Fixed hydraulic orifice accounting for flow inertia

Orifices

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 $$p={p}_{A}-{p}_{B}$$.

**Orifice area**Cross-sectional area of the orifice. The default value is

`1e-4`

m^2.**Orifice length**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.**Flow discharge coefficient**Semi-empirical parameter for orifice capacity characterization. The coefficient affects the resistive pressure drop in the orifice. The default value is

`0.6`

.**Critical Reynolds number**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`

.**Initial flow rate**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.

The block has the following ports:

`A`

Hydraulic conserving port associated with the orifice inlet.

`B`

Hydraulic conserving port associated with the orifice outlet.

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