/EOS/IDEAL-GAS or /EOS/IDEAL-GAS-VE

Format

(1)	(3)	(5)	(7)	(9)
/EOS/IDEAL-GAS/`mat_ID`/`unit_ID` or /EOS/IDEAL-GAS-VE/`mat_ID`/`unit_ID`
`eos_title`
$γ$	`P`₀	`P`_sh	`T`₀	$ρ_{0}$

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier. (Integer, maximum 10 digits)
`eos_title`	EOS title. (Character, maximum 100 characters)
$γ$	Heat capacity ratio $γ = \frac{C_{p}}{C_{v}}$ . (Real)
`P`₀	Initial pressure. (Real)	$[Pa]$
`P`_sh	Pressure shift. (Real)	$[Pa]$
`T`₀	Initial temperature. (Real)	$[K]$
$ρ_{0}$	Reference density. Default = material density (Real)	$[\frac{kg}{m^{3}}]$

Example (Air)

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/UNIT/1
unit for mat
                   g                  mm                  ms
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
/MAT/HYDRO/7/1
AIR
#              RHO_I               RHO_0
             1.22e-6                   0 
#                Knu                Pmin
              1.5E-2                   0
/EOS/IDEAL-GAS/7/1
EoS for Air at atmospheric pressure
#              GAMMA                  P0                 PSH                  T0                RHO0
                 1.4                0.10                   0               300.0             1.22E-6  
/ALE/MAT/7

#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata

Comments

Ideal-gas thermal EOS is:(1)
$P v = R T$

Where,

$v$

Specific volume

$R$

Specific gas constant

$T$

Temperature

Previous form of $P = P (v, T)$ can be written in the $P = P (μ, E)$ form.

Where,(2)
$µ = \frac{ρ}{ρ_{0}} - 1$
(3)
$E = \frac{E_{i n t}}{V_{0}}$
(4)
$P (μ, E) = (γ - 1) (1 + μ) E$

with (5)
$γ = \frac{C_{p}}{C_{v}}$

Where, $C_{p}$ and $C_{v}$ are constant parameters.

Consequently, the same equation of state can be built using /EOS/IDEAL-GAS-VT (Volume Temperature) defining the special case of a constant function:(6)
$C_{p} (T) = \frac{γ r}{γ - 1}$
Some characteristics of this equation of state:

Ideal Gas

$P (v, T)$

$P v = R T$

$P (μ, E)$

$(γ - 1) (1 + µ) E$

Sounce speed $c$

$c = \sqrt{\frac{γ P}{ρ}}$

$E_{0} = E (0)$

$\frac{P_{0}}{γ - 1}$
For this equation of state, $γ$ , $C_{p}$ and $C_{v}$ are constant parameters.
In other cases, /EOS/IDEAL-GAS-VT (Volume Temperature) must be used.

The heat capacity $C_{v}$ is computed from the initial data:(7)
$C_{v} = \frac{E_{0}}{ρ_{0} T_{0}}$

This parameter enables the calculation of the gas temperature since (8)
$Δ e = C_{v} Δ T$

Where,

$e = \frac{E_{i n t}}{m}$

Specific energy by mass
Equations of state are used by Radioss to compute the hydrodynamic pressure and are compatible with the material laws:
- /MAT/LAW3 (HYDPLA)
- /MAT/LAW4 (HYD_JCOOK)
- /MAT/LAW6 (HYDRO or HYD_VISC)
- /MAT/LAW10 (DPRAG1)
- /MAT/LAW12 (3D_COMP)
- /MAT/LAW49 (STEINB)
- /MAT/LAW102 (DPRAG2)
- /MAT/LAW103 (HENSEL-SPITTEL)