Fixed Orifice

Hydraulic orifice with constant cross-sectional area

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Orifices

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:

$q = C_{D} \cdot A \sqrt{\frac{2}{ρ}} \cdot \frac{p}{{(p^{2} + p_{c r}^{2})}^{1 / 4}}$

$Δ p = p_{A} - p_{B},$

where

q	Flow rate
p	Pressure differential
p_A, p_B	Gauge pressures at the block terminals
C_D	Flow discharge coefficient
A	Orifice passage area
ρ	Fluid density
p_cr	Minimum pressure for turbulent flow

The minimum pressure for turbulent flow, p_cr, 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:

p_cr = (p_avg + p_atm)(1 – B_lam)

p_avg = (p_A + p_B)/2

where

p_avg	Average pressure between the block terminals
p_atm	Atmospheric pressure, 101325 Pa
B_lam	Pressure 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:
$p_{c r} = \frac{ρ}{2} {(\frac{{Re}_{c r} \cdot ν}{C_{D} \cdot D_{H}})}^{2}$
$D_{H} = \sqrt{\frac{4 A}{π}}$
where
D_H Orifice hydraulic diameter
ν Fluid kinematic viscosity
Re_cr Critical 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 $Δ p = p_{A} - p_{B},$ .

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.

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.