Earlier this year, I wrote my master’s thesis about the flame structure in swirl-stabilized industrial gas turbine burners, the role of fuel staging and the effect of the latter on emissions of nitrogen oxides. A simulation with cantera and Python was used to determine NOx-levels with changing pressure, temperature and fuel staging. In the course of the work, I needed to generature reaction path diagrams of nitrogen. This feature is included in cantera, but creating those diagrams was harder to achieve than I had anticipated. In part, this was due to misleading or missing documentation of cantera. Not only that, it turned out that cantera simply lacks some essential features here. The combination of cantera and the graph visualization tool dot to create those diagrams made it extra confusing, so it took me some time to make cantera and dot do, what I wanted them to do.
As it turned out, not a lot of people have the need to create reaction path diagrams, so there were almost no discussions about it in the Cantera Users‘ Group. But it was essential for me. So I tried to work my way around the pitfalls and was eventually able to come up with some nice looking diagrams. For those of you that face the same problem, this article is for you.
I have written the code in this tutorial initially for cantera 2.2.1 and Python 3.4. For this article, I updated to cantera 2.3.0 and Python 3.6. There were no changes to the reaction path features of cantera in the latest update, so all the code works for the latest versions, respectively. There might be additions to cantera in newer version, and they may render some of the workarounds obsolete. I will try to update this article, but will not promise anything. I encourage you to an open discussion in the Cantera Users‘ Group or the comments here, where you possibly can help others with your input.
What do you need
There are a couple of things you need:
- Python (Reaction path diagrams are not available in cantera for Matlab) – Download here
- Cantera and some other python modules – Find the installation guide here.
- dot (as a part of graphviz) – Download here.
If you are reading this article, you probably came here from a search engine or from the cantera users‘ group. So I assume you already use cantera, that is why I will skip any installation instructions on python or cantera (also, I linked the installation guide above). So let’s start with what you probably don’t already have: dot.
Dot is a description language as well as a tool as part of the Graphviz software package. Graphviz is and open source tool for graph visualization (hence the name) that is used by computer science guys. With dot, you can pretty easily describe a graph, e.g. like this:
digraph graphname {
a -> b -> c;
b -> d;
}
Which turns into a graph like this:
Why am I telling you this? Personally, it always helps me if I really know what I am doing, and why I am doing it. The tool dot that comes with Graphviz is able to understand the notation in the example and can generate graphs like the one above. It is a command line tool that works for Windows, Mac OS and Linux likewise. So, what we are doing is, we use cantera to create the reaction path diagram as dot notation, and after that, we use dot to create the actual diagram. Sounds complicated? It’s not, you’ll see.
Cantera will call dot from the command line, so after you installed graphviz, you need to add dot to your system path variables. For windows users, add the path to dot.exe to the system path variables. The dot.exe can be found in the Graphviz program directory in \release\bin\ or \bin\. So your path should be something like C:\program files\graphviz-2.38\release\bin\. As you probably added python to your system path variables before, this shouldn’t be an issue. If you don’t know how to set your system path variables, please check this link or this one, that should help you.
To test if dot is in your system path variables, open a command line window and type dot -?. You should see the dot help screen:
Now you have everything you need, so let’s dive right in:
Creating a Reaction Path Diagram
Here is a minimal example with the absolute basics needed to generate a reaction path diagram. It defines a mixture of oxygen, nitrogen and methane at 1500 K and 1 bar and follows nitrogen in the reaction. It creates a .png file of the diagram in the same folder:
"""
Minimal reaction path diagram example
Author: Tilman Bremer
Date: June 21st 2017
Written for Python 3.6 with cantera 2.3.0 but might as well work with other versions.
"""
import os
import cantera as ct
# Define a gas mixture at a high temperature that will undergo a reaction:
gas = ct.Solution('gri30.xml')
gas.TPX = 1500, 100000, 'CH4:0.05,O2:0.21,N2:0.79'
# Define the element to follow in the reaction path diagram:
element = 'N'
# Initiate the reaction path diagram:
diagram = ct.ReactionPathDiagram(gas, element)
# Define the filenames:
dot_file = 'ReactionPathDiagram.dot'
img_file = 'ReactionPathDiagram.png'
# Write the dot-file first, then create the image from the dot-file with customizable
# parameters:
diagram.write_dot(dot_file)
# The last command requires dot to be in your system path variables, or your system
# will not undersand the command "dot".
# The command -Tpng defines the filetype and needs to fit your filename defined above,
# or else you will get errors opening the file later.
# The command -Gdpi sets the resolution of the generated image in dpi.
os.system('dot {0} -Tpng -o{1} -Gdpi=300'.format(dot_file, img_file))
The result are two files, a .dot and a .png file. The .dot file contains the notation as introduced before, as created by cantera:
digraph reaction_paths {
center=1;
s47 -> s37[fontname="Helvetica", style="setlinewidth(5.55)", arrowsize=2.78, color="0.7, 1.05, 0.9"
, label=" 0.552"];
s47 -> s34[fontname="Helvetica", style="setlinewidth(6)", arrowsize=3, color="0.7, 1.5, 0.9"
, label=" 1"];
s34 [ fontname="Helvetica", label="NNH"];
s37 [ fontname="Helvetica", label="N2O"];
s47 [ fontname="Helvetica", label="N2"];
label = "Scale = 1.1e-09\l ";
fontname = "Helvetica";
}
The reaction path diagram looks like this:
That was fairly easy. Now, if you look at the diagram and if you think „that doesn’t look very nice, is there a way to adjust the output?“, I have good and bad news for you. The good news are: There is a way. The bad news: It’s pretty limited, it’s buggy and it won’t do what you expect it to do. So, the next part is for the people like me, that just can’t let it be like it is.
Adjustments with cantera
The problem about adjusting the outcome in form of the reaction path diagram, is that we are dealing with two different softwares now. There are options available to control the dot file generated by cantera, and there are options to control how dot reads the .dot file and generates the actual image.
In the cantera docs, you will find the available options for the ReactionPathDiagram class: http://cantera.org/docs/sphinx/html/cython/kinetics.html?highlight=reaction%20path%20diagram#reaction-path-analysis
Let’s start with easy stuff that works. You can change the font used for the diagram with the font options. In the minimal example above, the diagram was initiated by
# Initiate the reaction path diagram: diagram = ct.ReactionPathDiagram(gas, element)
So after that, we can define the options by calling diagram. This is what I used to get the Latex serif font:
diagram.font='CMU Serif'
You can let it show details, like this:
diagram.show_details = True
The results looks like this:
If you look into the cantera docs, you will find a whole bunch of options. At first, this looks very promising, until it isn’t. Let me guide you through some of the options:
font |
Works fine. The name of the font needs to match the name of a system installed font. If you are using Windows and would like to use the Latex font, you should install this font. |
bold_color |
Doesn’t do anything. The color, as specified in the dot code as e.g. color="0.7, 1.05, 0.9" (hue, saturation, lightness) is hardcoded in the c++ code of the ReactionPathDiagram export function (if you are interested, see line 342 here). All lines will stay in a blueish color, because hue is hardcoded to 0.7. There were obviously plans to have the user decide the color scheme, but they never saw the light of day. |
dashed_color |
Same as for bold_color |
normal_color |
Same as for bold_color |
scale |
Scaling the fluxes. You can, for example, use diagram.scale = -1 (that is also the default value) to have the largest flux scaled to unity. If you use diagram.scale = 1, you get the correct net fluxes, the unit is kmol/m³s. I am mentioning that, because the unit is not in the docs, but I was told that it is kmol/m³s in the cantera user group.If you would like to remove the label with the scale, it’s not possible with cantera, because cantera hardcodes the label in the dot code (Line 366). However, it is possible with some additional work, see further below. |
title |
Pretty straight forward, it will print a title in the diagram. The title will be printed at the bottom below the scale notice. If you are using the reaction path diagrams in a scientific work, I recommend to add a caption there instead. |
threshold and label_threshold |
These command are working just fine and they are increadibly helpful to clean up the diagram. E.g. you can set diagram.scale=-1 so that the largest flux is unity. Then you set diagram.threshold=0.05 and all fluxes that are smaller than 5 % of the largest flux are removed. This can help you clean your diagram from irrelevant paths. |
flow_type |
Can be either NetFlow or OneWayFlow and it works just fine. Display element fluxes between species both ways or as a summed up net flux. |
dot_options |
That is quite an interesting option. It says in the cantera docs „Get/Set options for the ‘dot’ program“. What it does, is, it will take whatever you provide here and put it the first line of your reaction path dot code. For you to understand what this can do, you need to have a look in the documentation or the guide for dot (yay!). I will go into detail below, but to give you an example, diagram.dot_options='node[fontsize=20,shape="box"]' will change the fontsize and the shape of every node in your diagram. |
write_dot |
This is the final command, because it is the last one you make. This writes the dot code with all options to your specified location so you can then generate the diagram. |
Following is another example of a slightly more complex reaction path diagram. I took the same initial conditions as above, but I included a reactor to let the gas react a little while so it can reach 1800 K, there is time for more species to form and for more reactions to take place. That is also closer to what I did in my master’s thesis. I am not interested in artificial reaction paths but in the ones, that exist at a certain moment in my reactor in a certain state. Due to the high initial temperature, we have self-ignition and a lot of reactions happening, quite fast:
"""
Reaction path diagram example with some options
Author: Tilman Bremer
Date: June 29th 2017
Written for Python 3.6 with cantera 2.3.0 but might as well work with other versions.
"""
import os
import cantera as ct
# Define a gas mixture at a high temperature that will undergo a reaction:
gas = ct.Solution('gri30.xml')
gas.TPX = 1500, 100000, 'CH4:0.05,O2:0.21,N2:0.79'
# Define a reactor, let it react until the temperature reaches 1800 K:
r = ct.IdealGasReactor(gas)
net = ct.ReactorNet([r])
T = r.T
while T < 1800:
net.step()
T = r.T
# Define the element to follow in the reaction path diagram:
element = 'N'
# Initiate the reaction path diagram:
diagram = ct.ReactionPathDiagram(gas, element)
# Options for cantera:
diagram.show_details = False
diagram.font='CMU Serif Roman'
diagram.threshold=0.01
diagram.dot_options='node[fontsize=20,shape="box"]'
diagram.title = 'Reaction path diagram following {0}'.format(element)
# Define the filenames:
dot_file = 'ReactionPathDiagram.dot'
img_file = 'ReactionPathDiagram.png'
# Write the dot-file first, then create the image from the dot-file with customizable
# parameters:
diagram.write_dot(dot_file)
# The last command requires dot to be in your system path variables, or your system
# will not undersand the command "dot".
# The command -Tpng defines the filetype and needs to fit your filename defined above,
# or else you will get errors opening the file later.
# The command -Gdpi sets the resolution of the generated image in dpi.
os.system('dot {0} -Gdpi=300 -Tpng -o{1}'.format(dot_file, img_file))
The result:
Adjustments with dot
As I have shown, some styling is possible with cantera, but not really a lot. You will now understand why I introduced dot in the beginning, because everything else has to come from and has to go into dot code. dot is a powerful tool, so you can style your reaction path diagram in almost every detail, as long as you care to learn a little bit about dot.
There are two ways to adjust the reaction path diagram using dot commands. The first one is mentioned in the table above in the description for the dot_options command and line 33 of the example right above. The second one is the last line of both presented examples:
os.system('dot {0} -Gdpi=300 -Tpng -o{1}'.format(dot_file, img_file))
This line just calls the command line of your system, replaces {0} and {1} with the path to the dot_file and the img_file and executes the line dot {0} -Gdpi=300 -Tpng -o{1}. -Gdpi=300 and -Tpng are command-line options for dot. There are a couple of command line options, all can can be found on page 7 of this document. What you need to know is, that the commands consist of a first uppercase letter to define a command group and the actual command in lower case:
-T... |
File output formats |
-G... |
Graph attributes |
-N... |
Node attributes |
-E... |
Edge attributes |
-Ecolor |
The line color depends on the size of the flux and is defined by cantera. |
-Earrowtail |
For reasons I cannot figure out, it seems not to work to have arrowtails in reaction path diagrams from cantera. |
-Earrowsize |
Same as with -Ecolor, the arrow size depends on the flux and is set by cantera. |
-Estyle |
Cannot be set to dashed, dotted, etc., because cantera hardcodes a style argument for every edge in the dot file that is used to define the line width. |
fontname (edges and nodes) |
The font is set by canteras global font parameter, if not, Helvetica is the default font. In any case, cantera writes the font all over the place in the dot code, so you cannot change it individually for nodes or edges. |
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