The inflator capability in
Abaqus/Explicit
is suited for modeling the flow characteristics of inflators used for airbag
systems. You must associate the inflator definition with a name. You specify
the reference node of the fluid cavity that the inflator will fill with gas. A
single fluid cavity can have any number of inflators.
Defining the Inflator Property
The inflator property defines the mass flow rate and temperature as a
function of inflation time either directly or by entering tank test data. It
also defines the mixture of gases entering the fluid cavity. You must associate
the inflator property with a name. This name can then be used to associate a
certain property with an inflator definition.
Specifying the Gas Temperature and Mass Flow Rate Directly
The temperature and the mass flow rate of the gas entering the fluid cavity
can be given directly as functions of inflation time. Enter a table of mass
flow rate and temperature versus inflation time.
Using Tank Test Data
The mass flow rate and the temperature of the gas entering the fluid cavity
can be determined by the results of a tank test. In the test the inflator is
discharged into a closed, fixed volume tank, and the time history of pressure
in the tank is measured. The inflator mass flow rate can then be calculated
from the pressure history using the equations of gas dynamics. For an ideal
gas, conservation of energy for an adiabatic process is given by
where
is the temperature,
is the absolute zero on the temperature scale being used, and the subscripts
and
refer to quantities in the inflator and the rigid tank, respectively. Using
mass balance
and the equation of state for an ideal gas with constant volume gives
The mass flow rate can be found by combining the above equations
where
is the ratio of the constant pressure heat capacity, ,
and the constant volume heat capacity, :
To calculate the mass flow rate using the results of a tank test, enter a
table of tank pressure and inflator temperature versus inflation time, and
specify the volume of the tank.
Using the Dual Pressure Method
If both the inflator pressure, ,
and tank pressure, ,
time history curves can be measured during a tank test, the inflator mass flow
rate and temperature can then be calculated using the assumption of isentropic
flow (Wang and Nefske, 1988). The mass flow rate through the inflator orifice
can be described by
where C is the discharge coefficient,
A is the effective area, and the coefficient
is determined by assuming choked or sonic flow as
Comparing the expression for inflator mass flow rate obtained in a rigid
tank with that given above, the inflator temperature is given by
and the inflator mass flow rate is
To calculate the inflator mass flow rate and temperature using the dual
pressure method, enter a table of tank pressure and inflator pressure versus
inflation time; and specify the volume of the tank, the effective area, and the
discharge coefficient. The tank volume and effective area must be specified.
The discharge coefficient has a default value of 0.4.
Specifying the Inflator Pressure and Mass Flow Rate Directly
You can enter a table of the mass flow rate and inflator pressure versus
inflation time and specify the effective area and discharge coefficient. The
gas temperature in the inflator will be calculated by using the assumption of
isentropic flow. The effective area must be specified. The discharge
coefficient has a default value of 0.4.
Specifying the Gas Mixture
To define the inflator gas mixture, specify the number of gas species used
for the inflator, and enter a list of names of fluid behaviors and a table of
the mass fraction or molar fraction of the species. The mass fraction or molar
fraction of the species may be a function of inflation time. The sum of the
mass fractions or molar fractions for the species should be equal to one at any
given time.
Activating the Inflator Definition
Inflation does occur unless the inflation definition is activated in an
analysis step.
Relating Inflation Time to Analysis Time
Inflator property definition consists of specifying tables of gas variables
versus inflation time. In
Abaqus/Explicit
the inflation time, ,
is related to the value of an amplitude curve
by
Typically the amplitude variation is a step function stepping from zero to
one at the time the airbag should be deployed. This amplitude variation has the
effect of offsetting the inflation time from the analysis time.
Modifying the Mass Flow Rate
If the mass flow rate is prescribed directly in the inflator property
definition, you can modify it by specifying an amplitude definition during a
step. However, if the mass flow rate is calculated by using tank test data or
the dual pressure method, the amplitude definition will be ignored.
Activation in Multiple Steps
By default, when you modify the activation of a fluid inflator definition or
activate a new fluid inflator definition, all existing fluid inflator
activations in the step remain. When modifying an existing activation, all
applicable parameters must be respecified.
Activated inflator definitions remain active in subsequent steps unless
deactivated. You can choose to deactivate all fluid inflator definitions in the
model and optionally reactivate new ones. If you deactivate any fluid inflator
definition in a step, all fluid inflator definitions must be respecified.
References
Wang, J.T., and O. J. Nefske, “A
New CAL3D Airbag Inflation Model,” SAE paper
880654, 1988.