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Spring-Loaded Accumulator (IL)

Accumulator with a spring used for energy storage in an isothermal liquid system

  • Library:
  • Simscape / Fluids / Isothermal Liquid / Tanks & Accumulators

  • Spring-Loaded Accumulator (IL) block

Description

This block models a spring-charged accumulator in an isothermal liquid network. The accumulator consists of a preloaded spring and a liquid chamber.

As the liquid pressure at the accumulator inlet becomes greater than the preload pressure, liquid enters the accumulator and compresses the spring. A decrease in the liquid pressure causes the spring to decompress and discharge stored liquid into the system. The separator motion is restricted by a hard stop when the liquid volume is zero and when the liquid volume is at the liquid chamber capacity.

The inlet liquid resistance and spring properties, such as the spring inertia and damping, are not modeled. The spring pressure is assumed to be linear with respect to the liquid volume. The flow rate is positive if liquid flows into the accumulator.

This diagram represents a spring-loaded accumulator.

VL

Volume of the liquid in the accumulator.

VC

Liquid chamber capacity

pmax

Pressure at full capacity

pI

Liquid pressure in the liquid chamber, which is equal to the pressure at the accumulator inlet.

pHS

Hard-stop contact pressure.

KstiffHard-stop stiffness coefficient.
KspringSpring gain.
m˙A

Mass flow rate of liquid coming into port A.

ρI

Density of the liquid in the liquid chamber.

Conservation of Mass

Conservation of mass is represented by the following equation.

{p˙IdρIdpIVL+ρIV˙L=m˙A,     compressibility onρIV˙L=m˙A,                       compressibility off   

where

V˙L={p˙IKspring,            if 0 <VL<VCp˙IKspring+Kstiff,                  else

Conservation of Momentum

Conservation of momentum is represented by the following equation.

pI=pspring+pHS

where

pspring=ppr+KspringVL

pHS={(VLVC)Kstiff,    if VLVCVLKstiff,                          if VL  00,                                    else

Variables

To set the priority and initial target values for the block variables prior to simulation, use the Initial Targets section in the block dialog box or Property Inspector. For more information, see Set Priority and Initial Target for Block Variables.

Nominal values provide a way to specify the expected magnitude of a variable in a model. Using system scaling based on nominal values increases the simulation robustness. Nominal values can come from different sources, one of which is the Nominal Values section in the block dialog box or Property Inspector. For more information, see Modify Nominal Values for a Block Variable.

Ports

Conserving

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Hydraulic conserving port associated with the accumulator inlet. The flow rate is positive if liquid flows into the accumulator.

Parameters

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Amount of liquid that the accumulator can hold.

Spring pressure when the liquid chamber is empty.

Spring pressure when the liquid chamber is at capacity.

Proportionality constant of the hard-stop contact pressure with respect to the liquid volume penetrated into the hard stop. The hard stops are used to restrict the liquid volume between zero and liquid chamber capacity.

Whether to model any change in fluid density due to fluid compressibility. When Fluid compressibility is set to On, changes due to the mass flow rate into the block are calculated in addition to density changes due to changes in pressure. In the Isothermal Liquid Library, all blocks calculate density as a function of pressure.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2020a