The Air Orifice ISO6358 component models an orifice with flow-rate characteristics defined in standard ISO6358. This component calculates mainly pressure difference and mass flow rate.

In the ISO6358, the following equation is defined to calculate mass flow rate mflow.

$\mathrm{mflow}\=\left\{\begin{array}{cc}\mathrm{p\_\_a}\cdot C\cdot \mathrm{\ρ\_\_0}\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_a}}}\cdot \sqrt{1-{\left(\frac{\frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}-\mathrm{b\_\_cr}}{1-\mathrm{b\_\_cr}}\right)}^2}& \frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}\>\mathrm{b\_\_cr}\\ \mathrm{p\_\_a}\cdot C\cdot \mathrm{\ρ\_\_0}\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_a}}}& \mathrm{otherwise}\end{array}\right.$

Where$\mathrm{mflow}$ : mass flow rate [kg/s], $\mathrm{p\_\_a}$ : upstream pressure [Pa], $C$ : Sonic conductance [m3/s/Pa], $\mathrm{\ρ\_\_0}$ : density of air at reference condition [kg/m3], $\mathrm{T\_\_0}$ : temperature of air at reference condition [K], $\mathrm{T\_\_a}$ : upstream temperature [K], $\mathrm{p\_\_b}$ : downstream pressure [Pa], and $\mathrm{b\_\_cr}$ : critical pressure ratio [-].

The equation is modified for this component based on the reference book[1], and in order to have bi-directional flow.

$\mathrm{mflow}\&equals;\left\{\begin{array}{cc}\mathrm{p\_\_a}\cdot \mathrm{C\_\_act}\cdot \mathrm{\&rho;\_\_0}\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_a}}}& \frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}<\mathrm{b\_\_cr\_act}\\ \mathrm{p\_\_a}\cdot \mathrm{C\_\_act}\cdot \mathrm{\&rho;\_\_0}\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_a}}}\cdot \sqrt{1-{\left(\frac{\frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}-\mathrm{b\_\_cr\_act}}{1-\mathrm{b\_\_cr\_act}}\right)}^2}& \frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}<\mathrm{b\_\_lam}\\ \mathrm{k\_\_ab}\cdot \mathrm{p\_\_a}\cdot \&lpar;1-\frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}\&rpar;\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_a}}}& \frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}<1\\ -\mathrm{k\_\_ab}\cdot \mathrm{p\_\_b}\cdot \&lpar;1-\frac{\mathrm{p\_\_a}}{\mathrm{p\_\_b}}\&rpar;\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_b}}}& \frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}<{\mathrm{b\_\_lam}}^{-1}\\ -\mathrm{p\_\_b}\cdot \mathrm{C\_\_act}\cdot \mathrm{\&rho;\_\_0}\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_b}}}\cdot \sqrt{1-{\left(\frac{\frac{\mathrm{p\_\_a}}{\mathrm{p\_\_b}}-\mathrm{b\_\_cr\_act}}{1-\mathrm{b\_\_cr\_act}}\right)}^2}& \frac{\mathrm{p\_\_b}}{\mathrm{p\_\_a}}<{\mathrm{b\_\_cr\_act}}^{-1}\\ -\mathrm{p\_\_b}\cdot \mathrm{C\_\_act}\cdot \mathrm{\&rho;\_\_0}\cdot \sqrt{\frac{\mathrm{T\_\_0}}{\mathrm{T\_\_b}}}& \mathrm{otherwise}\end{array}\right.$

And,$$

$\mathrm{k\_\_ab}\&equals;1000 \cdot \mathrm{C\_\_act}\cdot \mathrm{\&rho;\_\_0}\cdot \sqrt{1-{\left(\frac{0.999-\mathrm{b\_\_cr\_act}}{1-\mathrm{b\_\_cr\_act}}\right)}^2}$

Where$\mathrm{mflow}$ : mass flow rate [kg/s], $\mathrm{p\_\_a}$ : upstream pressure [Pa], $\mathrm{C\_\_act}$ : Sonic conductance [m3/s/Pa], $\mathrm{\&rho;\_\_0}$ : density of air at reference condition [kg/m3], $\mathrm{T\_\_0}$ : temperature of air at reference condition [K], $\mathrm{T\_\_a}$ : upstream temperature [K], $\mathrm{p\_\_b}$ : downstream pressure [Pa], $\mathrm{T\_\_b}$ : downstream temperature [K], $\mathrm{b\_\_cr\_act}$ : critical pressure ratio [-], and $\mathrm{b\_\_lam}$ : pressure ratio at the boundary of laminar/turbulent [-]

(*) the above equation is used for both Dynamics of mass = Dynamic and Static.

Based on the parameter type, Sonic conductance $\mathrm{C\_\_act}$ and Critical pressure ratio $\mathrm{b\_\_cr\_act}$ are obtained as follow.

	Parameter Type = Sonic conductance
	Sonic conductance $\mathrm{C\_\_act}\= C$ Critical pressure ratio $\mathrm{b\_\_cr\_act}\=\mathrm{b\_\_cr}$

	Parameter Type = Effective area
	Sonic conductance $\mathrm{C\_\_act}\= \frac{S}{5}$ Critical pressure ratio $\mathrm{b\_\_cr\_act}\=0.5$

	Parameter Type = Flow area of restriction
	Sonic conductance $\mathrm{C\_\_act}\= \frac{0.512\cdot \mathrm{A\_\_r}}{\mathrm{Pi}}$ Critical pressure ratio $\mathrm{b\_\_cr\_act}\=\mathrm{b\_\_cr}$

Definitions related to Mass flow rate and pressure:

$\mathrm{dp}\&equals;\mathrm{`port\_a.p`}-\mathrm{`port\_b.p`}$

$\mathrm{pratio}\&equals;\frac{\mathrm{`port\_b.p`}}{\mathrm{`port\_a.p`}}$

$v\&equals;\frac{\mathrm{mflow}}{\&lcub;\begin{array}{cc}\mathrm{inStream}\left(\mathrm{`port\_a.rho`}\right)& \mathrm{dp}\ge 0\\ \mathrm{inStream}\left(\mathrm{`port\_b.rho`}\right)& \mathrm{others}\end{array}\cdot \mathrm{A\_\_act}}$

$\mathrm{`port\_a.mflow`}\&equals;\mathrm{mflow}$

$\mathrm{`port\_b.mflow`}\&equals;-\mathrm{mflow}$

Specific enthalpy is defined with:

$\mathrm{`port\_a.hflow`}\&equals;\mathrm{inStream}\left(\mathrm{`port\_b.hflow`}\right)$

$\mathrm{`port\_b.hflow`}\&equals;\mathrm{inStream}\left(\mathrm{`port\_a.hflow`}\right)$

If Fidelity of properties = Constant, density is calculated with:

$\mathrm{\&rho;\_\_0}\&equals;\frac{\mathrm{p\_\_0}}{\mathrm{`HeatTransfer.Properties.Fluid.SimpleAir.R\_gas`}\cdot \mathrm{T\_\_0}}$

(*) Regarding the value of properties for Constant, see more in Air Settings.

If Fidelity of properties = Ideal Gas (NASA Polynomial), Density is calculated with:

$\mathrm{\&rho;\_\_0}\&equals;\frac{\mathrm{p\_\_0}}{\mathrm{`HeatTransfer.Properties.Fluid.NASAPolyAir.R\_gas}\mathrm{\&sdot;T\_\_0}}$$$

(*) The properties are defined with NASA polynomials and coefficients, see more in Air Settings.

Port's variables are defined with:

$\mathrm{`port\_a.rho`}\&equals;\mathrm{inStream}\left(\mathrm{`port\_b.rho`}\right)$

$\mathrm{`port\_b.rho`}\&equals;\mathrm{inStream}\left(\mathrm{`port\_a.rho`}\right)$

$\mathrm{`port\_a.T`}\&equals;\mathrm{inStream}\left(\mathrm{`port\_b.T`}\right)$

$\mathrm{`port\_b.T`}\&equals;\mathrm{inStream}\left(\mathrm{`port\_a.T`}\right)$$$

	References
	[1] : Peter Beater (2006), "Pneumatic Drives - System Design, Modeling and Control", Springer

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