Spring-Loaded Accumulator (IL)

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

Since R2020a

Libraries:
Simscape / Fluids / Isothermal Liquid / Tanks & Accumulators

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.

`V_L`	Volume of the liquid in the accumulator.
`V_C`	Liquid chamber capacity
`p_max`	Pressure at full capacity
`p_I`	Liquid pressure in the liquid chamber, which is equal to the pressure at the accumulator inlet.
`p_HS`	Hard-stop contact pressure.
`K_stiff`	Hard-stop stiffness coefficient.
`K_spring`	Spring gain.
$\dot{m}$ `_A`	Mass flow rate of liquid coming into port A.
`ρ_I`	Density of the liquid in the liquid chamber.

Conservation of Mass

Conservation of mass is represented by the following equation.

${\begin{cases} {\dot{p}}_{I} \frac{d_{ρ_{I}}}{d_{p_{I}}} V_{L} + ρ_{I} {\dot{V}}_{L} = {\dot{m}}_{A}, c o m p r e s s i b i l i t y o n \\ ρ_{I} {\dot{V}}_{L} = {\dot{m}}_{A}, c o m p r e s s i b i l i t y o f f \end{cases}$

where

${\dot{V}}_{L} = {\begin{matrix} \frac{{\dot{p}}_{I}}{K_{s p r i n g}}, i f 0 < V_{L} < V_{C} \\ \frac{{\dot{p}}_{I}}{K_{s p r i n g} + K_{s t i f f}}, e l s e \end{matrix}$

Conservation of Momentum

Conservation of momentum is represented by the following equation.

$p_{I} = p_{s p r i n g} + p_{H S}$

where

$p_{s p r i n g} = p_{p r} + K_{s p r i n g} V_{L}$

$p_{H S} = {\begin{matrix} (V_{L} - V_{C}) K_{s t i f f}, i f V_{L} \geq V_{C} \\ V_{L} K_{s t i f f, i f V_{L} \leq 0} \\ 0, e l s e \end{matrix}$

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.

Examples

Closed-Circuit Hydraulic Actuator

A closed-circuit hydraulic actuator driven by a variable-speed pump. The actuator is arranged as a closed fluid system with two replenishment valves (check valves) and a spring-loaded accumulator serving as a replenishment reservoir. The pump speed is controlled by the difference between the commanded and measured piston position. The actuator acts against a spring, a damper, and a time-varying load.

Open Model

Diesel Engine In-Line Injection System

An in-line multi-element diesel injection system. It consists of a cam shaft, a lift pump, four in-line injection pumps, and four injectors.

Open Model

Ports

Conserving

expand all

A — Hydraulic conserving port
hydraulic conserving

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

Parameters

expand all

Liquid capacity — Liquid capacity
`8e-3 m^3` (default) | positive scalar

Amount of liquid that the accumulator can hold.

Preload pressure — Spring pressure
`1.01325 MPa` (default) | positive scalar

Spring pressure when the liquid chamber is empty.

Pressure at full capacity — Spring pressure
`3.01325 MPa` (default) | positive scalar

Spring pressure when the liquid chamber is at capacity.

Hard stop stiffness coefficient — Proportionality constant
`1e4 MPa/m^3` (default) | positive scalar

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.

Fluid dynamic compressibility — Fluid compressibility
`on` (default) | `off`

Whether to model any change in fluid density due to fluid compressibility. When you select Fluid dynamic compressibility, 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