# Constant Volume Chamber (TL)

Chamber with fixed volume of thermal liquid and variable number of ports

**Library:**Simscape / Foundation 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 can have between one and four inlets, labeled from **A** to **D**, through which fluid
can flow. The fluid volume can exchange heat with a thermal network, such as a network
representing the chamber surroundings, through the thermal port **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 the 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 the inlet and the interior of the chamber is assumed to be negligible. The pressure in the interior is therefore equal to the pressure at the inlet. 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 the temperature at the thermal port.

### Mass Balance

Mass can enter and exit the chamber through ports **A**, **B**, **C**, and **D**. 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**, **C**, and
**D**:

$$\left(\frac{1}{\beta}\frac{dp}{dt}-\alpha \frac{dT}{dt}\right)\rho V={\dot{m}}_{\text{A}}+{\dot{m}}_{\text{B}}+{\dot{m}}_{\text{C}}+{\dot{m}}_{\text{D}},$$

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.$$\dot{m}$$ is the mass flow rate.

### Energy Balance

Energy can enter and exit the chamber in two ways: with fluid flow through ports
**A**, **B**,
**C**, and **D**, 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 therefore equal the sum of the energy flow rates in through ports
**A**, **B**,
**C**, **D**, and
**H**:

$$\left[\left(\frac{h}{\beta}-\frac{T\alpha}{\rho}\right)\frac{dp}{dt}+\left({c}_{p}-h\alpha \right)\frac{dT}{dt}\right]\rho V={\varphi}_{\text{A}}+{\varphi}_{\text{B}}+{\varphi}_{\text{C}}+{\varphi}_{\text{D}}+\text{}{Q}_{\text{H}},$$

where the left-hand side is the rate of energy accumulation and:

*h*is the enthalpy.*ρ*is the density.*c*_{p}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 therefore equal
the pressure at ports **A**, **B**, **C**, and **D**:

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

### Variables

To set the priority and initial target values for the block variables prior to simulation, use
the **Variables** tab in the block dialog box (or the
**Variables** section in the block Property Inspector). For more
information, see Set Priority and Initial Target for Block Variables.

### Assumptions and Limitations

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

## Parameters

## Extended Capabilities

## See Also

**Introduced in R2013b**