/MONVOL/FVMBAG (Obsolete)

Block Format Keyword Describes the airbag with FVMBAG type. The input is similar to AIRBAG type.

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MONVOL/FVMBAG/monvol_ID/unit_ID
monvol_title
surf_IDex                  
Ascalet AscaleP AscaleS AscaleA AscaleD
        Pext T0 Iequi Ittf
γ i cpai cpbi cpci    
Number of injectors
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Njet                  
Define Njet injectors (four lines per injector)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
γ cpa cpb cpc    
fct_IDmas Iflow Fscalemas fct_IDT FscaleT sens_ID    
Isjet                  
fct_IDvel   Fscalevel            
Number of vent holes
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Nvent                  
Define Nvent vent holes (four lines per vent hole)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
surf_IDv Avent Bvent     Itvent    
Tvent Δ Pdef Δ tPdef fct_IDV FscaleV IdtPdef
fct_IDt fct_IDP fct_IDA   Fscalet FscaleP FscaleA
fct_IDt' fct_IDP' fct_IDA'   Fscalet' FscaleP' FscaleA'
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Vx3 Vy3 Vz3        
Vx1 Vy1 Vz1        
X0 Y0 Z0        
L1 L2 L3        
Nb1 Nb2 Nb3 grbrc_ID surf_IDin Iref        
Other FVMBAG parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Igmerg   Cgmerg Cnmerg Ptole    
qa qb Hmin        
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 1

(Integer)

 
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 ]
Pext External pressure

(Real)

[ Pa ]
T0 Initial temperature.

Default = 295 (Real)

[K]
Iequi Initial thermodynamic equilibrium flag.
= 0
The mass of gas initially filling the airbag is determined with respect to the volume at time zero.
= 1
The mass of gas initially filling the airbag is determined with respect to the volume at beginning of jetting.

(Integer)

 
Ittf Venting time shift flag. Active only when injection sensor is specified.
= 0 or 1
Time dependent porosity curves are not shifted by injection sensor activation time. Tvent and Tstop are ignored.
= 2
Time dependent porosity curves are shifted by Tinj (Tinj defined as the time of the first injector to be activated by the sensor).
Tvent and Tstop are ignored.
= 3
Time dependent porosity curves are shifted by Tinj +Tvent. Venting is stopped at Tinj + Tstop, when Tstop is specified.
 
γ i Ratio of specific heats at initial temperature 5

γ i = Cp i / Cv i

(Real)

 
cpai cpa coefficient in the relation cpi(T)

(Real)

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@
cpbi cpb coefficient in the relation cpi(T)

(Real)

[ J kg K 2 ]
cpci cpc coefficient in the relation cpi(T)

(Real)

[ J kg K 3 ]
Njet Number of injectors

(Integer)

 
γ Ratio of specific heats

γ = C p / C v

(Real)

 
cpa cpa coefficient in the relation cp(T)

(Real)

[ J kgK ] MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeaaciGaaiaabeqaamaabaabaaGcbaWaamWaaeaada WcaaqaaiaabQeaaeaacaqGRbGaae4zaiabgwSixlaabUeaaaaacaGL BbGaayzxaaaaaa@3DB3@
cpb cpb coefficient in the relation cp(T)

(Real)

[ J kg K 2 ]
cpc cpc coefficient in the relation cp(T)

(Real)

[ J kg K 3 ]
fct_IDmas Mass of injected gas versus time identifier

(Integer)

 
Iflow Mass versus time function input type flag
= 0
Mass is input
= 1
Mass flow is input

(Integer)

 
Fscalemas Scale factor on mass function

Default = 1.0 (Real)

[ kg ] or [ kg s ]
fct_IDT Temperature of injected gas versus time identifier

(Integer)

 
FscaleT Temperature scale factor

Default = 1.0 (Real)

[ K ]
sens_ID Sensor identifier to start injections

(Integer)

 
Isjet Injector surface identifier (must be different for each injectors)

(Integer)

 
fct_IDvel Injected gas velocity identifier

(Integer)

 
Fscalevel Injected gas 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)

 
surf_IDv Vent holes membrane surface (Real) or porous surface identifier

(Integer)

 
Avent If surf_IDv0: scale factor on surface.

Default = 1.0

If surf_IDv = 0: surface of vent holes.

Default = 0.0 (Real)

[ m 2 ] , if surf_IDV = 0
Bvent If surf_IDv0: scale factor on impacted surface

Default = 1.0

If surf_IDv = 0: Bvent is reset to 0

Default = 0.0 (Real)

[ m 2 ] , if surf_IDV = 0
Itvent Venting formulation 7
= 1
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.
= 2 (Default)
Venting velocity is computed from Bernoulli equation using local pressure in the airbag. Local density and energy are used to compute outgoing mass and energy.
= 3
Venting velocity is computed from Chemkin equation.

(Integer)

 
Tvent Start time for venting

Default = 0.0 (Real)

[ s ]
Δ P d e f Pressure difference to open vent hole membrane ( Δ P d e f = Pdef - Pext)

(Real)

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

(Real)

[ s ]
fct_IDV Outflow velocity 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@
IdtPdef Time delay flag when Δ P d e f is reached:
= 0
Pressure should be over Δ P d e f during a Δt P d e f cumulative time to activate venting.
= 1
Venting is activated Δt P d e f after Δ P d e f is reached.
 
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 when contact function identifier.

(Integer)

 
fct_IDP' Porosity versus pressure when contact function identifier.

(Integer)

 
fct_IDA' Porosity versus impacted surface 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)

 
Vx3 X component of vector V3 (in global frame).

(Real)

 
Vy3 Y component of vector V3 (in global frame).

(Real)

 
Vz3 Z component of vector V3 (in global frame).

(Real)

 
Vx1 X component of vector V1 (in global frame).

(Real)

 
Vy1 Y component of vector V1 (in global frame)

(Real)

 
Vz1 Z component of vector V1 (in global frame)

(Real)

 
X0 X coordinate of local origin O (in global frame)

(Real)

 
Y0 Y coordinate of local origin O (in global frame)

(Real)

 
Z0 Z coordinate of local origin O (in global frame)

(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. 25

(Integer)

 
Iref Flag for applying the automated FVM mesh on the reference geometry. 24
= 0 (Default)
No
= 1
Yes

(Integer)

 
Igmerg Global merging formulation flag. 19

Default = 1 (Integer)

 
Cgmerg Factor for global merging. 19

Default = 0.02 (Real)

 
Cnmerg Factor for neighborhood merging. 19

(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. 21

(Real)

[ m ]
Ilvout Output level
0 (Default)
1

(Integer)

 
Nlayer Estimated number of layers in airbag folding along direction V3 22

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

(Integer)

 

Comments

  1. surf_IDex must be defined using segments associated with 4-nodes or 3-nodes shell elements (possibly void elements).
  2. The volume must be closed and the normals must be oriented outwards.
  3. Abscissa scale factors are used to transform abscissa units in airbag functions, for example: (1)
    F ( t ' ) = fct _ ID ( t Ascale t )
    where, t is the time. (2)
    F ( p ' ) = fct _ ID ( p Ascale p )

    Where, p is the pressure.

  4. The initial pressure is set to Pext.
  5. If γ i = 0, the characteristics of the gas initially filling the airbag are set to the characteristics of the gas by the first injector.
  6. The gas flow in FVMBAG 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.
  7. 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:(4)
    m ˙ out = ρ v * vent _ holes _ surface * u
    The energy flow rate is given by:(5)
    E ˙ out = m ˙ out E ρ V = ( P ext P ) 1 γ * vent _ holes _ surface * u E V
    The venting velocity is computed by:(6)
    m out = ρ * vent _ holes _ surface * fct _ ID V * Fscale V ( P P ext )
  8. Vent hole membrane is deflated if T > Tvent or if the pressure exceeds Pdef during more than Δt P d e f .
  9. If surf_IDv0 (surf_IDv is defined). (7)
    vent _ holes _ surface = A vent * fct _ ID A ( A / A 0 ) * fct _ ID t ( t ) * fct _ ID P ( P P ext )

    Where, A is the Area of surface surf_ID and A0 is the initial Area of surface surf_IDv.

  10. If surf_IDv = 0 (surf_IDv is not defined) vent hole is ignored.(8)
    vent _ holes _ surface = A vent * fct _ ID t ( t ) * fct _ ID P ( P P ext )
  11. Functions fct_IDt and fct_IDP are assumed to be equal to 1, if they are not specified (null identifier).
  12. Function fct_IDA is assumed as the fct_IDA(A/A0) = 1, if it is not specified.
  13. Vent holes surface is computed as follows:(9)
    vent _ holes _ surface =A vent * A non _ impacted * fct _ ID t ( A non _ impacted / A 0 ) * fct _ ID P ( P P ext ) + B vent * A impacted * fct _ ID t ( A impacted / A 0 ) * fct _ ID P ( P P ext )
    with impacted surface:(10)
    A impacted = e S vent n c ( e ) n ( e ) A e
    and non-impacted surface:(11)
    A non _ impacted = e S vent ( 1 n c ( e ) n ( e ) ) A e

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


    Image12
    Figure 3. From Nodes Contact to Impacted/Non-impacted Surface
  14. Functions fct_IDt' and fct_IDP' are assumed to be equal to 1, if they are not specified (null identifier).
  15. In order to use porosity during contact, flag IBAG 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 Aimpacted and Anon_impacted.
  16. Automatic finite volume meshing parameters.

    monvol_finite_vol
    Figure 4.
  17. The finite volumes are generated in two steps.
    • The first step generates vertices lying exclusively on the envelope of the airbag. This allows to 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 5.

      This procedure requires the input of the direction V3, named cutting direction, and of the direction V1. A second direction V2 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 V1 and V2, 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 Wi = 2Li / Ni

      It is required that the box drawn in the horizontal plane (normal to V3) 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 especially required 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 V3) between two vertices lying on the envelope of the airbag (Figure 6). The local coordinates of the vertex within its reference segment remain constant throughout the inflation process.

      monvol_fvmbag
      Figure 6.

      The horizontal cutting width is given by W3 = 2L3 / N3. It is not necessary that the segment given in the V3 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 V3 direction, since at the second step only existing finite volumes are cut.

  18. Actual vector V1 used for automatic meshing is obtained after orthogonalization of the input vector with respect to vector V3.
  19. 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 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 merging: 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.
  20. In the case of both Cgmerg and Cnmerg are not equal to 0, means both merging approach will be used simultaneously. In case of a strong shock, it is recommended to set qa = 1.1 and qb = 0.05.
  21. 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.
  22. Nlayer, Nfacmax, 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.
  23. 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.
  24. Iref set to 1 only works with a reference geometry based on /REFSTA (not yet supported if the reference geometry is based on /XREF) for monitored volumes types FVMBAG or FVMBAG1.
  25. Only applicable to the Finite Volume Method, 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 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. 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.
  26. 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 c correction factor f computed at time t=0 is applied to the total vent hole surface:(12)
    f = S vent / ( S vent S injector )