Chamber with two ports and fixed volume of thermal liquid

**Library:**Thermal Liquid / Elements

The 2-Port 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 two inlets, labeled **A** and **B**, 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 can enter and exit the chamber through ports **A** and **B**. 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 rate in through ports **A** and
**B**:

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

*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 can enter and exit the chamber in two ways: with fluid flow through ports
**A** and **B** 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**, and
**H**:

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

*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.

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** and port **B**:

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

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.

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