## 2 Experimental Methodology  
The schematic of the overall combustion system and its external devices are shown in Figure 1. In this work, the sub-atmospheric pressure combustion environment within the furnace was achieved by three oil-free diaphragm vacuum pumps with capacities of 10 L-min\({}^{-1}\), 15 L-min\({}^{-1}\), and 20 L-min\({}^{-1}\), which was proven to be scientifically sound and feasible in many previous studies [20; 21]. The low air chamber has a minimum working pressure of 50 kPa with an accuracy of \(\pm\)50 Pa, a cylindrical quartz tube, an internal height of 1000 mm, and an internal diameter of 116 mm. To protect the oil-free diaphragm vacuum pump, the water and carbon black of the fine gas were filtered by the condensing-west tube, joint flask, and filter. The air was supplied through two air compressors. The CH\({}_{4}\) is supplied through a high-pressure gas cylinder (with the purity of higher than 99.999%) and a reducing value. The other species in the gas cylinder are mainly C\({}_{2}\)H\({}_{6}\), N\({}_{2}\), and H\({}_{2}\), which will not affect the CH\({}_{4}\) reactivity with such a low concentration. The burner consisted of two concentric stainless-steel tubes and consists of a central fuel-jet port (external diameter 8 mm and internal diameter 5 mm) and an outer air-jet port (external diameter 25 mm and internal diameter 21 mm). A metal sintered filter was placed in the air nozzle to minimize the instabilities in the initial air flow and create a uniform exit velocity, as shown in Figure 2. A quartz observation window was embedded on the heating furnace wall to facilitate visual observation during the test process. During the fuel combustion, the furnace wall is heated electrically, maintaining a constant temperature of 673 K to avoid the ambient temperature impact. In addition, the higher wall temperature can effectively stabilize combustion and avoid flue gas condensation. The centerline temperature was measured by using a 0.5 mm diameter, butt-welded, uncoated, K-type thermocouple. A gas analyzer (Testo 335) was adopted to measure the compositions of flue gas with a focus on determining the CO and NO concentrations. The main experimental equipment type specification and uncertainty are shown in Table 1.  
The environmental characteristics of low-atmospheric pressure and low-oxygen-mass concentration at high-altitude areas have a great impact on the aerodynamic parameters of gas-fired boilers. Some boilers are designed with fan selection based on low-altitude areas, which leads to a decrease in air volume. This greatly affects the efficient operation of the boiler. In recent years, the influence of low-atmospheric pressure on the operating performance of fans is gradually recognized and valued by boiler design and manufacturing enterprises. To ensure that the amount of oxygen mass concentration fed into the furnace remains unchanged and meets the fuel combustion needs, the fan power will generally scale according to the pressure. The impact of pressure on the combustion characteristics of gas within confined spaces was only investigated in our work. Therefore, the experiment was conducted under different pressure conditions by using the same air and gas mass flow rates. The specific experimental conditions selected in this work are shown in Table 2. The fuel flow was 4.44 mg/s, the pressure within the furnace varied from 61.66 to 97.75 kPa (about equal to 0-4000 m altitude), and the \(\alpha\) was varied from 0.8 to 1.3. In addition, the air flow rate was fixed at 5, 6, and 7 L-min\({}^{-1}\) and the fuel flow rate was slowly adjusted to the smoke point, at which the flame just begins to emit smoke when testing the smoke point. Each case was repeated three times and the root-mean-square error was used to represent the test error.  
Figure 1: Schematic of the overall combustion system and its external devices.  
Figure 2: Schematic of burner and metal sintered filter (titanium).