# Iform = 5

Block Format Keyword This boundary can simulate liquid inlet conditions for multi-material ALE laws (formulation: Iform = 0, 1, 10, or 11).

The boundary sub-material state is calculated from a state at a stagnation point which is provided by the user. When using this feature, it is no longer necessary to use imposed velocity (/IMPVEL) where the velocity is computed by numerical scheme.

The user provides the stagnation where ${\alpha }_{stagnation}={\alpha }_{0}$ , ${\rho }_{stagnation}={\rho }_{0}$ , ${E}_{stagnation}={E}_{0}$ ( $E$ is optional) which corresponds to the state for which $\upsilon$ =0. From a linear EOS: ${P}_{0}={C}_{0}+{C}_{1}\mu$ ; thus ${P}_{stagnation}={C}_{0}$ .

At each cycle Radioss computes the liquid inlet state so that the Bernoulli theory is satisfied () using velocity at inlet face.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
/MAT/LAW51/mat_ID/unit_ID
mat_title
Blank Format
Iform
#Global Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
Scaletime PEXT
#Material1 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
${\alpha }_{0}^{\mathit{mat}\text{ }_1}$ ${\rho }_{0}^{\mathit{mat}\text{ }_1}$ ${E}_{0}^{mat\text{ }_\text{​}\text{ }1}$ fct_IDα1 fct_ID $\rho$ 1 fct_IDE1
${C}_{1}^{mat\text{ }_1}$
$\Delta {P}_{min}^{\mathit{mat}_1}$ ${C}_{0}^{mat\text{ }_1}$
#Material2 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
${\alpha }_{0}^{\mathit{mat}\text{ }_2}$ ${\rho }_{0}^{\mathit{mat}\text{ }_2}$ ${E}_{0}^{mat\text{ }_\text{​}\text{ }2}$ fct_IDα2 fct_ID $\rho$ 2 fct_IDE2
${C}_{1}^{mat\text{ }_2}$
$\Delta {P}_{min}^{\mathit{mat}_2}$ ${C}_{0}^{mat\text{ }_2}$
#Material3 Parameters
(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
${\alpha }_{0}^{\mathit{mat}\text{ }_3}$ ${\rho }_{0}^{\mathit{mat}\text{ }_3}$ ${E}_{0}^{mat\text{ }_\text{​}\text{ }3}$ fct_IDα3 fct_ID $\rho$ 3 fct_IDE3
${C}_{1}^{mat\text{ }_3}$
$\Delta {P}_{min}^{\mathit{mat}_3}$ ${C}_{0}^{mat\text{ }_3}$

## Definition

Field Contents SI Unit Example
mat_ID Material identifier.

(Integer, maximum 10 digits)

unit_ID Unit Identifier.

(Interger, maximum 10 digits)

mat_title Material title.

(Character, maximum 100 characters)

Iform Formulation flag.
= 5
Liquid Inlet (computed from data at stagnation point).

(Integer)

Scaletime Abscissa scale factor for input functions. 2

Default = 1 (Real)

PEXT External (ambient) pressure. 3

(Real)

$\left[\text{Pa}\right]$
${\alpha }_{0}^{\mathit{mat}\text{ }_i}$ Initial volumetric fraction. 4

(Real)

${\rho }_{0}^{\mathit{mat}\text{ }_i}$ Initial density at stagnation point. 1

(Real)

$\left[\frac{\text{kg}}{{\text{m}}^{\text{3}}}\right]$
${E}_{0}^{mat\text{ }_\text{​}\text{ }i}$ Initial energy at stagnation point. 5

(Real)

$\left[\frac{\text{J}}{{\text{m}}^{\text{3}}}\right]$
fct_IDαi (Optional) Volumetric fraction scaling function ${\text{f}}_{{\alpha }_{i}}\left(t\right)$ identifier. 6
= 0
${\alpha }^{ma{t}_{i}}\left(t\right)={\alpha }_{0}^{ma{t}_{i}}$
> 0
${\alpha }^{ma{t}_{i}}\left(t\right)={\alpha }_{0}^{ma{t}_{i}}\cdot {f}_{{\alpha }_{i}}\left(t\right)$

(Integer)

fct_ID $\rho$ i (Optional) Density fraction scaling function ${\text{f}}_{{\rho }_{i}}\left(t\right)$ identifier.
= 0
${\rho }^{ma{t}_{i}}\left(t\right)={\rho }_{0}^{ma{t}_{i}}$
> 0
${\rho }^{ma{t}_{i}}\left(t\right)={\rho }_{0}^{ma{t}_{i}}.{\text{f}}_{{\rho }_{i}}\left(t\right)$

(Integer)

fct_IDEi (Optional) Energy fraction scaling function ${\text{f}}_{{E}_{i}}\left(t\right)$ identifier.
= 0
${E}^{ma{t}_{i}}\left(t\right)={E}_{0}^{ma{t}_{i}}$
> 0
${E}^{ma{t}_{i}}\left(t\right)={E}_{0}^{ma{t}_{i}}\cdot {f}_{{E}_{i}}\left(t\right)$

(Integer)

${C}_{1}^{mat\text{ }_\text{​}\text{ }i}$ Coefficient for perfect gas EOS. 5

(Real)

$\left[\text{Pa}\right]$
$\Delta {P}_{min}^{\mathit{mat}_i}$ Hydrodynamic cavitation pressure. 6

Default = -10-30 (Real)

$\left[\text{Pa}\right]$
${C}_{0}^{mat\text{ }_\text{​}\text{ }i}$ Coefficient for perfect gas EOS. 5

(Real)

$\left[\text{Pa}\right]$

1. Provided gas state from stagnation point ${\rho }_{\mathit{stagnation}}, {P}_{\mathit{stagnation}}$ is used to compute liquid inlet state. Bernoulli theory is applied:(1)
${P}_{\mathit{stagnation}}={P}_{\mathit{in}}+\frac{{\rho }_{\mathit{in}}{v}_{\mathit{in}}^{2}}{2}$
This leads to sub-material state in inlet boundary element:(2)
${\rho }_{in}=\frac{{C}_{1}\cdot {\rho }_{stagnation}}{{C}_{1}+\frac{{\rho }_{stagnation}{v}_{in}{}^{2}}{2}\left(1+{C}_{d}\right)}$
Where, ${C}_{d}$ is an optional drop parameter.(3)
${P}_{in}={P}_{stagnation}-\frac{{\rho }_{stagnation}{v}_{in}{}^{2}}{2}\left(1+{C}_{d}\right)$
(4)
${\left(\rho e\right)}_{in}=\left(1-\frac{{\rho }_{in}}{{\rho }_{stagnation}}\right){P}_{in}+{E}_{stagnation}$
Then global material state is determined by computing a mean value:
Pressure
$\Delta {P}_{in}=\sum _{i}{\alpha }^{ma{t}_{i}}\left(t\right)\Delta {P}_{in}^{mat_i}$
Density
${\rho }_{in}=\sum _{i}{\alpha }^{ma{t}_{i}}\left(t\right){\rho }_{in}^{mat_i}$
Energy
${\left(\rho e\right)}_{in}=\sum _{i}{\alpha }^{ma{t}_{i}}\left(t\right){\text{E}}_{in}^{mat_i}$
2. The optional scaling functions can be used such to scale the volumetric, density or energy fractions.
3. Parameter PEXT enables you to take the ambient pressure into account in case you want to work with relative pressure $\Delta {P}_{min}^{mat_i}$ . This parameter is required by Radioss for correct energy integration at each cycle. Otherwise, numerical EOS solving is generally incorrect. It represents pressure which must be added to EOS calculation to obtain total (physical) pressure. It has no influence on pressure contour in animation files.

Examples using linear EOS:

Total pressure: $P={P}_{amb}+{C}_{1}\mu$ , and also PEXT = 0

Relative Pressure: $\Delta P={C}_{1}\mu$ , and also ${P}_{EXT}={P}_{amb}$

4. Volumetric fractions enable the sharing of elementary volume within the three different materials.

For each material, ${\alpha }_{0}^{\mathit{mat}_i}$ must be defined between 0 and 1.

Sum of initial volumetric fractions ${\sum }_{i=1}^{3}{\alpha }_{0}^{\mathit{mat}_i}$ must be equal to 1.

For automatic initial fraction of the volume, refer to /INIVOL.

5. Linear EOS is:(5)
$P\left(\mu , E\right)={C}_{0}+{C}_{1}\mu$
This provides flexibility, depending on whether pressure and energy are total or relative:(6)
$P\left(\mu , E\right)={C}_{0}+{C}_{1}\mu$

Where, ${C}_{0}={P}_{\mathit{amp}}, {C}_{1}={\rho }_{0}{c}_{0}^{2}$ and ${P}_{EXT}=0$ .

This leads to usual form from $P\left(\mu , E\right)={C}_{0}+{C}_{1}\mu$ .(7)
$\Delta P\left(\mu , E\right)={C}_{1}\mu$

Where ${C}_{1}={\rho }_{0}{c}_{0}^{2}$ and ${P}_{EXT}={P}_{amb}$ .

6. $\Delta {P}_{min}^{\mathit{mat}_i}$ flag is the minimum value for the computed pressure.

Since $P=\text{Δ}P+{P}_{EXT}$ , defining ${P}_{EXT}=0$ implies $\text{Δ}P=P$ and $\text{Δ}{P}_{\mathrm{min}}={P}_{\mathrm{min}}$ .

Fluid materials pressure must remain positive to avoid any tensile strength, then, ${P}_{min}=0$ leads to $\text{Δ}{P}_{min}=-{P}_{EXT}$ .

For solid materials, the default value for $\Delta {P}_{min}^{\mathit{mat}_i}$ = 1030 is suitable.

7. Stagnation Energy is optional because this EOS does not depends on energy. The energy input value will only affect output value in animation files and time histories.
8. EOS parameters must be consistent with liquid EOS from adjacent MM-ALE domain.