## Adiabatic Flame Temperature using Python and Cantera - Reactor with Heat Loss

This project main objective is to calculate the Adiabatic Flame Temperature using Python and Cantera. In the first part of the project, the effect of the equivalence ratio for the methane combustion in a constant volume chamber is analyzed, and the python and cantera results are compared and explain. Then, the second part of the project takes into account possible heat loss in the constant pressure combustion of different hydrocarbons, and the results are again compared.

Please refer to the following link to find the code used in this project:

1) Effect of Equivalence Ratio on AFT

The constant volume adiabatic flame temperature is the temperature that results from a complete combustion process that occurs without any work, heat transfer or changes in kinetic or potential energy. This temperature is higher than the constant pressure combustion because none of the energy is used to change the volume of the system. In the first case, the AFL is computed by an internal energy equilibrium, while for the constant pressure combustion is calculated by an enthalpy equilibrium betweeen reactants and products.

The combustion of Methane is the one chosen for this analysis. The stoichiometric reaction is: CH4 + 2(O2 + 3.76N2) = CO2 + 2H20 + 7.52N2. For the Rich and Lean combustions, only one extra specie is selected for simplicity. An alaysis with more species is possible using the cinematic equilibrium constants, but the idea is to analyze the differences between Cantera (a more realistic simulation environment) and the simple program.

A) Python

As stated before, the Python program is base on a simple element and internal energy balance. This problem is simplified to a root finding problem, and it is solved using the Newton Raphson approach.

As expected, the maximum flame temperature takes place for the stoichiometric combustion, and the maximum temperature achieved is around 2800K.

B) Cantera

Cantera is a thermodynamics program that can be used in Python, Matlab or some other languages. The gas.equilibrate function allows the user to calculate the result of any given combustion with high accuracy, as the number of product species in the simulation is high.

Although this solution has the same trend than the previous one, it is clear that the temperatures are different. This is actually for the number of species simulated in Cantera. When any combustion takes place, the products are not just the regular products that we study as a simple model, but tens, hundreds or maybe thousands of other reactions are happening at the same time and forming different species. This process requires energy, and that is the reason the total temperature of the products is reduced when we take all these other reactions taking place (or at least some).

2) Constant Pressure Reactor with Heat Loss

The procedure to follow is the exact same than previously, but in this case the reactor is at constant pressure and with heat losses. For that, the root finding problem is simplified to:

Enthalpy of products - Enthalpy of reactants + F*MaximumQloss=0, where F is the fraction of heat lost.

A) Comparisson for C2H2, C2H4 and C2H6. F=0.35

The purpose of this section is to compare the AFL between an alkane, alkene and alkyne of the same number of carbons. In certain sense is trying to analyze how the double and triple bonds in a hydrocarbon affects to its hability as a fuel. Obviously, the effect of adding Heat Loss in the chamber is also analyzed here.

This results show that the maximum AFL occurs for the C2H2, while the minimum occurs for the C2H6. Why is this? In the alkyne, the fuel require a higher energy employed into breaking its triple bonds. Although the LHV of the last fuel might be higher, the higher number of hydrogen also indicates higher amount of products absorbing this energy. Because of this, it is possible that even having an smaller LHV, the first fuel produces the hottest flame.

Regarding the heat losses, indicate that the model is just an approximation, where the maximum heat loss is the LHV. For this, if you set the Hloss ratio to 1 (this is, all the enrgy is lost) it can be seen that the AFL is close to the standard conditions. Any variation from it is due to incaccuracy when selecting the AFL from internet.

B) Comparisson for a general Alkane. F=0

The purpose of this section is to compare the AFL between different alkanes species, with different number of carbons. This is, setting the heat loss to zero, analyze the impact of the number of carbons in a saturated specie's efficiency as a fuel.

In this case we can see that the higher number of carbons and hydrogens results in a higher AFL. This is because the bonds between the atoms in the three fuels are simple (not doble or triple bonds). Then, the bigger the fuel burned, this produces more energy released into the combustion. Even though the products of these higher fuels are going to have a bigger mass, the total temperature is still higher.

Also notice that the AFL calculated for the Methane, is way lower than the one computed at the beggining of the porject. As already mentioned, this is because the constant volume adiabatic flame temperature considers that no energy is emploted into changing the volume of the systems, what reflects into an overestimation with respect of the constant pressure case.

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