Ityp = 0

Block Format Keyword This law enables to model a gas inlet condition by providing data from stagnation point. Gas is supposed to be a perfect gas.

Format


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

Ityp = 0 - Gas Inlet (from stagnation point data)


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

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)
$ρ_{i}^{stagnation}$ $ρ_{i}^{stagnation}$	Initial stagnation density. 3 (Real)	$[\frac{kg}{m^{3}}]$ $[\frac{kg}{m^{3}}]$
$ρ_{0}^{stagnation}$ $ρ_{0}^{stagnation}$	Reference density used in E.O.S (equation of state). Default $ρ_{0}^{stagnation} = ρ_{i}^{stagnation}$ $ρ_{0}^{stagnation} = ρ_{i}^{stagnation}$ (Real)	$[\frac{kg}{m^{3}}]$ $[\frac{kg}{m^{3}}]$
`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)	$[Pa]$ $[Pa]$
`Fscale`_T	Time scale factor. 3 (Real)	$[s]$ $[s]$
`node_ID`_V	Node identifier for velocity computation. 4 = 0 $v_{in} = min nod e ε face {\to v}_{n o d e} \cdot \to n$ $v_{in} = \min_{nod e ε face} {\vec{v}}_{n o d e} \cdot \vec{n}$ > 0 $v_{in} = ∥ v_{node_ID} ∥$ $v_{in} = ‖ v_{node_ID} ‖$ (Integer)
$γ$ $γ$	Perfect gas constant. (Real)
`C`_d	Discharge coefficient. 5 (Real)
`fct_ID` $ρ$ $ρ$	Function $f_{ρ} (t)$ $f_{ρ} (t)$ identifier for stagnation density. 3 = 0 $ρ^{stagnation} (t) = ρ_{i}^{stagnation}$ $ρ^{stagnation} (t) = ρ_{i}^{stagnation}$ > 0 $ρ^{stagnation} (t) = ρ_{i}^{stagnation} \cdot f_{ρ} (t)$ $ρ^{stagnation} (t) = ρ_{i}^{stagnation} \cdot f_{ρ} (t)$ (Integer)
`fct_ID`_p	Function $f_{P} (t)$ $f_{P} (t)$ identifier for stagnation pressure. 3 = 0 $P^{stagnation} (t) = P_{0}^{stagnation}$ $P^{stagnation} (t) = P_{0}^{stagnation}$ > 0 $P^{stagnation} (t) = P_{0}^{stagnation} \cdot f_{P} (t)$ $P^{stagnation} (t) = P_{0}^{stagnation} \cdot f_{P} (t)$ (Integer)
$P_{0}^{stagnation}$ $P_{0}^{stagnation}$	Initial stagnation pressure. 3 (Real)	$[Pa]$ $[Pa]$
`fct_ID`_T	Function $f_{T} (t)$ $f_{T} (t)$ identifier for inlet temperature. 3 6 = 0 $T = T_{adjacent}$ $T = T_{adjacent}$ = n $T = T_{0} \cdot f_{T} (t)$ $T = T_{0} \cdot f_{T} (t)$ (Integer)
`fct_ID`_Q	Function $f_{Q} (t)$ $f_{Q} (t)$ identifier for inlet heat flux. 3 6 = 0 No imposed flux = n $Q = f_{Q} (t)$ $Q = f_{Q} (t)$ (Integer)

Comments

Provided gas state from stagnation point $(ρ_{stagnation,} P_{stagnation})$ $(ρ_{stagnation,} P_{stagnation})$ is used to compute inlet gas state.
A set of equations including Total Enthalpy formulation, Adiabatic Law and Equation of State allows for the complete definition of the inlet state:
$\begin{array}{l} ρ_{in} = ρ_{stagnation} \cdot {[1 - \frac{γ - 1}{2 γ} \cdot \frac{ρ_{stagnation}}{P_{stagnation}} \cdot (1 + C_{d}) \cdot v_{in}^{2}]}^{\frac{1}{γ - 1}} \\ P_{in} = P_{stagnation} {(\frac{ρ_{in}}{ρ_{stagnation}})}^{γ} \\ {(ρ e)}_{in} = \frac{P_{in}}{γ - 1} \end{array}$
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)).