# Orifice (IL)

**Libraries:**

Simscape /
Fluids /
Isothermal Liquid /
Valves & Orifices /
Orifices

## Description

The Orifice (IL) block models the flow through a local
restriction with a constant or variable opening area. For variable orifices, a control
member connected to port **S** sets the opening position. The opening
area is parametrized either linearly or by lookup table.

For orifices that open and close based on the displacement of a central spool, see Spool Orifice (IL).

The block conserves mass such that

$${\dot{m}}_{A}+{\dot{m}}_{B}=\rho {v}_{A}{A}_{A}+\rho {v}_{B}{A}_{B}=0.$$

This mass balance implies that there is an increase in velocity when there is a decrease in
area, and a reduction in velocity when the flow discharges into a larger area. In
accordance with the Bernoulli principle, this change in velocity results in a region of
lower pressure in the orifice and a higher pressure in the expansion zone. The resulting
increase in pressure, which is called *pressure recovery*, depends on
the discharge coefficient of the orifice and the ratio of the orifice and port
areas.

### Constant Orifices

For constant orifices, the orifice area,
*A*_{orifice}, does not change over the
course of the simulation.

**Using the**

`Constant`

Area ParameterizationThe block calculates the mass flow rate as

$$\dot{m}=\frac{{C}_{d}{A}_{orifice}\sqrt{2\overline{\rho}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{orifice}}{{A}_{port}}\right)}^{2}\right)}}\sqrt{{p}_{A}-{p}_{B}}\approx \frac{{C}_{d}{A}_{orifice}\sqrt{2\overline{\rho}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{orifice}}{{A}_{port}}\right)}^{2}\right)}}\frac{{p}_{A}-{p}_{B}}{{\left[{\left({p}_{A}-{p}_{B}\right)}^{2}+\Delta {p}_{crit}\right]}^{1/4}},$$

where:

*C*_{d}is the**Discharge coefficient**.*A*_{orifice}is the instantaneous orifice open area.*A*_{port}is the**Cross-sectional area at ports A and B**.$$\overline{\rho}$$ is the average fluid density.

*PR*_{loss} and
*Δp*_{crit} are calculated in the same
manner for constant and variable orifices and are defined in the Pressure Loss and Critical Pressure sections
below.

This approximation for $$\dot{m}$$ and the Local Restriction (IL) block are the same.

**Using the**

```
Tabulated data - Volumetric flow rate vs. pressure
drop
```

ParameterizationThe volumetric flow rate is determined from the tabulated values of the pressure
differential, *Δp*, which you can provide. If you provide only
non-negative values for both the volumetric flow rate and pressure drop vectors,
the block extrapolates the table to contain negative values. The volumetric flow
rate is interpolated from this extended table.

If the **Volumetric flow rate vector** and **Pressure
drop vector** parameters contain both negative and positive values
but no 0, the block inserts an origin into the vectors to ensure the valve does
not have nonzero flow rate when the pressure drop is 0, which is
non-physical.

### Variable Orifices

For variable orifices, setting **Opening orientation** to
`Positive control member displacement opens orifice`

opens the orifice when the signal at **S** is positive, while a
`Negative control member displacement opens orifice`

orientation opens the orifice when the signal at **S** is negative.
In both cases, the signal is positive and the orifice opening is set by the
magnitude of the signal.

**Using the**

`Linear - Area vs. control member position`

ParameterizationThe orifice area *A*_{orifice} is based on the
control member position and the ratio of orifice area and maximum control member
position:

$${A}_{orifice}=\frac{\left({A}_{\mathrm{max}}-{A}_{leak}\right)}{\Delta S}\left(S-{S}_{\mathrm{min}}\right)\epsilon +{A}_{leak},$$

where:

*S*_{min}is the control member position when the orifice is fully closed.*ΔS*is the**Control member travel between closed and open orifice**.*A*_{max}is the**Maximum orifice area**.*A*_{leak}is the**Leakage area**.*ε*is the**Opening orientation**.

When the valve is in a near-open or
near-closed position in the linear parameterization, you can maintain numerical
robustness in your simulation by adjusting the **Smoothing
factor** parameter. If the **Smoothing factor**
parameter is nonzero, the block smoothly saturates the orifice area between
*A _{leak}* and

*A*. For more information, see Numerical Smoothing.

_{max}The volumetric flow rate is determined by the pressure-flow rate equation:

$$\dot{m}=\frac{{C}_{d}{A}_{orifice}\sqrt{2\overline{\rho}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{orifice}}{A}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$$

where *A* is the **Cross-sectional
area at ports A and B**.

**Using the**

`Tabulated data - Area vs. control member position`

ParameterizationWhen you use the ```
Tabulated data - Area vs. control member
position
```

parameterization, the orifice area
*A*_{orifice} is interpolated from the
tabulated values of opening area and the control member position,
*ΔS*, which you can provide. As with the
`Linear - Area vs. control member position`

parameterization, the volumetric flow rate is determined by the pressure-flow
rate equation:

$$\dot{m}=\frac{{C}_{d}{A}_{orifice}\sqrt{2\overline{\rho}}}{\sqrt{P{R}_{loss}\left(1-{\left(\frac{{A}_{orifice}}{A}\right)}^{2}\right)}}\frac{\Delta p}{{\left[\Delta {p}^{2}+\Delta {p}_{crit}^{2}\right]}^{1/4}},$$

where *A*_{orifice} is:

*A*_{max}, the last element of the**Orifice area vector**, if the opening is larger than the maximum specified opening.*A*_{leak}, the first element of the**Orifice area vector**, if the orifice opening is less than the minimum opening.*A*_{orifice}if the calculated area is between the limits of the**Orifice area vector**.

*A*_{open} is a function of
the control member position received at port **S**. The block
queries between data points with linear interpolation and uses nearest
extrapolation for points beyond the table boundaries.

**Using the**

```
Tabulated data - Volumetric flow rate vs. control
member position and pressure drop
```

ParameterizationThe ```
Tabulated data - Volumetric flow rate vs. control member
position and pressure drop
```

parameterization interpolates the
volumetric flow rate directly from a user-provided volumetric flow rate table,
which is based on the control member position and pressure drop over the
orifice. The block queries between data points with linear interpolation and
uses linear extrapolation for points beyond the table boundaries.

This data can include negative pressure drops and negative opening values. If a negative pressure drop is included in the dataset, the volumetric flow rate will change direction. However, the flow rate will remain unchanged for negative opening values.

If the **Pressure drop vector, dp** parameter does not
contain a 0 and the **Volumetric flow rate table, q(s,dp)**
parameter does not contain a corresponding column of 0's, the block inserts them
to ensure the valve does not have nonzero flow rate when the pressure drop is 0,
which is non-physical.

### Pressure Loss

*Pressure loss* describes the reduction of pressure in the
valve due to a decrease in area. The pressure loss term,
*PR*_{loss} is calculated as:

$$P{R}_{loss}=\frac{\sqrt{1-{\left(\frac{{A}_{orifice}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}-{C}_{d}\frac{{A}_{orifice}}{{A}_{port}}}{\sqrt{1-{\left(\frac{{A}_{orifice}}{{A}_{port}}\right)}^{2}\left(1-{C}_{d}^{2}\right)}+{C}_{d}\frac{{A}_{orifice}}{{A}_{port}}}.$$

*Pressure recovery* describes the positive pressure change in the valve
due to an increase in area. If you do not wish to capture this increase in pressure,
clear the **Pressure recovery** check box. In this case,
*PR*_{loss} is 1.

### Critical Pressure

The critical pressure difference,
*Δp*_{crit}, is the pressure differential
associated with the **Critical Reynolds number**,
*Re*_{crit}, which is the point of
transition between laminar and turbulent flow in the fluid:

$$\Delta {p}_{crit}=\frac{\pi \overline{\rho}}{8{A}_{orifice}}{\left(\frac{\nu {\mathrm{Re}}_{crit}}{{C}_{d}}\right)}^{2}.$$

### Faults

To model a fault, in the **Faults** section,
click the **Add fault** hyperlink next to the fault that you want to model. In
the Add Fault window, specify the fault properties. For more information about fault modeling,
see Introduction to Simscape Faults.

The **Opening area when faulted** parameter has three fault options:

`Closed`

— The orifice freezes at its smallest value, depending on the**Orifice parameterization**:When

**Orifice parameterization**is set to`Linear - Area vs. control member position`

, the orifice freezes at the**Leakage area**.When

**Orifice parameterization**is set to`Tabulated data - Area vs. control member position`

, the orifice freezes at the first element of the**Orifice area vector**.When

**Orifice parameterization**is set to`Tabulated data - Volumetric flow rate vs. control member position and pressure drop`

, the orifice freezes at the first row of the**Volumetric flow rate table, q(s,dp)**.

`Open`

— The orifice freezes at its largest value, depending on the**Orifice parameterization**:When

**Orifice parameterization**is set to`Linear - Area vs. control member position`

, the orifice freezes at the**Maximum orifice area**.When

**Orifice parameterization**is set to`Tabulated data - Area vs. control member position`

, the orifice freezes at the last element of the**Orifice area vector**.When

**Orifice parameterization**is set to`Tabulated data - Volumetric flow rate vs. control member position and pressure drop`

, the orifice freezes at the last row of the**Volumetric flow rate table, q(s,dp)**.

`Maintain at last value`

— The orifice seizes at the open area or volumetric flow rate when the trigger occurs.

After the fault triggers, the orifice remains at the faulted area for the rest of the simulation.

## Ports

### Conserving

### Input

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2020a**