/EOS/NOBLE-ABEL

Block Format Keyword Describes the co-volume equation of state P ( v b ) = R T .

Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/EOS/NOBLE-ABEL/mat_ID/unit_ID
eos_title
b γ E0 Psh 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)

 
b Co-volume.

(Real)

[ m 3 k g ]
γ Heat Capacity ratio γ = C p C v .

(Real)

 
E0 Initial internal energy per unit reference volume.

(Real)

[ J m 3 ]
Psh Pressure shift.

(Real)

[ Pa ]
ρ 0 Reference density.

Default = material density (Real)

[ k g m 3 ]

Example (Noble-Abel)

#---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/HYDPLA/7
NOBLE_ABEL
#              RHO_I               RHO_0
             1.22e-6                   0
#                  E                  nu
                   0                   0
#                  a                   b                   n             eps_max           sigma_max
                1E30                   0                   0                   0                   0
#               Pmin                 Psh
                   0
/EOS/NOBLE-ABEL/7
NOBLE-ABEL EOS 
#                  b               GAMMA                  E0                 PSH                RHO0          
                1E-3                 1.4        0.2499999997                   0             1.22e-6
/ALE/MAT/7

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

Comments

  1. A generalization of the ideal-gas thermal EOS, P v = R T is the co-volume equation of state P ( v b ) = R T
    Where,
    v
    Specific volume
    b
    Covolume
    R
    Specific gas constant
    T
    Temperature

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

    Where,
    µ = ρ ρ 0 1
    E = E i n t V 0
    P ( μ , E ) = ( γ 1 ) ( 1 + μ ) E 1 b ρ 0 ( 1 + μ )

    with γ = C p C v

  2. This EOS applies to dense gases at high pressure for which the volume occupied by the molecules themselves is no longer negligible.
  3. Covolume b is usually in range [ 0.9 × 10 3 , 1.1 × 10 3 ] MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaqaaaaaaaaa Wdbmaadmaapaqaa8qacaaIWaGaaiOlaiaaiMdacqGHxdaTcaaIXaGa aGima8aadaahaaWcbeqaa8qacqGHsislcaaIZaaaaOGaaiilaiaaig dacaGGUaGaaGymaiabgEna0kaaigdacaaIWaWaaWbaaSqabeaacqGH sislcaaIZaaaaaGccaGLBbGaayzxaaaaaa@4890@ [ m 3 k g ]
  4. Some comparison with ideal gas EOS:
      IDEAL-GAS NOBLE-ABEL
    P ( v , T ) P v = R T P ( v b ) = R T
    P ( μ , E ) ( γ 1 ) ( 1 + μ ) E ( γ 1 ) ( 1 + μ ) E 1 b ρ 0 ( 1 + μ )
    Sound Speed

    c

    c = γ P ρ c = γ P ( 1 b ρ ) ρ
    E 0 = E ( 0 ) P 0 γ 1 P 0 ( 1 b ρ 0 ) γ 1
  5. 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)