Monitoring and Plotting Carbon

You compare the mass of carbon entering the computational domain with the mass of carbon leaving it. When the two mass flow rates reach the same value, you can assume that the solution has converged.

The mass flow rate of carbon at the inlet boundaries is calculated as a product of mass flow rate of coal at the injector, the mass fraction of carbon in the ultimate analysis, and the mass fraction of raw coal at the injector.

{\dot{m}}_{in, C} = 0.01162 \frac{k g}{s} * 0.8036 * 0.917 = 0.0085628 \frac{k g}{s}

By considering all species in the reaction mechanism that contain carbon, the mass outflow rate of carbon can be defined as:

{\dot{m}}_{out, C} = {\dot{m}}_{tot} (\frac{A_{r} (C)}{M_{W} (C O_{2})} Y_{CO 2} + \frac{A_{r} (C)}{M_{W} (C O)} Y_{CO} + \frac{2.803 A_{r} (C)}{M_{W} (C o a l V o l a t i l e)} Y_{CoalVolatile})

where ${\dot{m}}_{tot}$ is the total mass flow rate, $M_{W} (i)$ is the molecular weight, $A_{r} (i)$ is the atomic weight, and $Y_{i}$ is the mass fraction of species $i$ .

The mass flow rate of carbon can then be written as:

图 1. EQUATION_DISPLAY

{\dot{m}}_{out} (C) = {\dot{m}}_{tot} (0.27 Y_{CO 2} + 0.43 Y_{CO} + 0.673 Y_{CoalVolatile})

(5263)

From the ingoing and outgoing carbon mass flow rates, you create a monitor for a normalized carbon balance $({\dot{m}}_{in} - {\dot{m}}_{out}) / {\dot{m}}_{in}$ that you use later on to define a monitor-based stopping criterion.

To monitor and plot carbon:

Create a report for the mass flow rate of incoming carbon.

Right-click the Reports node and select New > User > Expression.
Rename the Expression 1 node as Carbon In.

Select the Carbon In node and set the following properties:


Property	Setting
Definition	0.0085628
Dimensions	Click (Custom Editor). In the Carbon In - Dimensions window, set Mass to 1, set Time to -1.

Create a report for the mass flow rate of carbon leaving the computational domain.

Right-click the Reports node and select New > User > Sum.
Rename the Sum 1 node as Carbon Out.

Select the Carbon Out node and set the following properties:


Property	Setting
Field Function	Carbon This user-defined field function has been pre-defined on the starting simulation file of the tutorial. Its definition corresponds to Eqn. (5263).
Parts	Regions > coalCombustor > Boundaries > OUTLET

Create a plot to display the ingoing and outgoing mass flow rate of carbon:
1. Multi-select the Carbon In and the Carbon Out report nodes, right-click one of the selected nodes and select Create Monitor and Plot from Report.
2. In the Create Plot From Reports dialog, click Single Plot.
3. Rename the Plots > Reports Plot node Carbon Balance.
Create a report and monitor to calculate the normalized carbon balance.
1. Right-click the Reports node and select New > User > Expression.
2. Rename the Expression 1 node as Normalized Carbon Balance.
3. Select the Normalized Carbon Balance node and Definition to (${Carbon In}-${Carbon Out})/${Carbon In}.
4. Right-click the Normalized Carbon Balance node and select Create Monitor from Report.
Create one more report to analyze the char burnout of the coal particles.
1. Right-click the Reports node and select New > Combustion > Char Burn Out.
2. Rename the Char Burn Out 1 node as Char Burnout.
3. Select the Char Burnout node and set Parts to Coal.
Within the Monitors node, multi-select the following nodes and set Normalization Option to Off.
- CO
- CO2
- CoalVolatile
- Continuity
- Energy
- H2
- H2O
- N2
- O2
- Tdr
- Tke
- SO2
- X-momentum
- Y-momentum
- Z-momentum
Save the simulation.