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Constant Area Pneumatic Orifice

Sharp-edged orifice in pneumatic systems

Library

None (example custom library)

  • Constant Area Pneumatic Orifice block

Description

Note

As of Release R2016b, the Gas block library replaces the Pneumatic library as the recommended way of modeling pneumatic systems. The former Pneumatic library is now included in the product installation as an example custom library. The pneumatic domain definition is still provided with the software, and all the pneumatic blocks in your legacy models continue to work as before. However, these blocks no longer receive full production support and can be removed in a future release.

The Constant Area Pneumatic Orifice block models the flow rate of an ideal gas through a sharp-edged orifice.

The flow rate through the orifice is proportional to the orifice area and the pressure differential across the orifice.

G=Cd·A·pi2γγ1·1RTi[(popi)2γ(popi)γ+1γ]

where

GMass flow rate
CdDischarge coefficient, to account for effective loss of area due to orifice shape
AOrifice cross-sectional area
pi, poAbsolute pressures at the orifice inlet and outlet, respectively. The inlet and outlet change depending on flow direction. For positive flow (G > 0), pi = pA, otherwise pi = pB.
γThe ratio of specific heats at constant pressure and constant volume, cp / cv
RSpecific gas constant
TAbsolute gas temperature

The choked flow occurs at the critical pressure ratio defined by

βcr=popi=(2γ+1)γγ1

after which the flow rate depends on the inlet pressure only and is computed with the expression

G=Cd·A·piγRTi·βcrγ+1γ

The square root relationship has infinite gradient at zero flow, which can present numerical solver difficulties. Therefore, for very small pressure differences, defined by po / pi > 0.999, the flow equation is replaced by a linear flow-pressure relationship

G=kCd·A·Ti0.5(pipo)

where k is a constant such that the flow predicted for po / pi is the same as that predicted by the original flow equation for po / pi = 0.999.

The heat flow out of the orifice is assumed equal to the heat flow into the orifice, based on the following considerations:

  • The orifice is square-edged or sharp-edged, and as such is characterized by an abrupt change of the downstream area. This means that practically all the dynamic pressure is lost in the expansion.

  • The lost energy appears in the form of internal energy that rises the output temperature and makes it very close to the inlet temperature.

Therefore, qi = qo, where qi and qo are the input and output heat flows, respectively.

The block positive direction is from port A to port B. This means that the flow rate is positive if it flows from A to B.

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Basic Assumptions and Limitations

  • The gas is ideal.

  • Specific heats at constant pressure and constant volume, cp and cv, are constant.

  • The process is adiabatic, that is, there is no heat transfer with the environment.

  • Gravitational effects can be neglected.

  • The orifice adds no net heat to the flow.

Parameters

Discharge coefficient, Cd

Semi-empirical parameter for orifice capacity characterization. Its value depends on the geometrical properties of the orifice, and usually is provided in textbooks or manufacturer data sheets. The default value is 0.82.

Orifice area

Specify the orifice cross-sectional area. The default value is 1e-5 m^2.

Ports

The block has the following ports:

A

Pneumatic conserving port associated with the orifice inlet for positive flow.

B

Pneumatic conserving port associated with the orifice outlet for positive flow.

Version History

Introduced in R2009b