Iform = 5

Block Format Keyword This boundary can simulate liquid inlet conditions for multi-material ALE laws (formulation: I_form = 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 $α_{s t a g n a t i o n} = α_{0}$ , $ρ_{s t a g n a t i o n} = ρ_{0}$ , $E_{s t a g n a t i o n} = E_{0}$ ( $E$ is optional) which corresponds to the state for which $υ$ =0. From a linear EOS: $P_{0} = C_{0} + C_{1} μ$ ; thus $P_{s t a g n a t i o n} = C_{0}$ .

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
`I`_form

#Global Parameters

(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)
`Scale`_time		`P`_EXT

#Material1 Parameters

(1)	(3)	(5)	(7)	(8)	(9)
$α_{0}^{mat_1}$	$ρ_{0}^{mat_1}$	$E_{0}^{m a t_ 1}$	`fct_ID`_α1	`fct_ID`_{$ρ$ 1}	`fct_ID`_E1
$C_{1}^{m a t_1}$
$Δ P_{min}^{mat_1}$	$C_{0}^{m a t_1}$

#Material2 Parameters

(1)	(3)	(5)	(7)	(8)	(9)
$α_{0}^{mat_2}$	$ρ_{0}^{mat_2}$	$E_{0}^{m a t_ 2}$	`fct_ID`_α2	`fct_ID`_{$ρ$ 2}	`fct_ID`_E2
$C_{1}^{m a t_2}$
$Δ P_{min}^{mat_2}$	$C_{0}^{m a t_2}$

#Material3 Parameters

(1)	(3)	(5)	(7)	(8)	(9)
$α_{0}^{mat_3}$	$ρ_{0}^{mat_3}$	$E_{0}^{m a t_ 3}$	`fct_ID`_α3	`fct_ID`_{$ρ$ 3}	`fct_ID`_E3
$C_{1}^{m a t_3}$
$Δ P_{min}^{mat_3}$	$C_{0}^{m a t_3}$

Definitions

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)
`I`_form	Formulation flag. = 5 Liquid Inlet (computed from data at stagnation point). (Integer)
`Scale`_time	Abscissa scale factor for input functions. 2 Default = 1 (Real)
`P`_EXT	External (ambient) pressure. 3 (Real)	$[Pa]$
$α_{0}^{mat_i}$	Initial volumetric fraction. 4 (Real)
$ρ_{0}^{mat_i}$	Initial density at stagnation point. 1 (Real)	$[\frac{kg}{m^{3}}]$
$E_{0}^{m a t_ i}$	Initial energy at stagnation point. 5 (Real)	$[\frac{J}{m^{3}}]$
`fct_ID`_αi	(Optional) Volumetric fraction scaling function $f_{α_{i}} (t)$ identifier. 6 = 0 $α^{m a t_{i}} (t) = α_{0}^{m a t_{i}}$ > 0 $α^{m a t_{i}} (t) = α_{0}^{m a t_{i}} \cdot f_{α_{i}} (t)$ (Integer)
`fct_ID`_{$ρ$ i}	(Optional) Density fraction scaling function $f_{ρ_{i}} (t)$ identifier. = 0 $P^{m a t_{i}} (t) = P_{0}^{m a t_{i}}$ > 0 $P^{m a t_{i}} (t) = P_{0}^{m a t_{i}} \cdot f_{P_{i}} (t)$ (Integer)
`fct_ID`_Ei	(Optional) Energy fraction scaling function $f_{E_{i}} (t)$ identifier. = 0 $E^{m a t_{i}} (t) = E_{0}^{m a t_{i}}$ > 0 $E^{m a t_{i}} (t) = E_{0}^{m a t_{i}} \cdot f_{E_{i}} (t)$ (Integer)
$C_{1}^{m a t_ i}$	Coefficient for perfect gas EOS. 5 (Real)	$[Pa]$
$Δ P_{min}^{mat_i}$	Hydrodynamic cavitation pressure. 6 Default = -10^-30 (Real)	$[Pa]$
$C_{0}^{m a t_ i}$	Coefficient for perfect gas EOS. 5 (Real)	$[Pa]$

Comments

Provided gas state from stagnation point $ρ_{stagnation}, P_{stagnation}$ is used to compute liquid inlet state. Bernoulli theory is applied:(1)
$P_{stagnation} = P_{in} + \frac{ρ_{in} v_{in}^{2}}{2}$

This leads to sub-material state in inlet boundary element:(2)
$ρ_{i n} = \frac{C_{1} \cdot ρ_{s t a g n a t i o n}}{C_{1} + \frac{ρ_{s t a g n a t i o n} v_{i n}^{2}}{2} (1 + C_{d})}$

Where, $C_{d}$ is an optional drop parameter.(3)
$P_{i n} = P_{s t a g n a t i o n} - \frac{ρ_{s t a g n a t i o n} v_{i n}^{2}}{2} (1 + C_{d})$
(4)
${(ρ e)}_{i n} = (1 - \frac{ρ_{i n}}{ρ_{s t a g n a t i o n}}) P_{i n} + E_{s t a g n a t i o n}$

Then global material state is determined by computing a mean value:

Pressure

$Δ P_{i n} = \sum_{i} α^{m a t_{i}} (t) Δ P_{i n}^{m a t_i}$

Density

$ρ_{i n} = \sum_{i} α^{m a t_{i}} (t) ρ_{i n}^{m a t_i}$

Energy

${(ρ e)}_{i n} = \sum_{i} α^{m a t_{i}} (t) E_{i n}^{m a t_i}$
The optional scaling functions can be used such to scale the volumetric, density or energy fractions.
Parameter P_EXT enables you to take the ambient pressure into account in case you want to work with relative pressure $Δ P_{min}^{m a t_i}$ . 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: $P = P_{a m b} + C_{1} μ$ , and also P_EXT = 0

Relative Pressure: $Δ P = C_{1} μ$ , and also $P_{E X T} = P_{a m b}$
Volumetric fractions enable the sharing of elementary volume within the three different materials.
For each material, $α_{0}^{mat_i}$ must be defined between 0 and 1.

Sum of initial volumetric fractions $\sum_{i = 1}^{3} α_{0}^{mat_i}$ must be equal to 1.

For automatic initial fraction of the volume, refer to /INIVOL.
Linear EOS is:(5)
$P (μ, E) = C_{0} + C_{1} μ$

This provides flexibility, depending on whether pressure and energy are total or relative:(6)
$P (μ, E) = C_{0} + C_{1} μ$

Where, $C_{0} = P_{amp}, C_{1} = ρ_{0} c_{0}^{2}$ and $P_{E X T} = 0$ .

This leads to usual form from $P (μ, E) = C_{0} + C_{1} μ$ .(7)
$Δ P (μ, E) = C_{1} μ$

Where $C_{1} = ρ_{0} c_{0}^{2}$ and $P_{E X T} = P_{a m b}$ .
$Δ P_{min}^{mat_i}$ flag is the minimum value for the computed pressure.
Since $P = Δ P + P_{E X T}$ , defining $P_{E X T} = 0$ implies $Δ P = P$ and $Δ P_{\min} = P_{\min}$ .

Fluid materials pressure must remain positive to avoid any tensile strength, then, $P_{m i n} = 0$ leads to $Δ P_{m i n} = - P_{E X T}$ .

For solid materials, the default value for $Δ P_{min}^{mat_i}$ = 10³⁰ is suitable.
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.
EOS parameters must be consistent with liquid EOS from adjacent MM-ALE domain.