/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_IDex                  
Ascalet AscaleP AscaleS AscaleA AscaleD
    μ Pext T0 equi Ittf
γ i cpai cpbi cpci    
Number of Injectors
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Njet                  
Define Njet injectors (3 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    
Ijet node_ID1 node_ID2 node_ID3            
Jetting Functions data (Read only if Ijet > 0)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
fct_IDPt fct_IDP θ fct_IDP θ   Fscalept Fscalep θ Fscalep δ
Number of vent holes
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Nvent                  
Define Nvent vent holes membranes (four lines per vent hole membrane)
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
surf_IDv Avent Bvent Tstop      
Tvent Δ P d e f Δt P d e f fct_IDV FscaleV IdtPdef
fct_IDt fct_IDP fct_IDA   Fscalet FscaleP FscaleA
fct_IDt' fct_IDP' fct_IDA'   Fscalet' FscaleP' FscaleA'  

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_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)

[ deg ]
AscaleD Abscissa scale factor for distance based functions

Default = 1.0 (Real)

[ m ]
mat_ID Initial gas material identifier (/MAT/GAS)

(Real)

 
μ Volumetric viscosity

Default = 0.01 (Real)

 
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

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 cpa coefficient in the relation cp(T)

(Real)

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

(Real)

[ J kg K 3 ]
surf_IDv Vent holes membrane 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
Tstop Stop time for venting

Default = 1E+30 (Real)

[ s ]
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 vs time function identifier

(Integer)

 
fct_IDP Porosity vs pressure function identifier

(Integer)

 
fct_IDA Porosity vs 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_IDmas Mass of injected gas vs time function identifier

(Integer)

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

(Integer)

 
Fscalemas Mass function scale factor

Default = 1.0 (Real)

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

(Integer)

 
FscaleT Temperature function scale factor

Default = 1.0 (Real)

[ K ]
sens_ID Sensor identifier

(Integer)

 
Ijet Jetting flag
= 0
No jetting
= 1
Jetting

(Integer)

 
node_ID1, node_ID2, node_ID3 Node identifiers N1, N2, and N3 for jet shape definition

(Integer)

 
fct_IDPt If Ijet = 1: identifier of the function number defining ΔPt

(Integer)

 
fct_IDP θ If Ijet = 1: identifier of the function number defining ΔP ( θ ) )

(Integer)

 
fct_IDP δ If Ijet = 1: identifier of the function number defining ΔP ( δ )

(Integer)

 
FscalePt If Ijet = 1: scale factor for fct_IDPt

Default = 1.0 (Real)

[ Pa ]
FscaleP θ If Ijet = 1: scale factor for fct_IDP θ

Default = 1.0 (Real)

[ Pa ]
FscaleP δ If Ijet = 1: scale factor for fct_IDP δ

Default = 1.0 (Real)

[ Pa ]
Nvent Number of vent holes

(Integer)

 
fct_IDt' Porosity vs time when contact function identifier

(Integer)

 
fct_IDP' Porosity vs pressure when contact function identifier

(Integer)

 
fct_IDA' Porosity vs 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)

 

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.

    For example, if your input data is in [ms], but you need a data in [s], you could set Ascale to 0.001.(2)
    F ( p ) = fct _ ID ( p Ascale p )

    Where, p is the pressure.

  4. Initial pressure is set to Pext.
  5. Initial thermodynamic equilibrium is written at time zero (Iequi =0) or at beginning of jetting (Iequi =1), based on the following equation with respect to the volume at time zero, or the volume at beginning of jetting: P ext V = R M 0 M i T 0
    where, M0 is the mass of gas initially filling the airbag, Mi 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 J mole K
  6. Ratio of specific heats at constant pressure per mass unit cpi of the gas initially filling the airbag is quadratic versus temperature:(4)
    cp i ( T ) = cpa + cpb i * T + cpc i * T 2
  7. Gas constant at initial temperature γ 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)
    ( γ 1 ) γ i cp i ( T o ) = R M i
    Where, Mi is the molar mass of the gas initially filling the airbag, and R is the gas constant depending on the units system.(6)
    R = 8.314 J mole K
  8. The characteristics of the gas initially filling the airbag must be defined (no default) and must be equal for each communicating airbag.
  9. If γ i = 0, the characteristics of the gas initially filling the airbag are set to the characteristics of the gas provided by the first injector.
  10. Ratio of specific heats at constant pressure per mass unit cpi of the gas is quadratic with regard to the temperature:(7)
    cp ( T ) = cpa + cpb * T + cpc * T 2
  11. Gas constant at initial temperature γ must be related to specific heat per mass unit at initial temperature and molar mass of the with respect to the following relation:(8)
    ( γ 1 ) γ cp ( T o ) = R M
    Where,
    M
    Molar mass of the gas
    R
    Gas constant depending on the units system
    (9)
    R = 8.314 J mole K
  12. If jetting is used, an additional Δ Pjet pressure is applied to each element of the airbag:(10)
    Δ P jet = Δ P ( t ) * Δ P ( θ ) * Δ P ( δ ) * max ( n * m , 0 )
  13. With m being the normalized vector between the projection of the center of the element upon segment (node_ID1 and node_ID3) and the center of the element; θ the angle between vectors MN2 and m (in degrees), δ is the distance between the center of the element and its projection upon segment (node_ID1 and node_ID3 ).
    The projection of a point upon segment (node_ID1 and node_ID3) is defined as the projection of the point in direction MN2 upon the line (node_ID1 and node_ID3) if it lies inside the segment (node_ID1 and node_ID3). If this is not the case, the projection of the point upon segment (node_ID1 and node_ID3) is defined as the closest node node_ID1 or node_ID3.

    clip0087
    Figure 1. Dihedral Shape of the Jet

    with M between N1 and N3

  14. If node_ID3 = 0, node_ID3 is set to node_ID1 and the dihedral shape is reduced to a conical shape.
  15. If fct_IDV = 0: isenthalpic outflow is assumed, else Chemkin model is used and outflow velocity is:(11)
    ν = Fscale V fct _ ID V ( P P ext )
    • 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) γ γ 1 P ρ = γ γ 1 P ext ρ vent + u 2 2 (vent hole)

      Applying the adiabatic conditions:

      (monitored volume) P ρ γ = P ext ρ vent γ (vent hole)

      Where, P is the pressure of gas into the airbag and ρ is the density of gas into the airbag.

      Therefore, the exit velocity is given by:(12)
      u 2 = 2 γ γ 1 P ρ ( 1 ( P ext P ) γ 1 γ )

      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)
      m ˙ out = ρ vent * vent _ holes _ surface * u = ρ ( P ext P ) 1 γ * vent _ holes _ surface * u
      The energy flow rate is given by:(14)
      E ˙ out = m ˙ out E ρ V = ( P ext P ) 1 γ * vent _ holes _ surface * u E V

      Where, V is the airbag volume and E is the internal energy of gas into the airbag.

    • Chemkin model(15)
      m ˙ out = vent _ holes _ surface * Fscale v * fct _ ID v ( P P ext ) * ρ

      Where, ρ is the density of the gas within the airbag.

  16. Vent holes surface is computed as follows:(16)
    vent _ holes _ surface =A vent * A non _ impacted * fct _ ID t ( A non _ impacted / A 0 ) * fct _ ID P ( P P ext )
    (17)
    + B vent * A impacted * fct _ ID t ( A impacted / A 0 ) * fct _ ID P ( P P ext )
    with impacted surface:(18)
    A impacted = e S vent n c ( e ) n ( e ) A e
    and non-impacted surface:(19)
    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 2. From Nodes Contact to Impacted/Non-impacted Surface
  17. Functions fct_IDt' and fct_IDP' are assumed to be equal to 1, if they are not specified (null identifier).
  18. Function fct_IDA' is assumed as the fct_IDA'(A) = A, if it is not specified.
  19. 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.
  20. 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 3-nodes shell elements.
    • The airbag external surface can not be defined with option /SURF/SEG (or with option /SURF/SURF if a sub-surface is defined with option /SURF/SEG).
    • Same restriction applies to vent hole surface.
    • Shells and 3-nodes shell elements included in vent hole surface have to also be included in external surface.
  21. Vent hole membrane is deflated if T > Tvent or if the pressure exceeds Pdef during more than Δt P d e f .