Fluid Cavity Definition

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.

FLUID CAVITY, REF NODE=n

Interaction module: Create Interaction: Fluid cavity: select the fluid cavity reference node

The fluid cavity must be completely enclosed by finite elements unless symmetry planes are modeled (see About Surface-Based Fluid Cavities). 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. By default, an error message is issued if the underlying elements of the surface do not have consistent normals. Alternatively, you can skip the consistency checking for the surface normals.

FLUID CAVITY, SURFACE=surface_name, CHECK NORMALS=YES

FLUID CAVITY, SURFACE=surface_name, CHECK NORMALS=NO

Interaction module: Create Interaction: Fluid cavity: select the fluid cavity boundary surface; toggle on or off Check surface normals

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. In Abaqus/Standard, along with the added volume, the surface forming the boundary of the fluid cavity must be specified.

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 in Abaqus/Explicit. If the volume of the cavity (which is equal to the actual volume plus the added volume) drops below the minimum, the minimum value is used to evaluate the fluid pressure.

You can specify the minimum volume either directly or as the initial volume of the fluid cavity. If the latter method is used and the initial volume of the fluid cavity is a negative value, the minimum volume is set equal to zero.

FLUID CAVITY, MINIMUM VOLUME=minimum volume

FLUID CAVITY, MINIMUM VOLUME=INITIAL VOLUME

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.

FLUID CAVITY, NAME=fluid_cavity_name, BEHAVIOR=behavior_name
FLUID BEHAVIOR, NAME=behavior_name

Interaction module: Create Interaction Property: Fluid cavity, Name: behavior_name

In Abaqus/Explicit you can define a fluid cavity behavior made of multiple gas species. To define a fluid cavity behavior made of multiple gas species, you specify multiple fluid behaviors to define the fluid properties. Specify the names of the fluid behaviors and the initial mass or molar fractions defining the mixture to associate a certain group of behaviors with a fluid cavity definition.

FLUID BEHAVIOR, NAME=behavior_name
FLUID CAVITY, NAME=fluid_cavity_name, MIXTURE=MASS FRACTION
out-of-plane surface thickness (if required; otherwise, blank)
behavior_name, initial mass fraction
...

FLUID BEHAVIOR, NAME=behavior_name
FLUID CAVITY, NAME=fluid_cavity_name, MIXTURE=MOLAR FRACTION
out-of-plane surface thickness (if required; otherwise, blank)
behavior_name, initial molar fraction
...

In Abaqus/Standard the fluid behavior can be defined in user subroutine UFLUID.

FLUID BEHAVIOR, USER

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) and predefined temperature fields (see Predefined Temperature) 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 reference fluid density, ${\rho }_R$, is specified at zero pressure and the initial temperature, ${\theta }_I$:

FLUID DENSITY

Interaction module: Create Interaction Property: Fluid cavity: Definition: Hydraulic: Fluid density: density 

The compressibility is described by the bulk modulus of the fluid:

where

p

is the current pressure,

$\theta$

is the current temperature,

K

is the fluid bulk modulus,

$V\left(p,\theta \right)$

is the current fluid volume,

$\rho \left(p,\theta \right)$

is the density at current pressure and temperature,

$V_0\left(\theta \right)$

is the fluid volume at zero pressure and current temperature,

$V_0\left({\theta }_I\right)$

is the fluid volume at zero pressure and initial temperature, and

${\rho }_0\left(\theta \right)$

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.

FLUID BULK MODULUS

Interaction module: Create Interaction Property: Fluid cavity: Definition: Hydraulic: Fluid Bulk Modulus tabbed page: toggle on Specify fluid bulk modulus, and enter the modulus value in the table

Toggle on Use temperature-dependent data, Number of field variables: n

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:

where ${\theta }_0$ is the reference temperature for the coefficient of thermal expansion and $\alpha \left(\theta \right)$ 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 ${\theta }_0$ is not needed.

Thermal expansion can also be expressed in terms of the fluid density:

FLUID EXPANSION, ZERO=${\theta }_0$

Interaction module: Create Interaction Property: Fluid cavity: Definition: Hydraulic: Fluid Expansion tabbed page: toggle on Specify fluid thermal expansion coefficients, and enter the mean coefficient of thermal expansion in the table

Toggle on Use temperature-dependent data, Reference temperature: ${\theta }_0$, Number of field variables: n

You must specify the value of the molecular weight of the ideal gas, $MW$.

MOLECULAR WEIGHT
$MW$

Interaction module: Create Interaction Property: Fluid cavity: Definition: Pneumatic, Ideal gas molecular weight: $MW$

You can specify the value of the universal gas constant, $\tilde{R}$.

PHYSICAL CONSTANTS, UNIVERSAL GAS CONSTANT=$\tilde{R}$

All modules: ModelEdit attributesmodel name: Physical Constants: toggle on Universal gas constant: $\tilde{R}$

You can specify the value of absolute zero temperature, ${\theta }^Z$.

PHYSICAL CONSTANTS, ABSOLUTE ZERO=${\theta }^Z$

All modules: ModelEdit attributesmodel name: Physical Constants: toggle on Absolute zero temperature: ${\theta }^Z$

By default, the fluid temperature is defined by the predefined temperature field at the cavity reference node. However, for rapid events the fluid temperature in Abaqus/Explicit 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

where the work done by the fluid cavity expansion is given as

and $\dot{Q}$ is the heat energy flow rate due to the heat transfer through the surface of the fluid cavity. A positive value for $\dot{Q}$ will generate the heat energy flow out of the primary fluid cavity. The specific energy is given by

where $E_I$ is the initial specific energy at the initial temperature ${\theta }_I$, $c_v$ is the specific heat at constant volume (or the constant volume heat capacity), which depends only upon temperature for an ideal gas, $H$ is the specific enthalpy, and V is the volume occupied by the gas. By definition, the specific enthalpy is

where $H_I$ is the initial specific enthalpy at the initial (or reference) temperature ${\theta }_I$ and $c_p$ 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.

FLUID CAVITY,  ADIABATIC

Interaction module: Create Interaction: Fluid cavity: Property definition: Pneumatic, toggle on Use adiabatic behavior

You must define the heat capacity at constant pressure 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

where the coefficients $\tilde{a}$, $\tilde{b}$, $\tilde{c}$, $\tilde{d}$, and $\tilde{e}$ are gas constants. These gas constants together with molecular weight are listed in Table 1 for some gases that are often used in airbag simulations. The constant pressure heat capacity can then be obtained by

The constant volume heat capacity, $c_v$, 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 $\tilde{a}$, $\tilde{b}$, $\tilde{c}$, $\tilde{d}$, and $\tilde{e}$. Alternatively, you can define a table of constant pressure heat capacity versus temperature and any predefined field variables.

CAPACITY, TYPE=POLYNOMIAL
$\tilde{a}$, $\tilde{b}$, $\tilde{c}$, $\tilde{d}$, $\tilde{e}$

CAPACITY, TYPE=TABULAR, DEPENDENCIES=n
${\tilde{c}}_p$, temperature, field_variable_1, etc...
...

Interaction module: Create Interaction Property: Fluid cavity: Definition: Pneumatic, toggle on Specify molar heat capacity: Polynomial, Polynomial Coefficients: $\tilde{a}$, $\tilde{b}$, $\tilde{c}$, $\tilde{d}$, $\tilde{e}$

Interaction module: Create Interaction Property: Fluid cavity: Definition: Pneumatic: toggle on Specify molar heat capacity: Tabular: enter the molar heat capacity

Toggle on Use temperature-dependent data, Number of field variables: n