Engee documentation

Gas-Charged Accumulator (TL)

Accumulator with gas chamber in a thermal liquid network.

gas charged accumulator tl

Description

Unit Gas-Charged Accumulator (TL) is an accumulator with a gas chamber in a thermal liquid network. The accumulator consists of a chamber pre-filled with gas and a thermal liquid chamber. The chambers are separated by an orifice plate, piston or any other separator.

*Accumulator diagram

gas charged accumulator tl 1 en

When the fluid pressure at the inlet to the accumulator becomes greater than the pressure in the pre-filled gas chamber, the fluid enters the accumulator and compresses the gas. The decrease in fluid pressure causes the gas to decompress and releases the accumulated fluid into the system.

The movement of the divider is restricted by a rigid restrictor when the liquid volume is zero or when the liquid volume is equal to the capacity of the liquid chamber. If the spring stiffness setting is too low, the fluid volume may briefly drop below zero or rise above the fluid chamber capacity. Use the Hard-stop stiffness coefficient parameters to correct this.

Mass Conservation

The mass conservation equation for a liquid in the chamber is:

where

  • - is the density of thermal liquid;

  • - isothermal modulus of elasticity;

  • - isobaric thermal expansion coefficient;

  • - pressure of thermal liquid;

  • - temperature of thermal liquid;

  • - mass flow rate of thermal liquid entering the accumulator through port A.

The block calculates the change in fluid chamber volume over time using Eqs:

where

  • - limiter stiffness coefficient, the value of the Hard-stop stiffness coefficient parameter;

  • - restrictor damping coefficient, value of the Hard-stop damping coefficient parameters;

  • - is the mass flow rate of fluid in the chamber when the accumulator separator contacts the upper hard stop:

  • - mass flow rate of liquid in the chamber when the accumulator divider contacts the lower rigid stop:

Saving the pulse

Conservation of momentum is represented by the following equation:

where is the contact pressure of the rigid limiter:

Conservation of energy

The equation of conservation of energy in the chamber for a liquid is of the form:

where

  • - is the specific internal energy of thermal liquid;

  • - energy flow into the fluid chamber through the inlet of the accumulator;

  • - energy flux into the liquid chamber through the accumulator wall.

Chamber volumes

The volume of liquid in the accumulator is the difference between the total volume of the accumulator and the volume of gas:

where

  • - is the total volume of the accumulator;

  • - volume of liquid in the accumulator;

  • - volume of gas in the accumulator;

Volumes of chambers

gas charged accumulator il 1

The fluid chamber operating volume is the difference between the total volume of the accumulator and the minimum volume of the gas chamber when the fluid chamber is full:

where

  • - is the volume of the liquid chamber;

  • - is the minimum volume of the gas chamber, the small portion of the chamber that remains filled with gas when the liquid chamber is full.

The dependence of pressure and gas volume between the current state and the precharge state is polytropic:

where

  • - is the pressure in the gas chamber at the given time step;

  • - is the volume of gas in the accumulator at the given time step;

  • - pressure in the gas chamber when the liquid chamber is empty;

  • - is the total volume of the liquid chamber;

  • - polytropy exponent.

Assumptions and limitations

  • Gas compression is considered as a polytropic process.

  • The load on the separator is not taken into account.

  • The effect of fluid inertia is not taken into account.

Ports

Conserving

# A — thermal liquid inlet port
thermal liquid

Details

Thermal liquid port, corresponds to the inlet to the accumulator. The flow rate is positive if the fluid enters the accumulator.

Program usage name

port

# H — heat port
heat

Details

A heat port related to the heat capacity of a volume of fluid.

Program usage name

thermal_port

Parameters

Parameters

# Total accumulator volume — total battery capacity
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi

Details

The total volume of the accumulator, including the liquid chamber and the gas chamber, it is equal to the sum of the volume of the liquid chamber and the minimum volume of the gas chamber.

Units

l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi
Default value

8e-3 m^3
Program usage name

V_capacity
Evaluatable

Yes

# Minimum gas volume — minimum gas chamber volume
l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi

Details

Minimum gas chamber volume, the small portion of the chamber that remains filled with gas when the liquid chamber is full.

The value of this parameters must be non-zero to avoid dividing by zero when the liquid chamber is full.

Units

l | gal | igal | m^3 | cm^3 | ft^3 | in^3 | km^3 | mi^3 | mm^3 | um^3 | yd^3 | N*m/Pa | N*m/bar | lbf*ft/psi | ft*lbf/psi
Default value

4e-5 m^3
Program usage name

dead_volume
Evaluatable

Yes

# Precharge pressure (gauge) — gas chamber pressure
Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar

Details

The initial overpressure in the empty accumulator chamber. Fluid enters the accumulator when the inlet pressure is equal to or greater than the pressure in the pre-filled gas chamber.

Units

Pa | GPa | MPa | atm | bar | kPa | ksi | psi | uPa | kbar
Default value

0.0 MPa
Program usage name

p_precharge
Evaluatable

Yes

# Specific heat ratio — specific heat capacity coefficient

Details

Specific heat capacity coefficient (adiabatic value).

Parameters are necessary to account for heat transfer, usually its value is between 1 and 2, depending on the properties of the gas in the chamber.

For dry air at 20°C, the value of the adiabatic exponent for an isothermal process is 1, and for an adiabatic (and isoentropic) process it is 1.4.

Default value

1.4
Program usage name

polytropic_exponent
Evaluatable

Yes

# Cross-sectional area at port A — cross-sectional area of the hole
m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2

Details

Cross-sectional area of the opening at the inlet to the accumulator.

Units

m^2 | cm^2 | ft^2 | in^2 | km^2 | mi^2 | mm^2 | um^2 | yd^2
Default value

0.01 m^2
Program usage name

port_area
Evaluatable

Yes

# Hard-stop stiffness coefficient — stiffness factor
MPa/m^3

Details

The stiffness coefficient of the upper and lower rigid accumulator limiters. Stiffeners are used to limit the fluid volume between zero and the fluid chamber volume.

Units

MPa/m^3
Default value

1e4 MPa/m^3
Program usage name

k_hard_stop
Evaluatable

Yes

# Hard-stop damping coefficient — damping factor
MPa*s/m^6

Details

The damping coefficients of the upper and lower rigid accumulator limiters. The rigid stops are used to limit the fluid volume between zero and the fluid chamber volume. The damping coefficients account for the dissipative part of the contact forces of the rigid stops.

Units

MPa*s/m^6
Default value

1e4 MPa*s/m^6
Program usage name

C_hard_stop
Evaluatable

Yes