# Orifice (TL)

Constant-area or variable-area orifice in a thermal liquid system

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• Simscape / Fluids / Thermal Liquid / Valves & Orifices

## Description

The Orifice (TL) 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.

The block conserves mass such that

`${\stackrel{˙}{m}}_{A}+{\stackrel{˙}{m}}_{B}=\rho {v}_{A}{A}_{A}+\rho {v}_{B}{A}_{B}=0.$`

This mass balance implies that there is an increase in velocity when there is a decrease in area, and there is 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, Aorifice, does not change over the course of the simulation.

Using the `Constant` Area Parameterization

The block calculates the mass flow rate as

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

where:

• Cd is the Discharge coefficient parameter.

• Aorifice is the instantaneous orifice open area.

• Aport is the Cross-sectional area at ports A and B parameter.

• $\overline{\rho }$ is the average fluid density.

PRloss and Δpcrit are calculated in the same manner for constant and variable orifices.

This approximation for $\stackrel{˙}{m}$ and the Local Resistance (TL) block are the same.

Using the ```Tabulated data - Volumetric flow rate vs. pressure drop``` Parameterization

The volumetric flow rate is determined from the tabular values of the pressure differential, Δp, which you can provide. If only non-negative values are provided for both the volumetric flow rate and pressure drop vectors, the table will be extrapolated to contain negative values. The volumetric flow rate is interpolated from this extended table.

### Variable Orifices

For variable orifices, when you set 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``` Parameterization

The orifice area Aorifice 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:

• Smin is the Control member position at closed orifice parameter.

• ΔS is the Control member travel between closed and open orifice parameter.

• Amax is the Maximum orifice area parameter.

• Aleak is the Leakage area parameter.

• ε is the Opening orientation parameter.

The volumetric flow rate is determined by the pressure-flow rate equation:

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

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

When the orifice is in a near-open or near-closed position in the linear parameterization, you can maintain numerical robustness in your simulation by adjusting the parameter. If the parameter is nonzero, the block smoothly saturates the opening area between Aleak and Amax. For more information, see Numerical Smoothing.

Using the ```Tabulated data - Area vs. control member position``` Parameterization

When you use the ```Tabulated data - Area vs. control member position``` parameterization, the orifice area Aorifice is interpolated from the tabular 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:

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

where Aorifice is:

• Amax, the last element of the Orifice area vector parameter, if the physical signal at port S is larger than the last element of the Control member position vector parameter.

• Aleak, the first element of the Orifice area vector parameter, if the physical signal at port S is smaller than the first element of the Control member position vector parameter.

• The linearly interpolated value of the Orifice area vector parameter if the calculated area is between the limits of the first and last element of the Control member position vector parameter.

Aorifice 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``` Parameterization

The ```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 nearest extrapolation with respect to control member position and linear extrapolation with respect to pressure drop.

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.

Using the ```Tabulated data - Mass flow rate vs. control member position and pressure drop``` Parameterization

```Tabulated data - Mass flow rate vs. control member position and pressure drop``` — Calculate the mass flow rate directly from the control member position and the pressure drop across the valve. The relationship between the three variables can be nonlinear and it is given by the tabulated data in the Control member position vector, s, Pressure drop vector, dp, and Mass flow rate table, mdot(s,dp) block parameters:

`${\stackrel{˙}{m}}_{\text{Tab}}=\frac{{\rho }_{\text{Avg}}}{{\rho }_{\text{Ref}}}\stackrel{˙}{m}\left(\Delta S,\Delta p\right),$`

where $\stackrel{˙}{m}$ is the tabulated form of the mass flow rate, a function of the control member position, h, and of the pressure drop across the orifice, Δp. The mass flow rate is adjusted for temperature and pressure by the ratio ρAvg/ρRef, where ρAvg is the average fluid density in the orifice and ρref is the reference density for the values of the Reference inflow temperature and Reference inflow pressure parameters.

### Pressure Loss

Pressure loss describes the reduction of pressure in the valve due to a decrease in area. The block calculates the pressure loss term, PRloss 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, set Pressure recovery to `Off`. In this case, PRloss is 1.

### Critical Pressure

The critical pressure difference, Δpcrit, is the pressure differential associated with the Critical Reynolds number parameter, Recrit, which is the point of transition between laminar and turbulent flow in the fluid:

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

### Energy Balance

The block treats the orifice as an adiabatic component. No heat exchange can occur between the fluid and the wall that surrounds it. No work is done on or by the fluid as it traverses from inlet to outlet. With these assumptions, energy can flow by advection only, through ports A and B. By the principle of conservation of energy, the sum of the port energy flows must always equal zero:

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

where ϕ is defined as the energy flow rate into the orifice through one of the ports (A or B).

## Ports

### Input

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Instantaneous displacement of the valve control member.

### Conserving

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Thermal liquid conserving port associated with the opening through which the flow can enter or exit the valve.

Thermal liquid conserving port associated with the opening through which the flow can enter or exit the valve.

## Parameters

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

• `Orifice area`—The assigned area does not change over the simulation.

• ```Tabulated data - Volumetric flow rate vs. pressure drop```—The area remains constant, but the volumetric flow rate through the orifice can vary. This value is interpolated directly from the Volumetric flow rate vector and the Pressure drop vector dataset.

• ```Tabulated data - Mass flow rate vs. pressure drop```—The area remains constant, but the volumetric flow rate through the orifice can vary. This value is interpolated directly from the Mass flow rate vector and the Pressure drop vector dataset.

When you set Orifice type to `Variable`, there are four options.

• ```Linear - Area vs. control member position```. Area is determined by a linear relationship to the control member position with respect to a fully open or fully closed orifice. The position is set by a varying physical signal at port S.

• ```Tabulated data - Area vs. control member position```. The opening area is interpolated from the Control member position vector and the Orifice area vector based on the control member position received at port S.

• ```Tabulated data - Volumetric flow rate vs. control member position and pressure drop```. The volumetric flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Volumetric flow rate table, q(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

• ```Tabulated data - Mass flow rate vs. control member position and pressure drop```. The mass flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Mass flow rate table, mdot(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

Method by which to model the opening characteristics of the orifice. The default setting prescribes a linear relationship between the orifice opening area and the orifice opening. The alternative settings allow for a general, nonlinear relationship to be specified in tabulated form, in one case between the opening area and the orifice opening, in the other case between the mass flow rate and both the orifice opening and the pressure drop between the ports.

#### Dependencies

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

When you set Orifice type to `Variable`, there are four options.

• ```Linear - Area vs. control member position```. Area is determined by a linear relationship to the control member position with respect to a fully open or fully closed orifice. The position is set by a varying physical signal at port S.

• ```Tabulated data - Area vs. control member position```. The opening area is interpolated from the Control member position vector and the Orifice area vector based on the control member position received at port S.

• ```Tabulated data - Volumetric flow rate vs. control member position and pressure drop```. The volumetric flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Volumetric flow rate table, q(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

• ```Tabulated data - Mass flow rate vs. control member position and pressure drop```. The mass flow rate is directly interpolated from the user- provided Control member position vector, s, Pressure drop vector, dp, and Mass flow rate table, mdot(s,dp) parameters based on the control member position received at port S and the pressure drop across ports A and B.

#### Dependencies

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

Cross-sectional area of the orifice opening.

#### Dependencies

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

Vector of pressure differential values for the tabular parameterization of volumetric flow rate. The values in this vector correspond one-to-one to values in the Volumetric flow rate vector parameter. The pressure drop vector values are listed in ascending order. The volumetric flow rate is interpolated directly from the Volumetric flow rate vector parameter, which depends on the Pressure drop vector parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Constant` and Orifice parameterization to ```Tabulated data - Volumetric flow rate vs. pressure drop```.

Vector of volumetric flow rate values for the tabular parameterization of volumetric flow rate. The values in this vector correspond one-to-one to values in the Pressure drop vector parameter. The volumetric flow rate is interpolated directly from the provided Volumetric flow rate vector parameter, which depends on the Pressure drop vector parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Constant` and Orifice parameterization to ```Tabulated data - Volumetric flow rate vs. pressure drop```.

Vector of mass flow rate values for the tabular parameterization of volumetric flow rate. The values in this vector correspond one-to-one to values in the Pressure drop vector parameter. The mass flow rate is interpolated directly from the provided Mass flow rate vector parameter, which depends on the Pressure drop vector parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Constant` and Orifice parameterization to ```Tabulated data - Mass flow rate vs. pressure drop```.

Initial control member offset when the variable orifice is fully closed.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and set Orifice parameterization to ```Linear – Area vs. control member position```.

Maximum distance the control member travels between closed and open 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.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Linear - Area vs. control member position```.

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

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Linear - Area vs. control member position```.

Maximum orifice area experienced during simulation. When using ```Tabulated data - Area vs. control member position```, the maximum orifice area is the last element of the Orifice area vector parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Linear - Area vs. control member position```.

Sum of all gaps when the valve is in fully closed position. Any area smaller than this value is maintained at the specified leakage area. This parameter contributes to numerical stability by maintaining continuity in the flow.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Linear - Area vs. control member position```.

Vector of control member positions for the tabular parameterization of orifice area. The vector elements correspond one-to-one to the values in the Orifice area vector parameter. The vector elements are listed in ascending order and the first element must be 0. The orifice opening area is interpolated from the Orifice area vector, which depends on the Control member position vector parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Tabulated data - Area vs. control member position```.

Vector of orifice area values for the tabular parameterization of orifice area. The values in this vector correspond one-to-one with the elements in the Control member position vector parameter. The first element of this vector is the orifice leakage area and the last element is the maximum orifice area. The orifice opening area is interpolated from the Orifice area vector parameter, which depends on the Control member position vector parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Tabulated data - Area vs. control member position```.

Correction factor that accounts for discharge losses in theoretical flows.

#### Dependencies

To enable this parameter, set either:

• Orifice type to `Variable` and Orifice parameterization to either ```Linear - Area vs. control member position``` or ```Tabulated data - Area vs. control member position```.

• Orifice type to `Constant` and Orifice parameterization to `Orifice area`.

Upper Reynolds number limit for laminar flow through the orifice.

#### Dependencies

To enable this parameter, set either:

• Orifice type to `Variable` and Orifice parameterization to either ```Linear - Area vs. control member position``` or ```Tabulated data - Area vs. control member position```.

• Orifice type to `Constant` and Orifice parameterization to `Orifice area`.

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 value to a nonzero value less than one to increase the stability of your simulation in these regimes.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Linear - Area vs. control member position```.

Whether to account for pressure increase when fluid flows from a region of smaller cross-sectional area to a region of larger cross-sectional area. This increase in pressure is not captured when Pressure recovery is set on `Off`.

#### Dependencies

To enable this parameter, set either:

• Orifice type to `Variable` and Orifice parameterization to either ```Linear - Area vs. control member position``` or ```Tabulated data - Area vs. control member position```.

• Orifice type to `Constant` and Orifice parameterization to `Orifice area`.

Vector of control member positions for tabular parametrization of volumetric flow rate. The control member position vector forms an independent axis with the Pressure drop vector, dp parameter for the 2-D dependent Volumetric flow rate table, q(s,dp) parameter. A positive displacement corresponds to valve opening. The values are listed in ascending order and the first element must be 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Tabulated data - Volumetric flow rate vs. control member position and pressure drop``` or ```Tabulated data - Mass flow rate vs. control member position and pressure drop```.

Vector of pressure drop values for tabular parametrization of volumetric flow rate. The pressure drop vector forms an independent axis with the Control member position vector, s parameter for the 2-D dependent Volumetric flow rate table, q(s,dp) parameter. The values are listed in ascending order and must be greater than 0. Linear interpolation is employed between table data points.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Tabulated data - Volumetric flow rate vs. control member position and pressure drop```.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Tabulated data - Volumetric flow rate vs. control member position and pressure drop``` or ```Tabulated data - Mass flow rate vs. control member position and pressure drop```.

M-by-N matrix of volumetric flow rates based on independent values of pressure drop and control member position. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Pressure drop vector, dp parameter.

• N is the number of elements in the parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Tabulated data - Volumetric flow rate vs. control member position and pressure drop```.

Mass flow rates based on independent values of pressure drop and control member position. M and N are the sizes of the corresponding vectors:

• M is the number of elements in the Pressure drop vector, dp parameter.

• N is the number of elements in the parameter.

#### Dependencies

To enable this parameter, set Orifice type to `Variable` and Orifice parameterization to ```Tabulated data - Mass flow rate vs. control member position and pressure drop```.

Nominal inlet temperature, with reference to absolute zero, at which to specify the tabulated data. This parameter is used to adjust the mass flow rate according to the temperature measured during simulation.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Tabulated data - Mass flow rate vs. opening and pressure drop```.

Nominal inlet pressure, with reference to absolute zero, at which to specify the tabulated data. This parameter is used to adjust the mass flow rate according to the pressure measured during simulation.

#### Dependencies

To enable this parameter, set Orifice parameterization to ```Tabulated data - Mass flow rate vs. opening and pressure drop```.

Cross-sectional area at the entry and exit ports A and B. This area is used in the pressure-flow rate equation that determines the mass flow rate through the orifice.

#### Dependencies

To enable this parameter, set either:

• Orifice type to `Variable` and Orifice parameterization to either ```Linear - Area vs. control member position``` or ```Tabulated data - Area vs. control member position```.

• Orifice type to `Constant` and Orifice parameterization to `Orifice area`.

## Version History

Introduced in R2022a