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Fixed Orifice

Hydraulic orifice with constant cross-sectional area

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Description

The Fixed Orifice block models a sharp-edged constant-area orifice, flow rate through which is proportional to the pressure differential across the orifice. The flow rate is determined according to the following equations:

q=CDA2ρp(p2+pcr2)1/4

p=pApB

where

qFlow rate
pPressure differential
pA, pBGauge pressures at the block terminals
CDFlow discharge coefficient
AOrifice passage area
ρFluid density
pcrMinimum pressure for turbulent flow

The minimum pressure for turbulent flow, pcr, is calculated according to the laminar transition specification method:

  • By pressure ratio — The transition from laminar to turbulent regime is defined by the following equations:

    pcr = (pavg + patm)(1 – Blam)

    pavg = (pA + pB)/2

    where

    pavgAverage pressure between the block terminals
    patmAtmospheric pressure, 101325 Pa
    BlamPressure ratio at the transition between laminar and turbulent regimes (Laminar flow pressure ratio parameter value)
  • By Reynolds number — The transition from laminar to turbulent regime is defined by the following equations:

    pcr=ρ2(RecrνCDDH)2

    DH=4Aπ

    where

    DHOrifice hydraulic diameter
    νFluid kinematic viscosity
    RecrCritical Reynolds number (Critical Reynolds number parameter value)

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, and the pressure differential is determined as p=pApB.

Variables

Use the Variables tab to set the priority and initial target values for the block variables prior to simulation. For more information, see Set Priority and Initial Target for Block Variables (Simscape).

Basic Assumptions and Limitations

  • Fluid inertia is not taken into account.

Parameters

Orifice area

Orifice passage area. The default value is 1e-4 m^2.

Flow discharge coefficient

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 0.7.

Laminar transition specification

Select how the block transitions between the laminar and turbulent regimes:

  • Pressure ratio — The transition from laminar to turbulent regime is smooth and depends on the value of the Laminar flow pressure ratio parameter. This method provides better simulation robustness.

  • Reynolds number — The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches the value specified by the Critical Reynolds number parameter.

Laminar flow pressure ratio

Pressure ratio at which the flow transitions between laminar and turbulent regimes. The default value is 0.999. This parameter is visible only if the Laminar transition specification parameter is set to Pressure ratio.

Critical Reynolds number

The maximum Reynolds number for laminar flow. The value of the parameter depends on the orifice geometrical profile. You can find recommendations on the parameter value in hydraulics textbooks. The default value is 12, which corresponds to a round orifice in thin material with sharp edges. This parameter is visible only if the Laminar transition specification parameter is set to Reynolds number.

Global Parameters

Parameters determined by the type of working fluid:

  • Fluid density

  • Fluid kinematic viscosity

Use the Hydraulic Fluid block or the Custom Hydraulic Fluid block to specify the fluid properties.

Ports

The block has the following ports:

A

Hydraulic conserving port associated with the orifice inlet.

B

Hydraulic conserving port associated with the orifice outlet.

Introduced in R2006a

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