/MAT/LAW37 (BIPHAS)

Block Format Keyword Describes the hydrodynamic bi-material liquid gas material. It is not recommended to use multi-material laws with Radioss single precision engine.

Format

(1)	(3)	(5)	(7)	(9)
/MAT/LAW37/`mat_ID`/`unit_ID` or /MAT/BIPHAS/`mat_ID`/`unit_ID`
`mat_title`
`P`_sh
$ρ_{0}^{l}$ $ρ_{0}^{l}$	$C_{l}$ $C_{l}$	$α_{l}$ $α_{l}$	$ν_{l}$ $ν_{l}$	$ν_{v o l _ l}$ $ν_{v o l _ l}$
$ρ_{0}^{g}$ $ρ_{0}^{g}$	$γ$ $γ$	$P_{0}$ $P_{0}$	$ν_{g}$ $ν_{g}$	$ν_{v o l _ g}$ $ν_{v o l _ g}$

Definition

Field	Contents	SI Unit Example
`mat_ID`	Material identifier. (Integer, maximum 10 digits)
`unit_ID`	Unit Identifier (Integer, maximum 10 digits)
`mat_title`	Material title. (Character, maximum 100 characters)
`P`_sh	Pressure shift. 5 Default: $P_{s h} = - P_{0}$ $P_{s h} = - P_{0}$ (Real)	$[Pa]$ $[Pa]$
$ρ_{0}^{l}$ $ρ_{0}^{l}$	Liquid reference density. (Real)	$[\frac{kg}{m^{3}}]$ $[\frac{kg}{m^{3}}]$
$C_{l}$ $C_{l}$	Liquid bulk modulus. (Real)	$[Pa]$ $[Pa]$
$α_{l}$ $α_{l}$	Initial mass fraction liquid proportion. = 0.0 Gas = 1.0 Liquid (Real)
$ν_{l}$ $ν_{l}$	Shear kinematic viscosity ( $= μ / ρ_{0}^{l}$ $= μ / ρ_{0}^{l}$ ). (Real)	$[\frac{m^{2}}{s}]$ $[\frac{m^{2}}{s}]$
$ν_{v o l _ l}$ $ν_{v o l _ l}$	Volumetric viscosity (kinematic) for liquid: $= \frac{3 λ + 2 μ}{ρ}$ $= \frac{3 λ + 2 μ}{ρ}$ Default = 0: Stokes Hypothesis ( $3 λ + 2 μ = 0$ $3 λ + 2 μ = 0$ ) (Real)	$[\frac{m^{2}}{s}]$ $[\frac{m^{2}}{s}]$
$ρ_{0}^{g}$ $ρ_{0}^{g}$	Reference gas density. (Real)	$[\frac{kg}{m^{3}}]$ $[\frac{kg}{m^{3}}]$
$γ$ $γ$	Perfect gas constant. (Real)
$P_{0}$ $P_{0}$	Reference gas initial pressure. (Real)	$[Pa]$ $[Pa]$
$ν_{g}$ $ν_{g}$	Shear kinematic viscosity = $= μ / ρ_{0}^{g}$ $= μ / ρ_{0}^{g}$ . (Real)	$[\frac{m^{2}}{s}]$ $[\frac{m^{2}}{s}]$
$ν_{v o l _ g}$ $ν_{v o l _ g}$	Volumetric viscosity (kinematic) for gas: $= \frac{3 λ + 2 μ}{ρ}$ $= \frac{3 λ + 2 μ}{ρ}$ Default = 0: Stokes Hypothesis ( $3 λ + 2 μ = 0$ $3 λ + 2 μ = 0$ ). (Real)	$[\frac{m^{2}}{s}]$ $[\frac{m^{2}}{s}]$

▸Example

#RADIOSS STARTER
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#-  1. MATERIALS:
#---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/LAW37/1/1
air (unit g_mm_ms)
#                Psh
                   0
#             RHO_l0                 C_l             ALPHA_l                NU_l            NU_VOL_l
                .001                2089                   0            1.787e-3                   0
#             RHO_G0               GAMMA                  P0                NU_g            NU_VOL_g
             1.22E-6                 1.4                  .1             1.48e-2                   
/ALE/MAT/1
#     Modif. factor.
                   0
/MAT/LAW37/2/1
water (unit g_mm_ms)
#                Psh
                   0
#             RHO_l0                 C_l             ALPHA_l                NU_l            NU_VOL_l
                .001                2089                   1            1.787e-3                   0
#             RHO_G0               GAMMA                  P0                NU_g            NU_VOL_g
             1.22E-6                 1.4                  .1             1.48e-2                   
/ALE/MAT/2
#     Modif. factor.
                   0
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|
#enddata
#---1----|----2----|----3----|----4----|----5----|----6----|----7----|----8----|----9----|---10----|

Comments

For each cycle equilibrium is computed between liquid and gas: $Δ P_{l} = Δ P_{g}$ $Δ P_{l} = Δ P_{g}$
Liquid EOS:(1)
$P_{l} = P_{0} + C_{l} μ$ $P_{l} = P_{0} + C_{l} μ$

with bulk modulus $C_{l} = ρ_{0}^{l} {(c_{0}^{l})}^{2}$ $C_{l} = ρ_{0}^{l} {(c_{0}^{l})}^{2}$

Where,

$ρ_{0}^{l}$ $ρ_{0}^{l}$

Initial liquid density

$c_{0}^{l}$ $c_{0}^{l}$

Initial sound speed

Gas EOS:(2)
$P v^{γ} = P_{0} v_{0}^{γ} = c o n s t a n t$ $P v^{γ} = P_{0} v_{0}^{γ} = c o n s t a n t$

Where,

P

Pressure

$v = \frac{V}{V_{0}}$ $v = \frac{V}{V_{0}}$

Specific volume

Stress Tension(3)
$σ = P + τ$ $σ = P + τ$
(4)
$τ_{i j} = λ {\dot{ε}}_{k k} δ_{i j} + 2 μ {\dot{ε}}_{i j}$ $τ_{i j} = λ {\dot{ε}}_{k k} δ_{i j} + 2 μ {\dot{ε}}_{i j}$

Where,

$σ$ $σ$

Stress tension

$P$ $P$

Spherical stress tension

$τ$ $τ$

Viscous stress tension

$λ$ $λ$

Shear viscosity (kinematic)

$μ$ $μ$

Dilatation viscosity (kinematic)
Multi-material LAW51 (/MAT/MULTIMAT) can emulate LAW37.
Anti-diffusive technique using MUSCL method is under implementation. It is already available for LAW51 (/ALE/MUSCL).
If inlet/outlet are needed LAW51 must be used instead. LAW51 has multi- material inlet/outlet formulations.
In Animation files:
/ANIM/ELEM/DENS37 enables to output submaterial densities.

/ANIM/BRIC/VFRAC allows to output volumetric fractions for each submaterial.

Refer to Time Histories in the Radioss Starter Input Manual, or to /ANIM/Eltyp/Restype in the Radioss Engine Input Manual.

By Default

P_{s h} = - P_{0}

$P_{s h} = - P_{0}$ . This means that computed pressure is shifted so that at initial time output pressure value relative to

P_{0}

$P_{0}$ value is 0.0.

To use total pressure, P_sh must be nullify using a small value such as -1e-20 Pressure P could be exported in animation with /ANIM/ELEM/P.

	Relative Pressure `P`_sh=-`P`₀ (Default)	Total Pressure `P`_sh = -1e-20
Initial Condition:	$P = Δ P = 0$ $P = Δ P = 0$	$P = P_{0}$ $P = P_{0}$
Expansion:	$P = Δ P < 0$ $P = Δ P < 0$	$P < P_{0}$ $P < P_{0}$
Compression:	$P = Δ P > 0$ $P = Δ P > 0$	$P > P_{0}$ $P > P_{0}$

Internal Energy is not computed with LAW37. Nevertheless, adiabatic condition $d E = - P \cdot d V$ $d E = - P \cdot d V$ is used through polytropic process equation:
(5)
$P V^{γ} = c o n s t .$ $P V^{γ} = c o n s t .$
LAW37 is not compatible with elementary boundary conditions (/EBCS).