Cantera/Adiabatic Flame Temperature Dilution - Revision history

Admin: Fix math syntax: collapse multi-line math tag to single line; replace deprecated <source> tags with <syntaxhighlight> (via update-page on MediaWiki MCP Server)

2026-06-14T23:10:29Z

Fix math syntax: collapse multi-line math tag to single line; replace deprecated <source> tags with <syntaxhighlight> (via update-page on MediaWiki MCP Server)

← Older revision		Revision as of 23:10, 14 June 2026
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	Translating that to real Python code,		Translating that to real Python code,

	<~~source~~ lang="python">		<syntaxhighlight lang="python">
	from Cantera import *		from Cantera import *
	from Cantera.Reactor import *		from Cantera.Reactor import *
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	n.advance(t)		n.advance(t)
	return r.temperature()		return r.temperature()
	</~~source~~>		</syntaxhighlight>

	Now we can feed a list of composition vectors or composition strings, and get a list of adiabatic flame temperatures.		Now we can feed a list of composition vectors or composition strings, and get a list of adiabatic flame temperatures.
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	A classical plot for adiabatic flame temperature is the adiabatic flame temperature versus equivalence ratio. The equivalence ratio is defined as:		A classical plot for adiabatic flame temperature is the adiabatic flame temperature versus equivalence ratio. The equivalence ratio is defined as:

	<math>		<math>\phi = \frac{ \mbox{fuel-oxidizer ratio} }{ \mbox{stoich fuel-oxidizer ratio} }</math>
	\phi = \frac{ \mbox{fuel-oxidizer ratio} }{ \mbox{stoich fuel-oxidizer ratio} }
	</math>

	Now we can continue building on the code above. Let's create a function to vary equivalence ratio, and compute a corresponding adiabatic flame temperature. We won't worry for now about how to go from an equivalence ratio to a gas composition.		Now we can continue building on the code above. Let's create a function to vary equivalence ratio, and compute a corresponding adiabatic flame temperature. We won't worry for now about how to go from an equivalence ratio to a gas composition.
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	Next, continuing the script above,		Next, continuing the script above,

	<~~source~~ lang="python">		<syntaxhighlight lang="python">

	def equivalence_ratio_test():		def equivalence_ratio_test():
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	plt.show()		plt.show()

	</~~source~~>		</syntaxhighlight>

	=Nitrogen and Carbon Dioxide Dilution=		=Nitrogen and Carbon Dioxide Dilution=
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	Translating this into Python code,		Translating this into Python code,

	<~~source~~ lang="python">		<syntaxhighlight lang="python">
	def nitrogen_co2_test():		def nitrogen_co2_test():
	T0 = 1073.15		T0 = 1073.15
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	plt.draw()		plt.draw()
	plt.show()		plt.show()
	</~~source~~>		</syntaxhighlight>

Admin at 08:56, 17 April 2017

2017-04-17T08:56:15Z

← Older revision		Revision as of 08:56, 17 April 2017
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	~~[[Category:Cantera]]~~		=Flags=

			{{CanteraFlag}}

Admin: /* The Final Script */

2016-04-20T15:58:02Z

The Final Script

← Older revision		Revision as of 15:58, 20 April 2016
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	plt.show()		plt.show()
	</source>		</source>

	~~=The Final Script=~~

	~~You can download the final script at http://charlesreid1.com/files/adiabflametempdilution.py~~



	[[Category:Cantera]]		[[Category:Cantera]]

Admin: /* The Final Script */

2016-04-20T15:56:15Z

The Final Script

← Older revision		Revision as of 15:56, 20 April 2016
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	=The Final Script=		=The Final Script=

	You can download the final script at http://~~charlesmartinreid~~.com/files/adiabflametempdilution.py		You can download the final script at http://charlesreid1.com/files/adiabflametempdilution.py



	[[Category:Cantera]]		[[Category:Cantera]]

Admin: /* Nitrogen and Carbon Dioxide Dilution */

2014-03-31T11:32:36Z

Nitrogen and Carbon Dioxide Dilution

← Older revision		Revision as of 11:32, 31 March 2014
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	I'll be analyzing the case of ethane combustion (mainly because ethane is slightly easier to ignite, meaning the combustion simulations are shorter and therefore faster).		I'll be analyzing the case of ethane combustion (mainly because ethane is slightly easier to ignite, meaning the combustion simulations are shorter and therefore faster).

			==Nitrogen vs Carbon Dioxide==

			(Comparison of physical properties, thermal heat capacities, etc.)

	==Diluting Function==		==Diluting Function==

Admin at 11:32, 31 March 2014

2014-03-31T11:32:09Z

← Older revision		Revision as of 11:32, 31 March 2014
Line 193:		Line 193:

	You can download the final script at http://charlesmartinreid.com/files/adiabflametempdilution.py		You can download the final script at http://charlesmartinreid.com/files/adiabflametempdilution.py



			[[Category:Cantera]]

Admin: /* Diluting Function */

2014-03-31T11:31:09Z

Diluting Function

← Older revision		Revision as of 11:31, 31 March 2014
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	<pre>		<pre>
	function component fraction to composition:		function component fraction to composition:
	moles of ethane = 1.0		moles of ethane = 1.0
	moles of oxygen = 2.0		moles of oxygen = 2.0
	total moles = moles of ethane + moles of oxygen		total moles = moles of ethane + moles of oxygen
	moles nitrogen = ( y / (1-y) ) * total moles		moles nitrogen = ( y / (1-y) ) * total moles
	assemble composition vector		assemble composition vector
	return composition vector		return composition vector
	</pre>		</pre>

Admin: /* Nitrogen and Carbon Dioxide Dilution */

2014-03-31T11:30:28Z

Nitrogen and Carbon Dioxide Dilution

← Older revision		Revision as of 11:30, 31 March 2014
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	return convert_composition_dict_to_string(d)		return convert_composition_dict_to_string(d)
	</pre>		</pre>

			==Adiabatic Flame Temperature Versus Diluant Concentration==

			Now we can get on with the business of computing our adiabatic flame temperature as a function of diluant concentration.

			For nitrogen concentration, let's analyze the range of 10% to 90%, not because we would actually dilute with nitrogen, but just to see what kind of functional dependence the model predicts.

			For carbon dioxide concentration, let's also analyze 10% to 90%. Then we can compare the trends, as well as identifying the CO2 dilution that gives the same adiabatic flame temperature as an air-fired flame.

			Starting with the pseudocode:

			<pre>
			for each nitrogen fraction:
			call component fraction to composition
			call compute adiabatic flame temperature

			for each carbon dioxide fraction:
			call component fraction to composition
			call compute adiabatic flame temperature
			</pre>

			We put the two in separate loops, in case we want a different number of dilution fractions for the species.

			Translating this into Python code,

			<source lang="python">
			def nitrogen_co2_test():
			T0 = 1073.15
			P0 = 3*OneAtm
			n2fracs = linspace(0.1,0.9,9)
			co2fracs = linspace(0.1,0.9,9)

			n2temps = []
			co2temps = []
			for n2frac in n2fracs:
			n2X = component_frac_to_X('N2',n2frac)
			n2temps.append(compute_adiabatic_flame_T(n2X,T0,P0))

			for co2frac in co2fracs:
			co2X = component_frac_to_X('CO2',co2frac)
			co2temps.append(compute_adiabatic_flame_T(co2X,T0,P0,1.0e-3))

			fig = plt.figure()
			ax = fig.add_subplot(111)
			ax.plot(n2fracs,n2temps,'bo-', label='N2')
			ax.plot(co2fracs,co2temps,'ro-',label='CO2')
			ax.set_xlabel('Diluant Fraction')
			ax.set_ylabel('Adiabatic Flame Temp [K]')
			ax.set_title('Adiab Flame Temp vs Diluant Fraction')
			fig.savefig('AFTvsDilFrac.eps')
			fig.savefig('AFTvsDilFrac.png')

			plt.draw()
			plt.show()
			</source>

			=The Final Script=

			You can download the final script at http://charlesmartinreid.com/files/adiabflametempdilution.py

Admin: /* Nitrogen and Carbon Dioxide Dilution */

2014-03-31T11:23:54Z

Nitrogen and Carbon Dioxide Dilution

← Older revision		Revision as of 11:23, 31 March 2014
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	Air is composed of a 3.7:1 mix of nitrogen and oxygen. To mimic air in an oxy-fired system, an operator would try and mimic the dilution of oxygen with carbon dioxide by mixing them in a similar ratio. However, this is a variable that the operator can (must) control, because not all of the properties of a carbon dioxide-diluted flame match those of a nitrogen-diluted flame. It can be varied to make those properties match more closely.		Air is composed of a 3.7:1 mix of nitrogen and oxygen. To mimic air in an oxy-fired system, an operator would try and mimic the dilution of oxygen with carbon dioxide by mixing them in a similar ratio. However, this is a variable that the operator can (must) control, because not all of the properties of a carbon dioxide-diluted flame match those of a nitrogen-diluted flame. It can be varied to make those properties match more closely.

	~~Just~~ to ~~start~~ with		I'll be analyzing the case of ethane combustion (mainly because ethane is slightly easier to ignite, meaning the combustion simulations are shorter and therefore faster).

			==Diluting Function==

			It will be useful to have a function that takes a diluant species (like 'N2' or 'CO2') and a fraction, and dilutes the mixture of fuel and oxidizer accordingly.

			If we have a mixture of N moles, and we are diluting it with a fraction y of nitrogen or carbon dioxide, we can dilute it in one of two ways:

			'''Method 1:''' Maintain N total moles by taking <math>(1-y)N</math> moles of the original mixture and <math>yN</math> moles of diluant.

			'''Method 2:''' Maintain N moles of original mixture by taking <math>N</math> moles of the original mixture and <math>\frac{y}{1-y} N</math> moles of diluant.

			Method 2 makes life easier, because that way we only have to modify one component - the diluent.

			Let's assume an equivalence ratio value <math>\phi</math> of (.............), which means our fuel to oxidizer ratio is (.......) The pseudocode, then, is:

			<pre>
			function component fraction to composition:
			moles of ethane = 1.0
			moles of oxygen = 2.0
			total moles = moles of ethane + moles of oxygen
			moles nitrogen = ( y / (1-y) ) * total moles
			assemble composition vector
			return composition vector
			</pre>

			Converting this to Python code,

			<pre>
			def component_frac_to_X(spname,frac):
			d = {}
			d['C2H6'] = 1.0
			d['O2'] = 2.0
			mole_sum = sum([d[k] for k in d.keys()])
			d[spname] = (frac/(1-frac))*mole_sum

			return convert_composition_dict_to_string(d)
			</pre>

Admin: /* Adiabatic Flame Temperature vs Equivalence Ratio */

2014-03-31T11:13:41Z

Adiabatic Flame Temperature vs Equivalence Ratio

← Older revision		Revision as of 11:13, 31 March 2014
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	</math>		</math>

	~~Continuing~~ on the code above,		Now we can continue building on the code above. Let's create a function to vary equivalence ratio, and compute a corresponding adiabatic flame temperature. We won't worry for now about how to go from an equivalence ratio to a gas composition.

			First, the pseudocode:

			<pre>
			for phi in range_of_phis:
			convert phi to composition
			call compute_adiabatic_flame_T
			</pre>

			Next, continuing the script above,

	<source lang="python">		<source lang="python">