Chamber with one port and fixed volume of gas

**Library:**Simscape / Foundation Library / Gas / Elements

The Constant Volume Chamber (G) block models mass and energy storage in a gas network. The chamber has one port and a constant volume of gas. The enclosure can exchange mass and energy with the connected gas network, as well as exchange heat with the environment, allowing its internal pressure and temperature to evolve over time. The pressure and temperature evolve based on the compressibility and thermal capacity of this gas volume.

Mass conservation relates the mass flow rates to the dynamics of the pressure and temperature of the internal node representing the gas volume:

$$\frac{\partial M}{\partial p}\cdot \frac{d{p}_{\text{I}}}{dt}+\frac{\partial M}{\partial T}\cdot \frac{d{T}_{\text{I}}}{dt}={\dot{m}}_{\text{A}}$$

where:

$$\frac{\partial M}{\partial p}$$ is the partial derivative of the mass of the gas volume with respect to pressure at constant temperature and volume.

$$\frac{\partial M}{\partial T}$$ is the partial derivative of the mass of the gas volume with respect to temperature at constant pressure and volume.

*p*_{I}is the pressure of the gas volume. Pressure at port A is assumed equal to this pressure,*p*_{A}=*p*_{I}.*T*_{I}is the temperature of the gas volume. Temperature at port H is assumed equal to this temperature,*T*_{H}=*T*_{I}.*t*is time.$$\dot{m}$$

_{A}is the mass flow rate at port A. Flow rate associated with a port is positive when it flows into the block.

Energy conservation relates the energy and heat flow rates to the dynamics of the pressure and temperature of the internal node representing the gas volume:

$$\frac{\partial U}{\partial p}\cdot \frac{d{p}_{\text{I}}}{dt}+\frac{\partial U}{\partial T}\cdot \frac{d{T}_{\text{I}}}{dt}={\Phi}_{\text{A}}+{Q}_{\text{H}},$$

where:

$$\frac{\partial U}{\partial p}$$ is the partial derivative of the internal energy of the gas volume with respect to pressure at constant temperature and volume.

$$\frac{\partial U}{\partial T}$$ is the partial derivative of the internal energy of the gas volume with respect to temperature at constant pressure and volume.

Ф

_{A}is the energy flow rate at port A.*Q*_{H}is the heat flow rate at port H.

The partial derivatives of the mass *M* and
the internal energy *U* of the gas volume with respect
to pressure and temperature at constant volume depend on the gas property
model. For perfect and semiperfect gas models, the equations are:

$$\begin{array}{l}\frac{\partial M}{\partial p}=V\frac{{\rho}_{I}}{{p}_{I}}\\ \frac{\partial M}{\partial T}=-V\frac{{\rho}_{I}}{{T}_{I}}\\ \frac{\partial U}{\partial p}=V\left(\frac{{h}_{I}}{ZR{T}_{I}}-1\right)\\ \frac{\partial U}{\partial T}=V{\rho}_{I}\left({c}_{pI}-\frac{{h}_{I}}{{T}_{I}}\right)\end{array}$$

where:

*ρ*_{I}is the density of the gas volume.*V*is the volume of gas.*h*_{I}is the specific enthalpy of the gas volume.*Z*is the compressibility factor.*R*is the specific gas constant.*c*_{pI}is the specific heat at constant pressure of the gas volume.

For real gas model, the partial derivatives of the mass *M* and
the internal energy *U* of the gas volume with respect
to pressure and temperature at constant volume are:

$$\begin{array}{l}\frac{\partial M}{\partial p}=V\frac{{\rho}_{I}}{{\beta}_{I}}\\ \frac{\partial M}{\partial T}=-V{\rho}_{I}{\alpha}_{I}\\ \frac{\partial U}{\partial p}=V\left(\frac{{\rho}_{I}{h}_{I}}{{\beta}_{I}}-{T}_{I}{\alpha}_{I}\right)\\ \frac{\partial U}{\partial T}=V{\rho}_{I}\left({c}_{pI}-{h}_{I}{\alpha}_{I}\right)\end{array}$$

where:

*β*is the isothermal bulk modulus of the gas volume.*α*is the isobaric thermal expansion coefficient of the gas volume.

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

The chamber walls are perfectly rigid.

There is no flow resistance between port A and the chamber interior.

There is no thermal resistance between port H and the chamber interior.

2-Port Constant Volume Chamber (G) | 3-Port Constant Volume Chamber (G) | Reservoir (G)

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