Air Orifice ISO6358

Orifice of Air based on the standard ISO6358 which is for compressible flow

 Description 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.

Equations

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 : 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}=\left\{\begin{array}{cc}\mathrm{p__a}\cdot \mathrm{C__act}\cdot \mathrm{ρ__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{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_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 (1-\frac{\mathrm{p__b}}{\mathrm{p__a}})\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 (1-\frac{\mathrm{p__a}}{\mathrm{p__b}})\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{ρ__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{ρ__0}\cdot \sqrt{\frac{\mathrm{T__0}}{\mathrm{T__b}}}& \mathrm{otherwise}\end{array}\right\$

And,

Where : mass flow rate [kg/s], $\mathrm{p__a}$ : upstream pressure [Pa], $\mathrm{C__act}$ : 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], $\mathrm{T__b}$ : 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 Critical pressure ratio $\mathrm{b__cr_act}=\mathrm{b__cr}$
 Parameter Type = Effective area Sonic conductance Critical pressure ratio $\mathrm{b__cr_act}=0.5$
 Parameter Type = Flow area of restriction Sonic conductance Critical pressure ratio $\mathrm{b__cr_act}=\mathrm{b__cr}$

Definitions related to Mass flow rate and pressure:

$\mathrm{dp}=\mathrm{port_a.p}-\mathrm{port_b.p}$

$\mathrm{pratio}=\frac{\mathrm{port_b.p}}{\mathrm{port_a.p}}$

$v=\frac{\mathrm{mflow}}{{\begin{array}{cc}\mathrm{inStream}\left(\mathrm{port_a.rho}\right)& \mathrm{dp}\ge 0\\ \mathrm{inStream}\left(\mathrm{port_b.rho}\right)& \mathrm{others}\end{array}\cdot \mathrm{A__act}}$

$\mathrm{port_a.mflow}=\mathrm{mflow}$

$\mathrm{port_b.mflow}=-\mathrm{mflow}$

Specific enthalpy is defined with:

$\mathrm{port_a.hflow}=\mathrm{inStream}\left(\mathrm{port_b.hflow}\right)$

$\mathrm{port_b.hflow}=\mathrm{inStream}\left(\mathrm{port_a.hflow}\right)$

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

$\mathrm{ρ__0}=\frac{\mathrm{p__0}}{\mathrm{HeatTransfer.Properties.Fluid.SimpleAir.R_gas}\cdot \mathrm{T__0}}$

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

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

$\mathrm{ρ__0}=\frac{\mathrm{p__0}}{\mathrm{HeatTransfer.Properties.Fluid.NASAPolyAir.R_gas}\mathrm{⋅T__0}}$

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

Port's variables are defined with:

$\mathrm{port_a.rho}=\mathrm{inStream}\left(\mathrm{port_b.rho}\right)$

$\mathrm{port_b.rho}=\mathrm{inStream}\left(\mathrm{port_a.rho}\right)$

$\mathrm{port_a.T}=\mathrm{inStream}\left(\mathrm{port_b.T}\right)$

$\mathrm{port_b.T}=\mathrm{inStream}\left(\mathrm{port_a.T`}\right)$

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

Variables

 Symbol Units Description Modelica ID $\mathrm{dp}$ $\mathrm{Pa}$ Pressure difference dp $\mathrm{pratio}$ $-$ Pressure ratio pratio $\mathrm{mflow}$ $\frac{\mathrm{kg}}{s}$ Mass flow rate mflow $v$ $\frac{m}{s}$ Velocity of flow v $\mathrm{C__act}$ $\frac{{m}^{3}}{s\cdot \mathrm{Pa}}$ Actual Sonic conductance C_act $\mathrm{b__cr_act}$ $-$ Actual critical pressure ratio b_cr_act $\mathrm{k__ab}$ $-$ Linear gain for Laminar flow k_ab $\mathrm{ρ__0}$ $\frac{\mathrm{kg}}{{m}^{3}}$ Density of air at reference condition rho0

Connections

 Name Units Condition Description Modelica ID $\mathrm{port__a}$  Air Port $\mathrm{port_a}$ $\mathrm{port__b}$  Air Port $\mathrm{port_b}$

Parameters

 Symbol Default Units Description Modelica ID $\mathrm{AirSettings1}$ $-$ Specify a component of Air simulation settings Settings $\mathrm{General}$ $-$ Select parameter type  - Sonic conductance  - Effective area  - Flow area of restriction TypeOfParam $A$ ${0.05}^{2}\cdot \mathrm{Pi}$ ${m}^{2}$ Flow area, only for monitoring flow velocity A $C$ $1e-7$ $\frac{{m}^{3}}{s\cdot \mathrm{Pa}}$ Sonic conductance C $\mathrm{A__r}$ $1e-5$ ${m}^{2}$ Flow area of the local restriction Ar $\mathrm{b__cr}$ $0.5$ $-$ Critical pressure ratio b_cr $S$ $5e-7$ ${m}^{2}$ Effective area S $\mathrm{b__lam}$ $0.999$ $-$ Pressure ratio at the boundary of laminar/turbulent [-] b_lam $\mathrm{p__0}$ $100000$ $\mathrm{Pa}$ Reference pressure p0 $\mathrm{T__0}$ 293.15 $K$ Reference temperature T0