## Abstract

Green hydrogen which could be produced from renewable sources by solar water splitting or photovoltaic electrolysis will play an important role in achieving net-zero in the near future. One possible approach will be to mix hydrogen with natural gas for power generation in gas turbine systems. It is necessary to know the physical properties of burning speed of the mixture of natural gas and hydrogen. Since natural gas is mainly made up of methane, the burning speed of mixtures of methane and hydrogen has been measured and reported in this paper. Adding hydrogen gas during the combustion of methane enhances flame stability, expands the lean flammability range, decreases pollutant emissions, and boosts the burning speed. Burning speed measurement is performed in a cylindrical and spherical chamber. The pressure rise due to combustion was measured by a pressure transducer on the top of cylindrical and spherical chambers. The Z-shaped Schlieren system, equipped with a high-speed complementary metal oxide semiconductor (CMOS) camera, obtains pictures of flame propagation. Laminar burning speed is measured exclusively for flames that have a smooth and spherical shape. In addition, burning speed is only measured for large flame radii with low stretch rates. Burning speed is calculated by a thermodynamic model with the pressure rise data as an input. Measurements cover a wide range of operating conditions. The hydrogen mole fraction is 0%, 20%, and 40%, with temperatures of 298–400 K, pressures between 0.5 and 5.5 atmospheres and equivalence ratios of 0.8, 1, and 1.2.

## 1 Introduction

Methane is a colorless, odorless, and highly flammable gas with the chemical formula of CH_{4}. It is the simplest hydrocarbon and belongs to the alkane group. As an essential component of natural gas, methane plays a crucial role in various natural processes and human activities. Hydrogen gas is a colorless, odorless, and highly flammable gas. It has various applications in industrial processes, fuel cell technology, transportation, and space exploration. The hydrogen molecule is crucial in many chemical reactions and serves as an important element in our daily lives and numerous industries.

Solar energy may be utilized to generate green hydrogen via a method known as solar water splitting or photovoltaic electrolysis. Solar panels or photovoltaic cells are used to directly convert sunlight into energy, which is then utilized to split water molecules into hydrogen (H_{2}) and oxygen (O_{2}) by electrolysis [1].

Mixing hydrogen into the combustion of hydrocarbons enhances flame stability [2], expands methane lean flammability limits, increases burning speed [3], and diminishes pollutant emissions [4].

One essential characteristic of a flammable mixture is its laminar burning speed, which can provide details about its diffusivity, exothermicity, and reactivity. Models of numerical chemical kinetics are frequently validated using it. The equivalence ratio, temperature, pressure, and other operating parameters affect the burning speed.

Various experimental methods can be used to determine laminar burning speed [5]. The methods can be categorized as stationary flame method and propagating flame method based on the flame type. The propagating flame method also can be classified into constant volume method and constant pressure method. Milton and Keck [6] used constant volume method to measure laminar burning speed in stoichiometric hydrogen and hydrogen-hydrocarbon gas mixtures. All mixtures were stoichiometric with air and pressures and temperatures varied between 0.5 and 7 atm, between 300 and 550 K. Kishore et al. [7] conducted an experiment to determine the laminar burning speed of natural gas using a heat flux method. They investigated how different levels of CO_{2} (ranging from 0% to 60%) affected flame attributes under various conditions, including equivalence ratios between 0.6 and 1.4, a temperature of 307 K, and atmospheric pressure. Elia et al. [8] measured the laminar burning speed of methane by a constant volume method. The measurements were made in the range of pressures (0.75–70 atm), unburned gas temperatures (298–550 K), fuel–air equivalence ratio (0.8–1.2), and diluent addition from 0% to 15% by volume. They also developed power-law correlations to fit the experimental results. Bai et al. [9] burned CH_{4}/CO_{2}/air mixtures and also established power-law correlations for the laminar burning speed of these mixtures for various equivalence ratios (0.8–1.2), pressures (0.5–6.9 atm), and temperatures (298–661 K), and CO_{2} concentrations (0–60%). They also utilized the constant volume method.

Halter et al. [10] used the constant pressure method to measure the laminar burning speed of methane–hydrogen–air mixtures for variable equivalence ratios (0.7–1.2), pressures (0.1, 0.3, 0.5 MPa) and the hydrogen mole fraction (0, 0.1 and 0.2). They also compared experimental results to computational calculation using a detailed chemical mechanism. Ilbas et al. [4] studied the laminar burning speed of various mixtures of hydrogen and methane with air, ranging from pure hydrogen to pure methane by using the constant pressure method. They measured the burning speed at ambient temperatures for variable equivalence ratios (0.8–3.2). Eckart et al. [11] generated laminar burning speed data for the range of temperature (298–373 K), pressure (1–5 bar), and hydrogen mole fraction(0–50%) by using the heat flux method and constant pressure method. They also proposed a power-law correlation for temperature and pressure.

As mentioned earlier, all three experiments [4,10,11] for measuring the laminar burning speed of methane–hydrogen–air mixtures used the constant pressure method. The main limitation of this method is flame radii are very small with very high stretch rates. Investigators use different methods of linear, polynomial, and logarithmic to predict the unstretched burning speeds unfortunately the prediction could be wrong. An additional limitation of using this method is for each experiment, only one laminar burning speed can be measured, and it is hard to measure laminar burning speed at high temperatures and pressure. In this work, the constant volume method is used to measure laminar burning speed. In current work, flame radii are large, and stretch effects are negligible. Also, for each experiment, a series of laminar burning speeds can be measured along an isentrope. Thus, laminar burning speeds can be measured for a broad range of temperatures and pressures.

The aim of this work is to measure the laminar burning speed of hydrogen–methane mixtures for a broad range of pressures from 0.5 atm to 5.5 atm, a broad range of temperatures ranging between 298 K and 400 K, and equivalence ratios between 0.8 and 1.2, and hydrogen mole fraction within the mixture of 0–40%. The measured range of data increases the range that was measured by previous researchers.

_{4}/H

_{2}/air is:

## 2 Experimental Setup

The experimental setup is made up of both spherical and cylindrical combustion chambers as presented in Fig. 1. The cylindrical chamber is constituted by a cylindrical vessel and two pieces of cylindrical fused silica glass. The cylindrical vessel is made of 316 stainless steel and the diameter and length of the cylindrical vessel are both 13.5 centimeters. The fused silica windows are fixed by the two stainless steel rings pressing from both sides allowing optical access in the chamber. A high-speed camera captured pictures of flames in a Z-shaped Schlieren system. The camera can take pictures up to 10,000 frames per second. In addition, pictures are utilized to study flame stability and instability and to monitor the shape of the flame. Only when the flame was smooth and spherical, the pressure–time data were collected and used to calculate laminar burning speed.

The spherical chamber is made of stainless steel and has an inner diameter of 15.24 cm. It consists of two hemispheres each having a thickness of 2.54 cm, designed to endure pressures of 400 atm maximum. Since the flame shape is inherently spherical, the cylindrical chamber geometry could have an impact on the pressure–time data for large radii. Therefore, the cylindrical chamber was utilized to analyze the morphology and stability of the flame in addition to taking flame propagation pictures that were used to confirm the flame was laminar, smooth, and spherical. A spherical chamber was utilized to collect pressure–time data. Figure 2 displays the pressure with time for experiments conducted in spherical and cylindrical containers. The experiments started at an initial pressure of 1 atm, an equivalence ratio of 1, an initial temperature of 298 K, and a hydrogen mole fraction of 20%. Point A occurs when the flame in the cylindrical vessel makes contact with the wall, but the flame in the spherical vessel does not make contact with the wall. The identical experimental circumstances were replicated in the spherical chamber to gather pressure-increase data and verify its repeatability. Additional details on the experimental equipment are available in other research papers [12–15].

## 3 Thermodynamic Model

The model can determine the laminar burning speed by analyzing the pressure increase within the combustion chamber. It is derived from prior work by Metghalchi and Keck [16,17]. The model supposes that the combustion chamber can be partitioned into burned and unburned parts which is shown in Fig. 3. There are a few assumptions, which are, that the burned and unburned gas behaves as an ideal gas, both gases are compressed isentropically and the burned and unburned regions are separated by a reaction layer of negligible thickness. The burned gas region is divided into “*n*” number of shells. Each shell has a different temperature and burned gases inside each shell remain in local chemical equilibrium. Experimental pressure increase data are used for calculating the temperature of each shell in burned gases and the mass fraction of burned gases, applying volume and energy balances. The burning speed is determined by the rate at which the mass fraction of burned gases changes over time. This model takes into account temperature gradients in the burned gas and preheat zone, the impacts of radiative and conductive energy losses to the chamber walls, the influence of wall and electrode boundary layers, and the consequences of conductive energy loss to the spark electrodes. Additional information on the model can be found in Refs. [18–25].

*p*and

*T*are pressure and temperature,

*v*is specific volume, and

*R*is the gas constant.

*m*is the total mass of the gas in the chamber, $mb$ is the mass of the burned gas, $Vc$ is the volume of the chamber and $Ve$ is the volume of the spark electrodes, and $pi$ and $Ti$ are the initial pressure and temperature.

*σ*represents the Stefan–Boltzman constant.

For given pressure, $p(t)$, Eqs. (11) and (12) were solved using the Newton–Raphson method to find the values of two unknowns: the temperature of the last shell burned gases, $Tb(t)$, and mass fraction, $xb(t)$.

*π*is the flame area,

*r*is the flame radius, and $re$ is the electrode radius.

Computational laminar burning speeds were also predicted by a 1D flame code from Cantera. Two different chemical kinetic mechanisms GRI-Mech 3.0 and AramcoMech 1.3 were used in the computational calculation. The GRI-Mech 3.0 contains 53 species and 325 reactions [26]. The AramcoMech 1.3 contains 124 species and 766 reactions [27].

## 4 Result and Discussion

Based on different initial conditions, laminar burning speed has been measured for temperatures ranging from 298 K to 400 K, pressures between 0.5 and 5.5 atmospheres, equivalence ratios between 0.8 and 1.2, and hydrogen mole fractions of 0%, 20%, and 40%.

Laminar burning speed were calculated only when the flame was smooth and spherical. In addition, burning speeds were calculated for flame radii larger than 40 mm resulting in a very low stretch rate. Pictures of flames were taken by a high-speed camera with a speed of 10,000 flames per second. Figure 4 shows flame pictures captured by the Schlieren system for different equivalence ratios and different initial pressures. There is an initial temperature of 298 K, an equivalence ratio of 1 with a flame radius of 63 mm for all cases. Timestamps are provided underneath every picture. The figures show that pressure adversely affects flame stability. and as the hydrogen mole fraction increases, flames become more cellular. The time of flame arrival to 63 mm radius is short when the hydrogen mole fraction increases and pressure decreases. It means that the burning speed increases with hydrogen mole fraction increasing or pressure decreasing.

*r*is the flame radius. The stretched laminar burning speed is not an intrinsic combustion property, but it is influenced by the flame's shape. To obtain the unstretched laminar burning speed, it is commonly extrapolated using several methods. In order to reduce the effects of stretch, it is preferable to measure laminar burning speeds at large flame radii.

Figure 5 presents the stretch rate as a function of normalized flame radius with respect to vessel radius. The initial condition for this experiment was at $pi=2atm,Ti=298K$, $\varphi =1$ and $X=0$. In this research normalized flame radii of larger than 0.58 have been used. For these cases, the maximum stretch rate is less than 95 s^{−1}, and it decreases as the flame radius increases. The effect of stretch on burning speed at these very low values is negligible.

*optimize.minimize*in the python SciPy library is used to find them, utilizing an unconstrained minimization strategy.

The experimental data were fitted to a power-law correlation Eq. (17) for different hydrogen mole fractions. The constants for power-law correlation are shown in Table 1. The coefficient of determination(*R*^{2}) is 0.9949, 0.9891 and 0.9940 for hydrogen mole fraction 0%, 20% and 40%. The coefficients in this table were only validated in temperatures of $298K<Tu<400K$, pressures of $0.5atm<p<5.5atm$, and equivalence ratios of $0.8<\varphi <1.2$.

Laminar burning speeds were also calculated using the Cantera code with two chemical kinetics mechanisms. GRI-Mech 3.0 [26] and AramacoMech 1.3 [27] were used in the computational calculation. Figure 6 compares the experimental laminar burning speeds along three isentropes and computational results predicted by two chemical mechanisms for different conditions. The initial pressures of the three conditions were 0.5 atm, 1 atm, and 2 atm. The circle symbols are the raw experiment data, the square symbols are the computational results predicted by GRI-Mech 3.0 and the triangle symbols are the computational results predicted by AramcoMech 1.3. It can be seen that for all those cases, AramcoMech 1.3 has a better agreement with experimental results than GRI-Mech 3.0. As a result, AramcoMech 1.3 has been used in the following work to determine computational laminar burning speeds.

Figure 7 compares the experimental results of the present work with Halter's and Eckart's experiment results at a temperature of 298 K, a pressure of 0.1 MPa, and hydrogen mole fraction of 20%. The experimental results of the present work based on power-law correlation are in good agreement with Halter et al.'s and Eckart et al.'s [10,11] experiment results except for Halter's result at $\varphi =1.2$.

Figures 8 through 16 show measured values of burning speed of methane/hydrogen/air mixtures across various temperatures, fuel–air equivalence ratios, pressures, and hydrogen mole fraction in the fuel. The circle symbols represent the measured values, the square symbols represent the computational results, and the solid curves represent the results of the power-law correlations based on Eq. (17).

Figure 8 displays the laminar burning speed of CH_{4}/H_{2}/air stoichiometric mixtures with varying initial pressure, initial temperature of 298 K, and hydrogen mole fraction of 0%. It also compares experimental results with computational results and Elia's [8] power-law correlation results. This figure shows laminar burning speed decreases with increasing initial pressure. Elia's power-law correlations are very close to the experimental results at initial pressures of 1 atm and 2 atm. However, the computational results are 5% higher than the experimental results for all the cases.

Figure 9 illustrates the laminar burning speed of CH_{4}/H_{2}/air mixtures along three isentropes with varying initial pressure, initial temperature of 298 K, equivalence ratio of 1.2, and hydrogen mole fraction of 40%. It also compares experimental results with computational results. This figure also shows laminar burning speed decreases with increasing initial pressure. The computational results are in excellent agreement with the experiment results.

Figure 10 shows the laminar burning speed of CH_{4}/H_{2}/air mixtures along three isentropes with varying hydrogen mole fraction, initial temperature of 298 K, initial pressure of 1 atm, and an equivalence ratio of 1.2. This figure shows that the laminar burning speed rises with an increase in hydrogen mole fraction. This is because the laminar burning speed of pure hydrogen is higher than the laminar burning speed of pure methane. The experimental results are in reasonable agreement with the computational results.

Figure 11 displays the laminar burning speed of CH_{4}/H_{2}/air mixtures along three isentropes with varying equivalence ratios, initial temperature of 298 K, initial pressure of 2 atm, and hydrogen mole fraction of 20%. This figure shows $\varphi =0.8$ case has the lowest laminar burning speed. Laminar burning speeds of $\varphi =1$ and $\varphi =1.2$ are close to each other. The computational results are 3–5% higher than the experimental results for all the cases.

Figure 12 shows the laminar burning speed of CH_{4}/H_{2}/air mixtures along three isentropes with varying equivalence ratios at an initial temperature of 298 K, an initial pressure of 0.5 atm, and the hydrogen mole fraction of 40%. The case with *ϕ* = 0.8 has the lowest laminar burning speed among the three cases. Laminar burning speeds of $\varphi =1$ and $\varphi =1.2$ are almost the same. The experimental results are very close to those of computational predictions. Nevertheless, the theoretical results are higher than the experimental results at an equivalence ratio of 0.8.

Figure 13 shows burning speed values as a function of fuel–air equivalence ratio at 320 K temperature and 1.3 atm pressure for three different mole fractions of hydrogen in a fuel mixture. Also shown are Elia's results [8]. It can be seen that the maximum laminar burning speed is at an equivalence ratio between 1 and 1.1. This is because the maximum adiabatic flame temperature also occurs at an equivalence ratio between 1 and 1.1. The experimental results are in good agreement with the computational results.

Figure 14 compares experimental correlation laminar burning speeds and computational predictions for CH_{4}/H_{2}/air stoichiometric mixtures as a function of pressures at an unburned gas temperature of 350 K and hydrogen mole fractions of 0%, 20%, and 40%. The circle symbols represent the raw experimental data while the solid curves are the power-law correlation. The square symbol is a computational prediction. The experimental correlation results are in good agreement with computational results.

Figure 15 compares experimental correlation laminar burning speeds and computational predictions for stoichiometric CH_{4}/H_{2}/air mixtures as a function of unburned gas temperatures at a pressure of 1.5 atm and hydrogen mole fraction of 0%, 20%, and 40%. The circle symbols represent the unprocessed experimental data while the solid curves represent the power-law correlation. The square symbols represent computational results. The experimental correlation results align well with computational results, indicating that burning speed rises with unburned gas temperature.

Figure 16 compares experimental results and computational predictions for CH_{4}/H_{2}/air stoichiometric mixtures along with varying hydrogen mole fractions at an unburned gas temperature of 350 K and pressures of 0.5, 1, and 2 atm. The circle symbols are the raw experimental data, and the square symbol is the computational results. The experimental correlation results are in excellent agreement with computational results.

## 5 Conclusions

In this work, laminar burning speeds of the mixture of methane, hydrogen, and air were measured for temperatures ranging between 298 K and 400 K, pressures ranging from 0.5 atm to 5.5 atm, fuel–air equivalence ratio $\varphi $ of 0.8, 1.0, and 1.2, as well as the hydrogen mole fraction *X* of 0, 20%, and 40%. In this research large flame radii were used to measure burning speed where there is no need to extrapolate to zero stretch. Also, the results of this research have increased the range of experimental data. Based on the experimental results, it can be concluded that laminar burning speed increases with temperature. An increase in pressure leads to a decrease in laminar burning speed and the flame will be more cellular. Also, as the hydrogen mole fraction increases, laminar burning speed increases as the tendency of flames becomes cellular.

## Conflict of Interest

There are no conflicts of interest. This article does not include research in which human participants were involved. Informed consent is not applicable. This article does not include any research in which animal participants were involved.

## Data Availability Statement

The datasets generated and supporting the findings of this article are obtainable from the corresponding author upon reasonable request.

## References

*Renewable Energy and Sustainable Buildings: Selected Papers From the World Renewable Energy Congress*WREC 2018