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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 / D_{H}) 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:
$$q={C}_{D}\cdot A\sqrt{\frac{2}{\rho}}\cdot \frac{{p}_{r}}{{\left({p}_{r}^{2}+{p}_{cr}^{2}\right)}^{1/4}}$$
$$p={p}_{in}+{p}_{r}$$
$${p}_{in}=\rho \frac{L}{A}\frac{dq}{dt}$$
$${p}_{cr}=\frac{\rho}{2}{\left(\frac{{\mathrm{Re}}_{cr}\cdot \nu}{{C}_{D}\cdot {D}_{H}}\right)}^{2}$$
$$\mathrm{Re}=\frac{\left|q\right|\cdot {D}_{H}}{A\cdot \nu}$$
$${D}_{H}=\sqrt{\frac{4A}{\pi}}$$
where
q | Volumetric flow rate |
p | Total pressure differential |
p_{in} | Inertial pressure drop |
p_{r} | Resistive pressure drop |
p_{cr} | Minimum pressure for turbulent flow |
C_{D} | Flow discharge coefficient |
A | Orifice passage area |
L | Orifice length |
D_{H} | Orifice hydraulic diameter |
ρ | Fluid density |
ν | Fluid kinematic viscosity |
Re | Instantaneous Reynolds number |
Re_{cr} | Critical Reynolds number |
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 $$p={p}_{A}-{p}_{B}$$.
Cross-sectional area of the orifice. The default value is 1e-4 m^2.
Total length of the orifice. Generally, increase the geometrical length of the orifice up to 2 · 0.8 · D_{H} (where D_{H} is the orifice hydraulic diameter) to take into account the added volumes of fluid on both sides of the orifice. The default value is 0.01 m.
Semi-empirical parameter for orifice capacity characterization. The coefficient affects the resistive pressure drop in the orifice. The default value is 0.6.
The maximum Reynolds number for laminar flow. The transition from laminar to turbulent regime is assumed to take place when the Reynolds number reaches this value. The default value is 10.
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. The default value is 0.
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.