# 3-Port Constant Volume Chamber (TL)

Chamber with three ports and fixed volume of thermal liquid

• Library:
• Thermal Liquid / Elements

## Description

The Constant Volume Chamber (TL) block models the accumulation of mass and energy in a chamber containing a fixed volume of thermal liquid. The chamber has three inlets, labeled A, B, and C, through which fluid can flow. The fluid volume can exchange heat with a thermal network, for example one representing the chamber surroundings, through a thermal port labeled H.

The mass of the fluid in the chamber varies with density, a property that in a thermal liquid is generally a function of pressure and temperature. Fluid enters when the pressure upstream of an inlet rises above that in the chamber and exits when the pressure gradient is reversed. The effect in a model is often to smooth out sudden changes in pressure, much like an electrical capacitor does with voltage.

The flow resistance between each inlet and the interior of the chamber is assumed to be negligible. The pressure in the interior is therefore equal to that at the inlets. Similarly, the thermal resistance between the thermal port and the interior of the chamber is assumed to be negligible. The temperature in the interior is equal to that at the thermal port.

### Mass Balance

Mass can enter and exit the chamber through ports A, B, and C. The volume of the chamber is fixed but the compressibility of the fluid means that its mass can change with pressure and temperature. The rate of mass accumulation in the chamber must exactly equal the mass flow rates in through ports A, B, and C:

`$\left(\frac{1}{\beta }\frac{dp}{dt}-\alpha \frac{dT}{dt}\right)={\stackrel{˙}{m}}_{\text{A}}+{\stackrel{˙}{m}}_{\text{B}}+{\stackrel{˙}{m}}_{\text{C}},$`
where the left-hand side is the rate of mass accumulation and:

• p is the pressure.

• T is the temperature.

• β is the isothermal bulk modulus.

• ɑ is the isobaric thermal expansion coefficient.

• $\stackrel{˙}{m}$ is the mass flow rate.

### Energy Balance

Energy can enter and exit the chamber in two ways: with fluid flow through ports A, B, and C, and with heat flow through port H. No work is done on or by the fluid inside the chamber. The rate of energy accumulation in the internal fluid volume must then equal the sum of the energy flow rates in through ports A, B, C, and H:

`$\left[\left(\frac{h}{\beta }-\frac{T\alpha }{\rho }\right)\frac{dp}{dt}+\left({c}_{p}-h\alpha \right)\frac{dT}{dt}\right]\rho V={\varphi }_{\text{A}}+{\varphi }_{\text{B}}+{\varphi }_{\text{C}}+\text{​}{Q}_{\text{H}},$`
where the left-hand side is the rate of energy accumulation and:

• h is the enthalpy.

• ρ is the density.

• cp is the specific heat.

• V is the chamber volume.

• ϕ is the energy flow rate.

• Q is the heat flow rate.

### Momentum Balance

The pressure drop due to viscous friction between the individual ports and the interior of the chamber is assumed to be negligible. Gravity is ignored as are other body forces. The pressure in the internal fluid volume must then equal that at port A, port B, and port C:

`$p={p}_{\text{A}}={p}_{\text{B}}={p}_{\text{C}}.$`

### Assumptions

• The chamber has a fixed volume of fluid.

• The flow resistance between the inlet and the interior of the chamber is negligible.

• The thermal resistance between the thermal port and the interior of the chamber is negligible.

• The kinetic energy of the fluid in the chamber is negligible.

## Ports

### Conserving

expand all

Opening through which fluid can enter and exit the chamber.

Opening through which fluid can enter and exit the chamber.

Opening through which fluid can enter and exit the chamber.

Interface through which the fluid in the chamber exchanges heat with a thermal network.

## Parameters

expand all

#### Parameters Tab

Volume of fluid in the chamber. This volume is constant during simulation.

Inlet area normal to the direction of flow.

Inlet area normal to the direction of flow.

Inlet area normal to the direction of flow.

#### Variables Tab

Pressure inside the chamber at the start of simulation.

Temperature inside the chamber at the start of simulation.

Internal energy per unit mass of fluid inside the chamber at the start of simulation.

Fluid density inside the chamber at the start of simulation.