# Experimental Study of Methane Combustion Efficiency in a High-Enthalpy Oxygen-Containing Flow
## 3 Experimental Results and Their Analysis
In order to identify the combustion modes, let us assume that for \(\varphi<1\) with a positive value of the derivative \(\partial\eta/\partial\varphi\), a 'kinetic' mode of methane combustion is realized. In the area, for which \(\partial\eta/\partial\varphi<0\), the 'diffusion' mode of methane combustion becomes the most probable. In the case of the local maximum presence which is characterized by the equality-to-zero of the derivative \(\partial\eta/\partial\varphi=0\), the combustion mode will be conventionally called 'diffusion-kinetic'. The presence of an extremum can be explained by the influence of two mutually influencing factors: on the one hand, an increase in the fuel excess coefficient leads to a decrease in the oxygen concentration and on the other hand--to an increase in temperature. Moreover, with an increase in the HOF enthalpy, the position of this extremum shifts to the area of smaller values \(\varphi\). Based on the analysis of the experimental data obtained, \(\varphi\) were determined, under which the maximum values of the combustion completeness coefficient in the HOF are realized and \(\partial\eta/\partial\varphi=0\). Let us call these \(\varphi\) values transitional. The results are shown in Figure 6. The figure also represents areas with predominantly kinetic and diffusion combustion modes. Figure 5: Dependence of the combustion completeness coefficient on the initial HOF enthalpy. 1–\(\eta_{max}\); 2–\(\eta_{-1}\). The dependence of the transitional value of fuel excess coefficient in the considered range can be approximated by a following linear dependence: \(\varphi=0.88\,-\,0.0005\)-\(H\). When \(\varphi\) is less than the transitional value, the combustion mode is 'kinetic'; and when it is greater, it is 'diffusion'. For further analysis, let us assume that the combustion completeness coefficient with a uniform flow in a constant cross-section channel can be represented as  
\[\eta_{x}=\eta_{0}+\int_{0}^{x}\frac{\partial\eta}{\partial x}dx,\]  
where \(\eta_{x}\) is the combustion completeness coefficient in the section with the longitudinal coordinate \(x\), \(\eta_{0}\) is the initial coefficient of methane combustion completeness (in the supply section). It should be noted that \(\eta_{0}\
eq 0\), since reverse currents occur during combustion in the fuel injection zone and methane is thrown 'upstream' [55; 56]. By solving the system of equations for momentum, energy and flow rate conservation [57], it is possible to determine the relationship between the combustion completeness coefficient and the static pressure distribution  
\[\frac{\partial\eta}{\partial x}=\mathrm{K}\frac{\partial p}{\partial x},\]  
where K is the mapping coefficient, which depends on the thermophysical gas properties, the relational heat release during combustion and the gas-dynamic parameters of the flow. It should be noted that during combustion in a subsonic flow, K < 0, and during combustion in a supersonic flow K > 0. According to the data obtained, for the considered flow modes in the experimental facility used, \(\eta_{0}=0.12\ldots 0.23\). In this case, with an increase of HOF enthalpy in the input the \(\eta_{0}\) increases as well. This is a consequence of an increase in the chemical reactions rate with an increase in enthalpy and some changes of the reverse currents zone. It is extremely important to analyze the dynamic processes during the methane combustion in constant cross-section channel. Thus, one of the main experimentally obtained parameters, which allow us to draw conclusions about the amplitude value and the dynamic processes frequency in a constant cross-section channel are the time realizations and  
Figure 6: Dependence of the fuel excess coefficient, corresponding to \(\partial\eta/\partial\varphi=0\) on the initial HOF enthalpy (1), the area of the diffusion combustion mode (2), and the kinetic combustion mode (3). spectrums of non-stationary pressure signals recorded during the tests.