Reactor Network

A reactor network is a collection of 0D chemical reactors connected together to rapidly simulate detailed chemistry in steady combustors.

The reactor network is calculated from a steady reacting flow solution, which is typically modeled with a flamelet model or the EBU model. Computational cells with similar states, by default temperature and equivalence ratio, are clustered into a specified number of reactors. Convective and diffusive mass fluxes between reactors are computed from the reacting flow solution. Finally, the species and temperature in the reactors are solved using the steady mass fluxes, and sources from a detailed chemistry mechanism.

Since clusters are by definition modeled as perfectly mixed reactors, the clustering algorithm is used to find cells that are close in composition space. Reactors that are non-contiguous in space are split, and finally reactors with the smallest number of cells are agglomerated to their closest neighbors until the specified number of reactors are reached.

After the reactors are created, the convection and diffusion flux matrix

{\dot{m}}_{i j}

is calculated from the cell face fluxes where

{\dot{m}}_{i j}

denotes the mass flux into reactor

i

from reactor

j

. The species mass sources are calculated from the boundary inlets and any volumetric mass sources, such as Lagrangian spray.

The total mass that flows into reactor

i

is:

Figure 1. EQUATION_DISPLAY

\dot{m_{i}} = Σ_{j = 1, j \neq i}^{N} \dot{m_{i j}} + Σ_{k = 1}^{K} S_{k}^{i}

(3827)

where:

$N$ is the total number of reactors
${\dot{m}}_{i j}$ is the mass flux into reactor $i$ from reactor $j$
$K$ is the total number of species
$S_{k}^{i}$ is the species mass source for reactor $i$ and species $k$
${\dot{r}}_{k}^{i}$ is the reaction rate for the $i$ th reactor and $k$ th species

There are two types of reactors in Simcenter STAR-CCM+: the Constant Pressure Reactor (CPR) and the Perfectly Stirred Reactor (PSR).

Constant Pressure Reactor (CPR): For CPRs, the mass weighted average species mass fraction entering into the $i$ th reactor $i$ is calculated as:
Figure 2. EQUATION_DISPLAY

$Y_{k, i n}^{i} = Σ_{j = 1, j \neq 1}^{N} \frac{{\dot{m}}_{i j} Y_{k}^{j}}{{\dot{m}}_{i}}$

(3828)
The mass fraction in the $i$ th reactor is calculated as:
Figure 3. EQUATION_DISPLAY

$Y_{k}^{i} = Y_{k, i n}^{i} + \int_{0}^{τ} {\dot{r}}_{k}^{i} d t$

(3829)
where ${\dot{r}}_{k}^{i}$ is the reaction rate for reaction $i$ and species $k$ , and $τ$ is the residence time in the $i$ th reactor, namely $\frac{m_{i}}{{\dot{m}}_{i}}$ .; The mass weighted average soot moment entering into the $i$ th reactor is calculated as:
Figure 4. EQUATION_DISPLAY

$M_{r, i n}^{i} = \sum_{j = 1, j \neq i}^{N} {\dot{m}}_{i j} M_{r}^{j} / {\dot{m}}_{i}$

(3830); and the soot moment in the $i$ th reactor is calculated as:
Figure 5. EQ2UATION_DISPLAY

$M_{r}^{i} = M_{r, i n}^{i} + \int_{0}^{τ} \frac{ω_{M_{r}}^{i}}{ρ} d t$

(3831)
Perfectly Stirred Reactor (PSR): The PSR governing equation set for the $i$ th of $N$ reactors is:
Figure 6. EQUATION_DISPLAY

$Σ_{j = 1, j \neq i}^{N} {\dot{m}}_{i j} Y_{k}^{j} - {\dot{m}}_{i} Y_{k}^{i} = m_{i} {\dot{r}}_{k}^{i} + S_{k}^{i}$

(3832)
where $Y_{k}^{i}$ is the $k$ th species mass fraction in reactor $i$ .; In the limit of a single reactor, the standard PSR equation is obtained:
Figure 7. EQUATION_DISPLAY

$\frac{Y_{k, i n} - Y_{k}}{τ} = {\dot{r}}_{k}$

(3833); The soot moment for a steady state PSR reactor is given by:
Figure 8. EQUATION_DISPLAY

$m_{i} {\dot{M}}_{r}^{i} = \sum_{j = 1, j \neq i}^{N} {\dot{m}}_{i j} M_{r}^{j} - {\dot{m}}_{i} M_{r}^{i} + \frac{{\dot{m}}_{i} {\dot{ω}}_{r}^{i}}{ρ} = 0$

(3834)

Since the mass and the volume of each reactor are constant, the density in each reactor is constant. Further, since the pressure is constant, the reactor temperature is calculated by default from the ideal gas equation of state:

Figure 9. EQUATION_DISPLAY

T_{i} = \frac{p_{i} {\bar{M}}_{w}_{i}}{R_{u} ρ_{i}}

(3835)

where $T_{i}$ is the temperature, $p_{i}$ the pressure, and $ρ_{i}$ the density of the $i$ th reactor. The only thing that changes due to the reactor network mass fractions is the mixture molecular weight of the reactor cell, ${\bar{M}}_{w}_{i}$ .

Optionally, the temperature can be calculated from the CFD enthalpy field and reactor network species solution, or taken from the frozen CFD solution.

Soot

Depending on the selected method, soot emissions are calculated by either the soot moment method or the soot sections method.

Soot Moments: The reactor network uses the soot moment method to simulate soot emissions. The general soot moment source term $ω_{M_{r}}$ , is given by Eqn. (3672) where $M_{r}$ is the $r$ th soot moment. The soot moments are solved coupled with the mass fraction equations in the ODE solver.

Soot Sections: The reactor network uses the soot sections method to simulate soot emissions. The general soot sections source term ${\tilde{Ω}}_{i, s o o t}$ , is given by Eqn. (3717).