## 3 Results and Discussion  
### Temperature Distribution  
Figure 3 shows the dependence of centerline temperature (\(T_{c}\)) on pressure under fuel-lean and -rich combustion. As the pressure decreases from 97.75 to 76.62 kPa and further to 61.66 kPa, there is an increase in the \(T_{c}\) at the front of furnace. This phenomenon can be attributable to two reasons. First, the fuel burning rate decreases with decreasing pressure [22]. Second, the reduced pressure reduces the oxygen and methane mass concentration gradient at the fuel-rich region [23]. As a result, the combined effect of the two leads to a decrease in the combustion intensity and heat release rate per unit volume. At the rear of the furnace, the combustion reaction ended. [PERSON] et al. [9] presented a correlation for predicting the buoyancy-driven flame fuel gas centerline temperature rise above the ambient temperature, as shown in Equation (1). The \(T_{c}\) at the rear of furnace is determined by the convective heat release rate and density of fuel gas. The convective heat release rate and density of fuel gas increase with decreasing pressure. Hence, compared with \(T_{c}\) at the front of furnace, a reverse effect of pressure at the rear of furnace on \(T_{c}\) is observed, and the value of \(T_{c}\) is higher with smaller pressure after point B. Interestingly, \(T_{c}\) is not dependent on pressure at an appropriate axial height, as shown in point B in Figure 3. This may be the coupling effect of radiation and convection heat. During the experiment, the wall temperature is fixed. According to Equation (2), the heat released per unit flame volume is related to the flame temperature or flu \begin{table}
\begin{tabular}{c c c c} \hline
**Equipment Type** & **Application** & **Measurement Span** & **Uncertainty** \\ \hline Mass flowmeter & Air/methane & Air: 10 L-min\({}^{-1}\) & \(\pm\)2\% \\  & Methane: 1 L-min\({}^{-1}\) & \(\pm\)0.5\% \\ K-type thermocouple & Centerline temperature & 0–1523 K & \(\pm\)0.5\% \\ Pressure gauge & Reactor pressure & 0–110 kPa & \(\pm\)0.1\% \\  & O\({}_{2}\) & 0–25\% & 5–25\% \\ Testo 335 & CO & 0–10,000 ppm & \(\pm\)10\%, 0–200 ppm; \(\pm\)5\%, 201–2000 ppm \\  & NO & 0–2000 ppm & \(\pm\)10\%, 0–99 ppm; \(\pm\)5\%, 100–1999 ppm \\ \hline \end{tabular}
\end{table} 
Table 1: Experimental equipment type specification and uncertainty. \begin{table}
\begin{tabular}{c c c c c c} \hline
**Case** & **P/kPa** & **Altitude/m** & **V\({}_{fuel}\)/m\(\cdot\)s\({}^{-1}\)** & \(\alpha\)** & **m\({}_{air}\)/mg\(\cdot\)s\({}^{-1}\)** \\ \hline
1 & & & & 0.8 & 61.63 \\
2 & & & & 0.9 & 69.33 \\
3 & & & & 1.0 & 77.03 \\
4 & 97.75 & 300  
absorption coefficient of flame. As the pressure decreases, the spectral absorption bands of the triatomic gas spectrum (CO\({}_{2}\), H\({}_{2}\)O) become narrow, and the absorption coefficient of the triatomic gas spectrum decreases [24]. For point A, \(T_{c,A}\) decreases with decreasing pressure. The radiant heat transfer between the flue gas and the wall will be reduced. The reduced radiation heat transfer leads to an increase in \(T_{c}\). In addition, from Equation (1), it is shown that the reduced convection heat transfer also leads to an increase in \(T_{c}\), and such a tendency of temperature was also observed in previous methane diffusion flames and four configurations of cardboard box fires under a sub-atmospheric pressure [9; 10; 25]. Whether fuel lean or rich combustion, the trends of \(T_{c}\) at the front and rear of furnace with pressure are both opposite. In addition, it is also shown in Figure 3 that as the pressure increases from 97.75 kPa to 61.66 kPa, the combustion intensity and heat release rate per unit volume decreases, and the maximum value of centerline temperature (\(T_{c,max}\)) in our work decreases by about 20-50 K at different \(\alpha\).