Experimental Investigation of the Continuous Transition of Flame-Spreading near the Blow-Off Limit

)is study investigates the continuous transition from flame-spreading to stabilized combustion near the blow-off limit in opposed forced flow by using expanding solid fuel duct that makes distribution of oxidizer velocity in the axial direction. )e stabilized combustion is a diffusion flame that appears in the Axial-Injection End-Burning Hybrid Rocket.)e boundary between flame-spreading and stabilized combustion has not been investigated in detail. Polymethyl methacrylate (PMMA) rectangular ducts were used as a fuel, and gaseous oxygen was used as an oxidizer. All firing tests were conducted at atmospheric pressure.)e diffusion flame traveled in the opposed-flow field where the oxidizer velocity increases continuously in the upstream direction. )e combustion mode changed when oxidizer velocity at the flame tip exceeded a certain value. )e oxidizer velocity used in this experiment ranges from 0.6 to 32.8m/s. Experimental results show that a threshold oxidizer velocity of the transition can be determined. In this study, the threshold velocity was 26.4m/s.


Introduction
Flame spread over combustible solids into an opposed flow of oxidizer has been investigated by various researchers [1]. In an opposed flow of a sufficiently large velocity (e.g., 20 m/ s), the diffusion flame spreading on the combustible flat plate extinguishes or cannot be ignited because the residence time for the gas mixture in the flow is insufficient. In a narrow fuel duct, however, Hashimoto et al. [2] observed that the diffusion flame does not extinguish when the opposed oxidizer flow velocity is sufficiently high, and slowly moves toward the upstream direction while widening the fuel. is combustion mode is called stabilized combustion ( Figure 1). In this combustion mode, the flame-traveling velocity (or flame spreading rate) is the velocity at which the flame widens the duct by fuel consumption. erefore, the flame spreading rate (V f ) is significantly low compared with flame-spreading combustion, e.g., V f � 0.7 mm/s for stabilized combustion and V f � 5.5 mm/s for flame spreading combustion under the conditions of atmospheric pressure, PMMA of the inner diameter of 2 mm, and pure oxygen [2]. us, the combustion mode can be distinguished by the flame spreading velocity and/or fuel regression shape. e boundary between the flame-spreading combustion and the stabilized combustion has been investigated. Hashimoto et al. showed that friction velocity at the boundary between the two combustion modes is constant for turbulent flow [3]. As for laminar flow, Matsuoka et al. [4] showed that friction velocity at the boundary is constant. ey also indicated that the constant friction velocity results in the constant critical Damköhler number (Da) at the boundary, and thus, the phenomenon of the transition to stabilized combustion is physically identical to the phenomenon of blow-off.
Stabilized combustion has been used for a new type of hybrid rocket. We "have been" investigating the hybrid rocket, Axial-Injection End-Burning Hybrid Rocket (EBHR), which uses a cylindrical fuel with an array of many small ports running in the axial direction, through which oxidizer gas flows [5][6][7]. Stabilized combustion is kept at each port exit. e fuel regresses due to heat input from these diffusion flames of the fuel end face (End-Burning). e researches reported that, in some cases, End-Burning could not persist because stabilized combustion mode suddenly changed to flame spreading combustion mode, possibly due to the influence of port accuracy. It is called the backfiring problem. erefore, from the viewpoint of the development of EBHR, the study about the transition of stabilized combustion is important and interesting. e influence of the oxidizer flow velocity in the port on each combustion mode has been investigated by conducting combustion experiments in which the oxidizer flow velocity is constant in each experiment [2][3][4]. Because the condition for appearing stabilized combustion was focused on in the abovementioned tests, the relation between the flame spreading rate and the oxidizer flow rate could only be investigated discretely, and the transition from flame spreading combustion to stabilized combustion modes has not been examined in detail. erefore, in this research, we focused on the transition of flame spreading near the blowoff limit. To observe the transition from flame-spreading combustion to the stabilized combustion, the expanding flow duct whose flow velocity increases continuously was used.

Fuel (Test Sample).
A fuel duct was designed to produce an opposed flow configuration where the oxidizer velocity increases continuously in the upstream direction. e fuel shape is shown in Figure 2, and its dimensions are specified in Table 1. e width of the fuel ducts was uniform in the axial direction, while the height of the ducts increased at an angle of 1 degree, resulting in an appropriate axial oxidizer velocity distribution. Because of the duct shape, the oxidizer flow velocity decreases as it flows downstream. Since the flame is ignited downstream, the oxidizer flow velocity at the tip of the flame increases as spreading upstream. An expanding flow path was created by bonding a flat plate with another plate which has an expanding groove. Transparent PMMA was used as fuel to measure the flame spreading rate by using a digital camera. In this study, to conduct experiments under the thermally thick condition, the vertical preheated length L sy ≈ [8] in the solid phase was predicted from the experimental results which were conducted by Fenandez-Pello et al. [9]. When the fuel thickness is larger than L sy , the fuel is thermally thick. Since the maximum value of L sy was 1.0 mm, we employed the thickness of at least 10 mm. e fuels were thermally thick under all observed velocity of flame propagation (V f ). Figure 3 schematically shows a test sample. e fuel connects to the gas inlet part made of stainless steel with epoxy resin. e gas inlet part connects to a gas supply line. From the fuel shape and mass flow rate, it is possible to calculate the oxidizer flow velocity distribution in the duct by using the following equation based on the continuity equation: (1) is an initial height of duct, L (m) is a duct length, and x (m) is a position of flame tip. Figure 4 shows a schematic of the experimental apparatus. It mainly consists of an oxygen tank, a nitrogen tank, and the test sample. Pure oxygen was used as an oxidizer and nitrogen was used for a purge. ere are 2 lines to supply gaseous oxygen and nitrogen. e oxygen line has a ball valve, needle valve, and nonreturn valve for flow/nonflow control, controlling gas flow rate, and preventing return flow, respectively. e nitrogen line has only a ball valve for flow/nonflow control. A mass flow meter measured the oxygen mass flow rate, and a pressure sensor measured the pressure at upstream of the fuel duct. e measured data are transmitted to the logger and stored. Table 2 shows the instruments used for the measurement and their accuracy. e oxidizer mass flow rate was adjusted and choked by a needle valve. While feeding oxygen into the test sample, the fuel duct was ignited downstream by an ignited incense or heated nichrome wire. en, the flame spreads into the fuel duct. A digital camera recorded the progress of the flame inside the fuel. When the flame reached the inlet, the oxygen    Mass flow meter CMS0500/azbil 5 ≤ Q < 50 L/min: ±1%FS ± 1 digit 50 ≤ Q < 500 L/min: ±3% RD ± 1 digit Maas flow meter CMS0050/azbil 0.5 ≤ Q < 5 L/min: ±1%FS ± 1 digi 5 ≤ Q < 50 L/min: ±3% RD ± 1 digit was switched to nitrogen for a purge. All tests were conducted at atmospheric pressure.

Flame Spreading Rate and Oxygen Velocity.
Oxygen mass flow rate and pressure were measured during firing tests. e flame spreading rate was calculated by tracking the position history of the flame tip in the video by ImageJ. From the time history of the flame tip position, the mass flow rate, and the pressure, oxygen velocity at the flame tip was calculated by equation (1). e pressure at the flame tip was identified by the pressure at the pressure port because pressure drop from pressure port to the duct outlet calculated from equation (2) was less than 0.5 kPa (around 107 kPa at test condition).
Since flame moves toward the upstream during a firing test, the actual pressure drop will be much less than 0.5 kPa. e resistance coefficient of the pipe was calculated by equation (3) for laminar flow and equation (4) for turbulent flow (Blasius resistance formula).

Boundary Velocity.
To evaluate the boundary, the bulk velocity equation (1) gives was employed. e boundary condition between the two combustion modes has been investigated [3,4]. e combustion mode depends upon whether flow separation exists or not at the flame leading edge. If the boundary layer over the solid surface receives enough momentum from the core flow, the flow does not separate from the surface, and the flame cannot spread against the flow. Accordingly, the turbulent momentum transfer from the core flow to the boundary layer decides whether the flame can spread against the flow or not. Due to this finding, they found that friction velocity is an important indicator deciding whether the mode is flame spreading or stabilizing combustion. e following equation gives friction velocity for the turbulent regime: where V o (m/s), μ (Pa s), ρ (kg/m 3 ), and d (m) are bulk velocity, viscosity, density of oxidiser, and port diameter. e boundary is expressed by a single value of the friction velocity regardless of other conditions [3]. Please note that the boundary expressed by a friction velocity is scale-independent. Near the transition point in this study, the Reynolds number was over 10,000, meaning that the flow was turbulent. By employing the friction velocity, we can use the result this paper provides to design EBHR at any scale. Accordingly, the discussion about the detailed velocity profile in the duct is not necessary. In this study, therefore, bulk velocity is used for boundary conditions.

Error Bias.
e value of the oxidizer velocity has some error bias B V o because of the accuracy of instruments. In this study, the error bias B V o is determined by equation (6) using each error bias B i of the instrument, which is summarised in Table 3.

Results and Discussion
Several firing tests were conducted to observe the behavior near the blow-off limit. Figure 5 shows typical images of the flame. e images show that the flame spreading rate slowed down at around 25 s; the flame slowly moves while widening the duct. is means the combustion mode has transited from flame-spreading combustion to stabilized combustion. Accordingly, the transition between combustion modes was successfully observed. Table 4 and Figure 6 summarize the results of the firing tests. In Figure 6, the horizontal axis represents the oxidizer flow velocity, and the vertical axis represents the flame spreading rate. e flame spreading rate changed as oxidizer flow velocity changed. e flame spreading rate increases with the flow velocity and then starts to decrease as the gas velocity increases. is trend qualitatively corresponds with the combustion on the plate [9]. For the high oxidizer velocity region (around 26 m/s, near the blow-off limit), V f -V o relation is changed when the oxidizer velocity over a certain value. is velocity is transition velocity. e V f -V o relation near the blow-off limit became clear. Figure 7 shows time histories of pressure and flame spreading rate in Test 6. e pressure marginally increased just after ignition and then decreased as the flame spreading rate decreased. When the flame spreading rate is fast, the flame increased the combustion area faster than it expanded combustion volume, so the pressure increased. For low flame spreading rate, however, the flame expanded the volume faster than it increased the area, so the pressure maintained constant. e pressure in tests 4-6 which were observed to have transition had the same tendency. Figure 8 is a diagram focusing on a region where the flame spreading velocity is sufficiently low in Figure 6.
When the oxidizer velocity exceeded around 26 m/s, flame spreading rate became much lower than before the flow rate exceeded the velocity and almost did not decelerate beyond V f � 0.6 mm/s. erefore, the threshold oxidizer velocity of the transition can be determined. Figure 9 shows the transition velocity of each test with error bias. From this figure, the threshold velocity is 26.4 m/s ± 2.0 m/s.

Conclusions
By using the expanding fuel duct, the continuous transition from flame spreading combustion to stabilized combustion was observed for the first time. e V f -V o relation near the blow-off limit was also clarified. From several firing tests, it was found that a threshold oxidizer velocity of the transition can be determined. In this study, the threshold velocity was 26.4 m/s ± 2.0 m/s. is result is expected to be useful for the design of the Axial-Injection End-Burning Hybrid Rocket to prevent the backfiring problem.

Data Availability
e data used to support the findings of this study are available from the corresponding author upon request.

Conflicts of Interest
e authors declare that there are no conflicts of interest regarding the publication of this paper. Journal of Combustion 7