Fixed hydraulic orifice accounting for flow inertia
The Fixed Orifice with Fluid Inertia block models a hydraulic fixed orifice and accounts for the fluid inertia, in addition to the static pressure loss.
Fluid inertia plays a noticeable role in orifices with a large ratio of orifice length to the orifice hydraulic diameter (L / DH) and in sharp-edged short orifices when the rate of change of flow rate (fluid acceleration) is relatively large.
The orifice is based on the following equations:
|q||Volumetric flow rate|
|p||Total pressure differential|
|pin||Inertial pressure drop|
|pr||Resistive pressure drop|
|CD||Flow discharge coefficient|
|A||Orifice passage area|
|pcr||Minimum 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
|pavg||Average pressure between the block terminals|
|patm||Atmospheric pressure, 101325 Pa|
|Blam||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:
|DH||Orifice hydraulic diameter|
|ν||Fluid kinematic viscosity|
|Recr||Critical Reynolds number (Critical Reynolds number parameter value)|
Connections A and B are conserving hydraulic ports associated with the orifice inlet and outlet, 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, and the pressure differential is determined as .
Cross-sectional area of the orifice. The default value is
Total length of the orifice. Generally, increase the geometrical
length of the orifice up to 2 · 0.8 · DH (where DH is
the orifice hydraulic diameter) to take into account the added volumes
of fluid on both sides of the orifice. The default value is
Semi-empirical parameter for orifice capacity characterization.
The coefficient affects the resistive pressure drop in the orifice.
The default value is
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.
Pressure ratio at which the flow transitions between laminar
and turbulent regimes. The default value is
This parameter is visible only if the Laminar transition
specification parameter is set to
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
10. This parameter is visible
only if the Laminar transition specification parameter
is set to
Flow rate through the orifice at the start of simulation. This
parameter specifies the initial condition for use in computing the
block's state at the beginning of a simulation run. For more information,
see Initial Conditions Computation (Simscape). The default value is
Parameters determined by the type of working fluid:
Fluid kinematic viscosity
The block has the following ports:
Hydraulic conserving port associated with the orifice inlet.
Hydraulic conserving port associated with the orifice outlet.