ConvectionP

Chemical Reactor Design Toolbox Reference Manual

ChemReactorDesign.Basic.Gas.Transport.ConvectionP

Description

The component generates a volumetric flow rate due to a pressure difference between the ports. To allow for a change in sign upon reversal of flow direction and to eliminate singularities due to flow reversal, which can pose a challenge for numerical solvers during simulation, the following relation is used

$\begin{equation*} y \, \Delta p = b_{0} \, q + b_{1} \, q \, \sqrt{q^2 + q_{small}^2} \end{equation*}$

with $y_{min} \leq y \leq 1$ as control signal to externally adjust the calculated volumetric flow rate.

If the option checkValve is set any flow reversal is prohibited, i.e. $q \stackrel{!}{\geq} 0$ .

Then the molar flow rates become

$\begin{equation*} F_{i} = q \, \left(\frac{x_{i} \, p}{z \, R \ T} \right)_{upstream} \end{equation*}$

The energy flow rate is determined as

$\begin{equation*} \Phi = \sum_{i}^{N} F_{i} \, \left({\overline H}_{i}(T)\right)_{upstream} + F_{tot} \, \Big(H_{res}(T,p)\Big)_{upstream} \end{equation*}$

with

$\begin{equation*} F_{tot} = \sum_{i}^{N} F_{i} \end{equation*}$

The positive flow direction is from port A to port B.

Ports

Conserving

Gas conserving port
```
Port_A = Gas;  %
```
Gas conserving port
```
Port_B = Gas;  %
```

Input

Physical control signal
```
yin = {0,'1'}; 
```
Dependencies: The port is only visible when controlInput is set to On.

Output

Physical signal that represents the volumetric flow rate at upstream conditions
```
qout = {1,'l/s'};
```
Dependencies: The port is only visible when flowOutput is set to On.

Parameters

Options

Option to select control input
```
controlInput = OnOff.Off;
```
Off | On
Option to select flow output
```
flowOutput = OnOff.Off; 
```
On | Off
Option to set check valve
```
checkValve = OnOff.Off; 
```
On | Off

Mass Transport

Laminar flow parameter
```
b0 = {1.0,'bar*s/m^3'};
```
Turbulent flow parameter
```
b1 = {1.0e-10,'bar*s^2/m^6'}; 
```

Assumptions and Limitations

The parameter $q_{small}$ is internally set to a value of $1.0 \times 10^-6 \, \frac{l}{s}$ .

Nomenclature

$b_{0}$	laminar flow parameter
$b_{1}$	turbulent flow parameter
$F_{i}$	molar flow rate of species A_i
${\overline H}_{i}(T)$	molar enthalpy of species A_i
$\Delta H_{res}$	departure enthalpy of the mixture
$N$	total number of species
$p$	pressure
$q$	volumetric flow rate
$t$	time
$T$	temperature
$x_{i}$	mole fraction of species A_i
$y$	control signal
$z$	compressibility
$\Phi$	energy flow rate