/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 | Iequi | Ittf | |||||
γi | cpai | cpbi | cpci |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
Njet |
(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 |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
fct_IDPt | fct_IDP θ | fct_IDP θ | Fscalept | Fscalep θ | Fscalep δ |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
Nvent |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) |
---|---|---|---|---|---|---|---|---|---|
surf_IDv | Avent | Bvent | Tstop | ||||||
Tvent | ΔPdef | ΔtPdef | fct_IDV | FscaleV | IdtPdef | ||||
fct_IDt | fct_IDP | fct_IDA | Fscalet | FscaleP | FscaleA | ||||
fct_IDt' | fct_IDP' | fct_IDA' | Fscalet' | FscaleP' | FscaleA' |
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) |
[m2] |
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.
(Integer) |
|
Ittf | Venting time shift flag.
Active only when injection sensor is specified.
|
|
γi | Ratio of specific heats at
initial temperature γi=cpicvi (Real) |
|
cpai | cpa
coefficient in the relation
cpi(T) (Real) |
[Jkg⋅K] |
cpbi | cpb
coefficient in the relation
cpi(T) (Real) |
[Jkg⋅K2] |
cpci | cpc
coefficient in the relation
cpi(T) (Real) |
[Jkg⋅K3] |
Njet | Number of
injectors (Integer) |
|
γ | Ratio of specific heats γ=CpCv (Real) |
|
cpa | cpa
coefficient in the relation cp(T) (Real) |
[Jkg⋅K] |
cpb | cpa
coefficient in the relation cp(T) (Real) |
[Jkg⋅K2] |
cpc | cpa
coefficient in the relation cp(T) (Real) |
[Jkg⋅K3] |
surf_IDv | Vent holes membrane
surface identifier (Integer) |
|
Avent | If
surf_IDv ≠
0: scale factor on surface Default = 1.0 If surf_IDv = 0: surface of vent holes Default = 0.0 (Real) |
[m2] , if surf_IDV = 0 |
Bvent | If
surf_IDv ≠
0: scale factor on impacted surface Default = 1.0 If surf_IDv = 0: Bvent is reset to 0. Default = 0.0 (Real) |
[m2] , if surf_IDV = 0 |
Tstop | Stop time for
venting Default = 1E+30 (Real) |
[s] |
Tvent | Start time for
venting Default = 0.0 (Real) |
[s] |
ΔPdef | Pressure difference to
open vent hole membrane (
ΔPdef
=
Pdef - Pext) (Real) |
[Pa] |
ΔtPdef | 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) |
[ms] |
IdtPdef | Time delay flag when
ΔPdef
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_IDmas | Mass of injected gas
versus time function identifier (Integer) |
|
Iflow | Mass versus time function
input type flag
(Integer) |
|
Fscalemas | Mass function scale
factor Default = 1.0 (Real) |
[kg] or [kgs] |
fct_IDT | Temperature of injected
gas versus time function identifier (Integer) |
|
FscaleT | Temperature function scale
factor Default = 1.0 (Real) |
[K] |
sens_ID | Sensor
identifier. (Integer) |
|
Ijet | Jetting flag.
(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 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) |
Comments
- surf_IDex must be defined using segments associated with 4-nodes or 3-nodes 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) F(t′)=fct_ID(tAscalet)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(pAscalep)Where, p is the pressure.
- Initial pressure is set to Pext.
- 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:
PextV=RM0MiT0
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=8.314Jmole⋅K - Ratio of specific heats
at constant pressure per mass unit
cpi of the gas initially
filling the airbag is quadratic versus temperature:
(4) cpi(T)=cpa+cpbi*T+cpci*T2 - 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)γicpi(To)=RMiWhere, 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=8.314Jmole⋅K - The characteristics of the gas initially filling the airbag must be defined (no default) and must be equal for each communicating airbag.
- 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.
- 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*T2 - 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)γcp(To)=RMWhere,- M
- Molar mass of the gas
- R
- Gas constant depending on the units system
(9) R=8.314Jmole⋅K - If jetting is used, an
additional Δ
Pjet pressure is applied to
each element of the airbag:
(10) ΔPjet=ΔP(t)*ΔP(θ)*ΔP(δ)*max(→n*→m,0) - 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.Figure 1. Dihedral Shape of the Jet
with M between N1 and N3
- If node_ID3 = 0, node_ID3 is set to node_ID1 and the dihedral shape is reduced to a conical shape.
- If
fct_IDV = 0:
isenthalpic outflow is assumed, else Chemkin model is used and outflow velocity
is:
(11) ν=FscaleV∗fct_IDV(P−Pext)- 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) γγ−1Pρ=γγ−1Pextρvent+u22 (vent hole)
Applying the adiabatic conditions:
(monitored volume) Pργ=Pextρventγ (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) u2=2γγ−1Pρ(1−(PextP)γ−1γ)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) ˙mout=ρvent*vent_holes_surface*u=ρ(PextP)1γ*vent_holes_surface*uThe energy flow rate is given by:(14) ˙Eout=˙moutEρV=(PextP)1γ*vent_holes_surface*uEVWhere, V is the airbag volume and E is the internal energy of gas into the airbag.
- Chemkin model
(15) ˙mout=vent_holes_surface*Fscalev*fct_IDv(P−Pext)*ρWhere, ρ is the density of the gas within the airbag.
- Isenthalpic model
- Vent holes surface is
computed as follows:
(16) vent_holes_surface=Avent*Anon_impacted*fct_IDt(Anon_impacted/A0)*fct_IDP(P−Pext)(17) +Bvent*Aimpacted*fct_IDt′(Aimpacted/A0)*fct_IDP′(P−Pext)with impacted surface:(18) Aimpacted=∑e∈Sventnc(e)n(e)Aeand non-impacted surface:(19) Anon_impacted=∑e∈Svent(1−nc(e)n(e))AeWhere 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.
Figure 2. From Nodes Contact to Impacted/Non-impacted Surface - Functions fct_IDt' and fct_IDP' are assumed to be equal to 1, if they are not specified (null identifier).
- Function fct_IDA' is assumed as the fct_IDA'(A) = A, if it is not specified.
- 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.
- 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.
- Vent hole membrane is deflated if T > Tvent or if the pressure exceeds Pdef during more than ΔtPdef .