J. Cent. South Univ. (2020) 27: 1880-1890

DOI: https://doi.org/10.1007/s11771-020-4415-x

A non-monotonic blow-off limit of micro-jet methane diffusion flame at different tube-wall thicknesses

LI Dan(李丹)¹, LIU Bing(刘冰)¹, HUANG Long(黄龙)¹, LIU Lei(刘磊)¹,

KE Wei-chang(柯炜昌)¹, WAN Jian-long(万建龙)², LIU Hao(刘豪)²

1. China Tobacco Hubei Industrial Limited Liability Company, Wuhan 430040, China;

2. State Key Laboratory of Coal Combustion, School of Energy and Power Engineering,Huazhong University of Science and Technology, Wuhan 430074, China

Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract: In order to provide guideline for choosing a suitable tube-wall thickness (d) for the micro-jet methane diffusion flame, the effect of tube-wall thickness on the blow-off limit is investigated via numerical simulation in the present work. The results show that the blow-off limit of micro-jet methane diffusion flame firstly increases and then decreases with the increase of tube-wall thickness. Subsequently, the underlying mechanisms responsible for the above non-monotonic blow-off limit are discussed in terms of the flow filed, strain effect and conjugate heat exchange. The analysis indicates that the flow field is insignificant for the non-monotonic blow-off limit. A smaller strain effect can induce the increase of the blow-off limit from d=0.1 to 0.2 mm, and a worse heat recirculation effect can induce the decrease of the blow-off limit from d=0.2 to 0.4 mm. The non-monotonic blow-off limit is mainly determined by the heat loss of flame to the tube-wall and the performance of tube-wall on preheating unburned fuel. The smallest heat loss of flame to the tube-wall and the best performance of tube-wall on preheating unburned fuel result in the largest blow-off limit at d=0.2 mm. Therefore, a moderate tube-wall thickness is more suitable to manufacture the micro-jet burner.

Key words: micro-jet diffusion flame; blow-off limit; flow field; strain effect; conjugate heat exchange

Cite this article as: LI Dan, LIU Bing, HUANG Long, LIU Lei, KE Wei-chang, WAN Jian-long, LIU Hao. A non-monotonic blow-off limit of micro-jet methane diffusion flame at different tube-wall thicknesses [J]. Journal of Central South University, 2020, 27(6): 1880-1890. DOI: https://doi.org/10.1007/s11771-020-4415-x.

1 Introduction

With the rapid development of micro electro-mechanic systems (MEMS), the demand of small power generation devices becomes more and more urgent. As the energy densities of hydrogen and hydrocarbon fuels are remarkably higher than that of electrochemical batteries, the miniature power generation apparatuses based on combustion have attracted much attention [1].

However, the flame is very hard to maintain stable in micro or mesoscale combustors mainly due to two issues. The first one, the large surface area-to-volume ratio easily leads to the wall radical capture and remarkably increases the heat losses to the ambient environment [2]. The second issue: the residence time of the fuel/oxidant mixture is very short. The above two issues lead to some unstable flame behaviors: such as the flame with repetitive extinction and ignition [3, 4], inclined flames [5-7], and spiral flame [8, 9].

Facing these issues, various methods were adopted to improve flame stabilization in small burners. For instance, enhancing heat recirculation effect was frequently employed to increase the fresh fuel mixture temperature and decrease the heat loss to the environment in small combustors. The “Swiss-roll” form is a high-efficient structure to use the heat recirculation effect, which significantly improves the flame stability in mesoscale combustors [10, 11]. The porous media in the micro combustor also can well preheat the upstream unburned fuel temperature and then expends the flame blowout limit [12, 13]. In addition, to form a flow recirculation zone via structural design (such as backward facing step, bluff body, and cavity) is another effective method to anchor the flame in small burners. For example, YANG et al [14] and KHANDELWAL et al [15] indicated that the recirculation zone behind the backward facing step makes the flames keep stable over a wide range of inlet velocity/equivalent ratio. The wall cavity also has a good ability to anchor the flame in micro- or meso-scale combustors [16, 17]. Moreover, the bluff body can significantly enlarge the blow-off limit of premixed flame [18-20].

All of the above works focus on the premixed flame in the micro- or meso-scale combustors. Considering the safety and convenience in practical cases, the diffusion flame might be more suitable as the micro heat source due to some advantages. For example, the stable operating range of diffusion flame is quite wide, and there does not exist the phenomenon of flashback (a dangerous flame propagation mode) for it. Therefore, the diffusion flame receives more and more attention. CHENG et al [21] studied the characteristics of micro hydrogen diffusion flame via experiment and simulation, and they pointed out that the buoyancy effect is insignificant for the convection–diffusion controlled flame. NAKAMURA et al [22] found that the far-field natural convection easily induces the extinction of micro-jet methane diffusion flame. Recently, GAO et al [23] quantitatively evaluated the anchoring effect of heat recirculation via solid wall on the micro-jet diffusion flame stabilization, and they demonstrated that the heat recirculation effect can significantly reduce the heat loss and enhance the flame temperature. These works help us to gain insight into the characteristics of micro-jet diffusion flame.

As we know, we need to select suitable geometrical sizes of micro-jet tube for practical case, and the tube-wall thickness is an important parameter because it can influence the flow field near the outlet of tube, the conjugate heat exchange between the flame and tube-wall, and the strain effect on the flame. However, the effect of tube-wall thickness on the anchoring performance of micro-jet diffusion flame has not been systematically studied, which will be carried out in the present work. We will display the flame blow-off limits for different tube-wall thickness at first, and then the underlying mechanisms are discussed in terms of flow field, strain effect, and conjugate heat exchange.

2 Numerical methods

2.1 Geometric model and boundary conditions

The schematic diagram of computation domain and boundary conditions is depicted in Figure 1. As you can see, the computational zone is axial symmetry with respect to the axis of micro tube. The radial (x direction) and axial (y direction) directions of the total computational zone are 16.0 and 30.0 mm, respectively. The height of tube-wall is 3.0 mm. In the present work, the tube-wall thickness (d) adopts three values (0.1, 0.2 and 0.4 mm). The methane ejects into the ambient air via a tube with an inner diameter of 0.3 mm.

The far field boundaries are set as pressure outlet. Uniform concentration and velocity distribution of 300 K are imposed at the inlet of micro tube. At first, the inlet velocity of fuel V_in is increased with a step of 1.0 m/s from V_in=1.0 m/s. Then, near the blow-off limit, V_in is increased with a step of 0.5 m/s until the flame blow-off occurs. The tube-wall is assumed to be non-slip and chemically inert boundary. The conjugate heat exchange between the flame and tube-wall, which can significantly affect the combustion characteristics [24], is considered by the method of “two-sided walls” [25]. The bottom surface of tube-wall is set as the heat loss boundary to the environment which includes the natural convection and radiation [17].

Figure 1 Schematic diagram of computation domain and boundary conditions

2.2 Mathematical model

Calculation indicates that the order of magnitude of Knudsen number K_n is 10^-5, which is much less than the critical value 10^-3, for the fuel mixture of methane/air, so the Navier–Stokes equations are still applicable to the present work [26]. As the Reynolds number of gaseous mixture in the micro tube is very small, the micro-jet flame can keep the laminar behavior, which has been confirmed by CHEN et al [27] and LI et al [28] via experiments, so the laminar model was adopted in numerical simulation by many other researchers [23, 27-30]. In the present work, a two-dimensional unsteady-state model is applied. Governing equations are presented below:

Continuity:

                 (1)

Momentum:

Axial direction:

  (2)

Radial direction:

                          (3)

Energy:

            (4)

Species:

     (5)

where p is the fluid pressure; μ is the stress on the fluid; ρ is the fluid density; D_m,i is the mass diffusion coefficient of species i; h_i is the formation enthalpy of species i; R_i is the generation or consumption rate of species i; Y_i is the mass fraction of species i; λ_f is the thermal conductivity of the fluid; T_f is the fluid temperature; u and v are the axial and radial components of the flow velocity, respectively.

In addition, the energy equation for the solid wall is given as

          (6)

where λ_s is the thermal conductivity of solid material; ρ_s and c_s are the density and specific heat capacity of the solid wall, respectively; T_s is the solid wall temperature.

2.3 Computation scheme

The quartz, which is resistant to high temperature, is adopted as solid material of tube-wall, whose specific heat capacity and thermal conductivity are 750 J/(kg·K) and 2.0 W/(m·K), respectively [27]. The combustion reaction of methane/air mixture is simulated by C1 mechanism [31], which consists of 18 species and 58 reversible reactions. The transport properties and thermodynamic of the reactive species were taken from the CHEMKIN databases [32]. The momentum, energy, mass and species conservation equations are solved by the computational fluid dynamics software, FLUENT 14.0 [25]. The combustion process is simulated via using the laminar-finite-rate model. A “temperature patch (2000 K)” on the fluid zone is used to ignite the methane/air mixture in the computation.

The numbers of grid nodes at x and y directions are 118 and 210, respectively. Further refinement of local meshes is employed near the outlet of micro-jet tube, and the minimum grid size is 25 μm. We compare the gas temperature profiles along the axis line of flame using the present grid system and a finer grid system (the minimum grid size is 10 μm) to check the grid-independency, as shown in Figure 2. It can be seen that the temperature profiles obtained by the above two grid systems are almost overlapped with each other, which demonstrates that the present gird system is sufficient fine to capture the methane/air non-premixed flame. A time-step of 1.0×10^-8 s is selected for the unsteady-state simulation [23]. Convergence of the simulation is judged based on the residuals to be less than 1.0×10^-6. It should be pointed out that the present geometrical model and numerical models are very similar or the same with that in Ref. [23], and the accuracy of the numerical models had been validated by GAO et al [23]. Therefore, it is expected that the numerical models adopted in the present paper are also reasonable accuracy.

Figure 2 Gas temperature profiles along centerline for different grid resolutions at d=0.2 mm and inlet velocity (V_in) of 2.0 m/s

3 Results and discussion

3.1 Blow-off limit

The flame blow-off limit is defined as the biggest flow velocity at the inlet of tube over which the flame is extinguished. Figure 3 shows that the blow-off limit firstly increases and then decreases with an increasing d, i.e., a non-monotonic function relation.

Figure 3 Blow-off limit of micro-jet methane diffusion flame for different wall thicknesses

The blow-off limit reaches the maximum at a moderate d. As we know, the change of tube-wall thickness can change the flow filed near the outlet of tube, the strain effect on the flame, and the conjugate heat exchange between the flame and tube-wall, which will affect the micro-jet flame stabilization. Next, the cases at V_in=2.0 m/s are adopted as examples to reveal the underlying mechanisms responsible for the non-monotonic blow-off limit in terms of the above three aspects.

3.2 Flow field

It has been confirmed that the mass fraction of CH (Y_CH) can be used to mark the diffusion flame front [23, 28]. For the convenience of quantitative discussion, based on our previous publication [33, 34], the normalised isoline of 15% maximum Y_CH is used to define and visualise the flame front boundary in the present study. In addition, the flame at the lowest location is defined as the flame root, and the highest location of the upstream boundary of flame is defined as the flame top. Figure 4 presents the mass fraction of CH contours overlaid with axial-velocity isolines for different d near the outlet of tube. It can be seen that there exist recirculation zones behind the top wall of tube at d=0.2 and 0.4 mm.

As we know, the recirculation zone can well anchor the flame, which is beneficial for the flame stabilization (the positive effect of flow field). However, the flame root is far away from the recirculation zone, which means that the generated recirculation zone is nearly insignificant for the flame root stabilization. In addition, the flow velocity magnitude decreases with the increase of d. This is probably because that the increase of d decreases the ejecting effect of the fuel with high speed on the air around the outlet of tube, which also influences the flame shape, as shown in Figure 5.

Figure 4 Mass fraction of CH contours overlaid with axial-velocity isolines for different wall thicknesses at V_in= 2.0 m/s:

Figure 5 demonstrates that the best ejecting effect of the fuel with high speed on the air at d= 0.1 mm makes the flame root can maintain at the most upstream location, and the flame almost presents a sphere-shape. For d=0.4 mm, the flame almost presents an umbrella-shape, and the anchoring location of flame root is higher than the outlet of tube. In order to directly observe the ejecting effect of fuel with high speed on the air around the outlet of tube for different d, Figure 6(a) displays the distributive profiles of axial-velocity around the outlet of tube.

Figure 6(a) presents that the average axial-velocity is decreasing with an increasing d, which means that the air can mix with the methane with a faster rate via convection for a smaller d. Therefore, the flame can maintain at a more upstream location (see Figure 5). Moreover,Figure 6(a) shows that, when l_s≥0.55 (l_s is horizontal distance to tube), the axial- velocity at d=0.2 mm is larger than that at d=0.1 mm, which is a competitive result of the flow velocity magnitude and the angle between the flame front and flow direction. As a result, the local axial-velocity at the anchoring location of flame root at d=0.2 mm reaches the maximum (see Figure 6(b)). It is known that the incoming flow can push the flame downstream (the negative effect of flow field), so a larger local axial-velocity is detrimental for the flame root stabilization. However, Figure 3 shows that the blow-off limit at d=0.2 mm is the largest, so it is deduced that the flow field is insignificant for the non-monotonic blow-off limit.

3.3 Strain effect

It is known that the strain effect has negative effect on the flame stabilization out of the recirculation zone [35]. Figure 7 presents the distribution characteristics of strain rate near the flame for different wall thicknesses. It can be seen that the magnitude of strain rate near the flame decreases with the increase of tube-wall thickness, as quantitatively demonstrated in Figure 8. It is indicated that, with the increase of tube-wall thickness, the strain rates at the flame top and root obviously decrease, and the differences also remarkably decrease. For example, the strain rates at the flame top for d=0.1, 0.2, and 0.4 mm are 930, 485 and 295 1/s, respectively. It means that the strain effect on flame is smaller for a thicker tube-wall, which is beneficial for the flame stabilization. Therefore, the smaller strain effect is one of the factors which decrease the blow-off limit from d=0.1 to 0.2 mm.

Figure 5 Flame front (15% maximum Y_CH isoline) for different wall thicknesses at V_in=2.0 m/s:

Figure 6 Axial-velocity profiles around outlet of tube at y=3.0 mm (a) (l_s is horizontal distance to tube), and axial-velocity at anchoring location of flame root (b) for different d at V_in=2.0 m/s

3.4 Conjugate heat exchange

The conjugate heat exchange between the flame and tube-wall has significant effect on the flame stabilization. On the one hand, the unburned fuel can be well preheated by the heat recirculation effect of tube-wall with high temperature (the positive effect on the flame stabilization). On the other hand, the flame loses heat to the tube-wall (the negative effect on the flame stabilization). At first, Figure 9 shows the temperature contours overlaid with flame front for different tube-wall thicknesses. It can be seen that the tube-wall can be heated to a high temperature by the flame, and the temperature of upstream tube-wall at d=0.4 mm is obviously higher than that at d=0.1 and 0.2 mm mainly due to a smaller thermal-conduction resistance.

In order to quantitatively observe the conjugate heat exchange effect between the flame and tube-wall, we display the heat flux profiles of the inner wall, top wall and outer wall of tube in Figure 10. Figure 10(a) presents that the unburned fuel is preheated by the inner wall of tube all the time, and the total heat flux decreases with the increase of tube-wall thickness, which leads to a lower fuel temperature at the outlet of tube for a thicker tube-wall, as shown in Figure 11. Moreover,a larger section area of tube at a bigger d results in a better performance of thermal conduction towards upstream, so the upstream heat flux density (y≤1.2 mm) is slightly increasing with the increase of tube-wall thickness. For the top wall of tube, the surface area of top wall heated by the flame and the total heat flux significantly increase with the increase of d (see Figure 10(b)).In addition,Figure 10(c) presents the heat flux profiles along the outer wall of tube, which indicates that the absorbed heat flux of outer wall decreases but the heat loss from the outer wall of tube to the ambient environment increases with the increase of d. This is mainly because that the flame root slightly shifts downstream and the thermal-conduction resistance towards upstream decreases with an increasing d. Next, we will quantitatively calculate the total heat flux of heat recirculation, heat loss to the environment, and absorptive heat of tube-wall from the flame, as shown in Figure 12.

Figure 7 Strain rate isolines overlaid with 15% maximum Y_CH isoline for different d at V_in=2.0 m/s:

Figure 8 Strain rates at flame top and root for different d at V_in=2.0 m/s

At first, let us observe the positive effect of heat recirculation on the flame stabilization.Figure 11 shows the unburned fuel temperature at the outlet of tube for different tube-wall thicknesses. It can be seen that the unburned fuel temperature obviously decreases with the increase of tube-wall thickness, and the average fuel temperature at d=0.1, 0.2 and 0.4 mm are 1197.7, 1126.1 and 1067.0 K, respectively, which is consist with the distribution characteristic of heat flux in Figure 10(a). As we know, a lower unburned fuel temperature is detrimental for the flame stabilization, which is one of the factors decreasing the blow-off limit from d=0.2 to 0.4 mm.

Furthermore, it should be pointed out that the absorptive heat of tube-wall is the heat loss for the flame. It is known that a smaller heat loss of flame is beneficial for the flame stabilization. Figure 12 indicates that the heat loss of flame to the tube-wall at d=0.2 mm is the smallest. This is a competitive result of the distance between the flame and tube and the absorptive heat area of tube-wall. For d= 0.2 mm, the distance between the flame and tube is farther and the absorptive heat area of tube-wall is smaller, which results in the smallest heat loss of flame.

Figure 9 Temperature contours overlaid with 15% maximum Y_CH isoline for different wall thicknesses at V_in=2.0 m/s:

Figure 10 Heat flux profiles of the inner wall (a), top wall (b) and outer wall (c) of tube for different wall thicknesses at V_in=2.0 m/s

In addition, Figure 12 shows that the total heat flux of heat recirculation at d=0.2 mm is smaller, but the percent of heat recirculation in the total absorption of heat at d=0.2 mm is the largest. In other words, the performance of absorptive heat of tube-wall from the flame on preheating the unburned fuel at d=0.2 mm is the best. This is mainly because that the thermal-conduction resistance towards upstream at d=0.2 mm is larger, the heat loss of tube-wall to the environment is smaller, which is beneficial for increasing the percentage of heat recirculation. These consist with the non-monotonic blow-off limit. Therefore, it is deduced that the smallest heat loss of flame to the tube-wall and the best performance of tube-wall at d=0.2 mm on preheating unburned fuel are two main factors to determine the non-monotonic blow-off limit.

Figure 11 Gas temperature profiles at outlet of tube for different wall thicknesses at V_in=2.0 m/s

Figure 12 Total heat flux of heat recirculation and absorptive heat, and percent of heat recirculation in total absorption of heat at V_in=2.0 m/s

4 Conclusions

The present work studies the effect of tube-wall thickness on the blow-off limit of the micro-jet methane diffusion flame. It is unexpected that the blow-off limit firstly increases and then decreases with an increasing d, and the underlying mechanisms responsible for the non-monotonic blow-off limit are revealed in terms of the flow filed, the strain effect and the conjugate heat exchange. For the flow field, even though there are recirculation zones behind the top wall of tube at a larger tube-wall thickness, the flame root is far away from the recirculation zone, so it is deduced that the recirculation zone is insignificant for the flame stabilization. The local axial-velocity at the flame root reaches the maximum d=0.2 mm, which is detrimental for the flame root stabilization. However, the blow-off limit at d=0.2 mm is the largest. It is indicated that the flow field is insignificant for the non-monotonic blow-off limit. The strain effect on the flame is smaller for a thicker tube-wall, which is beneficial for the flame stabilization, so it is deduced that the smaller strain effect is one of the factors which increase the blow-off limit from d=0.1 to 0.2 mm. For the conjugate heat exchange, a worse heat recirculation effect is one of the factors which decrease the blow-off limit from d=0.2 to 0.4 mm. In addition, at d=0.2 mm, the heat loss of flame to the tube-wall is the smallest, and the percent of heat recirculation in the total absorption of heat is the largest, which is consist with the non-monotonic blow-off limit. Therefore, the heat loss of flame to the tube-wall and the performance of tube-wall on preheating unburned fuel are two main factors to determine the present blow-off limit. In one word, a moderate tube-wall thickness is more suitable to manufacture the micro-jet combustor.

References

[1] MARUTA K. Micro and mesoscale combustion [J]. Proceedings of the Combustion Institute, 2011, 33(1): 125-150. DOI: 10.1016/j.proci.2010.09.005.

[2] LEACH T T, CADOU C P. The role of structural heat exchange and heat loss in the design of efficient silicon micro-combustors [J]. Proceedings of the Combustion Institute, 2005, 30(2): 2437-2444. DOI: 10.1016/j.proci. 2004.08.229.

[3] MARUTA K, KATAOKA T, KIM N II, MINAEV S, FURSENKO R. Characteristics of combustion in a narrow channel with a temperature gradient [J]. Proceedings of the Combustion Institute, 2005, 30(2): 2429-2436. DOI: 10.1016/j.proci.2004.08.245.

[4] KANG X, GOLLAN R J, JACOBS P A, VEERARAGAVAN A. Suppression of instabilities in a premixed methane–air flame in a narrow channel via hydrogen/carbon monoxide addition [J]. Combustion and Flame, 2016, 173: 266-275. DOI: 10.1016/j.combustflame.2016.07.003.

[5] XU Bo, JU Yi-guang. Experimental study of spinning combustion in a mesoscale divergent channel [J]. Proceedings of the Combustion Institute, 2007, 31(2): 3285-3292. DOI: 10.1016/j.proci.2006.07.241.

[6] LIU Lei, ZHAO Liang, FAN Ai-wu. Effects of wall thickness and material on flame stability in a planar micro-combustor [J]. Journal of Central South University, 2019, 26: 2224-2233. DOI: 10.1007/s11771-019-4168-6.

[7] WAN Jian-long, SHANG Cheng, ZHAO Hai-bo. Dynamics of methane/air premixed flame in a mesoscale diverging combustor with/without a cylindrical flame holder [J]. Fuel, 2018, 232: 659-665. DOI: 10.1016/j.fuel.2018.06.026.

[8] KUMAR S, MARUTA K, MINAEV S. On the formation of multiple rotating Pelton-like flame structures in radial microchannels with lean methane–air mixtures [J]. Proceedings of the Combustion Institute, 2007, 31(2): 3261-3268. DOI: 10.1016/j.proci.2006.07.174.

[9] FAN Ai-wu, WAN Jian-long, MARUTA K, NAKAMURA H, YAO Hong, LIU Wei. Flame dynamics in a heated meso-scale radial channel [J]. Proceedings of the Combustion Institute, 2013, 34(2): 3351-3359. DOI: 10.1016/j.proci.2012.06.083.

[10] KUO C H, RONNEY P D. Numerical modeling of non-adiabatic heat-recirculating combustors [J]. Proceedings of the Combustion Institute, 2007, 31(2): 3277-3284. DOI: 10.1016/j.proci.2006.08.082.

[11] FAN Ai-wu, ZHANG He, WAN Jian-long. Numerical investigation on flame blow-off limit of a novel microscale Swiss-roll combustor with a bluff-body [J]. Energy, 2017, 123: 252-259. DOI: 10.1016/j.energy.2017.02.003.

[12] LI J, CHOU S K, LI Z W, YANG W M. Experimental investigation of porous media combustion in a planar micro-combustor [J]. Fuel, 2010, 89(3): 708-715. DOI: 10.1016/j.fuel.2009.06.026.

[13] LIU Yi, FAN Ai-wu, YAO Hong, LIU Wei. Numerical investigation of filtration gas combustion in a mesoscale combustor filled with inert fibrous porous medium [J]. International Journal of Heat and Mass Transfer, 2015, 91:18-26. DOI: 10.1016/j.ijheatmasstransfer.2015.07.100.

[14] YANG W M, CHOU S K, SHU C, LI Z W, XUE H. Combustion in micro-cylindrical combustors with and without a backward facing step [J]. Applied Thermal Engineering, 2002, 22(16): 1777-1787. DOI: 10.1016/ S1359-4311(02)00113-8.

[15] KHANDELWAL B, SAHOTA G P S, KUMAR S. Investigations into the flame stability limits in a backward step micro scale combustor with premixed methane–air mixtures [J]. Journal of Micromechanics and Microengineering, 2010, 20(9): 095030. DOI: 10.1088/0960- 1317/20/9/095030.

[16] WAN Jian-long, YANG Wei, FAN Ai-wu, LIU Yi, YAO Hong, LIU Wei, DU Yi-qing, ZHAO Dai-qing. A numerical investigation on combustion characteristics of H₂/air mixture in a micro-combustor with wall cavities [J]. International Journal of Hydrogen Energy, 2014, 39(15): 8138-8146. DOI: 10.1016/j.ijhydene.2014.03.116.

[17] WAN Jian-long, FAN Ai-wu, LIU Yi, YAO Hong, LIU Wei, GOU Xiao-long, et al. Experimental investigation and numerical analysis on flame stabilization of CH₄/air mixture in a mesoscale channel with wall cavities [J]. Combustion and Flame, 2015, 162(4): 1035-1045. DOI: 10.1016/ j.combustflame.2014.09.024.

[18] WAN Jian-long, ZHAO Hai-bo. Effect of thermal condition of solid wall on the stabilization of a preheated and holder-stabilized laminar premixed flame [J]. Energy, 2020, 200: 117548. DOI: 10.1016/j.energy.2020.117548.

[19] WAN Jian-long, WU Yong-jia, ZHAO Hai-bo. Excess enthalpy combustion of methane-air in a novel micro non-premixed combustor with a flame holder and preheating channels [J]. Fuel, 2020, 271: 117518. DOI: 10.1016/ j.fuel.2020.117518.

[20] WAN Jian-long, CHENG Xiao-bei. Numerical investigation of the local extinction and re-ignition mechanisms of premixed flame in a micro combustor with a flame holder and preheating channels [J]. Fuel, 2020, 264: 116837. DOI: 10.1016/j.fuel.2019.116837.

[21] CHENG T S, CHAO Y C, WU C Y, LI Y H, NAKAMURA Y, LEE K Y, YUANB T, LEU T S. Experimental and numerical investigation of microscale hydrogen diffusion flames [J]. Proceedings of the Combustion Institute, 2005, 30(2): 2489-2497. DOI: 10.1016/j.proci.2004.07.025.

[22] NAKAMURA Y, YAMASHITA H, SAITO K. A numerical study on extinction behaviour of laminar micro-diffusion flames [J]. Combustion Theory and Modelling, 2006, 10(6): 927-938. DOI: 10.1080/13647830600941704.

[23] GAO Jian, HOSSAIN A, MATSUOKA T, NAKAMURA Y. A numerical study on heat-recirculation assisted combustion for small scale jet diffusion flames at near-extinction condition [J]. Combustion and Flame, 2017, 178: 182-194. DOI: 10.1016/j.combustflame.2016.12.028.

[24] WAN Jian-long, ZHAO Hai-bo. Effect of conjugate heat exchange of flame holder on laminar premixed flame stabilization in a meso-scale diverging combustor [J]. Energy, 2020, 198: 117294. DOI: 10.1016/j.energy.2020.117294.

[25] ANSYS FLUENT Release 14.0 [M]. Canonsburg, PA: ANSYS Inc., 2011.

[26] XIN Yu-xuan, SUNG C J, LAW C K. A mechanistic evaluation of Soret diffusion in heptane/air flames [J]. Combustion and Flame, 2012, 159(7): 2345-2351. DOI: 10.1016/j.combustflame.2012.03.005.

[27] CHEN C P, CHAO Y C, CHENG T S, CHEN G B, WU C Y. Structure and stabilization mechanism of a microjet methane diffusion flame near extinction [J]. Proceedings of the Combustion Institute, 2007, 31(2): 3301-3308. DOI: 10.1016/j.proci.2006.08.069.

[28] LI Xing, ZHANG Jing, YANG Hao-lin, JIANG Li-qiao, WANG Xiao-han, ZHAO Dai-qing. Combustion characteristics of non-premixed methane micro-jet flame in coflow air and thermal interaction between flame and micro tube [J]. Applied Thermal Engineering, 2017, 112: 296-303. DOI: 10.1016/j.applthermaleng.2016.10.082.

[29] ZHANG J, LI X, YANG H, JIANG L, WANG X, ZHAO D. Study on the combustion characteristics of non-premixed hydrogen micro-jet flame and the thermal interaction with solid micro tube [J]. International Journal of Hydrogen Energy, 2017, 42(6): 3853-3862. DOI: 10.1016/j.ijhydene. 2016.07. 255.

[30] GAO Jian, HOSSAIN A, NAKAMURA Y. Flame base structures of micro-jet hydrogen/methane diffusion flames [J]. Proceedings of the Combustion Institute, 2017, 36(3): 4209-4216. DOI: 10.1016/j.proci.2016.08.034.

[31] BILGER R W, STARNER S H. On reduced mechanisms for methane air combustion in nonpremixed flames [J]. Combustion and Flame, 1990, 80(2): 135-149. DOI: 10.1016/0010-2180(90)90122-8.

[32] KEE R J, GRCAR J F, SMOOKE M D, MILLER J A. Sandia National Laboratories Report, SAND85-8240 [R]. San Diego, CA: Reaction Design Inc, 1994.

[33] WAN Jian-long, FAN Ai-wu. Effect of solid material on the blow-off limit of CH₄/air flames in a micro combustor with a plate flame holder and preheating channels [J]. Energy Conversion and Management, 2015, 101: 552-560. DOI: 10.1016/j.enconman.2015.06.010.

[34] WAN Jian-long, FAN Ai-wu, YAO Hong. Effect of the length of a plate flame holder on flame blowout limit in a micro-combustor with preheating channels [J]. Combustion and Flame, 2016, 170: 53-62. DOI: 10.1016/ j.combustflame.2016.05.015.

[35] LAW C K. Combustion physics [M]. Cambridge: Cambridge University Press, 2006.

(Edited by FANG Jing-hua)

中文导读

不同管壁厚度下甲烷扩散微射流火焰的非单调吹熄极限

摘要：为给选择合适的射流喷管壁面厚度提供指导，本文先通过数值模拟研究了固体壁面厚度对火焰吹熄极限的影响。结果表明，微射流甲烷扩散火焰吹熄极限随壁面厚度的增大而先增大后减小。之后，从流场、拉伸应力和耦合热传导三方面对出现非单调火焰吹熄极限的内在机制进行了讨论。分析表明，流场在其中无明显作用，较小的火焰拉伸应力使得壁厚0.2 mm时吹熄极限大于0.1 mm时的吹熄极限，对燃料较差的预热作用使得壁厚0.4 mm时吹熄极限大于0.2 mm时的吹熄极限。非单调的火焰吹熄极限主要由火焰对固体壁面的散热损失和固体壁面对燃料的预热性能决定。最小的火焰散热损失和对燃料最好的预热性能使得壁面厚度为0.2 mm时的火焰吹熄极限最大。因此，适中的壁面厚度更适合用来加工微射流燃烧器。

关键词：微射流扩散火焰；吹熄极限；流场；拉伸作用；耦合热传导

Foundation item: Project(51876074) supported by the National Natural Science Foundation of China

Received date: 2019-12-16; Accepted date: 2020-04-14

Corresponding author: WAN Jian-long, PhD, Lecturer; Tel: +86-27-87545526-8604; E-mail: jlw@hust.edu.cn; ORCID: 0000-0002- 3175-7239; LIU Hao, PhD, Associate Professor; Tel: +86-27-87544779-8329; E-mail: liuhao@hust.edu.cn; ORCID: 0000-0002-5620-4948