# Experimental Study of Coflow Propane--Air Laminar Diffusion Flames at Subatmospheric Pressures
## 3 Results and Discussion  
### Physical Flame Structure  
The images of visible flames at different pressures ranging from 30 kPa to 101 kPa are shown in Figure 3. Flame shape changes significantly with the declining pressure. There were two distinct parts: the yellow luminous region (i.e., the sooting region) and the blue luminous region (i.e., the premixed region). As the pressure decreased, the sooting region moved upward and the blue premixed region expanded, as also observed in the previous high pressure [8; 21] and low pressure [15] studies. This observation indicates that soot yield was suppressed by the reduction in pressure. For the diffusion flames produced by a circular burner, flame height can be predicted using [PERSON]'s [22] correlation:  
\[H_{f}=\frac{Q\Big{(}T_{0}/T_{f}\Big{)}^{0.67}}{4\cdot\pi\cdot D_{0}\cdot ln \Big{(}1+\frac{1}{s}\Big{)}} \tag{1}\]  
where \(Q\) is the volumetric fuel flow rate, \(T_{0}\) is the ambient temperature, \(T_{f}\) is the average flame temperature, \(D_{0}\) is the diffusion coefficient at ambient temperature and \(S\) is the stoichiometric molar oxidizer-to-fuel ratio. Considering the trivial pressure dependence of \(T_{0}/T_{f}\), Equation (1) can be simplified as:  
\[H_{f}\propto\frac{Q}{D_{0}}\propto\frac{u_{f}\cdot A}{D_{0}} \tag{2}\]  
where \(u_{f}\) is the mean velocity of the fuel flow, which is proportional to pressure, and \(A\) is the area of the fuel nozzle. Since \(D_{0}\) is proportional to \(1/P\), according to Equation (2), flame height is independent from pressure. With \(T_{f}=1800\) K, \(D_{0}=11.1\) mm\({}^{2}\)/s and \(S=25\), \(H_{f}~{}\approx~{}25\) mm. This calculated value is slightly different from the experimental flame height which moderately increased with pressure from about 23 mm to 27 mm. Such a tendency of flame height to slightly increase with the increase in pressure can be attributed to soot formation in flames since soot radiation reduces flame temperature \(T_{f}\) and the soot oxidation region extends the visible flame height. As shown in Figure 4, the maximum diameter (\(D_{f}\)) of the flame's cross-section expanded as pressure decreased. The dependence of the maximum flame diameter on pressure for \(r_{\mathrm{(fuel/air)}}=1\) and 0.5 is shown in Figure 4. The maximum diameter could  
Figure 3: A schematic of the coflow burner. be fitted with a power law function of pressure (excluding the pressure of 30 kPa for \(r_{v(\text{fuel/air})}=0.5\) where the flame was lifted off), where exponent \(n=-0.4\) and \(-0.53\), respectively, for \(r_{v(\text{fuel/air})}=1\) and 0.5. Those exponents are similar to the results of the experimental study by [PERSON] (19) and [PERSON] (20) for coflow methane-air diffusion flames at high pressure; they noted that the flame's cross-section area was proportional to \(p^{-1}\). Such an inverse dependence of the flame's cross-section area on pressure implies that the average velocity along the flame's axis direction is independent from pressure. Therefore, the residence time of reactants moving from the nozzle to the flame tip is considered identical at different pressures, in consideration of the nearly fixed flame length. The reduction in soot formation results mainly from suppression of the soot production rate at low pressures ([PERSON] et al., 2018). Remarkable differences in flame shape were observed between the flames at \(r_{v(\text{fuel/air})}=1\) and \(r_{v(\text{fuel/air})}=0.5\), as shown in Figure 4. Flame diameter grew with \(r_{v(\text{fuel/air})}\) decreasing from 1 to 0.5 and the increment became more observable as the pressure decreased to a low level, as shown in Figure 5. For \(r_{v(\text{fuel/air})}=0.5\), the sooting region shrunk in the low-pressure range from 50 kPa to 40 kPa, which corresponds to a rapid expansion in flame diameter. As the pressure decreased from 40 kPa to 30 kPa, the flame lifted off at \(r_{v(\text{fuel/air})}=0.5\). The lifted flame had a unique appearance, with the sooting region completely covered by the premixed blue flame sheet.