### 20.4.1 Hydrostatic fluid models

Products: ABAQUS/Standard  ABAQUS/Explicit

### Overview

The hydrostatic fluid models:

• are used to model fluid-filled cavities;

• can be used in ABAQUS/Standard to model incompressible (hydraulic) fluids, compressible (pneumatic) fluids, or user-defined fluids;

• can be used in ABAQUS/Explicit to model only compressible (pneumatic) fluids;

• do not take the inertia of the fluid into account; and

• do not require a material definition.

### Hydraulic (incompressible) fluids

The hydraulic fluid model is used to model incompressible or nearly incompressible fluid behavior in ABAQUS/Standard. By default, the fluid is considered to be incompressible; the density is independent of the pressure but may depend on the temperature. Compressibility of a hydraulic fluid can be introduced, as described below. In both cases you define the density at the reference temperature and its temperature dependence as described below.

 Input File Usage: `*FLUID PROPERTY, TYPE=HYDRAULIC`

#### Defining the reference fluid density

The reference fluid density, , is specified at zero pressure and the initial temperature:

It is used to convert mass fluxes, as defined using a fluid flux load (Modeling fluid-filled cavities, Section 11.5.1) or in the fluid link elements (Fluid link elements, Section 26.8.3), to volume fluxes. Hence, the density can be given in arbitrary units, as long as the same units are used in the fluid flux load or fluid link element definition.

 Input File Usage: `*FLUID DENSITY`

#### Defining the compressibility

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

where

K

is the fluid bulk modulus,

p

is the fluid pressure,

is the current temperature,

is the initial temperature,

is the current fluid volume,

is the fluid volume at zero pressure and current temperature,

is the fluid volume at zero pressure and initial temperature,

is the current fluid density,

is the density at zero pressure and current temperature, and

is the reference fluid density.

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`

#### Defining the fluid expansion

The thermal expansion coefficients are interpreted as total expansion coefficients from a reference temperature. The change in fluid volume due to thermal expansion is determined as follows:

where

is the fluid volume at zero pressure and temperature ,

is the fluid volume at zero pressure and initial temperature ,

is the reference temperature for the coefficient of thermal expansion,

is the mean coefficient of thermal expansion,

are the current values of the predefined field variables, and

are the initial values of the predefined field variables given as initial conditions.

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:

where is the fluid density at zero pressure and temperature and is the reference fluid density.

 Input File Usage: `*FLUID EXPANSION`

### Pneumatic (compressible) fluids

Compressible or pneumatic fluids are modeled as an ideal gas satisfying the law

where

is the fluid density,

is the total fluid pressure,

is the temperature,

is the absolute zero on the temperature scale being used, and

C

is a constant.

The hydrostatic fluid model is applicable only for situations where the pressure and temperature of the fluid in a particular cavity can be assumed to be uniform at any point in time. For cases where a spatially varied pressure and temperature is required, ABAQUS/Explicit provides an ideal gas equation of state model (Equation of state, Section 17.9.1).

 Input File Usage: In ABAQUS/Standard use the following option: `*FLUID PROPERTY, TYPE=PNEUMATIC`In ABAQUS/Explicit use the following option:`*FLUID PROPERTY`

#### Defining the reference fluid density

The reference fluid density, , is specified at a reference gauge pressure and temperature:

It is used to convert mass fluxes, as defined using a fluid flux load (Modeling fluid-filled cavities, Section 11.5.1) or in the fluid link elements (Fluid link elements, Section 26.8.3), to volume fluxes. Hence, the density can be given in arbitrary units, as long as the same units are used in the fluid flux load or fluid link element definition. However, you must ensure that the density defined at the specified reference pressure and temperature is consistent with the gas law.

The reference gauge pressure and temperature are assumed to be zero unless you specify these values when you define the reference fluid density.

 Input File Usage: `*FLUID DENSITY, PRESSURE=, TEMPERATURE=`

#### Specifying the value of absolute zero

You can specify the value of absolute zero as a physical constant.

 Input File Usage: `*PHYSICAL CONSTANTS, ABSOLUTE ZERO=`

#### Converting gauge pressure to total pressure

Since the equilibrium problem is generally expressed in terms of the “gauge” pressure in the fluid cavity (that is, ambient atmospheric pressure is ignored as a loading of the solid parts of the system), you can specify an ambient pressure to convert gauge pressure to total pressure, , used in the ideal gas law. 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 a value for it. Temperature variations are not permitted in ABAQUS/Explicit.

 Input File Usage: `*FLUID PROPERTY, AMBIENT=`

### User-defined fluids

In ABAQUS/Standard the fluid density and the fluid compliance for user-defined fluids are defined in user subroutine UFLUID.

 Input File Usage: `*FLUID PROPERTY, TYPE=USER`

### Elements

The hydrostatic fluid models can be used only with hydrostatic fluid elements (Hydrostatic fluid elements, Section 26.8.1).