## 5 Results and Discussion  
### Effect of the Power Supply  
The ignition probability is tested under intake air flow velocity of 1.4 m/s and diesel flow rate of 10 mL/min. The ambient temperature and intake air temperature are 20 \({}^{\circ}\)C in this section. The varying trends of the input power of the intake manifold burner under different voltages are shown in Figure 3. The electrical power of the heating elements shows the highest value at the starting time, then decreases with time elapse and reaches a stable value. Figure 4 presents the temperature of the heating rods of the intake manifold burner. With the power supply switching on, the temperature of the heating rods increases with time elapses until a stable value is reached. The electrical power of the intake manifold burner decreases with the decreasing voltage, leading to a lower surface temperature of the heating rods. This leads to poor fuel evaporation, making it more difficult to ignite the fuel-air mixture. Therefore, the ignition probability is 100% under the voltages of 23 V and 24 V, and it decreases significantly from 100% to 0% when the voltage decreases from 23 to 20 V.  
Figure 2: (**a**) The structure of the intake manifold burner, (**b**) schematic of the model and (**c**) the model validation.  
Under the voltage of 20 V, the surface temperature of the heating rods is too low to ignite the mixture of fuel and air. Therefore, the flame propagation of the intake manifold burner is presented with the voltage ranging from 20.5 to 24 V. In this section, the air flow velocity is fixed to 1.4 m/s, and the fuel flow rate is set to 10 mL/min.  
The combustion process under the voltages of 24 V and 20.5 V are shown in Figures 5 and 6. When the fuel-air mixture is ignited, the flame can be seen from holes in the flame shroud at 0 s. Then, the flame rushes out the flame burner, and a flame-developing stage is shown. Eventually, the flame area reaches the maximum value at about 1.2918 s under 24 V and enters the steady stage.  
Figure 4: (**a**) The increasing temperature and (**b**) the peak temperature of the heating rods in the intake manifold burner.  
Figure 3: (**a**) Electrical power and (**b**) ignition probability of the intake manifold burner.  
During the developing and steady stage, flame stripping happens, which is denoted by the yellow dotted circle. Thus, the flame area decreased abruptly as a result of flame stripping. The occurrence probability of the stripped flame is almost the same with different operating voltages, indicating that flame swirl motion is irrelevant to voltage.  
As shown in Figure 7, when the power supply increases from 20.5 to 24 V, the flame area in the steady stage shows an overall increasing trend, indicating the promotion of the power supply on the combustion. With the increase of the voltage, the surface temperature of the heating rods is higher, which promotes diesel evaporation and makes the mixture of air and diesel vapor better. Besides, higher surface temperature makes the ignition easier. Thus, higher flame area in the steady stage is shown.  
Figure 5: Flame propagation under the voltage of 24 V.  
Figure 6: Flame propagation under the voltage of 20.5 V.  
Figure 7: (**a**) Flame area with time elapses and (**b**) the average flame area in the steady stage with different power supply.