Ityp = 1

Block Format Keyword This law enables to model a liquid inlet condition by providing data from stagnation point. Liquid behavior is modeled with linear EOS.

Format

(1)	(3)	(5)
/MAT/LAW11/`mat_ID`/`unit_ID` or /MAT/BOUND/`mat_ID`/`unit_ID`
`mat_title`
$ρ_{i}^{stagnation}$	$ρ_{0}^{stagnation}$
`Ityp`	`P`_sh	`Fscale`_T

Ityp = 1 - Liquid Inlet (from stagnation point data)

(1)	(2)	(3)	(7)
`node_ID`_V		`C`₁	`C`_d
$fct_{ID}_{ρ}$
`fct_ID`_p		$P_{0}^{stagnation}$
`fct_ID`_E		$E_{0}^{stagnation}$
Blank Format
Blank Format
`fct_ID`_T	`fct_ID`_Q

Definitions

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)
$ρ_{i}^{stagnation}$	Initial stagnation density. 3 (Real)	$[\frac{kg}{m^{3}}]$
$ρ_{0}^{stagnation}$	Reference density used in E.O.S (equation of state). Default $ρ_{0}^{stagnation} = ρ_{i}^{stagnation}$ (Real)	$[\frac{kg}{m^{3}}]$
`Ityp`	Boundary condition type. 1 = 0 Gas inlet (from stagnation point data) = 1 Liquid inlet (from stagnation point data) = 2 General inlet/outlet = 3 Non-reflecting boundary (Integer)
`P`_sh	Pressure shift. 2 (Real)	$[Pa]$
`Fscale`_T	Time scale factor. 3 (Real)	$[s]$
`node_ID`_V	Node identifier for velocity computation. 4 = 0 $v_{in} = \min_{nod e ε face} {\vec{v}}_{n o d e} \cdot \vec{n}$ > 0 $v_{in} = ‖ v_{node_ID} ‖$ (Integer)
`C`₁	Liquid bulk modulus. 9 (Real)
`C`_d	Discharge coefficient. 5 Default = 0.0 (Real)
`fct_ID` $ρ$	Function $f_{ρ} (t)$ identifier for stagnation density. 3 = 0 $ρ^{stagnation} (t) = ρ_{i}^{stagnation}$ > 0 $ρ^{stagnation} (t) = ρ_{i}^{stagnation} \cdot f_{ρ} (t)$ (Integer)
`fct_ID`_p	Function $f_{P} (t)$ identifier for stagnation pressure. 3 = 0 $P^{stagnation} (t) = P_{0}^{stagnation}$ > 0 $P^{stagnation} (t) = P_{0}^{stagnation} \cdot f_{P} (t)$ (Integer)
$P_{0}^{stagnation}$	Initial stagnation pressure. 3 (Real)	$[Pa]$
`fct_ID`_E	Function $f_{E} (t)$ identifier for stagnation density. 3 = 0 $E^{stagnation} (t) = E_{0}^{stagnation}$ > 0 $E^{stagnation} (t) = E_{0}^{stagnation} \cdot f_{E} (t)$ (Integer)
$E_{0}^{stagnation}$	Initial specific volume energy at stagnation point. 3 8 (Real)	$[Pa]$
`fct_ID`_T	Function $f_{T} (t)$ identifier for inlet temperature. 3 6 = 0 $T = T_{adjacent}$ = n $T = T_{0} \cdot f_{T} (t)$ (Integer)
`fct_ID`_Q	Function $f_{Q} (t)$ identifier for inlet heat flux. 3 6 = 0 No imposed flux = n $Q = f_{Q} (t)$ (Integer)

Comments

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

This leads to inlet state:(2)
$\begin{array}{l} ρ_{in} = \frac{C_{1} \cdot ρ_{stagnation}}{C_{1} + \frac{ρ_{stagnation} v_{in}^{2}}{2} (1 + C_{d})} \\ P_{in} = P_{stagnation} - \frac{ρ_{stagnation} v_{in}^{2}}{2} (1 + C_{d}) \\ {(ρ e)}_{in} = (1 - \frac{ρ_{in}}{ρ_{stagnation}}) P_{in} + E_{stagnation} \end{array}$
The P_sh parameter enables shifting the output pressure, which also becomes P-P_sh. If using P_sh=P(t=0), the output pressure will be $Δ P$ , with an initial value of 0.0.
If no function is defined, then related quantity $(P_{stagnation}, ρ_{stagnation}, T, or Q)$ remains constant and set to its initial value. However, all input quantities $(P_{stagnation}, ρ_{stagnation}, T, and Q)$ can be defined as time dependent function using provided function identifiers. Abscissa functions can also be scaled using Fscale_T parameter which leads to use f (Fscale_t* t) instead of f(t).
Inlet velocity $v_{in}$ is used in Bernoulli theory.
Discharge coefficient accounts for entry loss and depends on shape orifice.

Figure 2.
With thermal modeling, all thermal data ( $T_{0}, ρ_{0} C_{P}$ , ...) can be defined with /HEAT/MAT.
It is not possible to use this boundary material law with multi-material ALE laws 37 (/MAT/LAW37 (BIPHAS)) and 51 (/MAT/LAW51 (MULTIMAT)).
Definition of stagnation energy is optional. Default value recommended: $E_{0}^{stagnation} = 0.0$ ; since linear EOS $Δ P = C_{1} μ$ does not depends on energy pressure is not affected and the initial energy is also set by you.
Specific volume energy E is defined as $E = \frac{E_{int}}{V}$ , where $E_{int}$ is the internal energy. It can be output using /TH/BRIC.

Specific mass energy e is defined as $e = \frac{E_{int}}{m}$ . This leads to $ρ e = E$ . Specific mass energy e can be output using /ANIM/ELEM/ENER. This may be a relative energy depending on user modeling.
Liquid bulk modulus is usually set to $C_{1} = ρ_{0} c_{0}^{2}$ , where $c_{0}$ is sound speed.