/MONVOL/FVMBAG1

Block Format Keyword Describes Finite Volume Method Airbag, which has more flexible input than the similar obsolete keyword /MONVOL/FVMBAG (Obsolete).

  • 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.
  • Automatic Finite Volume meshing in specified coordinate system, given by a frame.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MONVOL/FVMBAG1/monvol_ID/unit_ID
monvol_title
surf_IDex   Hconv            
Ascalet AscaleP AscaleS AscaleA AscaleD
mat_ID       Pext T0 Iequil Ittf
Number of injectors
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Njet                  
For each injector
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
inject_ID sens_ID surf_IDinj              
fct_IDvel   Fscalevel            
Number of vent holes and porous fabric surfaces
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Nvent Nporsurf                
Define Nvent vent holes (four lines per vent hole)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
surf_IDv Iform Avent Bvent     vent_title
Tstart Tstop Δ P d e f Δ t P d e f   IdtPdef
fct_IDt fct_IDP fct_IDA   Fscalet FscaleP FscaleA
fct_IDt' fct_IDP' fct_IDA'   Fscalet' FscaleP' FscaleA'
Insert for each porous surface
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
surf_IDps Iformps Iblockage           surface_title
Tstart Tstop Δ P d e f Δ t P d e f    
Chemkin model data (read only if Iform =2 or Iformps = 2)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDV   FscaleV            
Finite volume meshing parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
frame_ID kmesh Tswitch   Iswitch Pswitch    
L1 L2 L3        
Nb1 Nb2 Nb3 grbric_ID surf_IDin Iref        
Igmerg   Cgmerg Cnmerg Ptole    
qa qb Hmin Δ T sca Δ T min
Ilvout Nlayer Nfacmax Nppmax Ifvani          

Definition

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_IDex External surface identifier. 12

(Integer)

 
Hconv Heat transfer coefficient. 24

(Real)

[ W m 2 K ]
Ascalet Abscissa scale factor for time based functions.

Default = 1.0 (Real)

[ s ]
AscaleP Abscissa scale factor for pressure based functions.

Default = 1.0 (Real)

[ Pa ]
AscaleS Abscissa scale factor for area based functions.

Default = 1.0 (Real)

[ m 2 ]
AscaleA Abscissa scale factor for angle based functions.

Default = 1.0 (Real)

[ rad ]
AscaleD Abscissa scale factor for distance based functions.

Default = 1.0 (Real)

[ m ]
mat_ID Initial gas material identifier.

(Integer)

 
Pext External pressure.

(Real)

[ Pa ]
T0 Initial temperature.

Default = 295K (Real)

[ K ]
Iequil Initial thermodynamic equilibrium flag.
= 0
The mass of gas initially filling the airbag is determined with respect to the volume at time zero.
= 1
Start of the FVM simulation is shifted to TTF (time to fire) specified in an injector sensor.

(Integer)

 
Ittf 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.
= 0 (Default)
=1 and 2
Obsolete
=3
All options are shifted. 8

(Integer)

 
Njet Number of injectors.

(Integer)

 
inject_ID Injector property identifier.

(Integer)

 
sens_ID Sensor identifier.

(Integer)

 
surf_IDinj Injector surface identifier (must be different for each injector).

(Integer)

 
fct_IDvel Injected gas velocity identifier.

(Integer)

 
Fscalevel Injected gas velocity scale factor.

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
Nvent Number of vent holes.

(Integer)

 
Nporsurf Number of porous surfaces. 15

(Integer)

 
surf_IDv Vent holes area surface identifier.

(Integer)

 
Iform Venting formulation. 6
= 0
Set to 1
= 1 (Default)
Isenthalpic
= 2
Chemkin
= 3
Local
= 4
Isenthalpic with possible gas. (mat_ID) flow in

(Integer)

 
Avent Scale factor on vent hole area.

Default = 1.0 (Real)

 
Bvent Scale factor on impacted vent hole area.

Default = 1.0 (Real)

 
vent_title Vent hole title.

(Character, maximum 20 characters)

 
Tstart Start time for venting.

Default = 0 (Real)

[ s ]
Tstop Stop time for venting.

Default = 1030 (Real)

[ s ]
Δ P d e f Pressure difference to open vent hole membrane.

Δ P d e f = P d e f P e x t

Default = 0 (Real)

[ Pa ]
Δ t P d e f Minimum duration pressure exceeds Pdef to open vent hole membrane.

Default = 0 (Real)

[ s ]
IdtPdef Time delay flag when Δ P d e f is reached:
= 0
Pressure should be over Δ P d e f during a Δ t P d e f cumulative time to activate venting.
= 1
Venting is activated Δ t P d e f after Δ P d e f is reached.

(Integer)

 
fct_IDt Porosity versus time function identifier.

(Integer)

 
fct_IDP Porosity versus pressure function identifier.

(Integer)

 
fct_IDA Porosity versus area function identifier.

(Integer)

 
Fscalet Scale factor for fct_IDt.

Default = 1.0 (Real)

 
FscaleP Scale factor for fct_IDP.

Default = 1.0 (Real)

 
FscaleA Scale factor for fct_IDA.

Default = 1.0 (Real)

 
fct_IDt' Porosity versus time function identifier during contact.

(Integer)

 
fct_IDP' Porosity versus pressure function identifier during contact.

(Integer)

 
fct_IDA' Porosity versus impacted surface function identifier during contact.

(Integer)

 
Fscalet' Scale factor for fct_IDt'.

Default = 1.0 (Real)

 
FscaleP' Scale factor for fct_IDP'.

Default = 1.0 (Real)

 
FscaleA' Scale factor for fct_IDA'.

Default = 1.0 (Real)

 
surf_IDps Porous surface identifier.

(Integer)

 
Iformps Porosity formulation.
= 1 (Default)
Bernouilli (Wang & Nefske).
= 2
Chemkin.
= 3
Graefe.

(Integer)

 
Iblockage Block leakage flag, if contact (Iformps > 0).
= 0
No
= 1
Yes

(Integer)

 
surface_title Porous surface title.

(Character, maximum 20 characters)

 
fct_IDV Outflow velocity versus relative pressure function identifier.

(Integer)

 
FscaleV Scale factor on fct_IDV.

Default = 1.0 (Real)

[ m s ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada Wcaaqaaiaab2gaaeaacaqGZbaaaaGaay5waiaaw2faaaaa@39DE@
frame_ID Frame identifier used to define vectors V 1 , V 2 , V 3 and origin O .

Default = global frame is used (Integer)

 
kmesh FVMBAG automatic meshing option. 26
Only used if grbric_ID = 0.
= 1
Polyhedron airbag volume meshing based on geometric plane cutting.
= 2
Tetrahedron airbag volume meshing using internal and external airbag surfaces.
= 4
Tetrahedron airbag volume meshing using internal and external airbag surfaces with output of the created tetra mesh in Radioss format.
= 12
Tetrahedron airbag volume meshing using internal and external airbag surfaces using the HyperMesh tetramesher.
= 14
Tetrahedron airbag volume meshing using internal and external airbag surfaces using the HyperMesh tetramesher. The tetra mesh is output in the Radioss format to a file.

(Integer)

 
Tswitch Amount of time after airbag time to fire to switch from FVM to UP (Uniform Pressure) formulation. 31

Default = 1e30 (Real)

[ s ]
Iswitch Flag to switch from FVM to UP.
= 0 (Default)
No switch to uniform pressure. The finite volume method is used.
= 1
Switch to uniform pressure is performed when either Pswitch or Tswitch criteria is reached.
= 2
Switch to single finite volume is performed when either Pswitch or Tswitch criteria is reached.

(Integer)

 
Pswitch Ratio of FV standard deviation pressure to average pressure which triggers FVM to UP switch. 33

Default = 0.0 (Real)

 
L1 Length L1.

(Real)

[ m ]
L2 Length L2.

(Real)

[ m ]
L3 Length L3.

(Real)

[ m ]
Nb1 Number of finite volumes in direction 1.

Default = 1 (Integer)

 
Nb2 Number of finite volumes in direction 2.

Default = 1 (Integer)

 
Nb3 Number of finite volumes in direction 3.

Default = 1 (Integer)

 
grbric_ID User-defined solid group identifier.

(Integer)

 
surf_IDin Internal surfaces identifier. 27

(Integer)

 
Iref Flag for applying the automated FVM mesh on the reference geometry. Only used if, kmesh=1. 25
= 0 (Default)
Folded airbag is used for meshing.
= 1
Reference airbag is used for meshing.

(Integer)

 
Igmerg Global merging formulation flag. 20
= 1 (Default)
Current mean volume is used for merging.
= 2
Initial mean volume is used for merging.

(Integer)

 
Cgmerg Factor for global merging. 20

(Real)

 
Cnmerg Factor for neighborhood merging. 20

(Real)

 
Ptole Tolerance for finite volume identification.

Default = 10-5 (Real)

 
qa Quadratic bulk viscosity.

Default = 0.0 (Real)

 
qb Linear bulk viscosity.

Default = 0.0 (Real)

 
Hmin Minimum height for triangle permeability. 22

(Real)

[ m ]
Δ T sca Scale factor for airbag time step.

Using /DT/FVMBAG in the Engine will override this value.

Default = 0.9

 
Δ T min Minimum time step for the airbag.

Using /DT/FVMBAG in the Engine will override this value.

 
Ilvout Output level.
= 0 (Default)
Limited information about FVM airbag is printed out.
= 1
All possible information about FVM is printed out.

(Integer)

 
Nlayer Estimated number of layers in airbag folding along direction V 3 . 23

Default = 10 (Integer)

 
Nfacmax Estimated maximum number of airbag segments concerned by a finite volume in the first automatic meshing step.

Default = 20 (Integer)

 
Nppmax Estimated maximum number of vertices of a polygon.

Default = 20 (Integer)

 
Ifvani Write finite volumes in Radioss Starter Animation A000 File flag.
= 0
No
= 1
Yes

(Real)

 

Comments

  1. The airbag external surface should be built only from 4- and 3-noded shell elements. The airbag external surface cannot be defined with option /SURF/SEG, nor with /SURF/SURF, if a sub-surface is defined in /SURF/SEG.
  2. External surfaces shall compose a closed volume with normals must oriented outwards.
  3. Abscissa scale factors are used to transform abscissa units in airbag functions, for example:(1)
    F ( t ) = f t ( t Ascale t )
    Where,
    t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWG0baaaa@3757@
    Time
    f t
    Function of fct_IDt
    (2)
    F ( P ) = f P ( P Ascale P )
    Where,
    P MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGqbaaaa@3733@
    Pressure
    f P
    Function of fct_IDP
    The options are obsolete. Normally, the curve scaling parameters are used instead.
  4. Pressure and temperature of external air and the initial pressure and temperature of air inside of airbag is set to Pext and T0.
  5. The gas flow in FVMBAG1 is solved using finite volumes.

    Some of these finite volumes can be entered by you through a group of solids, located inside the airbag and filling a part or the total internal volume. If there still exists a part of the internal volume which is not discretized by user-defined solids, an automatic meshing procedure produces the remaining volumes. This can be used for example to model a canister.

    A finite volume consists in a set of triangular facets. Their vertices do not necessarily coincide with the nodes of the airbag. The airbag envelope can be modeled with 4-node or 3-node membranes; however, 3 nodes are recommended.

    monvol_airbag-env
    Figure 1.

    monvol_airbag2
    Figure 2.
  6. Venting through vent holes:

    If Iform = 1, venting velocity is computed from Bernoulli equation using local pressure in the airbag.

    The exit velocity is given by:(3)
    u 2 = 2 γ γ 1 P ρ ( 1 ( P ext P ) γ 1 γ )

    The mass out flow rate is given by:

    If Iform = 2, venting velocity is computed from the Chemkin equation:(4)
    v = F s c a l e v f v ( P P e x t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODaiabg2 da9iaadAeacaWGZbGaam4yaiaadggacaWGSbGaamyzamaaBaaaleaa caWG2baabeaakiabgwSixlaadAgadaWgaaWcbaGaamODaaqabaGcca GGOaGaamiuaiabgkHiTiaadcfadaWgaaWcbaGaamyzaiaadIhacaWG 0baabeaakiaacMcaaaa@4A01@

    Where, f v MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzamaaBa aaleaacaWG2baabeaaaaa@3809@ is defined by fct_IDv.

    If Iform = 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.

  7. When there is no sensor which activates gas injection, the vent holes and porosity becomes active, if time T becomes greater than the Tstart, or if the pressure P exceeds Pdef value longer than the time given in Δ t P d e f .
  8. When at least one of the injectors is activated by the sensor, then activation of venting and porosity options is controlled by Ittf.

    Tinj is the time of the first injector to be activated by the sensor.

    Ittf = 0
      Venting, Porosity
    Activation When P > Δ P d e f longer than the time Δ t P d e f , or T > T s t a r t
    Deactivation Tstop
    Time dependent functions No shift
    Ittf = 3
      Venting, Porosity
    Activation When T > T i n j and P > Δ P d e f longer than the time Δ t P d e f , or T > T i n j + T s t a r t
    Deactivation T i n j + T s t o p
    Time dependent functions Shifted by T i n j + T s t a r t

    All other related curves are active when the corresponding venting, porosity or communication option is active.

    The variety of Ittf values comes from historical reasons. Values Ittf=1 and 2 are obsolete and should not be used. Usual values are Ittf=0 (no shift) or Ittf=3 (all relative options are shifted by Tinj).

  9. If surf_IDv0 (surf_IDv is defined) the vent hole area is computed as:(5)
    v e n t _ h o l e s _ a r e a   = A v e n t f A ( A A 0 ) f t ( t ) f P ( P P e x t ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadAhacaWGLbGaamOBaiaadshacaGGFbGaamiAaiaad+gacaWG SbGaamyzaiaadohacaGGFbGaamyyaiaadkhacaWGLbGaamyyaiaabc cacqGH9aqppaGaamyqamaaBaaaleaacaWG2bGaamyzaiaad6gacaWG 0baabeaakiabgwSixlGacAgadaWgaaWcbaGaamyqaaqabaGcdaqada qaamaalaaabaGaamyqaaqaaiaadgeadaWgaaWcbaGaaGimaaqabaaa aaGccaGLOaGaayzkaaGaeyyXICTaciOzamaaBaaaleaacaWG0baabe aakmaabmaabaGaamiDaaGaayjkaiaawMcaaiabgwSixlGacAgadaWg aaWcbaGaamiuaaqabaGcdaqadaqaaiaadcfacqGHsislcaWGqbWaaS baaSqaaiaadwgacaWG4bGaamiDaaqabaaakiaawIcacaGLPaaaaaa@65A1@
    Where,
    A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGbbaaaa@3725@
    Area of surface surf_IDv
    A 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWGbbWaaS baaSqaaiaaicdaaeqaaaaa@380B@
    Initial area of surface surf_IDv
    f t , f P and f A
    Functions of fct_IDt, fct_IDP and fct_IDA
  10. In the case of activated venting closure the vent holes surface is computed as:(6)
    vent_holes_area = A vent A non_impacted f t ( t ) f P ( P P ext ) f A ( A non_impacted A 0 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa WdbiaadAhacaWGLbGaamOBaiaadshacaGGFbGaamiAaiaad+gacaWG SbGaamyzaiaadohacaGGFbGaamyyaiaadkhacaWGLbGaamyyaiaabc cacqGH9aqppaGaamyqamaaBaaaleaacaWG2bGaamyzaiaad6gacaWG 0baabeaakiabgwSixlaadgeadaWgaaWcbaGaamOBaiaad+gacaWGUb Gaai4xaiaadMgacaWGTbGaamiCaiaadggacaWGJbGaamiDaiaadwga caWGKbaabeaakiabgwSixlGacAgadaWgaaWcbaGaamiDaaqabaGcda qadaqaaiaadshaaiaawIcacaGLPaaacqGHflY1ciGGMbWaaSbaaSqa aiaadcfaaeqaaOWaaeWaaeaacaWGqbGaeyOeI0IaamiuamaaBaaale aacaWGLbGaamiEaiaadshaaeqaaaGccaGLOaGaayzkaaGaeyyXICTa ciOzamaaBaaaleaacaWGbbaabeaakmaabmaabaWaaSaaaeaacaWGbb WaaSbaaSqaaiaad6gacaWGVbGaamOBaiaac+facaWGPbGaamyBaiaa dchacaWGHbGaam4yaiaadshacaWGLbGaamizaaqabaaakeaacaWGbb WaaSbaaSqaaiaaicdaaeqaaaaaaOGaayjkaiaawMcaaaaa@7F75@
    (7)
    + B vent A impacted f t ( t ) f P ( P P ext ) f A ( A impacted A 0 )
    With impacted surface:(8)
    A impacted = e S vent n c ( e ) n ( e ) A e
    and non-impacted surface:(9)
    A non _ impacted = e S vent ( 1 n c ( e ) n ( e ) ) A e

    Image12
    Figure 3.
    Where for each element e of the vent holes surf_IDv, n c ( e ) means the number of impacted nodes among the n ( e ) nodes defining the element.

    A0 is the initial area of surface surf_IDv

    ft, fP and fA are functions of fct_IDt, fct_IDP and fct_IDA

    ft', fP' and fA' are functions of fct_IDt', fct_IDP' and fct_IDA'

  11. Radioss ends with a Starter error, if surf_IDv = 0 (surf_IDv is not defined) (Iform=1 or 2).
  12. Functions fct_IDt and fct_IDP are equal to 1, if they are not specified (null identifier).
  13. Function fct_IDA is assumed to be equal to 1, if it is not specified.
  14. To account for contact blockage of vent holes and porous surface areas, flag IBAG 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 Aimpacted and Anon_impacted.
  15. Leakage by porosity formulations, the mass flow rate flowing out is computed as:
    • Iformps = 1 m ˙ out = A eff 2 P ρ Q 1 γ γ γ 1 [ 1 Q γ 1 γ ] (Isentropic - Wang Nefske)
    • Iformps = 2 m ˙ out = A eff ρ v ( P P ext )

      Where, v is the outflow gas velocity (Chemkin)

    • Iformps = 3 m ˙ out = A eff 2 ρ ( P P ext ) (Graefe)

    The effective venting area Aeff is computed according to the input in the /LEAK/MAT input for fabric materials of TYPE19 or TYPE58.

  16. If leakage blockage is activated, Iblockage=1, the effective venting area is modified as:(10)
    A eff = A non _ impacted

    A non _ impacted is non-impact surface 10

    The blockage will be active only if flag IBAG is set to 1 in the concerned contact interfaces (line 3 of interface TYPE7 and TYPE23).

  17. Automatic finite volume meshing parameters.
  18. The finite volumes are generated in two steps.
    • The first step generates vertices lying exclusively on the envelope of the airbag. You can update the finite volume along with the deformation of the envelope and correspond to the following procedure (displayed in 2D for purpose of clarity):

      monvol_step1
      Figure 4.
      This procedure requires the input of the direction V 3 , named cutting direction, and of the direction V 1 . A second direction V 2 in the plan normal to the cutting direction will be computed. In order to position the finite volumes and to determine the cutting width in both direction V 1 and V 2 , an origin O must be provided as well as a length Li, counted both positively and negatively from the origin, and a number of steps Ni. The cutting width is then given by:(11)
      W i = 2 L i N i

      It is required that the box drawn in the horizontal plane (normal to V 3 ) by the origin O and the length Li, counted both positively and negatively from O, includes the bounding-box of the envelope of the volume to mesh projected in this plane. This is necessary to ensure that this volume in entirely divided into finite volumes.

    • The second step performs horizontal cutting of the finite volumes, and may be useless in many cases of tightly folded airbags. It is required especially when injection is made in a canister filled by the injected gas before unfolding the airbag.
    This second step may generate vertices located inside the airbag. In order for them to be moved along with the inflation of the airbag, each is attached to a vertical segment (parallel to direction V 3 ) between two vertices lying on the envelope of the airbag (Figure 4). The local coordinates of the vertex within its reference segment remain constant throughout the inflation process.

    monvol_fvmbag
    Figure 5.
    The horizontal cutting width is given by:(12)
    W 3 = 2 L 3 N 3

    It is not necessary that the segment given in the V 3 direction by the origin O and length L3, counted both positively and negatively, includes the bounding-box of the envelope of the volume to mesh projection on the V 3 direction, since at the second step only existing finite volumes are cut.

  19. Actual vector V 1 used for automatic meshing is obtained after orthogonalization of the input vector with respect to vector V 3 .
  20. 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 merge: 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 Igmerg determines if the mean volume to use is the current mean volume (Igmerg =1) or the initial mean (Igmerg =2). The factor giving the minimum volume from the mean volume is Cgmerg.
    • Neighborhood merge: a finite volume is merged if its volume becomes less than a certain factor multiplying the mean volume of its neighbors. The factor giving the minimum volume from the mean volume is Cnmerg.
  21. In the case of both Cgmerg and Cnmerg are not equal to 0, means both merging approaches will be used simultaneously. In case of a strong shock, it is recommended to set qa = 1.1 and qb = 0.05.
  22. When two layers of fabric are physically in contact, there should be no possible flow between finite volumes, which is numerically not the case because of interface gap. Hmin represents a minimum height for the triangular facets below which the facet is impermeable. Its value should be close to the gap of the self-impacting interface of the airbag.
  23. Nlayer, Nfacmax, and Nppmax are memory parameters that help the finite volume creation process. Changing their value cannot cause the calculation to stop. Increasing the leads to a higher amount of memory and a smaller computation time for automatic meshing.
  24. During the finite volume creation process, plane polygons are first created, which are then assembled into closed polyhedra and decomposed into triangular facets. Nppmax is the maximum number of vertices of these polygons.
  25. Automatic finite volume meshing based on reference geometry can be activated with flag Iref=1. It only works with a reference geometry based on /REFSTA and /XREF. The flag is not supported when disjointed reference geometry /EREF is used. Note that for Iref=1, the frame definition for automatic meshing should refer to non-folded reference geometry.
  26. The option kmesh controls type of FVM meshing of internal airbag volume. The polyhedron meshing method, kmesh =1 was the default method used in 2017.2 and before. If grbric_ID ≠ 0, kmesh is ignored and the tetra FVM mesh is specified by the user created.
  27. Surface surf_IDin is used to take internal surfaces or baffles into account as obstacles to the gas flow inside the monitored volume. Internal surfaces are taken into account in FVM only if the monitored volume is meshed automatically with polyhedron or if it is filled with solid elements, like TETRA4 (possibly HEXA and PENTA) with nodes coinciding with the monitored volume external and internal surface nodes (these solids must be declared in grbrick_ID). A porosity ranging from 0: no porosity up to 1: full porosity (vent) can be applied to internal surface fabrics only if their material model is LAW19 or LAW58. Injector surface can also be defined on an internal surface in which case the gas flow direction is opposite to the internal surface normal orientation.
  28. The lost heat flow is given by:(13)
    Q ˙ ( x , t ) = H conv Area ( x , t ) ( T ( x , t ) T 0 )
  29. If an element of a vent hole surface (surf_IDv) belongs to an injector (surf_IDinj) 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:(14)
    f = S vent S vent S injector
  30. If an element of a porous surface also belongs to an injector (surf_IDinj), it will be ignored from the porous surface.
  31. The time to switch Tswitch to Uniform Pressure is relative to the time to fire.
  32. With option Iswitch=2, the airbag is always computed with finite volume method, even when only 1 finite volume remains. The gas parameters are identical before and after switching to a single finite volume. Some variation of pressure or gas parameters may be seen with a switch to uniform pressure method (Iswitch=1).
  33. Pswitch is the ratio of standard deviation of the Finite Volume pressures to the airbag average pressure.(15)
    P s w i t c h = SD(FV pressure) Average pressure MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamiuamaaBa aaleaacaWGZbGaam4DaiaadMgacaWG0bGaam4yaiaadIgaaeqaaOGa eyypa0ZaaSaaaeaacaqGtbGaaeiraiaabIcacaqGgbGaaeOvaiaabc cacaqGWbGaaeOCaiaabwgacaqGZbGaae4CaiaabwhacaqGYbGaaeyz aiaabMcaaeaacaqGbbGaaeODaiaabwgacaqGYbGaaeyyaiaabEgaca qGLbGaaeiiaiaabchacaqGYbGaaeyzaiaabohacaqGZbGaaeyDaiaa bkhacaqGLbaaaaaa@5916@

    This ratio can be output using the /TH/MONVOL variable UPCRIT. Pswitch approaches zero as the pressure in each finite volume approaches the average pressure in the airbag.