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Constant- or variable-area orifice in a two-phase fluid network

**Library:**Simscape / Fluids / Two-Phase Fluid / Valves & Orifices

The Orifice (2P) block models pressure loss due to a constant or variable area orifice
in a two-phase fluid network. The orifice can be constant or variable. When
**Orifice type** is set to `Variable`

, the
physical signal at port **S** sets the position of the control member,
which opens and closes the orifice.

Fluid properties inside the valve are calculated from inlet conditions. There is no heat exchange between the fluid and the environment, and therefore phase change inside the orifice only occurs due to a pressure drop or a propagated phase change from another part of the model.

A number of block parameters are based on nominal operating conditions, which correspond to the orifice rated performance, such as a specification on a manufacturer datasheet.

When you set **Orifice type** to
`Constant`

, the orifice has a constant area. The mass
flow rate through the orifice is:

$${\dot{m}}_{A}={\dot{m}}_{nom}\left[\sqrt{\frac{{v}_{nom}}{2\Delta {p}_{nom}}}\right]\sqrt{\frac{2}{{v}_{in}}}\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{lam}^{2}\right)}^{0.25}},$$

where:

*Δp*is the pressure drop over the orifice,*p*._{A}̶ p_{B}*Δp*is the pressure transition threshold between laminar and turbulent flow, which is calculated from the_{lam}**Laminar flow pressure ratio**,*B*:_{lam}$$\Delta {p}_{lam}=\frac{\left({p}_{A}+{p}_{B}\right)}{2}\left(1-{B}_{lam}\right).$$

$${\dot{m}}_{nom}$$ is the

**Nominal mass flow rate**.*Δp*is the_{nom}**Nominal pressure drop rate**.*v*is the nominal inlet specific volume. This value is determined from the fluid properties tabulated data based on the_{nom}**Nominal inlet condition specification**parameter.*v*is the inlet specific volume._{in}

When you set **Orifice type** to
`Variable`

, the block is configured for a variable
opening, which is set by the control member position at **S**. The
block calculates the mass flow rate through the variable-area orifice as:

$${\dot{m}}_{A}=\lambda {\dot{m}}_{nom}\left[\sqrt{\frac{{v}_{nom}}{2\Delta {p}_{nom}}}\right]\sqrt{\frac{2}{{v}_{in}}}\frac{\Delta p}{{\left(\Delta {p}^{2}+\Delta {p}_{lam}^{2}\right)}^{0.25}},$$

where *λ* is the orifice opening
fraction.

The orifice opening, which is expressed as a fraction of the total orifice
open area, is determined by the input signal at **S**, the
**Control member travel between closed and open orifice**
parameter, *ΔS*, and a leakage value that improves numerical
stability when the orifice is closed:

$$\lambda =\epsilon \left(1-{f}_{leak}\right)\frac{\left(S-{S}_{\mathrm{min}}\right)}{\Delta S}+{f}_{leak},$$

where:

*ε*is the**Opening orientation**. This value is`+1`

when the setting is`Positive control member displacement opens orifice`

and`-1`

when the setting is`Negative control member displacement opens orifice`

.*f*is the_{leak}**Closed orifice leakage as a fraction of nominal flow**.*S*is the_{min}**Control member position at closed orifice**.

When the fluid at the orifice inlet is a liquid-vapor mixture, the block calculates the specific volume as:

$${v}_{in}=\left(1-{x}_{dyn}\right){v}_{liq}+{x}_{dyn}{v}_{vap},$$

where:

*x*is the inlet vapor quality. The block applies a first-order lag to the inlet vapor quality of the mixture._{dyn}*v*is the liquid specific volume of the fluid._{liq}*v*is the vapor specific volume of the fluid._{vap}

If the inlet fluid is liquid or vapor,
*v _{in}* is the respective liquid or
vapor specific volume.

If the inlet vapor quality is a liquid-vapor mixture, the block applies a first-order time lag:

$$\frac{d{x}_{dyn}}{dt}=\frac{{x}_{in}-{x}_{dyn}}{\tau},$$

where:

*x*is the dynamic vapor quality._{dyn}*x*is the current inlet vapor quality._{in}*τ*is the**Inlet phase change time constant**.

If the inlet fluid is a subcooled liquid or superheated vapor,
*x _{dyn}* is equal to

Mass is conserved in the orifice:

$${\dot{m}}_{A}+{\dot{m}}_{B}=0,$$

where:

$${\dot{m}}_{A}$$ is the mass flow rate at port

**A**.$${\dot{m}}_{B}$$ is the mass flow rate at port

**B**.

Energy is conserved in the orifice:

$${\Phi}_{A}+{\Phi}_{B}=0,$$

where:

*Φ*is the energy flow at port_{A}**A**.*Φ*is the energy flow at port_{B}**B**.

The block does not model pressure recovery downstream of the valve.

There is no heat exchange between the valve and the environment.

The block does not model choked flow.

Check Valve (2P) | Pressure-Reducing Valve (2P) | Pressure Relief Valve (2P) | Thermostatic Expansion Valve (2P)