Gas-Charged Accumulator (IL)

Gas-charged accumulator in an isothermal liquid network

Since R2020a

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

Description

The Gas-Charged Accumulator (IL) block represents a gas-charged accumulator in an isothermal liquid network. The accumulator consists of a precharged gas chamber and a liquid chamber. The chambers are separated by a bladder, a piston, or any kind of a diaphragm.

As the liquid pressure at the accumulator inlet becomes greater than the precharge pressure, liquid enters the accumulator and compresses the gas through a polytropic process. A decrease in the liquid pressure causes the gas 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 liquid chamber capacity is the total accumulator volume minus the minimum gas volume.

Inlet liquid resistance, and separator properties such as inertia and damping are not modeled. The flow rate is positive if liquid flows into the accumulator.

This diagram represents a gas-charged accumulator. The total accumulator volume, VT, is divided into the liquid chamber on the left and the gas chamber on the right by the vertical separator. The distance between the left side and the separator defines the liquid volume, VL. The distance between the right side and the separator defines the gas volume, VG. The liquid chamber capacity, VC, is less than the total accumulator volume, so that the gas volume never becomes zero:

$$\begin{array}{l}{V}_L=V_T-V_G\\ V_C=V_T-V_{dead}\end{array}$$

where:

• V_T is the total volume of the accumulator, including the liquid chamber and the gas chamber.

• V_L is the volume of the liquid in the accumulator.

• V_G is the volume of the gas in the accumulator.

• V_C is the liquid chamber capacity.

• V_dead is the gas chamber dead volume, a small portion of the gas chamber that remains filled with gas when the liquid chamber is at capacity.

The hard stop contact pressure is modeled 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 polytropic and pressure is balanced at the separator:

$$p_G{V}_G^{k_{sh}}=p_{pr}{V}_T^{k_{sh}},$$

where:

• p_G is the gas pressure in the gas chamber.

• p_pr is the pressure in the gas chamber when the liquid chamber is empty

• k_sh is the specific heat ratio (adiabatic index).

Conservation of Mass

Conservation of mass is represented by the following equation.

$$\{\begin{array}{l}{\dot{p}}_I\frac{d_{{\rho }_I}}{d_{p_I}}{V}_L+{\rho }_I{\dot{V}}_L={\dot{m}}_A\text{, }compressibilityon\\ {\rho }_I{\dot{V}}_L={\dot{m}}_A\text{, }compressibilityoff\end{array}$$

where:

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

• $$\dot{m}$$_A is the mass flow rate of liquid coming into port A.

• ρ_I is the density of the liquid in the liquid chamber.

$${\dot{V}}_L=\{\begin{array}{c}\frac{{\dot{p}}_I}{k_{sh}\frac{p_G}{V_G}}\text{, }if0<V_L<V_C\\ \frac{{\dot{p}}_I}{k_{sh}\frac{p_G}{V_G}+K_{stiff}},else\end{array}$$

where K_stiff is the hard-stop stiffness coefficient.

Conservation of Momentum

Conservation of momentum is represented by:

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

where p_HS is the hard-stop contact pressure.

$${\text{p}}_{HS}=\{\begin{array}{c}(V_L-V_C)K_{stiff},if{V}_L\ge V_C\\ V_L{K}_{stiff,if{V}_L\le \text{ 0}}\\ 0,else\end{array}$$

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

Water Hammer Effect

This demo shows how the Isothermal Liquid library can be used to model water hammer in a long pipe. After opening a valve to slowly establish steady flow in the pipe, the valve is quickly shut. If the Valve is shut quickly enough, it triggers a water hammer effect. A water hammer arrestor suppresses the pressure spikes.

• Open Model

Ports

Conserving

A — Liquid port

isothermal liquid

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

Parameters

Total accumulator volume — Accumulator volume

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

Total volume of the accumulator, including the liquid chamber and the gas chamber. It is the sum of the liquid 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, which is defined as a small portion of the gas chamber that remains filled with gas when the liquid chamber is filled to capacity. The block requires a nonzero value to avoid divide-by-zero when the liquid chamber is at capacity.

Precharge pressure — Gas chamber pressure

1.101325 MPa (default) | positive scalar

Pressure in the gas chamber when the liquid chamber is empty.

Specific heat ratio — Specific heat ratio

1.4 (default) | positive scalar

Specific heat ratio (adiabatic index). To account for heat exchange, set it to a value normally 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 or 1.4 for an adiabatic (and isentropic) process.

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