/EOS/LSZK

Block Format Keyword Describes the Landau-Stanyukovich-Zeldovich-Kompaneets EOS for detonation products.

Format

(1)	(3)	(5)	(7)	(9)
/EOS/LSZK/`mat_ID`/`unit_ID`
`eos_title`
$γ$	`P`₀	`P`_sh	`A`	`b`
$ρ_{0}$

Definitions

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)	$[Pa]$
`A`	EOS parameter. (Real)	$[Pa]$
`b`	EOS parameter. (Real)
$ρ_{0}$	Reference density. Default = material density (Real)	$[\frac{kg}{m^{3}}]$

Example (Gas)

#---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/7/1
IDEAL-GAS
#              RHO_I               RHO_0
             1.22e-3             1.22e-3
#                  E                  nu
                   0                   0
#                  a                   b                   n             eps_max           sigma_max
                1E30                   0                   0                   0                   0
#               Pmin
                   0
/EOS/LSZK/7/1
det products   
#              GAMMA                  P0                 PSH                   A                   B      
                2.71                1.00                   0                  10                 2.5
#               RHO0
             1.22e-3
/ALE/MAT/7

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

Comments

The Landau-Stanyukovich-Zeldovich-Kompaneets EOS ¹ for detonation products is:(1)
$P (ρ, e) = (γ - 1) ρ e + a ρ^{b}$

Where,

$ρ$

Density

e

Internal energy density by mass

b

Material parameters

(2)
$μ = \frac{ρ}{ρ_{0}} - 1 = \frac{V_{0}}{V} - 1$

This leads to:(3)
$P (μ, E) = (γ - 1) (1 + μ) E + A {(1 + μ)}^{b}$

Which is the form used by Radioss where,(4)
$A = a ρ_{0}^{b}$

Where,

E

Internal energy by initial volume

A and b

Material parameters
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)

¹ Needham, Charles E. Blast Waves. Springer, 2003

² Lutzky, Morton. The Flow Field Behind a Spherical Detonation in TNT Using the Landau-Stanyukovich Equation of State for Detonation Products. No. NOLTR-64-40. Naval Ordance Lab White Oak, MD, 1964