# Orifice (2P)

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

Since R2021a

Libraries:
Simscape / Fluids / Two-Phase Fluid / Valves & Orifices

## Description

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.

### Constant Area

When you set Orifice type to `Constant`, the orifice has a constant area. The mass flow rate through the orifice is:

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

where:

• Δp is the pressure drop over the orifice, pA ̶ pB.

• Δplam is the pressure transition threshold between laminar and turbulent flow, which is calculated from the Laminar flow pressure ratio, Blam:

`$\Delta {p}_{lam}=\frac{\left({p}_{A}+{p}_{B}\right)}{2}\left(1-{B}_{lam}\right).$`

• ${\stackrel{˙}{m}}_{nom}$ is the Nominal mass flow rate.

• Δpnom is the Nominal pressure drop rate.

• vnom is the nominal inlet specific volume. This value is determined from the fluid properties tabulated data based on the Nominal inlet condition specification parameter.

• vin is the inlet specific volume.

### Variable Area

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:

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

where λ is the orifice opening fraction.

Control Member Displacement

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```.

• fleak is the Closed orifice leakage as a fraction of nominal flow.

• Smin is the Control member position at closed orifice.

### Fluid Specific Volume Dynamics

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:

• xdyn is the inlet vapor quality. The block applies a first-order lag to the inlet vapor quality of the mixture.

• vliq is the liquid specific volume of the fluid.

• vvap is the vapor specific volume of the fluid.

If the inlet fluid is liquid or vapor, vin is the respective liquid or vapor specific volume.

Vapor Quality Lag

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:

• xdyn is the dynamic vapor quality.

• xin is the current inlet vapor quality.

• τ is the Inlet phase change time constant.

If the inlet fluid is a subcooled liquid or superheated vapor, xdyn is equal to xin.

### Mass Balance

Mass is conserved in the orifice:

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=0,$`

where:

• ${\stackrel{˙}{m}}_{A}$ is the mass flow rate at port A.

• ${\stackrel{˙}{m}}_{B}$ is the mass flow rate at port B.

### Energy Balance

Energy is conserved in the orifice:

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

where:

• ΦA is the energy flow at port A.

• ΦB is the energy flow at port B.

### Assumptions and Limitations

• 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.

## Ports

### Conserving

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Fluid entry or exit port.

Fluid entry or exit port.

### Input

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Control member position that sets the orifice opening.

#### Dependencies

To enable this port, set Orifice type to `Variable`.

## Parameters

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Type of orifice. When set to `Variable`, the orifice area varies according to the input signal received at port S.

Typical, rated, or design mass flow rate through a constant orifice.

#### Dependencies

To enable this parameter, set Orifice type to `Constant`.

Typical, rated, or design pressure drop through a constant orifice.

#### Dependencies

To enable this parameter, set Orifice type to `Constant`.

Control member offset, or the value at S when the orifice is fully closed.

#### Dependencies

To enable this parameter, set Orifice type to `Variable`.

Distance the control member travels between a closed and open orifice. When you set Opening orientation to ```Positive control member displacement opens orifice```, the orifice is fully open at the sum of the Control member position at closed orifice and Control member travel between closed and open orifice parameters. When you set Opening orientation to ```Negative control member displacement opens orifice```, the orifice is fully open at the difference between the Control member position at closed orifice and Control member travel between closed and open orifice parameters.

#### Dependencies

To enable this parameter, set Orifice type to `Variable`.

Direction of member displacement that opens a variable orifice. A positive orientation means that an increase in the signal at S opens the orifice. A negative orientation means that a decrease in the signal at S opens the orifice.

#### Dependencies

To enable this parameter, set Orifice type to `Variable`.

Mass flow rate through a fully open orifice under typical, design, or rated conditions.

#### Dependencies

To enable this parameter, set Orifice type to `Variable`.

Pressure drop over a fully open orifice under typical, design, or rated conditions.

#### Dependencies

To enable this parameter, set Orifice type to `Variable`.

Method of determining inlet fluid state. The orifice nominal inlet specific volume is determined from the fluid properties tabulated data based on the Nominal inlet pressure and the setting of the Nominal inlet condition specification parameters.

Inlet pressure in nominal conditions. The inlet specific volume is determined from the fluid properties tabulated data based on the Nominal inlet pressure and the setting of the Nominal inlet condition specification parameters.

Inlet fluid temperature in nominal operating conditions.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to `Temperature`.

Inlet mixture vapor quality by mass fraction in nominal operating conditions. A value of `0` means that the inlet fluid is subcooled liquid. A value of `1` means that the inlet fluid is superheated vapor.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Vapor quality```.

Inlet mixture volume fraction in nominal operating conditions. A value of `0` means that the inlet fluid is subcooled liquid. A value of `1` means that the inlet fluid is superheated vapor.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Vapor void fraction```.

Inlet specific enthalpy in nominal operating conditions.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Specific enthalpy```.

Inlet specific internal energy in nominal operating conditions.

#### Dependencies

To enable this parameter, set Nominal inlet condition specification to ```Specific internal energy```.

Area of the orifice ports A and B.

Fractional flow rate through the orifice when it is fully closed. This parameter contributes to numerical stability by maintaining continuity in the fluid network.

Continuous smoothing factor that introduces a layer of gradual change to the flow response when the orifice is in near-open or near-closed positions. Set this parameter to a nonzero value less than one to increase the stability of your simulation in these regions.

Ratio of the orifice outlet pressure to orifice inlet pressure at which the fluid transitions between the laminar and turbulent regimes. The pressure loss corresponds to the mass flow rate linearly in laminar flows and quadratically in turbulent flows.

Time lag for liquid-vapor mixtures in computing the fluid specific volume. This parameter does not influence the specific volume when the inlet fluid is a fully supercooled liquid or fully superheated vapor.

## Version History

Introduced in R2021a