inj}  Injector surface
identifier (must be different for each
injector). (Integer) 

N_{vent}  Number of vent
holes. (Integer) 

N_{porsurf}  Number of porous surfaces.
(Integer) 

surf_ID_{v}  Vent holes area surface
identifier. (Integer) 

I_{form}  Venting formulation. 5
(Integer) 

A_{vent}  If surf_ID_{v} ≠ 0: scale factor on vent
hole area. Default = 1.0 (Real) 

If surf_ID_{v} = 0: vent hole
area. Default = 0.0 (Real) 
$\left[{\text{m}}^{2}\right]$  
B_{vent}  If surf_ID_{v} ≠ 0: scale factor on
impacted vent hole area. Default = 1.0 (Real) 

If surf_ID_{v} = 0:
B_{vent} is
reset to 0 for vent hole area. Default = 0.0 (Real) 
$\left[{\text{m}}^{2}\right]$  
vent_title  Vent hole
title. (Character, maximum 20 characters) 

T_{start}  Start time for
venting. Default = 0 (Real) 
$\left[\text{s}\right]$ 
T_{stop}  Stop time for
venting. Default = 10^{30} (Real) 
$\left[\text{s}\right]$ 
$\text{\Delta}{P}_{def}$  Pressure difference to
open vent hole membrane. $\text{\Delta}{P}_{def}={P}_{def}{P}_{ext}$ Default = 0 (Real) 
$\left[\text{Pa}\right]$ 
$\text{\Delta}t{P}_{def}$  Minimum duration pressure
exceeds P_{def} to
open vent hole membrane. Default = 0 (Real) 
$\left[\text{s}\right]$ 
I_{dtPdef}  Time delay flag when
$\text{\Delta}{P}_{def}$
is reached:
(Integer) 

fct_ID_{t}  Vent area scale factor vs
time function identifier. (Integer) 

fct_ID_{P}  Vent area scale factor vs
pressure function identifier. (Integer) 

fct_ID_{A}  Vent area scale factor vs
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_{t'}  Vent area scale factor vs
time during contact function identifier. (Integer) 

fct_ID_{P'}  Vent area scale factor vs
pressure during contact function identifier. (Integer) 

fct_ID_{A'}  Vent area scale factor vs
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) 

fct_ID_{v}  Outflow velocity function
identifier (Chemkin model, only if I_{form} = 2). (Integer) 

Fscale_{v}  Scale factor on
fct_ID_{v}. Default = 1.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
surf_ID_{ps}  Porous surface
identifier. (Integer) 

Iform_{ps}  Porosity formulation.
(Integer) 

Iblockage  Block porous leakage flag,
when in contact
(Iform_{ps} > 0).
(Integer) 

surface_title  Porous surface
title. (Character, maximum 20 characters) 

fct_ID_ps_{V}  Outflow velocity versus
relative pressure function identifier. (Integer) 

Fscale_ps_{V}  Scale factor on
fct_ID_ps_{V}. Default = 1.0 (Real) 
$\left[\frac{\text{m}}{\text{s}}\right]$ 
C_{gmerg}  Factor for global merging.
16
Default = 0.02 (Real) 

T_{switch}  Amount of time after
airbag time to fire to switch from FVM to UP (Uniform Pressure)
formulation. 20 Default = 1e30 (Real) 
$\left[\text{s}\right]$ 
I_{switch}  Flag to switch from FVM to UP.
(Integer) 

P_{switch}  Ratio of FV standard
deviation pressure to average pressure which triggers FVM to UP
switch. 21 Default = 0.0 (Real) 

$\text{\Delta}{T}_{sca}$  Scale factor for airbag
time step. Using /DT/FVMBAG in the Engine will override this value. Default = 0.9 

$\text{\Delta}{T}_{\mathrm{min}}$  Minimum time step for the
airbag. Using /DT/FVMBAG in the Engine will override this value. 
Comments
 The airbag external surface should be built only from 4 and 3noded shell elements. The airbag external surface cannot be defined with option /SURF/SEG, nor with /SURF/SURF, if a subsurface is defined in /SURF/SEG.
 External surfaces shall compose a closed volume with normals must oriented outwards.
 The correct model units must defined in /BEGIN or a local /UNIT referenced by unit_ID. The gas constants, injection velocity, and predefined gas materials are set based on the units defined in the model.
 Pressure and temperature of external air and the initial pressure and temperature of air inside of airbag is set to P_{ext} and T_{0}.
 Venting through vent
holes:
If I_{form} = 1, venting velocity is computed from Bernoulli equation using local pressure in the airbag.
The exit velocity is given by:(1) $${u}^{2}=\frac{2\gamma}{\gamma 1}\frac{P}{\rho}\left(1{\left(\frac{{P}_{\mathit{ext}}}{P}\right)}^{\frac{\gamma 1}{\gamma}}\right)$$The mass out flow rate is given by:
If I_{form} = 2, venting velocity is computed from the Chemkin equation:(2) $$v=Fscal{e}_{v}\cdot {f}_{v}(P{P}_{ext})$$Where, ${f}_{v}$ is defined by fct_ID_{v}.
If I_{form} = 3, venting velocity is equal to the component of the local fluid velocity normal to vent hole surface. Local density and energy are used to compute outgoing mass and energy through the hole.
 When there is no sensor which activates gas injection, the vent holes and porosity becomes active, if time T becomes greater than the T_{start}, or if the pressure P exceeds P_{def} value longer than the time given in $\text{\Delta}t{P}_{def}$ .
 When at least one of the
injectors is activated by the sensor, then activation of venting and porosity
options is controlled by
I_{ttf}.
T_{inj} is the time of the first injector to be activated by the sensor.
I_{ttf} = 0Venting, Porosity Activation When $P>\text{\Delta}{P}_{def}$ longer than the time $\text{\Delta}t{P}_{def}$ , or $T>{T}_{start}$ Deactivation T_{stop} Time dependent functions No shift I_{ttf} = 3Venting, Porosity Activation When $T>{T}_{inj}$ and $P>\text{\Delta}{P}_{def}$ longer than the time $\text{\Delta}t{P}_{def}$ , or $T>{T}_{inj}+{T}_{start}$ Deactivation ${T}_{inj}+{T}_{stop}$ Time dependent functions Shifted by ${T}_{inj}+{T}_{start}$ All other related curves are active when the corresponding venting, porosity or communication option is active.
The variety of I_{ttf} values comes from historical reasons. Values I_{ttf}=1 and 2 are obsolete and should not be used. Usual values are I_{ttf}=0 (no shift) or I_{ttf}=3 (all relative options are shifted by T_{inj}).
 If surf_ID_{v} ≠ 0 (surf_ID_{v} is defined) the vent hole area is
computed as:
(3) $$vent\_holes\_area\text{}={A}_{vent}\cdot {\mathrm{f}}_{A}\left(\frac{A}{{A}_{0}}\right)\cdot {\mathrm{f}}_{t}\left(t\right)\cdot {\mathrm{f}}_{P}\left(P{P}_{ext}\right)$$Where, $A$
 Area of surface surf_ID_{v}
 ${A}_{0}$
 Initial area of surface surf_ID_{v}
 ${\mathrm{f}}_{t}$ , ${\mathrm{f}}_{P}$ and ${\mathrm{f}}_{A}$
 Functions of fct_ID_{t}, fct_ID_{P} and fct_ID_{A}
 In the case of activated
venting closure the vent holes surface is computed as:
(4) $$vent\_holes\_area\text{}={A}_{vent}\cdot {A}_{non\_impacted}\cdot {\mathrm{f}}_{t}\left(t\right)\cdot {\mathrm{f}}_{P}\left(P{P}_{ext}\right)\cdot {\mathrm{f}}_{A}\left(\frac{{A}_{non\_impacted}}{{A}_{0}}\right)$$(5) $$+{B}_{\mathit{vent}}\cdot {A}_{\mathit{impacted}}\cdot {\text{f}}_{{t}^{\prime}}\left(t\right)\cdot {\text{f}}_{{P}^{\prime}}\left(P{P}_{\mathit{ext}}\right)\cdot {\text{f}}_{{A}^{\prime}}\left(\frac{{A}_{\mathit{impacted}}}{{A}_{0}}\right)$$With impacted surface:(6) $${A}_{\mathit{impacted}}=\sum _{e\in {S}_{\mathit{vent}}}\frac{{n}_{c}\left(e\right)}{n\left(e\right)}{A}_{e}$$and nonimpacted surface:(7) Where for each element e of the vent holes surf_ID_{v}, ${n}_{c}\left(e\right)$ means the number of impacted nodes among the $n\left(e\right)$ nodes defining the element.$${A}_{\mathit{non}\_\mathit{impacted}}=\sum _{e\in {S}_{\mathit{vent}}}\left(1\frac{{n}_{c}\left(e\right)}{n\left(e\right)}\right){A}_{e}$$A_{0} is the initial area of surface surf_ID_{v}
f_{t}, f_{P} and f_{A} are functions of fct_ID_{t}, fct_ID_{P} and fct_ID_{A}
f_{t'}, f_{P'} and f_{A'} are functions of fct_ID_{t'}, fct_ID_{P'} and fct_ID_{A'}
 Radioss ends with a Starter error, if surf_ID_{v} = 0 (surf_ID_{v} is not defined) for Chemkin venting formulation (I_{form}=2).
 Functions fct_ID_{t} and fct_ID_{P} are equal to 1, if they are not specified (null identifier).
 Function fct_ID_{A} is assumed to be equal to 1, if it is not specified.
 To account for contact blockage of vent holes and porous surface areas, flag I_{BAG} must be set to 1 in the correspondent interfaces (Line 3 of interface /INTER/TYPE7 or /INTER/TYPE23). 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}.
 Leakage by porosity
formulations, the mass flow rate flowing out is computed as:
 Iform_{ps} = 1 ${\dot{m}}_{\mathit{out}}={A}_{\mathit{eff}}\sqrt{2P\rho}{Q}^{\frac{1}{\gamma}}\sqrt{\frac{\gamma}{\gamma 1}\left[1{Q}^{\frac{\gamma 1}{\gamma}}\right]}$ (Isentropic  Wang Nefske)
 Iform_{ps} = 2
${\dot{m}}_{\mathit{out}}={A}_{\mathit{eff}}\rho v(P{P}_{\mathit{ext}})$
Where, v is the outflow gas velocity (Chemkin)
 Iform_{ps} = 3 ${\dot{m}}_{\mathit{out}}={A}_{\mathit{eff}}\sqrt{2\rho (P{P}_{\mathit{ext}})}$ (Graefe)
The effective venting area A_{eff} is computed according to the input in the /LEAK/MAT input for fabric materials of TYPE19 or TYPE58.
 If leakage blockage is
activated, Iblockage=1, the effective
venting area is modified as:
(8) $${A}_{\mathit{eff}}={A}_{\mathit{non}\_\mathit{impacted}}$$${A}_{\mathit{non}\_\mathit{impacted}}$ is nonimpact surface
The blockage will be active only if flag I_{BAG} is set to 1 in the concerned contact interfaces (line 3 of interface TYPE7, TYPE19 and TYPE23).
 When a finite volume fails
during the inflation process of the airbag (volume becoming negative, internal
mass or energy becoming negative), it is merged to one of its neighbors so that
the calculation can continue. Two merging approaches are used:
 Global merging: a finite volume is merged if its volume becomes less than a certain factor multiplying the mean volume of all the finite volumes. The flag I_{gmerg} determines if the mean volume to use is the current mean volume (I_{gmerg} =1) or the initial mean (I_{gmerg} =2). The factor giving the minimum volume from the mean volume is C_{gmerg}.
 Time step dependent merging: if the time step for a finite volume becomes less than the value defined in /DT/FVMBAG, the finite volume is merged with neighboring finite volumes.
 The lost heat flow is
given by:
(9) $$\dot{\text{Q}}\left(x,t\right)={H}_{\mathit{conv}}\cdot \text{Area}\left(x,t\right)\cdot \left(\text{T}\left(x,t\right){T}_{0}\right)$$  If an element of a vent
hole surface (surf_ID_{v}) belongs to an injector (surf_ID_{inj}) it will be ignored from the vent
hole. A constant correction factor f computed at time t=0 is
applied to the total vent hole surface:
(10) $$f=\frac{{S}_{\mathit{vent}}}{{S}_{\mathit{vent}}{\text{S}}_{\mathit{injector}}}$$  If an element of a porous surface also belongs to an injector (surf_ID_{inj}), it will be ignored from the porous surface.
 The time to switch T_{switch} to Uniform Pressure is relative to the time to fire. The switch is automatic, if there is only one finite volume left.
 P_{switch} is
the ratio of standard deviation of the Finite Volume pressures to the airbag
average pressure.
(11) $${P}_{switch}=\frac{\text{SD(FVpressure)}}{\text{Averagepressure}}$$This ratio can be output using the /TH/MONVOL variable UPCRIT. P_{switch} approaches zero as the pressure in each finite volume approaches the average pressure in the airbag.