adiabatic flame temperature

Image:Propan Lewis.svg]]

File:Alkane IUPAC1.svg (2,2,4-Trimethylpentane)]]

In daily life, the vast majority of flames one encounters are those caused by rapid oxidation of hydrocarbons in materials such as wood, wax, fat, plastics, propane, and gasoline. The constant-pressure adiabatic flame temperature of such substances in air is in a relatively narrow range around {{cvt|1950|C|K F|abbr=on}}.{{cn|date=June 2024}} This is mostly because the heat of combustion of these compounds is roughly proportional to the amount of oxygen consumed, which proportionally increases the amount of air that has to be heated, so the effect of a larger heat of combustion on the flame temperature is offset. Incomplete reaction at higher temperature further curtails the effect of a larger heat of combustion.{{cn|date=June 2024}}

Because most combustion processes that happen naturally occur in the open air, there is nothing that confines the gas to a particular volume like the cylinder in an engine. As a result, these substances will burn at a constant pressure, which allows the gas to expand during the process.

Assuming initial atmospheric conditions (1{{nbsp}}bar and 20 °C), the following tableSee under "Tables" in the external references below. lists the flame temperature for various fuels under constant pressure conditions. The temperatures mentioned here are for a stoichiometric fuel-oxidizer mixture (i.e. equivalence ratio φ = 1).

Note that these are theoretical, not actual, flame temperatures produced by a flame that loses no heat. The closest will be the hottest part of a flame, where the combustion reaction is most efficient. This also assumes complete combustion (e.g. perfectly balanced, non-smoky, usually bluish flame). Several values in the table significantly disagree with the literature or predictions by online calculators.

Image:Adiabatic flame temperature (diagram).jpg

From the first law of thermodynamics for a closed reacting system we have

:$\{\}\_RQ\_P\; -\; \{\}\_RW\_P\; =\; U\_P\; -\; U\_R$

where, $\{\}\_RQ\_P$ and $\{\}\_RW\_P$ are the heat and work transferred from the system to the surroundings during the process, respectively, and $U\_R$ and $U\_P$ are the internal energy of the reactants and products, respectively.

In the constant volume adiabatic flame temperature case, the volume of the system is held constant and hence there is no work occurring:

: $\{\}\_RW\_P\; =\; \backslash int\backslash limits\_R^P\; \{pdV\}\; =\; 0$

There is also no heat transfer because the process is defined to be adiabatic: $\{\}\_RQ\_P\; =\; 0$. As a result, the internal energy of the products is equal to the internal energy of the reactants: $U\_P\; =\; U\_R$.

Because this is a closed system, the mass of the products and reactants is constant and the first law can be written on a mass basis,

: $U\_P\; =\; U\_R\; \backslash Rightarrow\; m\_P\; u\_P\; =\; m\_R\; u\_R\; \backslash Rightarrow\; u\_P\; =\; u\_R$.

Image:hrhp.jpg versus temperature diagram illustrating closed system calculation]]

In the case of the constant pressure adiabatic flame temperature, the pressure of the system is held constant, which results in the following equation for the work:

: $\{\}\_RW\_P\; =\; \backslash int\backslash limits\_R^P\; \{pdV\}\; =\; p\backslash left(\; \{V\_P\; -\; V\_R\; \}\; \backslash right)$

Again there is no heat transfer occurring because the process is defined to be adiabatic: $\{\}\_RQ\_P\; =\; 0$. From the first law, we find that,

:$-\; p\backslash left(\; \{V\_P\; -\; V\_R\; \}\; \backslash right)\; =\; U\_P\; -\; U\_R\; \backslash Rightarrow\; U\_P\; +\; pV\_P\; =\; U\_R\; +\; pV\_R$

Recalling the definition of enthalpy we obtain $H\_P\; =\; H\_R$. Because this is a closed system, the mass of the products and reactants is the same and the first law can be written on a mass basis:

: $H\_P\; =\; H\_R\; \backslash Rightarrow\; m\_P\; h\_P\; =\; m\_R\; h\_R\; \backslash Rightarrow\; h\_P\; =\; h\_R$.

We see that the adiabatic flame temperature of the constant pressure process is lower than that of the constant volume process. This is because some of the energy released during combustion goes, as work, into changing the volume of the control system.

File:Adiabatic flame temperatures and pressures as function of stoichiometry (chart).jpg. A ratio of 1 corresponds to the stoichiometric ratio]]

File:Constant volume flame temperature (chart for multiple fuels).jpg

If we make the assumption that combustion goes to completion (i.e. forming only {{chem|C|O|2}} and {{chem|H|2|O}}), we can calculate the adiabatic flame temperature by hand either at stoichiometric conditions or lean of stoichiometry (excess air). This is because there are enough variables and molar equations to balance the left and right hand sides,

:$\{\backslash rm\{C\}\}\_\backslash alpha\; \{\backslash rm\{H\}\}\_\backslash beta\; \{\backslash rm\{O\}\}\_\backslash gamma\; \{\backslash rm\{N\}\}\_\backslash delta\; +\; \backslash left(\; \{a\{\backslash rm\{O\}\}\_\{\backslash rm\{2\}\}\; +\; b\{\backslash rm\{N\}\}\_\{\backslash rm\{2\}\}\; \}\; \backslash right)\; \backslash to\; \backslash nu\; \_1\; \{\backslash rm\{CO\}\}\_\{\backslash rm\{2\}\}\; +\; \backslash nu\; \_2\; \{\backslash rm\{H\}\}\_\{\backslash rm\{2\}\}\; \{\backslash rm\{O\}\}\; +\; \backslash nu\; \_3\; \{\backslash rm\{N\}\}\_\{\backslash rm\{2\}\}\; +\; \backslash nu\; \_4\; \{\backslash rm\{O\}\}\_\{\backslash rm\{2\}\}$

Rich of stoichiometry there are not enough variables because combustion cannot go to completion with at least {{chem|C|O}} and {{chem|H|2}} needed for the molar balance (these are the most common products of incomplete combustion),

:$\{\backslash rm\{C\}\}\_\backslash alpha\; \{\backslash rm\{H\}\}\_\backslash beta\; \{\backslash rm\{O\}\}\_\backslash gamma\; \{\backslash rm\{N\}\}\_\backslash delta\; +\; \backslash left(\; \{a\{\backslash rm\{O\}\}\_\{\backslash rm\{2\}\}\; +\; b\{\backslash rm\{N\}\}\_\{\backslash rm\{2\}\}\; \}\; \backslash right)\; \backslash to\; \backslash nu\; \_1\; \{\backslash rm\{CO\}\}\_\{\backslash rm\{2\}\}\; +\; \backslash nu\; \_2\; \{\backslash rm\{H\}\}\_\{\backslash rm\{2\}\}\; \{\backslash rm\{O\}\}\; +\; \backslash nu\; \_3\; \{\backslash rm\{N\}\}\_\{\backslash rm\{2\}\}\; +\; \backslash nu\; \_5\; \{\backslash rm\{CO\}\}\; +\; \backslash nu\; \_6\; \{\backslash rm\{H\}\}\_\{\backslash rm\{2\}\}$

However, if we include the water gas shift reaction,

: $\{\backslash rm\{CO\}\}\_\{\backslash rm\{2\}\}\; +\; H\_2\; \backslash Leftrightarrow\; \{\backslash rm\{CO\}\}\; +\; \{\backslash rm\{H\}\}\_\{\backslash rm\{2\}\}\; \{\backslash rm\{O\}\}$

and use the equilibrium constant for this reaction, we will have enough variables to complete the calculation.

Different fuels with different levels of energy and molar constituents will have different adiabatic flame temperatures.

Image:Constant pressure flame temperature of a number of fuels.jpg

File:Flame temperature and pressure chart (nitromethane vs isooctane).jpg

We can see by the following figure why nitromethane (CH₃NO₂) is often used as a power boost for cars. Since each molecule of nitromethane contains an oxidant with relatively high-energy bonds between nitrogen and oxygen, it can burn much hotter than hydrocarbons or oxygen-containing methanol. This is analogous to adding pure oxygen, which also raises the adiabatic flame temperature. This in turn allows it to build up more pressure during a constant volume process. The higher the pressure, the more force upon the piston creating more work and more power in the engine. It stays relatively hot rich of stoichiometry because it contains its own oxidant. However, continual running of an engine on nitromethane will eventually melt the piston and/or cylinder because of this higher temperature.

Image:Adiabatic Flame Temperature Dissociation.jpg

In real world applications, complete combustion does not typically occur. Chemistry dictates that dissociation and kinetics will change the composition of the products. There are a number of programs available that can calculate the adiabatic flame temperature taking into account dissociation through equilibrium constants (Stanjan, NASA CEA, AFTP). The following figure illustrates that the effects of dissociation tend to lower the adiabatic flame temperature. This result can be explained through Le Chatelier's principle.

• Flame speed

• {{Cite web

| last = Babrauskas

| first = Vytenis

| title = Temperatures in flames and fires

| work = Fire Science and Technology Inc.

| accessdate = 2008-01-27

| date = 2006-02-25

| url = http://www.doctorfire.com/flametmp.html

| archiveurl = https://web.archive.org/web/20080112141325/http://www.doctorfire.com/flametmp.html

| archivedate = 12 January 2008

| url-status = dead

}}

• [http://elearning.cerfacs.fr/combustion/n7masterCourses/adiabaticflametemperature/index.php Computation of adiabatic flame temperature]
• [http://web.mit.edu/16.unified/www/SPRING/propulsion/notes/node111.html Adiabatic flame temperature]

• {{Cite web

| title = Adiabatic Flame Temperature

| work = The Engineering Toolbox

| accessdate = 2008-01-27

| url = http://www.engineeringtoolbox.com/adiabatic-flame-temperature-d_996.html

| archiveurl= https://web.archive.org/web/20080128053804/http://www.engineeringtoolbox.com/adiabatic-flame-temperature-d_996.html| archivedate= 28 January 2008 | url-status= live}} adiabatic flame temperature of hydrogen, methane, propane and octane with oxygen or air as oxidizers

• {{Cite web

| title = Flame Temperatures for some Common Gases

| work = The Engineering Toolbox

| accessdate = 2008-01-27

| url = http://www.engineeringtoolbox.com/flame-temperatures-gases-d_422.html

| archiveurl= https://web.archive.org/web/20080107164751/http://www.engineeringtoolbox.com/flame-temperatures-gases-d_422.html| archivedate= 7 January 2008 | url-status= live}}

• [http://hypertextbook.com/facts/1998/JamesDanyluk.shtml Temperature of a blue flame and common materials]

• [http://elearning.cerfacs.fr/combustion/tools/adiabaticflametemperature/index.php Online adiabatic flame temperature calculator] using Cantera
• [https://web.archive.org/web/20101022164211/http://people.ku.edu/~depcik/aftp/aftp.htm Adiabatic flame temperature program]
• [http://www.gaseq.co.uk Gaseq], program for performing chemical equilibrium calculations.
• [https://web.archive.org/web/20150521041644/http://astronautics.usc.edu/utility/flame_temperature.php Flame Temperature Calculator] - Constant pressure bipropellant adiabatic combustion
• [http://www.engr.colostate.edu/~allan/thermo/page12/adia_flame/Flamemain.html Adiabatic Flame Temperature calculator]

Category:Combustion

Category:Temperature

Category:Threshold temperatures