# Controlled Volumetric Flow Rate Source (TL)

Generate time-varying volumetric flow rate

## Library

Thermal Liquid/Sources

## Description

The Controlled Volumetric Flow Rate Source (TL) block generates a time-varying volumetric flow rate through its outlet. The source is ideal. It maintains the specified flow rate regardless of the pressure differential between the inlet and outlet. Losses due to friction are assumed negligible.

The flow rate input is a physical signal that you connect to port V. This input controls the volumetric flow rate at the outlet. The rate at the inlet can differ from the input signal if the specific volume changes within the source. However, due to mass conservation, the mass flow rates at the inlet and outlet are always identical.

The ports representing the inlet and outlet change with the flow rate sign. If the flow rate is positive, fluid flows from port A to port B and the outlet is at port B. If the flow rate is negative, fluid flows from port B to port A and the outlet is at port A.

The volumetric and mass flow rates at the source outlet are related through the expression

`$\stackrel{˙}{V}=\left\{\begin{array}{cc}\stackrel{˙}{m}{v}_{B},& \stackrel{˙}{V}\ge 0\\ \stackrel{˙}{m}{v}_{A},& \stackrel{˙}{V}<\text{\hspace{0.17em}}0\end{array},$`
where:

• $\stackrel{˙}{V}$ is the volumetric flow rate.

• $\stackrel{˙}{m}$ is the mass flow rate from port A to port B.

• vA is the specific volume at port A.

• vB is the specific volume at port B.

The energy balance at the source is a function of the energy flow rates through ports A and B and the work done on the fluid:

`${\varphi }_{A}+{\varphi }_{B}+{\varphi }_{work}=0,$`
where:

• ϕA is the energy flow rate into the source through port A.

• ϕB is the energy flow rate into the source through port B.

• ϕwork is the isentropic work done on the fluid.

The isentropic work term is

`${\varphi }_{work}=\stackrel{˙}{m}\left({p}_{B}-{p}_{A}\right){v}_{avg},$`
where:

• ϕwork is the isentropic work done on the thermal liquid.

• pA is the pressure at port A.

• pB is the pressure at port B.

• vavg is the average of the specific volumes at ports A and B,

`${v}_{avg}=\frac{{v}_{A}+{v}_{B}}{2}.$`

### Variables

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.

### Assumptions and Limitations

• The source is ideal. Losses due to friction are assumed negligible.

• The source is adiabatic. Heat exchange with the surroundings is assumed negligible.

• Work done by the source is isentropic—that is, reversible and adiabatic.

## Parameters

Cross-sectional area at ports A and B

Area normal to the direction of flow at the source inlet and outlet. The two cross-sectional areas are assumed identical. The default value is `0.01` m^2.

Characteristic longitudinal length

Average distance the fluid traverses in the source before it reaches the outlet. The default value is `0.1`m.

## Ports

• A — Thermal Liquid conserving port representing source inlet A

• B — Thermal Liquid conserving port representing source inlet B

• V — Physical signal input port for specifying the volumetric flow rate