Product: ABAQUS/Explicit
A surface-based fluid cavity:
can be used to model a liquid-filled or gas-filled structure;
is associated with a node known as the cavity reference node;
is defined by specifying a surface that fully encloses the cavity;
is applicable only for situations where the pressure and temperature of the fluid in a particular cavity are uniform at any point in time;
can be used to model an airbag using the assumptions of an ideal gas mixture under adiabatic conditions; and
has a name that can be used to identify history output associated with the cavity.
You must associate a name with each fluid cavity.
| Input File Usage: | *FLUID CAVITY, NAME=name |
Every fluid cavity must have an associated cavity reference node. Along with the fluid cavity name, the reference node is used to identify the fluid cavity. In addition, it may be referenced by fluid exchange and inflator definitions. The reference node should not be connected to any elements in the model.
| Input File Usage: | *FLUID CAVITY, REF NODE=n |
The fluid cavity must be completely enclosed by finite elements unless symmetry planes are modeled (see “Surface-based fluid cavities: overview,” Section 7.13.1). Surface elements can be used for portions of the cavity surface that are not structural. The boundary of the cavity is specified using an element-based surface covering the elements that surround the cavity with surface normals pointing inward.
| Input File Usage: | *FLUID CAVITY, SURFACE=surface_name |
An additional volume can be specified for a fluid cavity. The additional volume will be added to the actual volume when the boundary of the cavity is defined by a specified surface. If you do not specify a surface forming the boundary of the fluid cavity, the fluid cavity is assumed to have a fixed volume that is equal to the added volume.
| Input File Usage: | *FLUID CAVITY, ADDED VOLUME=r |
When the volume of a fluid cavity is extremely small, transients in an explicit dynamic procedure can cause the volume to go to zero or even negative causing the effective cavity stiffness values to tend to infinity. To avoid numerical problems, you can specify a minimum volume for the fluid. If the volume of the cavity (which is equal to the actual volume plus the added volume) drops below the minimum, the minimum value will be used to evaluate the fluid pressure.
| Input File Usage: | *FLUID CAVITY, MINIMUM VOLUME=r |
The fluid cavity behavior governs the relationship between cavity pressure, volume, and temperature. To define a fluid cavity behavior made of a single fluid, specify a single fluid behavior to define the fluid properties. You must associate the fluid behavior with a name. This name can then be used to associate a certain behavior with a fluid cavity definition.
| Input File Usage: | Use the following options: |
*FLUID CAVITY, NAME=fluid_cavity_name, BEHAVIOR=behavior_name *FLUID BEHAVIOR, NAME=behavior_name |
To define a fluid cavity behavior made of multiple gas species, specify multiple fluid behaviors to define the fluid properties. Specify the names of the fluid behaviors and the initial molar fractions defining the mixture to associate a certain group of behaviors with a fluid cavity definition.
| Input File Usage: | *FLUID BEHAVIOR, NAME=behavior_name *FLUID CAVITY, NAME=fluid_cavity_name, MIXTURE out-of-plane surface thickness (if required; otherwise, blank) behavior_name, initial molar fraction |
| Repeat the second data line as often as necessary to define the initial gas mixture. |
For pneumatic fluids the equilibrium problem is generally expressed in terms of the “gauge” pressure in the fluid cavity (that is, ambient atmospheric pressure does not contribute to the loading of the solid and structural parts of the system). You can choose to convert gauge pressure to absolute pressure 
as used in the constitutive law. For hydraulic fluids you can define the ambient pressure, which can be used to calculate the pressure difference in the fluid exchange between a fluid cavity and its environment. The pressure value given as degree of freedom 8 at the cavity reference node is the value of the gauge pressure. The ambient pressure, 
, is assumed to be zero if you do not specify it.
| Input File Usage: | *FLUID CAVITY, AMBIENT PRESSURE= |
For hydraulic fluids and pneumatic fluids in problems of long time duration, it is reasonable to assume that the temperature is constant or a known function of the environment surrounding the cavity. In this case the temperature of the fluid can be defined by specifying initial conditions (see “Defining initial temperatures” in “Initial conditions,” Section 19.2.1) and predefined temperature fields (see “Predefined temperature” in “Predefined fields,” Section 19.6.1) at the cavity reference node. For a pneumatic fluid the pressure and density of the gas are calculated from the ideal gas law, conservation of mass, and the predefined temperature field.
The hydraulic fluid model is used to model nearly incompressible fluid behavior. Compressibility is introduced by assuming a linear pressure-volume relationship. The required behavior parameters are the bulk modulus and the reference density. Temperature dependence of the density can be modeled as a thermal expansion of the fluid.
| Input File Usage: | *FLUID CAVITY, BEHAVIOR=behavior_name |
The reference fluid density, 
, is specified at zero pressure and the initial temperature, 
:
| Input File Usage: | *FLUID DENSITY |
The compressibility is described by the bulk modulus of the fluid:
is the current pressure,
is the current temperature,
is the fluid bulk modulus,
is the current fluid volume,
is the density at current pressure and temperature,
is the fluid volume at zero pressure and current temperature,
is the fluid volume at zero pressure and initial temperature, and
is the density at zero pressure and current temperature.
It is assumed that the bulk modulus is independent of the change in fluid density. However, the bulk modulus can be specified as a function of temperature or predefined field variables.
| Input File Usage: | *FLUID BULK MODULUS |
The thermal expansion coefficients are interpreted as total expansion coefficients from a reference temperature, which can be specified as a function of temperature or predefined field variables. The change in fluid volume due to thermal expansion is determined as follows:
is the reference temperature for the coefficient of thermal expansion and 
is the mean (secant) coefficient of thermal expansion.If the coefficient of thermal expansion is not a function of temperature or field variables, the value of is not needed.
Thermal expansion can also be expressed in terms of the fluid density:
| Input File Usage: | *FLUID EXPANSION, ZERO= |
Compressible or pneumatic fluids are modeled as an ideal gas in ABAQUS/Explicit (see “Equation of state,” Section 10.9.1). The equation of state for an ideal gas (or the ideal gas law) is given as
is defined as 
is the ambient pressure, is the gauge pressure, 
is the gas constant, is the current temperature, and 
is absolute zero on the temperature scale being used. The gas constant, , can also be determined from the universal gas constant, 
, and the molecular weight, 
, as follows:
is the mass of the fluid, 
is the mass flow rate into the fluid cavity, and 
is the mass flow rate out of the fluid cavity.By default, the fluid temperature is defined by the predefined temperature field at the cavity reference node. However, for rapid events the fluid temperature can be determined from the conservation of energy assumed in an adiabatic process. With this assumption, no heat is added or removed from the cavity except by transport through fluid exchange definitions or inflators. An adiabatic process is typically well suited for modeling the deployment of an airbag. During deployment, the gas jets out of the inflator at high pressure and cools as it expands at atmospheric pressure. The expansion is so quick that no significant amount of heat can diffuse out of the cavity.
The energy equation can be obtained from the first law of thermodynamics. By neglecting the kinetic and potential energy, the energy equation for a fluid cavity is given by
is the initial specific energy at the initial temperature , 
is the specific heat at constant volume (or the constant volume heat capacity), which depends only upon temperature for an ideal gas, 
is the specific enthalpy, and 
is the volume occupied by the gas. By definition, the specific enthalpy is 
is the initial specific enthalpy at the initial (or reference) temperature and 
is the specific heat at constant pressure, which depends only upon temperature for an ideal gas. The pressure, temperature, and density of the gas are obtained by solving the ideal gas law, the energy balance, and mass conservation.Adiabatic behavior will always be used for the fluid cavity if an adiabatic or coupled procedure is used.
| Input File Usage: | *FLUID CAVITY, ADIABATIC |
You must specify the value of the molecular weight of the ideal gas, .
| Input File Usage: | *MOLECULAR WEIGHT |
The heat capacity at constant pressure must be specified when modeling an adiabatic process for the ideal gas. It can be defined either in polynomial or tabular form. The polynomial form is based on the Shomate equation according to the National Institute of Standards and Technology. The constant pressure molar heat capacity can be expressed as
, 
, 
, 
, and 
are gas constants. These gas constants together with molecular weight are listed in Table 7.13.2–1 for some gases that are often used in airbag simulations. The constant pressure heat capacity can then be obtained by
, can be determined by
You can use the polynomial form for specifying the heat capacity at constant pressure, in which case you enter the coefficients , , , , and . Alternatively, you can define a table of constant pressure heat capacity versus temperature and any predefined field variables.
Table 7.13.2–1 Properties of some commonly used gases (SI units).
| Gas | MW | | | | | | |
|---|---|---|---|---|---|---|---|
| (× 10–3) | (× 10–6) | (× 10–9) | (× 106) | (Kelvin) | |||
| Air | 0.0289 | 28.110 | 1.967 | 4.802 | –1.966 | 0.0 | 273–1800 |
| Nitrogen | 0.028 | 26.092 | 8.218 | –1.976 | 0.1592 | 0.0444 | 298–6000 |
| Oxygen | 0.032 | 29.659 | 6.137 | –1.186 | 0.0957 | –0.219 | 298–6000 |
| Hydrogen | 0.00202 | 33.066 | –11.36 | 11.432 | –2.772 | –0.158 | 273–1000 |
| Carbon monoxide | 0.028 | 25.567 | 6.096 | 4.054 | –2.671 | 0.131 | 298–1300 |
| Carbon dioxide | 0.044 | 24.997 | 55.186 | –33.691 | 7.948 | –0.136 | 298–1200 |
| Water vapor | 0.0180 | 32.240 | 1.923 | 0.105 | –3.595 | 0.0 | 273–1800 |
| Input File Usage: | Use the following option to specify the heat capacity in polynomial form: |
*CAPACITY, TYPE=POLYNOMIAL Use the following option to specify the heat capacity in tabular form: *CAPACITY, TYPE=TABULAR, DEPENDENCIES=n |
You can specify the value of the universal gas constant, .
| Input File Usage: | *PHYSICAL CONSTANTS, UNIVERSAL GAS CONSTANT= |
You can specify the value of absolute zero temperature, .
| Input File Usage: | *PHYSICAL CONSTANTS, ABSOLUTE ZERO= |
ABAQUS/Explicit can model a mixture of ideal gases in the fluid cavity. For ideal gas mixtures the Amagat-Leduc rule of partial volumes is used to obtain an estimate of the molar-averaged thermal properties (Van Wylen and Sonntag, 1985). Let each species have constant pressure and volume heat capacities, 
and 
; molecular weight, 
; and mass fraction, 
. The constant pressure and volume heat capacities for the mixed gas are then given by
If the output of the state of the fluid inside the cavity is requested for a node set that contains more than one fluid cavity, the averaged properties of the multiple fluid cavities will also be output automatically. The average pressure is calculated by volume weighting cavity pressure contributions. The average temperature for an adiabatic ideal gas is obtained by mass weighting cavity temperature contributions. Let each fluid cavity have pressure 
, temperature 
, volume 
, gas constant 
, and mass 
. The average pressure of the fluid cavity cluster is then defined as
