/EOS/IDEAL-GAS-VT

Block Format Keyword Describes the equation of state for ideal gas (volume - temperature).

Describes the equation of state for ideal gas P=ρrT ; where, cp is temperature dependent and described with Janaf model: cp(T)=A0+A1T+A2T2+A3T3+A4T4 (SI: J.kg1.K1 )

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/IDEAL-GAS-VT/mat_ID/unit_ID
eos_title
r T0 P0 Psh
A0 A1 A2 A3 A4

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)

r Ideal gas constant.

(Real)

[J.kg1.K1]
T0 Initial temperature. If P0 not defined, refer to Comment 3.

(Real)

[K]
P0 Initial pressure. If T0 is not defined, refer to Comment 3.

(Real)

[Pa]
Psh Pressure shift.

(Real)

[Pa]
A0 Specific heat capacity parameter.

(Real)

[Jkg.K]
A1 Specific heat capacity parameter.

(Real)

[Jkg.K2]
A2 Specific heat capacity parameter.

(Real)

[Jkg.K3]
A3 Specific heat capacity parameter.

(Real)

[Jkg.K4]
A4 Specific heat capacity parameter.

(Real)

[Jkg.K5]

Example (Air)

Comments

  1. Ideal gas EOS is PV=RT
    Where,
    V
    Volume
    R
    Universal ideal gas constant (SI: J.kg1mol1 )
    T
    Temperature

    It can also be written Pv=rT or P=ρrT .

    Where,
    v
    Specific volume ( v=1/ρ )
    r
    Gas constant (SI: J.kg1K1 ), r=R/M ; where, M is molecular mass
  2. Alternative form of ideal gas is /EOS/IDEAL-GAS-VE (Volume Energy):
    P(μ,E)=(γ1)(1+μ)E
    Where,
    γ=cpcv
    Is constant
    µ=ρρ01
    E=EintV0
    In this case, equation of state /EOS/IDEAL-GAS-VT (Volume Temperature) is used when γ is not constant, which is why the cp(T) function is required. γ=cpcv=cpcpr , since cv=cpr .

    Consequently, when γ is constant, defining A0=cp=γrγ1 , and A1=A2=A3=A4=0 will provide the same equation of state as /EOS/IDEAL-GAS-VE formulation.

  3. If T0 is defined, then P0 is computed:
    P0=r.ρ0.T0

    Otherwise, if P0 is defined, then T0 is computed:

    T0=P0/r.ρ0

  4. The cp(T) function is provided with Janaf model:
    cp(T)=A0+A1T+A2T2+A3T3+A4T4

    (SI: J.kg1.K1 )

  5. Equations of state are used by Radioss to compute the hydrodynamic pressure and are compatible with the material laws: