# Flow Rate Source (2P)

Generate constant or time-varying mass flow rate or volumetric flow rate in two-phase fluid network

*Since R2023b*

**Libraries:**

Simscape /
Foundation Library /
Two-Phase Fluid /
Sources

## Description

The Flow Rate Source (2P) block represents an ideal
mechanical energy source in a two-phase fluid network. The source can maintain the specified
mass flow rate or volumetric flow rate regardless of the pressure differential. There is no
flow resistance and no heat exchange with the environment. You specify the flow rate type by
using the **Flow rate type** parameter.

The block icon changes depending on the values of the **Source type** and
**Flow rate type** parameters.

Ports **A** and **B** represent the source inlet and
outlet. The input physical signal at port **M** or **V**,
depending on the flow rate type, specifies the flow rate. Alternatively, you can specify a
fixed flow rate as a block parameter. A positive flow rate causes gas to flow from port
**A** to port **B**.

### Mass Balance

The volume of fluid in the source is considered negligible and is ignored in a model. There is no fluid accumulation between the ports and the sum of all mass flow rates into the source must therefore equal zero:

$${\dot{m}}_{\text{A}}+\text{}{\dot{m}}_{\text{B}}=0,$$

where $$\dot{m}$$ denotes the mass flow rate into the source through a port.

When you set the **Flow rate type** parameter to ```
Volumetric
flow rate
```

, the mass flow rate at port **A**
is calculated from the volumetric flow rate:

$$\stackrel{.}{{m}_{A}}=\{\begin{array}{ll}\frac{\dot{V}}{{v}_{\text{B}}},\hfill & \text{if}\dot{V}\ge 0\hfill \\ \frac{\dot{V}}{{v}_{\text{A}}},\hfill & \text{otherwise}\hfill \end{array},$$

where $$\dot{V}$$ is volumetric flow rate and *v* is specific
volume.

### Energy Balance

By default, the source maintains the specified flow rate by performing isentropic work on the incoming fluid, though the block provides the option to ignore this term. The rate at which the source does work, if considered in the model, must equal the sum of the energy flow rates through the ports:

$${\varphi}_{\text{A}}+\text{}{\varphi}_{\text{B}}+\text{}{\varphi}_{\text{Work}}=0,$$

where *ϕ* denotes the energy flow rate into the source
through a port or by means of work. The energy flow rate due to work is equal to the power
generated by the source. Its value is calculated from the specific total enthalpies at the ports:

$${\varphi}_{\text{Work}}={\dot{m}}_{\text{A}}\left({h}_{\text{A}}-{h}_{\text{B}}\right).$$

The specific total enthalpy *h* is defined as:

$${h}_{*}={u}_{*}+{p}_{*}{v}_{*}+\frac{1}{2}{\left(\frac{{\dot{m}}_{*}{v}_{*}}{S}\right)}^{2},$$

where the asterisk denotes a port (**A** or
**B**) and:

*u*is specific internal energy.*p*is pressure.*S*is flow area.

The specific internal energy in the equation is obtained from the tabulated
data of the Two-Phase Fluid Properties (2P)
block. Its value is uniquely determined from the constraint that the work done by the source
is isentropic. The specific entropy, a function of specific internal energy, must then have
the same value at ports **A** and **B**:

$${s}_{\text{A}}\left({p}_{\text{A}},{u}_{\text{A}}\right)={s}_{\text{B}}\left({p}_{\text{B}},{u}_{\text{B}}\right),$$

where *s* is specific entropy. If the **Power
added** parameter is set to `None`

, the specific total
enthalpies at the ports have the same value ($${h}_{\text{A}}={h}_{\text{B}}$$) and the work done by the source reduces to zero ($${\varphi}_{\text{Work}}=0$$).

### Assumptions and Limitations

There are no irreversible losses.

There is no heat exchange with the environment.

## Ports

### Input

### Conserving

## Parameters

## Extended Capabilities

## Version History

**Introduced in R2023b**