Fluid material models define constitutive relations for fluids used in structural analyses. These models are available for hydrostatic fluid elements, HSFLD241 and HSFLD242.
For more details on the fluid material models presented here, see Fluids in the Material Reference.
Liquid material can be used to model a compressible linear (Newtonian) isotropic elastic non-viscous fluid. Using the stress-strain relationship for linear elastic material as given in Structural Fundamentals, the constitutive equation for liquid can be written as:
 | (4–375) |
with
 | (4–376) |
 | (4–377) |
where:
| K = bulk modulus |
| εvolf = volumetric strain for fluid |
| ΔVf = change in fluid volume |
| V0f = initial fluid volume |
| P = current fluid pressure |
| P0 = initial fluid pressure (use the IC command) |
The thermal properties of liquid material are defined by coefficient of linear thermal expansion, which determines the change of fluid volume due to change of temperature:
 | (4–378) |
where:
| α = coefficient of linear thermal expansion |
| T = current fluid temperature |
| Tref = reference temperature (use TREF or MP command) |
Initial fluid density (needed when prescribing fluid mass flow
rate) can be specified using the TBcommand with Lab = FLUID and TBOPT =
LIQUID.
Change in fluid volume also affects fluid density. If fluid mass is kept fixed, current density for liquid material can defined as:
 | (4–379) |
where:
| ρ0f = initial fluid density |
This material model is defined through theTB command with
Lab = FLUID and
TBOPT = LIQUID; in addition, use
the TBDATA command to define the bulk modulus, K,
coefficient of linear thermal
expansion, α, and initial fluid density,
ρ0f, as material constants C1,
C2, and C3, respectively.
The Ideal Gas Law is written as:
 | (4–380) |
where:
| ρ = density |
| P = pressure |
| R = universal gas constant |
| T = temperature |
The Ideal Gas Law is used to define the constitutive equation for gas material:
 | (4–381) |
where:
| m = mass of fluid |
| R = universal gas constant |
| Tt = Toff + T = total fluid temperature |
| Toff = temperature offset from absolute zero to zero (use TOFFST command) |
| Pt = Pref + P = total fluid pressure |
| Pref = reference fluid pressure (specified as a real constant PREF) |
Current density for gas material is defined in terms of initial density as:
 | (4–382) |
where:
| T0t = Toff + Tref = initial total temperature |
| Tref = reference temperature (use TREF or MP command) |
| P0t = Pref + P0 = initial total fluid pressure |
To define a gas material, use theTB command
with Lab = FLUID, TBOPT = GAS, and initial fluid density, ρ0f, as material constant C1 on the TBDATA command.
To completely define the initial state of the gas material, also specify
a reference pressure, Pref, as a real constant
(use the R command) for the hydrostatic fluid element,
a temperature offset from absolute zero to zero temperature, Toff, (use the TOFFST command), and
a reference temperature, Tref (use the TREF or MP command).
For compressible fluids that do not follow the constitutive equation for liquid or Ideal Gas Law, a pressure-volume curve may be used to define a pressure-volume relationship.
Current fluid density for this material model can be defined as:
 | (4–383) |
where the current fluid volume is given by the pressure-volume curves based on the current fluid pressure and temperature.
A pressure-volume curve can be defined through the TB command with Lab = FLUID
and TBOPT = PVDATA, along with the TBTEMP command to define temperature, and the TBPT command to define pressure-volume data points for
each temperature. The pressure-volume data points must be defined
in terms of total pressure and total volume of the fluid in the containing
vessel.