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Hydraulic accumulator with gas as compressible medium

This block models a gas-charged accumulator. The accumulator consists of a precharged gas chamber and a fluid chamber connected to a hydraulic system. The chambers are separated by a bladder, piston, or another kind of elastic diaphragm.

If the fluid pressure at the accumulator inlet becomes higher than the preload pressure, fluid enters the accumulator chamber and compresses the gas, thus storing hydraulic energy. A drop in the fluid pressure at the inlet forces the stored fluid back into the system.

Normally, pressure in the gas chamber is equal to that of the
fluid chamber. But if pressure at the accumulator inlet (*p*)
drops below the accumulator's preload value (*p*_{pr}),
the gas chamber gets isolated from the system with the inlet valve.
In this case, pressure in the gas chamber remains constant and equal
to the preload value, while pressure at the inlet depends on pressure
in the system to which the accumulator is connected. If pressure at
the inlet builds up to the preload value or higher, the chambers start
interacting again.

To improve computational convergence and efficiency, the accumulator inlet chamber is assumed to be compliant. As a result, the fluid starts accumulating in the chamber even before the preload pressure is reached, so that at preload pressure the accumulator already stores a certain volume of fluid. The structural compliance can be set to a very small value, but not to zero.

The accumulator is described with the following equations:

where

V_{F} | Volume of fluid in the accumulator |

V_{A} | Accumulator capacity |

V_{pr} | Volume of fluid at preload pressure |

p | Inlet gauge pressure |

p_{pr} | Preload pressure |

p_{a} | Atmospheric pressure |

K_{s} | Structural compliance of the accumulator inlet port structure |

k | Specific heat ratio |

q | Volumetric flow rate |

t | Time |

The gas compression is determined on the basis of the thermodynamics of ideal gases.

The process is assumed to be polytropic.

No loading on the separator, such as inertia, friction, and so on, is considered.

Fluid compressibility is not taken into account.

**Capacity**Accumulator capacity. The default value is

`0.008`m^3.**Preload pressure (gauge)**Preload gauge pressure. The default value is

`1e6`Pa.**Specific heat ratio**Specific heat ratio (adiabatic index). No units. The default value is

`1.4`. To account for heat exchange, you can set it to a value between 1 and 2, depending on the properties of the gas being used in the accumulator. For example, for dry air at 20 degrees C, this value will be within a range between 1 (isothermal process) and 1.4 (adiabatic process).**Initial volume**Initial volume of fluid in the accumulator. This parameter specifies the initial condition for use in computing the block's initial state at the beginning of a simulation run. For more information, see Initial Conditions Computation. The default value is

`0`.**Structural compliance**The compliance of the inlet port structure. This parameter is introduced to improve convergence and computational efficiency. It must be greater than zero. Values less than 1e-16 m^3/Pa may result in numerical instability. The default value is

`1e-13`m^3/Pa.

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