2.1 Two-staged in-tandem combustor

In this study, a scaled-down experimental test rig is designed and used to capture the main characteristics of the afterburner by feeding the combustion products from the main combustor to the afterburner. Figure 1 shows an in-tandem combustor with a main combustor and an afterburner used in this study. As shown in Fig. 1(a), the horizontal main combustor has a circular cross-section with a radius of 51.15 mm. The length of the main combustor is 523 mm, and the main combustor is connected to the afterburner by a 90 degree elbow. The water jacket around the main combustor prevents the thermal damage to the main combustor. Air and methane are used as the oxidiser and fuel, respectively, for the main combustor. The air and methane are mixed as jets-in-crossflow and the mixture passes through an axial swirler before entering the main combustor. The swirler has a diameter of 35 mm and has 10 swirl vanes with a swirl angle of 30 degrees. At the downstream end of the main combustor, dilution air is introduced to lower the temperature of the combustion products from the main combustor and to supply additional oxidiser for the afterburner. One dynamic pressure sensor (DP1) and one temperature sensor (TC1) are installed at the upstream end of the main combustor.

Figure 1.

Schematic of the in-tandem combustor: (a) the main combustor with swirler and (b) the afterburner with V-gutter.

Figure 1(b) shows the afterburner which is installed on the 90 degree elbow vertically. The afterburner is composed of a flow strainer and three modules, and the rectangular cross-section of the afterburner is 45 × 70 mm². The flow strainer is a plate with 135 holes with a diameter of 2.54 mm and is used to reduce the flow inhomogeneity caused by the 90 degree elbow. The afterburner uses the combustion products from the main combustor and dilution air as reactants and the liquid test fuel is additionally introduced at the upstream section of the afterburner as reactant. The length of the afterburner is about 1,400 mm and the downstream end of the afterburner is set as an acoustic open boundary condition. The liquid test fuel injector at the first module of the afterburner consists of two holes with 6.5 mm apart on the top of the injector and the orifice diameter is 0.32 mm. Both holes are oriented perpendicular to the cross-flow direction, so the liquid test fuel and the products from the main combustor are mixed as jets-in-crossflow. The flame holder at the second module is a V-gutter type with a vertex angle of 60° and a side length of 28 mm. The flame holder’s blockage ratio (V-gutter width/test section width) is 40%. The flame holder is placed 413 mm downstream after the liquid test fuel injector. Hydrogen torch igniters are mounted upstream end of the main combustor and before the flame holder to ignite the flames, respectively. Two quartz windows are employed on each sidewall on the two modules for optical access for the test fuel injector and the flame holder, respectively.

2.3 Liquid test fuel characteristics

The research using NJFCP test fuels focuses on the characteristics of two types of test fuels: category A and C. Category A fuels represent conventional petroleum-derived fuels with typical properties (viscosity, flash point, aromatic content, etc.) [Reference Edwards44]. On the other hand, category C fuels are experimental fuels specifically designed to explore the extreme boundaries of jet fuel composition and properties [Reference Edwards44]. Due to their distinct physical and chemical properties, each test fuel exhibits variations in combustion characteristics such as lean blowoff, flashback, and combustion instability.

This study investigates the combustion characteristics of a total of five NJFCP test fuels (Jet-A, A-2, C-1, C-5, and C-9) and a JP-8/HRJ. A total of six fuel samples were prepared by the National Research Council (NRC). Table 1 shows the characteristics of each test fuel. Each test fuel has similar heat of combustion, but with a DCN difference of up to 3.7 times. Figures 3(a) and (b) show the properties of category A fuels and the distillation curves for category C fuels, respectively. A-2 is a test fuel with the average value of Jet-A characteristics. C-1 has a very low cetane number. C-5 has a flat boiling point. C-9 is a mixture of 80% hydrotreated renewable jet (HRJ) biofuel and 20% dodecane, and JP-8/HRJ is a mixture of 50% HRJ and 50% Jet-8.

Table 1.

Characteristics of test fuels used in this study [Reference Colket, Heyne, Rumizen, Gupta, Edwards, Roquemore, Andac, Boehm, Lovett, Williams, Condevaux, Turner, Rizk, Tishkoff, Li, Moder, Friend and Sankaran1, Reference Kang, Kim, Kalaskar, Violi and Boehman6, Reference Yang, Stachler and Heyne45]

Figure 3.

(a) Test fuel properties of category A fuels and (b) distillation curves for category C fuels [Reference Colket, Heyne, Rumizen, Gupta, Edwards, Roquemore, Andac, Boehm, Lovett, Williams, Condevaux, Turner, Rizk, Tishkoff, Li, Moder, Friend and Sankaran1].

2.4 Experimental conditions

Table 2 shows the detailed experimental conditions of this study. The flow rate of air and methane used at the main combustor are kept constant at 1,000 and 69.45 slpm, respectively, so that the equivalence ratio is kept at 0.66. The test SAF supplied to the afterburner is kept at 1,500 g/h, and the equivalence ratio at the second stage burner is controlled as the dilution air flow rate is changed from 50 to 500 slpm. The inlet pressures of the air, methane, SAF, and dilution air are ambient condition. The inlet temperature of the afterburner is approximately 1,100 K, and this varies depending on the amount of dilution air.

Table 2.

Experimental test conditions

2.5 Measurement and diagnostics

Three dynamic pressure sensors (DPs) (PCB, 112A22, uncertainty = ± 1% of full scale) and three thermocouples (TCs, K-type) are used to measure the pressure perturbation and temperatures, respectively, at the main combustor, after the flow strainer, and at the flame holder. The dynamic pressure sensors and thermocouples are operated at 10 kHz and 10 Hz rates, respectively. To prevent thermal damage to the TCs, temperatures near the wall were measured within the temperature range suitable for K-type TCs.

The global OH^*-chemiluminescence (CL) intensity near the flame holder is measured by a photomultiplier tube (PMT) (Hamamatsu, H11526-20-NF) at 10 kHz rates. CH^*-CL images are captured at 10 Hz with an intensified charged-coupled device (ICCD) camera (Princeton Instruments, PI-MAX) using a UV-enhanced lens (LaVision, f = 100 mm, f/2.8) with a 430 nm bandpass filter. Direct images are obtained using a digital single-lens reflex (DSLR) camera (Nikon, D750). The fields of view (FOVs) of the CH^*-CL and direct images are 35 mm × 175 mm and 35 mm × 720 mm, respectively, as denoted in Fig. 1.

3.1 Lean blowoff (LBO) and flashback characteristics

In the following, we present and discuss comparative results of the six sample fuels. The characteristics of LBO and flashback are identified by varying the global equivalence ratio at the afterburner ( ${\phi _{af}}$ ), while keeping the condition for the main combustor the same. In Fig. 4, the operational limits of each test fuel are presented in the order of its DCN. It clearly shows the implications regarding the significance of DCN on the LBO and flashback characteristics.

Figure 4.

Operational limits of each test fuel.

Figure 5 shows the LBO equivalence ratio for each test fuel. Blowoff occurs when the flow residence time scale is less than the chemical time scale. Since the flame speed decreases and the flow speed increases as decreasing ${\phi _{af}}$ (by increasing the dilution air flow rate) in this study, the possibility of blowoff increases as decreasing ${\phi _{af}}$ . The LBO occurs at ${\phi _{af}}$ of about 0.42 for the C-1 with the lowest DCN in this study, but the LBO equivalence ratio decreases for the test fuel with higher DCN and LBO occurs at ${\phi _{af}}$ of about 0.3 for the C-9 with the highest DCN in this study.

Figure 5.

${\phi _{af}}$ at the lean blowoff (LBO) for each test fuel.

The DCN is a chemical property of fuels [Reference Won, Rock, Lim, Nates, Carpenter, Emerson, Lieuwen, Edwards and Dryer15] and the DCN indicates the chemical reactivity potential [Reference Won, Veloo, Dooley, Santner, Haas, Ju and Dryer46, Reference Won, Haas, Dooley, Edwards and Dryer47]. Therefore, a small DCN means a high chemical time scale [Reference Gowdagiri, Wang and Oehlschlaeger33] and a low Da under the same residence time scale according to Equation (1). According to the previous studies [Reference Gowdagiri, Wang and Oehlschlaeger33, Reference Wang and Oehlschlaeger34], the chemical time scale is lower for higher DCN fuel. Also, in previous studies [Reference Kalghatgi32, 48], the relational expression between the ignition delay time ( ${\tau _i}$ ) of diesel fuel and DCN was identified within the range of ignition delay time of 3.1–6.5 ms, which is shown in Equation (6).

(6) \begin{align}DCN = 83.99{( {{\tau _i} - 1.512} )^{ - 0.658}} + 3.547\end{align}

Since Equation (6) was derived for diesel fuels comprising ASTM National Exchange Group (NEG) check fuels, heptamethylnonane, cetane, and an in-house check fuel [48] at 2.137 MPa and 545 °C, it is difficult to apply it directly to our cases, but it can be seen that ignition delay time is closely related to DCN. However, research on the ignition time for NJFCP test fuels is not sufficient yet.

Since the total flow rate is kept same regardless of the test fuel at the same ${\phi _{af}}$ , there will be almost no change in the residence time as shown in Equation (2). Therefore, in our case, Da number will increase with the increase of DCN as chemical time scale decreases (ignition delay time decreases) and residence time is almost constant.

In other words, test fuels with a small DCN are more easily blown-off. As shown in Fig. 5, the LBO equivalence ratio decreases as the DCN increases since the flame can be sustained even at a faster flow speed due to a small chemical time scale, which is consistent with the results of previous studies.

Figure 6 shows ${\phi _{{\rm{af}}}}$ when flashback occurs for each test fuel. Flashback occurs when the flame speed is faster than the flow speed. In this study, the flashback propensity increases as ${\phi _{{\rm{af}}}}$ increases by decreasing the dilution air flow rate since the flame speed increases and the flow speed decreases. Here, for C-9 with the highest DCN in this study, flashback occurs at ${\phi _{{\rm{af}}}}$ of about 0.48. However, for test fuels with lower DCN, flashback occurs at a higher ${\phi _{{\rm{af}}}}$ . This indicates that flashback has a strong correlation with DCN in a similar way to blowoff, which has not been discussed in previous studies.

Figure 6.

${\phi _{af}}$ at the onset of the flashback for each test fuel.

Behind the V-gutter, the flow speed is low owing to the recirculation zone, resulting in high Da and stable flame. However, for flashback to occur, flames need to propagate toward the upstream direction of V-gutter, where the flow speed is fast. Therefore, flow time scale becomes smaller, so Da becomes smaller, resulting in a high possibility to be extinguished. Since the fuel with a high DCN has a small chemical time scale, even if the flow time scale becomes smaller, the flame can be sustained and flashback can occur. Therefore, the flashback of C-9 flame with the highest DCN in this study occurs at a faster flow speed and the flashback of test fuels with lower DCN occurs at a lower flow speed. However, for the flames by the C-1 and C-5 test fuels with even smaller DCNs, blowoff occurs instead of flashback. This will be discussed later.

3.2 Effect of shear layer reactivity on flame characteristics

The flame at the afterburner in this study is anchored to the V-gutter which acts as a flame holder. According to the previous study [Reference Shanbhogue, Husain and Lieuwen14, Reference Chaudhuri, Kostka, Renfro and Cetegen20, Reference Chaudhuri, Kostka, Tuttle, Renfro and Cetegen49, Reference Fan, Wan, Liu, Pi, Yao and Liu50], the shear layer at the V-gutter tip has a strong influence on the stability and characteristics for the bluff body flame. Despite the ongoing debate surrounding the efficacy of CH^* as a reliable indicator for accurately assessing the local heat release rate or reactivity [Reference Hossain and Nakamura51, Reference Sardeshmukh, Bedard and Anderson52], it remains a good marker commonly utilised in numerous studies [Reference Sardeshmukh, Bedard and Anderson52, Reference Yan, Gong, Guo, Yu and Wang53]. Consequently, this study also incorporated CH^* as an indicator to evaluate shear layer reactivity. To examine the reactivity of the shear layer, the ratio of image intensity inside the red box shown in Fig. 7 to that of the averaged total flame is calculated as shown in Equation (7).

(7) \begin{align}I = \frac{{intensity{\rm{\;}}of{\rm{\;}}red{\rm{\;}}box}}{{average{\rm{\;}}intensity{\rm{\;}}of{\rm{\;}}flame}}\end{align}

$I$ represents the relative reactivity in the shear layer compared to the average total flame. Therefore, a high $I$ corresponds to a case where the flame is concentrated in the shear layer region and is strongly anchored to the V-gutter. Here, since the $I$ is calculated using both CH^*-CL and direct images because of the FOV limitation and lack of CH^*-CL data due to operational constraints of the experimental setup and test fuels, the $I$ is standardised by the $I$ at ${\phi _{{\rm{af}}}}$ of 0.5 to compare the results from both of them.

Figure 7.

CH^*-CL image (upper) and direct image (lower) of A-2 under ${\phi _{af}}$ = 0.6.

Figure 8 shows the shear layer reactivity standardised by the $I$ at ${\phi _{{\rm{af}}}}$ of 0.5 ( $I/{I_{{\phi _{{\rm{af}}}} = 0.5}}$ ). As shown in Fig. 8, it shows a trend that the value of $I/{I_{{\phi _{{\rm{af}}}} = 0.5}}$ decreases as ${\phi _{{\rm{af}}}}$ decreases when the equivalence ratio is below a certain specific value to each fuel, indicating that the flame anchoring at the V-gutter is weakened. In other words, as the combustion condition approaches to a leaner condition by decreasing ${\phi _{{\rm{af}}}}$ , the flame speed decreases and the flow speed increases, resulting in a decrease in Da. Therefore, the flame anchoring to the V-gutter is weakened, eventually causing blowoff.

Figure 8.

Relative shear layer reactivity standardised using ${I_{{\phi _{af}} = 0.5}}$ of (a) Jet-A, (b) A-2, (c) C-1, (d) C-5, (e) C-9, and (f) JP-8/HRJ.

Figure 9 shows the change in the average flame shape as decreasing the ${\phi _{{\rm{af}}}}$ for the A-2 flame. The upper side of Fig. 9 shows the CH^*-CL image and the bottom side of Fig. 9 shows the flame edge obtained through Sobel edge detection of the upper side image. It can be seen that the average flame front is gradually pushed downstream as the ${\phi _{{\rm{af}}}}$ decreases. In other words, as the ${\phi _{{\rm{af}}}}$ decreases, the $I/{I_{{\phi _{{\rm{af}}}} = 0.5}}$ decreases and the average flame front is also pushed downstream, so when the ${\phi _{{\rm{af}}}}$ becomes lower, it can be seen that the flame blowoff occurs by detaching from the V-gutter.

Figure 9.

The changes in averaged A-2 fueled flame shape according to the global equivalence ratio at the afterburner: (a) ${\phi _{af}}$ = 0.47, (b) ${\phi _{af}}$ = 0.41, and (c) ${\phi _{af}}$ = 0.36.

In contrast, as the ${\phi _{{\rm{af}}}}$ increases, Da increases and the flame is better anchored to the V-gutter, increasing the shear layer reactivity. However, the shear layer reactivity of Jet-A, A-2, C-9, and JP-8/HRJ flames tends to decrease after a certain ${\phi _{{\rm{af}}}}$ due to the occurrence of flashback as shown in Fig. 8. When flashback happens, the reactivity of the shear layer is weakened because the reactants are already reacted before reaching the shear layer. Since flashback does not occur in C-1 and C-5 flames, the shear layer reactivity does not decrease as the ${\phi _{{\rm{af}}}}$ increases. Figure 10 shows the change in the average flame shape as increasing the ${\phi _{{\rm{af}}}}$ for the A-2 flame. As in Fig. 9, the upper side and bottom side of Fig. 10 show the CH^*-CL image and the edge of the flame, respectively. As the ${\phi _{{\rm{af}}}}$ increases, the flame front shifts upstream, eventually leading to flashback.

Figure 10.

The changes in averaged A-2 fueled flame shape according to the global equivalence ratio at the afterburner: (a) ${\phi _{af}}$ = 0.48, (b) ${\phi _{af}}$ = 0.58, (c) ${\phi _{af}}$ = 0.68, and (d) ${\phi _{af}}$ = 0.77.

Figure 11 shows the relationship between the ${\phi _{{\rm{af}}}}$ where flashback occurs and the ${\phi _{{\rm{af}}}}$ where the $I/{I_{{\phi _{{\rm{af}}}} = 0.5}}$ is the maximum in Fig. 8. It can be seen that the two ${\phi _{{\rm{af}}}}$ have a proportional relationship and the shear layer reactivity and flame shape are closely related. However, shear layer reactivity was not measured under all combustible ${\phi _{{\rm{af}}}}$ for all fuels, so additional measurement and analysis are needed in future work.

Figure 11.

Relationship between ${\phi _{af}}$ where the shear layer reactivity is highest and ${\phi _{af}}$ where the flashback occurs.

3.3 Combustion instability characteristics

With the increase of the ${\phi _{af}}$ , the flame speed increases, while the flow speed decreases due to reduced dilution air, so Da increases and the likelihood of blowoff decreases. Indeed, for the flames by Jet-A, A-2, C-9, and JP-8/HRJ test fuels, as the ${\phi _{af}}$ increases, blowoff does not occur until flashback occurs. However, as mentioned in Chapter 3.1, for flames using C-1 and C-5 test fuels, blowoff occurs before flashback occurs as ${\phi _{af}}$ increases. This is deemed to be related to the pressure perturbation. As can be seen in Fig. 1, pressure perturbations ( $p'_{2}$ and $p'_{3}$ ) are measured by a high frequency pressure transducers ported just after the honeycomb (DP2) and near the V-gutter (DP3). $p'_{2}$ is the pressure perturbation upstream end of the afterburner, which represents the pressure perturbation affecting the turbine blade, and $p'_{3}$ is the pressure perturbation near the V-gutter, which is closely related to the heat release rate fluctuation from the flame at the afterburner. Therefore, $p'_{2}$ and $p'_{3}$ were measured and analysed for the strength of pressure perturbation and the phase difference between the pressure perturbation and the heat release rate fluctuation, respectively.

Figure 12 shows the pressure perturbations ( $p'_{2}$ and $p'_{3}$ ) according to the change in the ${\phi _{af}}$ for each test fuel. The plots are obtained by varying the dilution air flow rate while maintaining a steady liquid test fuel flow. The RMS pressures start with the low RMS pressure at the low ${\phi _{af}}$ for all test fuels, then rapidly increase with the increase in the ${\phi _{af}}$ until they reach a plateau region or blowoff. This is similar to the results of previous studies [Reference Stouffer, Hendershott, Monfort, Diemer, Corporan, Wrzesinski and Caswell54, Reference Monfort, Stouffer, Hendershott, Wrzesinski, Foley and Rein55], which examined the pressure perturbations for some NJFCP test fuels and found that pressure perturbation increased sharply above a certain equivalence ratio. For comparison among test fuels, curve fits are performed for the RMS pressures of A-2 and these curve fits are plotted in the red and blue lines along with the RMS pressures. It can be seen that C-1 and C-5 flames have notably different tendency between the RMS pressures and the ${\phi _{af}}$ while other test fuels show similar trend. In overall, they show much higher RMS pressures compared to other test fuels. In addition, C-1 and C-5 flames don’t have flat RMS pressure region at the low ${\phi _{af}}$ because they are blown off at higher ${\phi _{af}}$ than other test fuels. They are also blown off at a high ${\phi _{af}}$ of near 0.64 and 0.58 before flashback happens, respectively. Therefore, flammability limit for C-1 and C-5 flames are narrower than that of the other test fuels.

Figure 12.

RMS pressure perturbations measured just after the honeycomb ( $p'_{2}$ ) and near the V-gutter ( $p'_{3}$ ) for each of the test fuels ((a) Jet-A, (b) A-2, (c) C-1, (d) C-5, (e) C-9, and (f) JP-8/HRJ) according to the ${\phi _{af}}$ along with the curve fits of the RMS pressures for the A-2 test fuel (shown as the red and blue lines).

Figure 13 shows the three-dimensional phase space of A-2 flame obtained from $p'_{2}$ for different ${\phi _{af}}$ . When ${\phi _{af}}$ is 0.32, the trajectories fill the core of the phase space, which means $p'_{2}$ does not have deterministic dynamic characteristics. With the increase of ${\rm{\;}}{\phi _{af}}$ , it is clearly seen that the trajectory deviates from the core of the phase space and limit cycle is formed. This indicates that the periodicity of the dominant pressure perturbations becomes stronger. This trend happens similarly for all test fuels including C-1 and C-5 universally.

Figure 13.

Three-dimensional phase space [ $p'_{2}$ ( $t$ ), $p'_{2}$ ( $t - \tau $ ), $p'_{2}$ ( $t - 2\tau $ )] for different ${\phi _{af}}$ using A-2.

In addition, Rayleigh index, which represents the relationship between the pressure perturbation and the heat release fluctuations, is calculated by Equation (8). Here, both the pressure perturbation ( $p'_{3}$ ) and the heat release rate fluctuation ( $q'$ ) for calculating the Rayleigh index are measured near the V-gutter, where ${t_p}$ is the period of oscillation.

(8) \begin{align}{\rm{Rayleigh\;index}} = {1 \over {{t_p}}}\mathop \int \nolimits_0^{{t_p}} p'_{3}( t ) \cdot q'(t)dt\end{align}

As shown in Fig. 14, as the Rayleigh index increases, the strength of pressure perturbation also increases. The Rayleigh index refers to the degree of interaction between the pressure perturbation inside the afterburner and the heat release rate fluctuation. Therefore, the pressure perturbations shown in Fig. 12 are attributed to the thermo-acoustic combustion instability. Especially, the Rayleigh indexes of C-1 and C-5 are mostly positive and greater than those of other test fuels, which means that the strength of combustion instability of C-1 and C-5 flames is stronger than that of other flames. Therefore, as the equivalence ratios increase, C-1 and C-5 flames show strong combustion instability caused by constructive interference between the pressure perturbation and the heat release rate fluctuation leading to blowoff.

Figure 14.

RMS of $p'_{2}$ for each of the test fuels according to the Rayleigh index.

Figure 15 shows the RMS of $p'_{2}$ according to the phase difference between the pressure perturbation ( $p'_{3}$ ) and the heat release rate fluctuation ( $q'$ ) for each test fuel. As shown in Fig. 15, RMS of $p'_{2}$ is strong when the phase difference between $p'_{3}$ and $q'$ is near zero. Therefore, it can be also seen that the perturbation inside the afterburner is caused by the thermo-acoustic combustion instability.

Figure 15.

RMS of $p'_{2}$ according to the phase difference for each test fuel.

Figure 16 shows the joint probability density distribution between the pressure perturbation at DP3 and the heat release rate fluctuation measured by PMT for each test fuel at the ${\phi _{af}}$ of 0.58. For the flames by Jet-A, A-2, C-9, and JP-8/HRJ test fuel, the distribution of $p'_{3}$ and $q'$ is circular in the centre and the order of the coefficient of linear relationship corresponds to O(-2). However, for the flames by C-1 and C-5, the distribution shows an upward-sloping trend and the order of the coefficient of linear relationship corresponds to O(-1). In other words, the interaction between the pressure and heat release rate perturbations is weak for the flames by Jet-A, A-2, C-9, and JP-8/HRJ, so perturbations are not strong. However, for the flames by C-1 and C-5, the interaction is stronger so the pressure and heat release rate perturbations are amplified strongly. In other words, the combustion instability occurs strongly for C-1 and C-5 flames due to the relatively strong interaction between the pressure perturbation and the heat release rate fluctuation at the high ${\phi _{af}}$ , which makes the flame detach from the V-gutter and eventually causes the blowoff. In contrast, the flames by Jet-A, A-2, C-9, and JP-8/HRJ test fuels can be sustained without the blowoff even at the high ${\phi _{af}}$ since the interaction between the pressure perturbation and heat release rate fluctuation is weak and the DCN of the flames is also high.

Figure 16.

Joint probability density distribution between $p'_{3}$ and $q'$ under ${\phi _{af}}$ = 0.58 of (a) Jet-A, (b) A-2, (c) C-1, (d) C-5, (e) C-9, and (f) JP-8/HRJ flames.

Using chemiluminescence images of A-2, C-1, C-9, and JP-8/HRJ test fuel flames, the intensity centre within the chemiluminescence FOV was measured. Figure 17 shows the phase difference between pressure and heat release rate with respect to the intensity centre. The intensity centre is set at zero at the position of the V-gutter tip, with the upstream direction being positive and the downstream direction being negative. As the equivalence ratio increases, the intensity centre moves closer to the V-gutter tip. As shown in Fig. 17, as the intensity centre moves upstream, the phase difference between pressure perturbation and heat release rate fluctuation decreases. This is because the delay time between pressure perturbation and heat release rate fluctuation changes as the distance between the fuel injector and flame centre changes according to the equivalence ratio [Reference Lieuwen56, Reference Bae, Jeong and Yoon57]. Additionally, when the position of the intensity centre was around -30 mm, the phase difference was close to zero for all test fuels. For C-1 flame, the intensity centre was mostly located at -30 mm under most chemiluminescence measurement conditions, indicating a stronger oscillation intensity compared to other test fuels since the phase difference was close to zero.

Figure 17.

Phase difference between $p'_{3}$ and $q'$ for each test fuel according to the location of intensity centre from V-gutter tip.