Calculation of the main parameters involved in the combustion process of CH 4 -H 2 mixtures at different proportions

. By setting clear targets for reducing pollutant emissions, the researchers in the field of combustion are pushed lately to find new alternatives for cleaner combustion. The partial or total transition to other types of fuels, such as hydrogen, involves substantial changes in the combustion process and possible necessary constructive changes. In the study of the combustion of CH 4 -H 2 mixtures, both numerically and experimentally, preliminary calculations are required, which will help to easily establish the parameters and working regimes and then to use for verifying the results. This paper aims to find an easier method of calculating these parameters, depending on the percentage of gas in the fuel mixture. The calculated values resulted this way will lead to some logical estimates of important aspects of combustion, such as flame field and temperature variation, related to the variation of the amount of hydrogen in the mixture. The method can be a useful tool in the preliminary design of a combustion chamber for CH 4 -H 2 mixtures.


Introduction
Starting from the environmental problems form the past decades, the scientific world is lately in a constant search for less pollutant and more efficient fuels. Hydrogen is studied as a possible alternative, since new ways for producing and transporting it developed in the past few years [1]. For example, from wind or solar energy, hydrogen can be produced on site by electrolysis and can be transported with the existing natural gas distribution network and then used for different existing or new applications. In the field of energy, it could be interesting to use this new fuel in gas turbines, at industrial level, in order to produce electricity and heat.
The new resulting gas, as a mixture of hydrogen and natural gas, depending on the proportions, can change significantly the combustion parameters of the final application, due to the different mixtures properties. From this perspective, numerical and experimental investigations are needed. Various studies and experiments were made with results pointing that above 15-20% H 2 , some structural modifications of the equipment are requested [2] [3] [4].
For both numerical simulations and experimental sessions, the preliminary calculations of the input values and nominal regimes are needed. In order to find the main operating parameters of the combustion, formulas and calculations are usually required, based on theory and literature. These calculations and the preliminary results obtained can be later used to define the input and output parameters in the numerical simulations and to establish the operating regimes, air and fuel flows, temperatures, pressures and stability limits in the experiments. The present paper will point below a method to easily calculate the excess air, the calorific value of the fuel mixture, adiabatic temperature and other important parameters in the combustion chamber and the variation of the products in the combustion gases, according to this mixture's different proportions between methane and hydrogen. Hence, the acquired formulas can be used for obtaining useful values that can be used both as starting data and also for verifying the experimental measured results.

Excess air -mixture ratio -gas analysis
The combustion process for a C n H m , hydrocarbon fuel, as a global stoichiometric reaction using air as an oxidizer, is written as [5] [6]: Although the air contains other compounds in small quantities, beside oxygen (20.95%) and nitrogen (78.08%) and other [5], here is simply considered to be composed only of oxygen (21%) and nitrogen (79%). Thus the molar ratio between the two compounds is considered to be 3.76 in the above relationship.
Therefore, for the combustion of each mole of fuel are required (n+m/4)(1+3.76) moles of air, resulting in 4.76(n+m/4)+m/4 moles of reaction products.

Combustion of CH 4
The overall reaction for stoichiometric combustion process in the case of CH 4 is written as follows [7]: The molar mass of CH 4 is 16.043 g/mol . Thus, the fuel / stoichiometric air ratio is: To burn 1 kg of CH 4 requires 17.16 kg of air, an amount known in the literature as Lmin CH4 , or L 0 CH4 .

Combustion of H 2
The overall reaction for stoichiometric combustion in the case of H 2 is: The molar mass of H 2 is 2.016 g/mol. Thus the fuel/stoichiometric air ratio is: To burn 1 kg of H 2 requires 34.32 kg of air, an amount known in the literature as Lmin H2 or Lo H2 .

Combustion of CH 4 + H 2 mixtures
The classical stoichiometric method of calculation is adopted, writing the individual equations for CH 4 Then the stoichiometric equations are multiplied by the molar fractions of the fuel mixture. For this paper, the following notations and rule are adopted: the molar fraction (or the volume percentage by multiplying by 100) for CH 4 is noted with x, and for H 2 it is noted with y. The condition is x + y = 1; (1 = 100% as percentage). In these conditions: * [CH + 2(O + 3.76N ) → CO + 2H O + 2 * 3.76 * N ] The minimum theoretical air required [8] [kg air /kg fuel ] : Where: Mair = 28.84 [kg/kmol] is the molar mass of air; Mfuel = (1-y) * 16+y * 2 [kg/kmol] is the molar mass of the fuel mixture It results: The excess air is further defined by an excess air coefficient, known also as air-fuel equivalence ratio [5] [9]: where: ̇ -air flow ̇ -fuel mixture flow Fuel-air equivalence ratio, is defined as: Thus, for lean fuel combustion (ϕ ≤1; λ ≥1) the relation (11), can be redefined, obtaining the global equation in the form: Starting from the above, the excess air and dosage are defined (required for comparisons with data from the literature, where dosage is used as a basis): Stoichiometric dosage: The table below shows the variations of these parameters, depending on the composition of the mixture: The flue gas analysis results from the relation (17), depending on the volume fraction of H 2 and on the excess air: Considering that in practice, when using the gas analyzer, water is condensed on the well path, or at the inlet through the special installation in the analyzer, the analysis of dry flue gases, respectively CO 2 , is considered as the main reference element: It results: Or by transforming the relationship (24) : These latter relationships will be used during the experiments to determine the excess air, as an additional, and more accurate, verification of the measured CH 4  3 Adiabatic temperature -mixture ratio It starts from the relationship known for defining the efficiency of combustion: [11] ζ * Hi = (1 + * L ) * h − * L * h The enthalpy can be defined by the following relationship [12]: It was considered that the reference temperature is T -air-fuel equivalence ratio (equation (15) With the two calculation relations for the calorific values by mass, the differences are:  It can be observed that over 40% H 2 (y=0.4) the rising of the lower calorific value is increasing, which is also observed in the diagram below, in which the slope of the curve changes essentially after this value. This observation correlates with the reports in the literature, in which experiments say that up to 10-15% by volume H 2 , there are not special problems for the combustion process [14]. This should be monitored during experiments. In addition to this, the variation of the fuel mixture's flow for CH 4 -H 2 will be considered, which will be adjusted with the change of the percentage of H 2 , in order to obtain the same constant thermal power.
To determine the specific heats, the literature and the common methods indicates various ways, or charts to calculate. One example is presented and used in the program and calculation procedures for combustion chambers used in 1968 by NASA [15]. After transformations, the specific heats can be written: The procedure is iterative (2-3 iterations), in which we start from a specific heat value and depending on the resulting temperature, the calculation is repeated with the value of the specific heat corresponding to the temperature resulting in the first iteration. The method is often used in the field, with different calculation relationships [8] [15] [16].
The presented relations do not take into account the thermal dissociation. In order to make the dissociation correction, we will start from the correction concept according to which the lower calorific value is diminished by the energy lost by dissociation [15] [16]: where Hi dissociation is approximated with the relation [15]: where: f -fuel-air ratio; T 3 -flue gases temperature [K]; After transformations and adaptation to the CH 4 -H 2 mixture, the relationship becomes: where: T 2 -air temperature; T 3 -adiabatic temperature above, T 3 is iterative, as in the case of specific heats Results of calculations using these relationships are presented in the following graph adiabatic temperature of combustion (in the equation is iterative, as in the case of specific heats Cp flgas . Results of calculations using these relationships are presented in the following graphs: for the mixture CH 4   As it can be seen, the deviations are small and of both positive and negative values, not only in one direction (which would suggest a methodological error).

Conclusions
The work here does not aim in this phase to bring special innovations in the field of combustion for CH 4 -H 2 mixtures, it starts from known formulas, specific to the physical and chemical processes that take place in the combustion chambers. However, going deeper into the calculation details for the peculiarities of burning CH 4 and H 2 mixtures, new aspects come to light, highlighting specific tendencies that should direct numerical or experimental research for a certain course. For example, a clear picture of the variation in lower calorific value, depending on the variation in the percentage of hydrogen in the fuel mixture, can lead to some logical estimates of important aspects of combustion, such as flame field and temperature variation, related to the variation of the amount of hydrogen.
Moreover, in this paper very useful formulas have been developed for establishing the starting parameters for possible numerical calculations, as well as for establishing operating regimes for experiments. Finally, the data obtained with these calculations can be compared with those obtained by CFD analysis, or from experiments, as a very useful, correct and easy verification. This work has been funded by the European Social Fund from the Sectorial Operational Programme Human Capital 2014-2020, through the Financial Agreement with the title "Scholarships for entrepreneurial education among doctoral students and postdoctoral researchers (Be Antreprenor!)", Contract no. 51680/09.07.2019 -SMIS code: 124539.