Gas-Charged Accumulator

(To be removed) Hydraulic accumulator with gas as compressible medium

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead. (since R2020a)

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.

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Libraries:
Simscape / Fluids / Hydraulics (Isothermal) / Accumulators

Description

The Gas-Charged Accumulator block models a gas-charged accumulator that consists of a precharged gas chamber and a fluid chamber. The fluid chamber is connected to a hydraulic system. The chambers are separated by a bladder, a piston, or any kind of a diaphragm.

As the fluid pressure at the accumulator inlet becomes greater than the precharge pressure, fluid enters the accumulator and compresses the gas, storing hydraulic energy. A decrease in the fluid pressure causes the gas to decompress and discharge the stored fluid into the system.

During typical operations, the pressure in the gas chamber is equal to the pressure in the fluid chamber. However, if the pressure at the accumulator inlet drops below the precharge pressure, the gas chamber becomes isolated from the system. In this situation, the fluid chamber is empty and the pressure in the gas chamber remains constant and equal to the precharge pressure. The pressure at the accumulator inlet depends on the hydraulic system to which the accumulator is connected. If the pressure at the accumulator inlet builds up to the precharge pressure or higher, fluid enters the accumulator again.

The motion of the separator between the fluid chamber and the gas chamber is restricted by two hard stops that limit the expansion and contraction of the fluid volume. The fluid volume is limited when the fluid chamber is at capacity and when the fluid chamber is empty. The hard stops are modeled with finite stiffness and damping. This means that it is possible for the fluid volume to become negative or greater than the fluid chamber capacity, depending on the values of the hard-stop stiffness coefficient and the accumulator inlet pressure.

The diagram represents a gas-charged accumulator. The vertical separator divides the total accumulator volume, V_T, into the fluid chamber on the left and the gas chamber on the right. The distance between the left side and the separator defines the fluid volume, V_F. The distance between the right side and the separator defines the gas volume, V_T – V_F. The fluid chamber capacity, V_C, is less than the total accumulator volume, V_T, so that the gas volume never becomes zero.

The block models the hard stop contact pressure with a stiffness term and a damping term. The relationship of the gas pressure and gas volume between the current state and the precharge state is given by the polytropic relation, with pressure balanced at the separator

$$\left(p_G+p_A\right){\left(V_T-V_F\right)}^k=\left(p_{pr}+p_A\right)V_T^k$$

$$p_F=p_G+p_{HS}$$

$$V_C=V_T-V_{dead}$$

$$p_{HS}=\{\begin{array}{ll}{K}_S\left(V_F-V_C\right)+K_d{q}_F^{+}\left(V_F-V_C\right)\hfill & \text{if }{V}_F\ge V_C\hfill \\ K_S{V}_F-K_d{q}_F^{-}{V}_F\hfill & \text{if }{V}_F\le 0\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$$

$$q_F^{+}=\{\begin{array}{ll}{q}_F\hfill & \text{if }{q}_F\ge 0\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$$

$$q_F^{-}=\{\begin{array}{ll}{q}_F\hfill & \text{if }{q}_F\le 0\hfill \\ 0\hfill & \text{otherwise}\hfill \end{array}$$

where:

VT	Total volume of the accumulator, including the fluid chamber and the gas chamber
VF	Volume of fluid in the accumulator
Vinit	Initial volume of fluid in the accumulator
VC	Fluid chamber capacity, which is the difference between total accumulator volume and the gas chamber dead volume
Vdead	Gas chamber dead volume, which is a small portion of the gas chamber that remains filled with gas when the fluid chamber is at capacity
pF	Fluid pressure (gauge) in the fluid chamber, which is equal to the pressure at the accumulator inlet
ppr	Pressure (gauge) in the gas chamber when the fluid chamber is empty
pA	Atmospheric pressure
pG	Gas pressure (gauge) in the gas chamber
pHS	Hard-stop contact pressure
Ks	Hard-stop stiffness coefficient
Kd	Hard-stop damping coefficient
k	Specific heat ratio (adiabatic index)
qF	Fluid flow rate into the accumulator, which is positive if fluid flows into the accumulator

The flow rate into the accumulator is the rate of change of the fluid volume:

$$q_F=\frac{d{V}_F}{dt}.$$

At t = 0, the initial condition is V_F = V_init, where V_init is the value you assign to the Initial fluid volume parameter.

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.

Assumptions and Limitations

• The process in the gas chamber is assumed to be polytropic.

• Loading on the separator, such as inertia or friction, is not considered.

• Inlet hydraulic resistance is not considered.

• Fluid compressibility is not considered.

Examples

Engine Cooling System

Model an engine cooling system with an oil cooling circuit.

• Open Model

House Heating System

Model a simple house heating system. The model contains a heater, a controller, and a house structure with four radiators and four rooms. Each room exchanges heat with the environment through its exterior walls, roof, and windows. Each path is simulated as a combination of a thermal convection, thermal conduction, and the thermal mass. It is assumed that heat is not transferred internally between rooms. The heater consists of a furnace, a boiler, an accumulator, and a pump to circulate hot water in the system. The controller starts admitting fuel into the furnace if the overall average temperature of rooms falls below 21 degree C and it stops if the temperature exceeds 25 degree C. The simulation calculates the heating cost and indoor temperatures.

• Open Model

Ports

Conserving

A — Accumulator inlet

hydraulic

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

Parameters

Total accumulator volume — Accumulator volume, including fluid chamber and gas chamber

8e-3 m^3 (default) | positive scalar

Total volume of the accumulator, including the fluid chamber and the gas chamber. This value is the sum of the fluid chamber capacity and the minimum gas volume.

Minimum gas volume — Gas chamber dead volume

4e-5 m^3 (default) | positive scalar

Gas chamber dead volume, a small portion of the gas chamber that remains filled with gas when the fluid chamber is at capacity. A nonzero volume is necessary so that the gas pressure does not become infinite when the fluid chamber is at capacity.

Precharge pressure (gauge) — Pressure in gas chamber when fluid chamber is empty

10e5 Pa (default) | positive scalar

Pressure (gauge) in the gas chamber when the fluid chamber is empty.

Specific heat ratio — Adiabatic index

1.4 (default) | scalar, typically between 1 and 2

Specific heat ratio, also known as the adiabatic index. To account for heat exchange, set this parameter to a value, typically between 1 and 2, depending on the properties of the gas in the gas chamber. For dry air at 20°C, this value is 1 for an isothermal process and 1.4 for an adiabatic and isentropic process.

Hard-stop stiffness coefficient — Proportionality constant for hard-stop stiffness

1e10 Pa/m^3 (default) | nonnegative scalar

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

Hard-stop damping coefficient — Proportionality constant for hard-stop damping

1e10 Pa*s/m^6 (default) | nonnegative scalar

Proportionality constant of the hard-stop contact pressure with respect to the flow rate and the fluid volume penetrated into the hard stop. The block uses the hard stops to restrict the fluid volume between zero and fluid chamber capacity.

Extended Capabilities

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

Version History

Introduced in R2006a

R2023a: To be removed

The Hydraulics (Isothermal) library will be removed in a future release. Use the Isothermal Liquid library instead.

For more information on updating your models, see Upgrading Hydraulic Models to Use Isothermal Liquid Blocks.