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Hydraulic accumulator with spring used for energy storage

This block represents a spring-loaded accumulator, where fluid entering the accumulator compresses the spring, thus storing hydraulic energy. Since the spring compression increases as fluid enters the chamber and decreases as the accumulator is discharged, the pressure is not constant. The spring is preloaded. If the fluid pressure at the accumulator inlet becomes higher than the preload pressure, fluid enters the accumulator chamber and compresses the spring, thus storing hydraulic energy. A drop in the fluid pressure at the inlet forces the stored fluid back into the system.

To improve computational convergence and efficiency, the accumulator shell 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

p | Pressure at the accumulator inlet |

q | Flow rate into accumulator |

V_{max} | Accumulator capacity (maximum volume) |

V_{F} | Instantaneous volume of fluid in the accumulator |

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

p_{pr} | Preload pressure |

p_{max} | Pressure needed to fully fill the accumulator |

K_{s} | Structural compliance of the accumulator shell |

k | Gain coefficient |

The block positive direction is from port A into the accumulator. This means that the flow rate is positive if it flows into the accumulator.

The spring has linear characteristics.

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

Fluid compressibility is not taken into account.

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

`0.008`m^3.**Preload pressure (gauge)**Pressure at which fluid starts entering the chamber. The default value is

`1e6`Pa.**Maximum pressure**Pressure at which the accumulator is fully charged. The default value is

`3e6`Pa.**Initial fluid 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 accumulator shell. 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

`4e-15`m^3/Pa.

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