/MONVOL/FVMBAG2

• 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

Definitions

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. 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.
4. Pressure and temperature of external air and the initial pressure and temperature of air inside of airbag is set to P_ext and T₀.
5. 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.

6. 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 $\text{Δ}t{P}_{def}$ .
7. 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 = 0

   	Venting, Porosity
   Activation	When $P>\text{Δ}{P}_{def}$ longer than the time $\text{Δ}t{P}_{def}$ , or $T>T_{start}$
   Deactivation	Tstop
   Time dependent functions	No shift

   I_ttf = 3

   	Venting, Porosity
   Activation	When $T>T_{inj}$ and $P>\text{Δ}{P}_{def}$ longer than the time $\text{Δ}t{P}_{def}$ , 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).

8. If surf_ID_v ≠ 0 (surf_ID_v is defined) the vent hole area is computed as:(3)
   $$vent\_holes\_area=A_{vent}\cdot {\mathrm{f}}_A\left(\frac{A}{A_0}\right)\cdot {\mathrm{f}}_t\left(t\right)\cdot {\mathrm{f}}_P\left(P-P_{ext}\right)$$
   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

9. In the case of activated venting closure the vent holes surface is computed as:(4)
   $$vent\_holes\_area=A_{vent}\cdot A_{non\_impacted}\cdot {\mathrm{f}}_t\left(t\right)\cdot {\mathrm{f}}_P\left(P-P_{ext}\right)\cdot {\mathrm{f}}_A\left(\frac{A_{non\_impacted}}{A_0}\right)$$
   (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 non-impacted surface:(7)

   $$A_{\mathit{non}\_\mathit{impacted}}=\sum _{e\in S_{\mathit{vent}}}\left(1-\frac{n_c\left(e\right)}{n\left(e\right)}\right)A_e$$

   
   
   Figure 1.

   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.

   A₀ 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'

10. Radioss ends with a Starter error, if surf_ID_v = 0 (surf_ID_v is not defined) for Chemkin venting formulation (I_form=2).
11. Functions fct_ID_t and fct_ID_P are equal to 1, if they are not specified (null identifier).
12. Function fct_ID_A is assumed to be equal to 1, if it is not specified.
13. 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}.
14. 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.

15. 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 non-impact 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).

16. 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.
17. The lost heat flow is given by:(9)
    $$\dot{\text{Q}}\left(x,t\right)=H_{\mathit{conv}}\cdot \text{Area}\left(x,t\right)\cdot \left(\text{T}\left(x,t\right)-T_0\right)$$
18. 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)
    $$f=\frac{S_{\mathit{vent}}}{S_{\mathit{vent}}-{\text{S}}_{\mathit{injector}}}$$
19. If an element of a porous surface also belongs to an injector (surf_ID_inj), it will be ignored from the porous surface.
20. The time to switch T_switch to Uniform Pressure is relative to the time to fire.
21. With option I_switch=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 (I_switch=1).
22. P_switch is the ratio of standard deviation of the Finite Volume pressures to the airbag average pressure.(11)
    $$P_{switch}=\frac{\text{SD(FV pressure)}}{\text{Average pressure}}$$

    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.