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air flames in a mesoscale cavity-combustor
Energy 91 (2015) 102e109
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Effect of pressure on the blow-off limits of premixed CH4/air flames in a mesoscale cavity-combustor Jianlong Wan, Aiwu Fan*, Hong Yao, Wei Liu State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 May 2015 Received in revised form 5 August 2015 Accepted 13 August 2015 Available online 3 September 2015
The blow-off limits of CH4/air flames in a mesoscale cavity-combustor under various pressures (P ¼ 1.0 e3.0 atm) are investigated numerically. The results show that the flame blow-off limit increases first and then decreases with an increasing pressure. Three typical pressures (P ¼ 1, 2 and 3 atm) are selected to perform numerical analysis with a detailed reaction mechanism. The analysis demonstrates that the reaction intensity in the cavity is enhanced as the pressure is raised, which is beneficial for flame stability. On the other hand, the flame front is prolonged at a higher pressure. This leads to more intense stretching effect, which is detrimental for flame stability. Therefore, the flame blow-off limit depends on the competition between the positive and negative sides. When the pressure is increased from 1 atm to 2 atm, the enhancement of anchoring ability in the cavity overwhelms the augmentation of stretching effect, which leads to an increase in flame blow-off limit. However, as the pressure is further raised from 2 atm to 3 atm, the stretching effect becomes the dominated side, which results in a decrease in flame blow-off limit. In summary, these complicated interactions determine that the flame blow-off limit is a non-monotonic function of the pressure. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Mesoscale combustor Cavity Elevated pressure Blow-off limit Reaction rate Stretching effect
1. Introduction With the rapid development of MEMS (micro-electro-mechanical systems) technology, the demand for micro power generation devices becomes more and more urgent. Currently, the primary power sources for portable electronics are conventional electrochemical batteries. However, the batteries have disadvantages including a short life span, a long recharging period and a low energy density. Micro-power-MEMS are considered to be promising alternatives due to their much higher energy densities [1,2]. However, there exist some challenges to maintain a stable combustion in micro- and meso-scale combustors. First, the large surface-area-to-volume ratio leads to a considerable increase in the heat-loss ratio as the combustor is scaled down. Moreover, the residence time of the gaseous mixture flowing through the combustor is very short, which sometimes makes it hard to achieve a complete combustion for the fuel [2]. Due to those problems, various unstable flames occur in small combustors [3e5]. Hence, it
* Corresponding author. 1037 Luoyu Road, Wuhan 430074, China. Tel.: þ86 27 87542618; fax: þ86 27 87540724. E-mail addresses: [email protected], [email protected] (A. Fan). http://dx.doi.org/10.1016/j.energy.2015.08.026 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
is vital to develop flame stabilization technologies for those miniature combustors. By far, many methods have been used to promote the flame stability in micro- and meso-scale combustors. Heat management is a frequently applied strategy [6e11]. To name a few, Kuo and Ronney [9] studied the combustion characteristics in micro “Swissroll” combustors, and the results showed that a better heat recirculation effect can extend the operational limit of inlet velocity more effectively. Jiang et al. [10] proposed a miniature combustor with a porous wall that can enhance the flame stability by reducing the heat loss and the preheating effect on the fresh mixture. Wang et al. [11] pointed out that the inert porous media can significantly extend the operating range of gas flow rate and equivalence ratio of CH4/air mixture. Moreover, the catalytic combustion is a good way to stabilize flame under small scales. Chen et al. [12] investigated the catalytic combustion of H2/air mixture in a micro combustor, which demonstrated that the flame stability can be significantly improved by the catalyst. Choi et al. [13] confirmed that combustion can occur in a catalytic combustor of sub-millimeter scale. Baigmohammadi et al. [14,15] numerically studied the impacts of wire insertion on premixed CH4/air flame and catalytic segmented bluff body on CH4/H2/air flame in a micro combustor, respectively. Their results show that the inserted wire and catalytic segmented
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bluff body have significant effects on flame stabilization and can also modify the flame location within the micro combustor. Forming a recirculation zone or low-velocity zone in the flow field is another effective way to stabilize the flame in microcombustors. Yang et al. [16] investigated the flame stability in micro combustors with one backward facing step. They found that the flame can remain stable in different combustor configurations over wide ranges of inlet velocity and equivalence ratio. Khandelwal et al. [17] experimentally studied the flame stabilization in a micro combustor with three steps, and the flame can be anchored with improved flammability limits. Wan et al. [18] and Fan et al. [19] developed micro bluff-body combustors that can expand the blow-off limit by several times compared with the straight channel. Recently, Wan et al. [20e22] and Yang et al. [23] studied the combustion characteristics of H2/air mixtures in micro combustors with wall cavities. They found that although the flame blow-off is greatly extended by the cavity, the “flame tip opening phenomenon” occurred at relatively high velocity which leads to a sharp drop in the combustion efficiency. Very recently, Wan et al. [24] investigated the flame behaviors of CH4/air flames in a mesoscale channel with cavities experimentally and numerically. The flame blow-off limits of this cavity-combustor are several times the corresponding burning velocities of incoming mixtures, indicating that the cavities have a strong ability to extend the operational range of inlet velocity. They also investigated the effect of channel gap distance on the flame blow-off limit [25] and a monotonic dependence was found. Moreover, the impact of wall thermal conductivity was examined and they revealed a nonmonotonic tendency [26]. Those findings provide a guideline for an optimum design of this type of micro- and meso-scale combustor. It is well known that the pressure has a significant effect on combustion characteristics. In the present work, we numerically investigated the flame blow-off limits of a mesoscale cavity-combustor at normal and elevated pressures. A nonmonotonic variation trend of the flame blow-off limit versus the pressure was found and analyzed.
20 mm, 4 mm and 70 mm respectively, while the wall thickness (W3) is 3 mm. The cavity length (L2) and depth (W2) are 4.5 mm and 1.5 mm, respectively. The angle of the ramped cavity wall (q) is set as 45 . The distance from the combustor entrance to the vertical cavity wall (L1) is 10 mm. The solid material of combustor walls is quartz glass.
2.2. Mathematical model First, the value of the Knudsen number, Kn ¼ Lg/Lc, was estimated, where Lg is the mean free path of gas and Lc is the characteristic scale of the combustor. The calculation shows that the order of magnitude of Kn is 105 for CH4 and O2, which is much less than the criterion of 103. Thus, the mixture can be reasonably regarded as a continuum and the NaviereStokes equations are suitable for the present study [27]. As the largest Reynolds number of the incoming mixture is approximately 1,750, a three-dimensional, unsteady laminar model was adopted. The governing equations for the mixture are shown below, Continuity:
vr v v v þ ðrvx Þ þ rvy þ ðrvz Þ ¼ 0 vt vx vy vz
(1)
Momentum:
X direction :
vðrvx Þ vðrvx vx Þ v rvx vy vðrvx vz Þ vp ¼ þ þ vt vx vz vx vy vtxx vtxy vtxz þ þ þ vx vy vz (2)
Y direction :
2. Numerical method 2.1. Geometric model
103
Z direction :
Fig. 1 shows the schematic of the mesoscale combustor with cavities. The width (W0), height (W1) and length (L0) of the channel are
v rvy v rvy vx v rvy vy v rvy vz vp ¼ þ þ vy vt vx vy vz vtyx vtyy vtyz þ þ þ vx vy vz (3) vðrvz Þ vðrvz vx Þ v rvz vy vðrvz vz Þ vp ¼ þ þ vt vx vz vz vy vtzx vtzy vtzz þ þ þ vx vy vz (4)
Energy:
v rcp T v rvx cp T v rvy Cp T v rvz cp T þ þ þ vt vx vy vz v lf vT v lf vT v lf vT X v vYi rc ¼ þ þ þ TD p;i m;i vx vx vx2 vy2 vz2 i X v vY v vY þ rcp;i TDm;i i þ rcp;i TDm;i i þ hi Ri vy vz vy vz i (5) Species:
Fig. 1. Schematic of the mesoscale combustor with cavities: (a) longitudinal cross section, (b) vertical cross section. The origin of coordinates is located at the center of the combustor.
vðrYi Þ vðrYi vx Þ v rYi vy vðrYi vz Þ þ þ þ vt vx vz vy v vYi v vYi v vY rDm;i rDm;i rDm;i i þ Ri þ þ ¼ vx vy vz vx vy vz
(6)
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where Yi, Ri, Cp,i and hi denote the mass fraction, generation or consumption rate, specific heat capacity and formation enthalpy of species i, respectively. lf is the thermal conductivity of the fluid. It has been widely confirmed that the heat conduction in the solid walls affects the micro- and meso-scale combustion significantly [19]. Therefore, heat transfer in the combustor walls was considered in our computation. The energy equation for the solid walls is given as
v rw cp;w Tw v vTw v vTw v vTw ls ls ls ¼ þ þ vx vy vz vt vx vy vz
(7)
where ls, rw and cp,w are the thermal conductivity, density, and specific heat of the solid wall, respectively.
overlapped with each other. Therefore, the cell size of Dx ¼ Dy ¼ Dz ¼ 200 mm is sufficiently fine to capture the flame structure. Further refinement of the meshes near the local region of cavities was conducted and a non-uniform grid system with 1,576,960 cells was applied in final computations, as presented in Fig. 3. A time step of 105 s was adopted for the iterations. The convergence of the CFD simulation was judged based on the residuals of all governing equations to be less than 1.0 106. The blow-off limit is defined as the largest combustible velocity over which the flame is blown out of the combustion chamber. Under small inlet velocity, the flame can be stabilized in the cavities. Then, we increase the inlet velocity step by step with a small interval (e.g., 0.05 m/s or even less). When the flame blow-off occurs, there is no flame in the combustor and the whole temperature field is uniform with a same value as the incoming mixture (i.e., 300 K).
2.3. Computation schemes
2.4. Model validation
The density of gaseous mixture was calculated using the ideal gas assumption, while the viscosity, specific heat and thermal conductivity were calculated based on a mass-fraction-weighted average of the species’ properties [28]. The detailed chemistry, C1 mechanism, which includes 18 species and 58 elementary reactions, was applied to simulate the premixed CH4/air combustion. The thermodynamic and transport properties of the species were taken from the CHEMKIN databases [29,30]. As the combustor was specially processed (e.g., annealed in oxygen atmosphere) and the interior surfaces was made chemically inert, the surface reactions were not considered in the computation. The density, specific heat and thermal conductivity of the quartz material at 300 K are 2650 kg/m3, 750 J/(kg$K) and 1.05 W/(m,K), respectively. Temperature dependences of the specific heat and thermal conductivity of the solid wall were incorporated using polynomial functions based on the handbook [31]. The boundary conditions are specified as follows. Uniform velocity distributions and concentration of CH4/air mixture were set at the entrance with a temperature of 300 K. A Neumann boundary condition was given at the exit of combustor. The DO (discrete ordinates) model was adopted to consider the effect of interior surface radiation. Temperature continuity at the interface was applied to link the solid and fluid phases. In addition, a non-slip boundary condition was considered for the inner wall. The heat-loss rate from the outer wall surfaces of the combustor was calculated through Eq. (8):
The accuracy of the present numerical model has been evaluated in our recent paper [24], where we conducted experimental and numerical investigation in the blow-off limits of CH4/air flames at atmospheric pressure, as shown in Fig. 4. The maximum relative deviation is 6.25% which demonstrates that the predictions agree well with experimental data. This confirms the reasonable accuracy of the numerical model adopted in the current work.
4 4 q ¼ hs TW;O T∞ þ εs s TW;O T∞
(8)
where hs is the natural convection heat transfer coefficient (20 W m2 K1) [32], T∞ is the ambient temperature (300 K), Tw,o is the outer wall temperature, εs is the emissivity of the quartz glass (0.92), and s is the StefaneBoltzmann constant, 5.67 108 W m2 K4. The mass, energy, momentum, and species conservation equations, together with the conjugated heat conduction in solid walls, were solved by the CFD (computational fluid dynamics) software, FLUENT 6.3 [28]. A “temperature patch (2000 K)” near the exit of combustor was set to initiate the combustion reaction in the computation. Additionally, the “SIMPLE” algorithm was employed to decouple the velocity and pressure. The convection and diffusion terms are discretized using the second-order upwind scheme. The grid independency was checked by using three sets of grid system, i.e., Dx ¼ Dy ¼ Dz ¼ 200, 100 and 50 mm, respectively. The mass fraction profiles of two key radicals (HCO and OH) along the centerline of the yz plane are shown in Fig. 2. This figure illustrates that the results obtained by these three grid systems were almost
3. Results and discussion 3.1. Flame blow-off limits under various pressures Fig. 5 shows the blow-off limits of the mesoscale cavitycombustor for premixed CH4/air flames under different pressures and equivalence ratios. This figure demonstrates that for a same pressure, the flame blow-off limit increases with the increase of mixture equivalence ratio. For instance, when P ¼ 2 atm, the blowoff limits of f ¼ 0.8, 0.9 and 1.0 are 3.0, 3.7 and 4.1 m/s, respectively, which are ~15 times larger than the corresponding laminar burning velocities of the incoming CH4/air mixtures, whose values are 0.21 m/s, 0.24 m/s and 0.28 m/s, respectively [33]. Moreover, it is interesting to see from Fig. 4 that the flame blow-off limit exhibits a non-monotonic trend versus the pressure. To be more specific, when the pressure is lower than 2 atm, the flame blow-off limit increases as the pressure is increased, and reaches a peak at P ¼ 2 atm; then it decreases with the further increase in the pressure. In the following section we will discuss the reasons for this non-monotonic variation. 3.2. Discussion It is expected that the flame-anchoring ability in the mesoscale cavity-combustor depends mainly upon two competitive aspects. The first one is the stabilization of the flame root, which is affected by both the reaction intensity in the cavity and the heat recirculation via the upstream walls; while the other aspect is the stretching effect on the flame front, especially for the flame tip. The former is considered to be positive whereas the latter is detrimental for flame stabilization. Therefore, the flame blow-off limit relies on the competition between these two sides. 3.2.1. Effect of pressure on the heat recirculation via upstream wall Because the preheating effect via the upstream wall can affect the combustion intensity in the wall cavity, we study the effect of pressure on the heat recirculation in this section as a first step. It is easy understanding that the heat release amount at a higher pressure is larger than that at a lower one. The first reason is that
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Fig. 2. Local profiles of the mass fractions of HCO and OH for different grid resolutions along the centerline of the yz plane under the condition of f ¼ 1.0, Vin ¼ 0.5 m/s.
Fig. 3. The mesh generation near (30 mm < y < 0 mm, 5 mm < z < 5 mm) in the yz plane.
the
cavities
Fig. 5. Blow-off limits of premixed CH4/air flames in the mesoscale cavity-combustor under different pressures and equivalence ratios.
Fig. 4. Experimental and numerical flame blow-off limits of the mesoscale combustor with cavities for different equivalence ratios [24].
the reaction rate in the cavity is increased with the increase of the pressure. The second reason is that the mass flow rate is proportional to the density of the gaseous mixture which has a linear relationship with the pressure according to the ideal gas state equation (r ¼ P/RT). As a result, the temperature level in the
mesoscale cavity-combustor increases with the pressure. To verify this, Fig. 6 shows the temperature fields of the whole combustor at different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9. It is known from this figure that the maximum temperatures for P ¼ 1 atm, 2 atm and 3 atm are 1929.4 K, 2095.5 K and 2174.6 K, respectively. Fig. 7 depicts the gas temperature profiles in the vicinity of the upstream inner wall (z ¼ 1.975 mm), and in the cross-section at the cavity entrance (y ¼ 25 mm) under the same condition (Vin ¼ 1.0 m/s, f ¼ 0.9). From Fig. 7a, it is seen that for a larger pressure (i.e., P ¼ 2 atm and 3 atm), the gas temperature near the upstream inner wall rises up to a higher level. This is because that, at a larger pressure, more heat energy is released in the cavity and transferred to the upstream solid wall. However, it is also obviously noted from Fig. 7b that, the gas temperature level far from the wall (i.e., mainstream temperature) is comparatively lower for a larger pressure. This is mainly because the mass flow rate is larger at a higher pressure. These distinct temperature patterns have essential influences on the flame shapes (both the locations of flame root and flame tip) at different pressures.
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Fig. 6. Temperature fields of the mesoscale cavity-combustor at different pressures under the condition of Vin ¼ 1.0 m/s, f ¼ 0.9.
Fig. 7. Gas temperature profiles at different locations under the same condition of Vin ¼ 1.0 m/s, f ¼ 0.9: (a) in the vicinity of upstream inner wall (z ¼ 1.975 mm); (b) in the crosssection at the cavity entrance (y ¼ 25 mm).
3.2.2. Effect of pressure on the reaction intensity in the cavity Nikolaou and Swaminathan [34] indicated that for near stoichiometric CH4/air flames, the reaction rate of H þ CH2O ¼ HCO þ H2 (hereafter referred as R-1) serves as a good marker of the heat release rate. Our previous study [24,25] reveals that the flame root is anchored by the vertical cavity wall. Thus, we show the Arrhenius rate of R-1 in the vicinity of the vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) in Fig. 8. It is evident
from Fig. 8 that the reaction rate of R-1 increases drastically from P ¼ 1 atm to P ¼ 2 atm and then slows down from P ¼ 2 atm to P ¼ 3 atm. The maximum reaction rates for P ¼ 1 atm, 2 atm and 3 atm are 0.14 kgmol/m3s, 1.02 kgmol/m3s and 1.38 kgmol/m3s, respectively. Hassan et al. [33] pointed that the chemical reactions exhibit the similar largest sensitivities at low and high pressures. For C1 mechanism, the main chain propagation reactions are R-2
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Fig. 8. Arrhenius rate profiles of R1(H þ CH2O ¼ HCO þ H2) in the vicinity of the vertical cavity wall (y ¼ 24.975 mm) for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
Fig. 10. Gas temperature profiles in the vicinity of vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
(OH þ CO ¼ H þ CO2) and R-3 (H þ O2 ¼ O þ OH). Fig. 9 depicts the Arrhenius rate profiles of R-2 and R-3 in the vicinity of vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) at different pressures, which exhibits similar variation tendencies with that of R-1. As a result, the gas temperature level near the vertical cavity wall is much higher at P ¼ 2, 3 atm compared with that at P ¼ 1 atm, as shown in Fig. 10. The peak values of these three curves are 879.46 K, 1017.09 K and 1073.96 K for P ¼ 1 atm, 2 atm and 3 atm, respectively. It is well known that the radical HCO can be used to identify the flame front [35]. Here, we show the mass fraction profiles of HCO in the vicinity of the vertical cavity wall for different pressures in Fig. 11. The peak of HCO mass fraction is indicated by a dashed line, which can be used to identify the location of flame root. It is noted from Fig. 11 that the maximum mass fraction of HCO decreases with the increase of pressure. This is because that the rates of the chemical reactions that consume HCO increase with an increasing pressure [36]. Furthermore, Fig. 11 demonstrates that the location of the flame root shifts towards the combustor center
(corresponding to a smaller z value) as the pressure is increased. To be more specific, the distance between the flame root and the combustor center at P ¼ 1 atm, 2 atm and 3 atm are 2.76 mm, 2.72 mm and 2.53 mm, respectively. In conclusion, a higher pressure leads to larger reaction rate and larger heat release rate in the cavity, which is beneficial for anchoring the flame root near the vertical cavity wall. In other words, this is a positive factor for a larger flame blow-off limit.
3.2.3. Effect of pressure on the flame stretch The mass fraction profiles of HCO along the combustor centerline are shown in Fig. 12. The peak of HCO is used to mark the location of flame tip. Meanwhile, the flame shapes under different pressures are schematically shown in Fig. 13, which are drawn based on the locations of both flame root and flame tip. Here, we define the flame height as the distance between the flame tip and the vertical cavity wall (i.e., flame root). It turns out that the flame heights are around 7.1 mm, 9.2 mm and 10.1 mm for P ¼ 1 atm, 2 atm and 3 atm, respectively. Accordingly, the ratios of flame
Fig. 9. Arrhenius rate profiles of R-2 (OH þ CO ¼ H þ CO2) and R-3 (H þ O2 ¼ O þ OH) in the vicinity of vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) at different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
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reflects the maximum stretching effect along the flame surface, is augmented as the pressure is increased. 3.3. Brief summary
Fig. 11. Mass fraction profiles of HCO in the vicinity of the vertical cavity wall (y ¼ 24.975 mm) for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
From the above discussion, the flame stabilization ability depends mainly on the anchoring ability of the flame root and the stretching effect of flame front. The former is a positive factor while the latter is a negative one for flame stabilization. Therefore, the flame blow-off limit is a result of the competition between these two sides. As have been shown in Fig. 8 that the reaction rate increases significantly with the increase of pressure. A larger reaction rate results in a stronger flame root, which is beneficial for flame stabilization. Thus, when the pressure is increased from 1 atm to 2 atm, the anchoring ability of the flame root overwhelms the stretching effect, which leads to an increase in the flame blow-off limit. However, as the pressure is raised from 2 atm to 3 atm, the stretching effect becomes the dominated factor, which results in a decrease in the flame blow-off limit. In summary, the flame blowoff limit is a non-monotonic function of the pressure. 4. Conclusions
Fig. 12. Mass fraction profiles of HCO along the centerline of the combustor for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
height to flame width are 1.29, 1.69 and 2.0 for the three cases. These values illustrate that the flame inclination angle (a) decreases with the increase of pressure, which means that the curvature of the flame tip increases with the increase of pressure. Moreover, the strain rates at the flame tips for P ¼ 1 atm, 2 atm, and 3 atm are 2845.3 s1, 3758.6 s1 and 4149.5 s1, respectively. As the flame stretch depends on both the curvature and strain rate [37], it can be deduced that the stretching effect on the flame tip, which
The blow-off limits of premixed CH4/air flames in a mesoscale cavity-combustor were investigated numerically under atmospheric and elevated pressures. The results show that the flame blow-off limit exhibits a non-monotonic variation versus the pressure and it achieves a maximum at a moderate pressure. Three typical pressures (i.e., P ¼ 1 atm, 2 atm, 3 atm) are adopted to analyze the influence of pressure on the flame blow-off limit in terms of heat recirculation, chemical reaction near the flame root (i.e., in the cavity) and flame stretch. The former two aspects are considered to be positive functions for flame-anchoring, whereas the latter is detrimental for flame stabilization. Therefore, the flame blow-off limit relies on the competition between the positive and negative sides. Analysis demonstrates that the heat recirculation via the upstream wall and the reaction intensity of the flame root are enhanced as the pressure is raised. However, the stretching effect is also strengthened at a higher pressure. When the pressure is increased from 1 atm to 2 atm, the anchoring ability of the flame root overwhelms the stretching effect, which leads to an increase in the flame blow-off limit. However, as the pressure is further raised from 2 atm to 3 atm, the stretching effect becomes the dominated factor, which results in a decrease in the flame blow-off limit. In summary, the flame blow-off limit is a non-monotonic function of the pressure. Acknowledgements This work was supported by the Natural Science Foundation of China (Grant No.51576084) and the Foundation of State Key Laboratory of Coal Combustion, China (Grant No. FSKLCCA1503). References
Fig. 13. Schematic of the flame shapes under different pressures. The numbers 1, 2 and 3 indicate the flame fronts at P ¼ 1 atm, 2 atm and 3 atm, respectively.
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[21] Wan JL, Fan AW, Yao H, Liu W. Effect of thermal conductivity of solid wall on combustion efficiency of a micro-combustor with cavities. Energy Convers Manag 2015;96:605e12. [22] Wan JL, Fan AW, Yao H, Liu W. Flame-anchoring mechanisms of a micro cavity-combustor for premixed H2/air flame. Chem Eng J 2015;275:17e26. [23] Yang W, Fan AW, Wan JL, Liu W. Effect of external surface emissivity on flamesplitting limit in a micro cavity-combustor. Appl Therm Eng 2015;83:8e15. [24] Wan JL, Fan AW, Liu Y, Yao H, Liu W, Gou XL, et al. Experimental investigation and numerical analysis on flame stabilization of CH4/air mixture in a mesoscale channel with wall cavities. Combust Flame 2015;162(4):1035e45. [25] Wan JL, Fan AW. Effect of channel gap distance on the flame blow-off limit in mesoscale channels with cavities for premixed CH4/air flames. Chem Eng Sci 2015;132:99e107. [26] Wan JL, Fan AW, Yao H. A non-monotonic variation of blow-off limit of premixed CH4/air flames in mesoscale cavity-combustors with different thermal conductivities. Fuel 2015;159:1e6. [27] Beskok A, Karniadakis G. A model for flows in channels, pipes, and ducts at micro and nano scales. Microscale Thermophys Eng 1999;3:43e77. [28] Fluent 6.3 user's guide. Lebanon, New Hampshire: Fluent Inc; 2006. [29] Kee RJ, Rupley FM, Miller JA. Sandia national laboratories report. SAND878215B. 1990. http://www.osti.gov/scitech/biblio/7073290. [30] Kee RJ, Grear JF, Smooke MD, Miller JA. Sandia national laboratories report. SAND85-8240. 1985. http://www.researchgate.net/publication/260388319. [31] Ma Q, Fang R, Xiang L. Handbook of thermo-physical properties. Bejing: China Agricultural Machinery Press; 1986 (in chinese). [32] Holman JP. Heat transfer. 9th ed. New York: McGraw-Hill; 2002. [33] Hassan MI, Aung KT, Faeth GM. Measured and predicted properties of laminar premixed methane/air flames at various pressures. Combust Flame 1998;115: 539e50. [34] Nikolaou ZM, Swaminathan N. Heat release rate markers for premixed combustion. Combust Flame 2014;161(12):3073e84. [35] Najm HN, Paul PH, Mueller CJ, Wyckoff PS. On the adequacy of certain experimental observables as measurements of flame burning rate. Combust Flame 1998;113:312e32. [36] Goswami M, Derks SCR, Coumans K, Slikker WJ, de Andrade Oliveira MH, Bastiaans RJM, et al. The effect of elevated pressures on the laminar burning velocity of methaneþair mixtures. Combust Flame 2013;160(9):1627e35. [37] Law CK. Combustion physics. Cambridge: Cambridge University Press; 2006.
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Effect of pressure on the blow-off limits of premixed CH4/air flames in a mesoscale cavity-combustor Jianlong Wan, Aiwu Fan*, Hong Yao, Wei Liu State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan 430074, China
a r t i c l e i n f o
a b s t r a c t
Article history: Received 1 May 2015 Received in revised form 5 August 2015 Accepted 13 August 2015 Available online 3 September 2015
The blow-off limits of CH4/air flames in a mesoscale cavity-combustor under various pressures (P ¼ 1.0 e3.0 atm) are investigated numerically. The results show that the flame blow-off limit increases first and then decreases with an increasing pressure. Three typical pressures (P ¼ 1, 2 and 3 atm) are selected to perform numerical analysis with a detailed reaction mechanism. The analysis demonstrates that the reaction intensity in the cavity is enhanced as the pressure is raised, which is beneficial for flame stability. On the other hand, the flame front is prolonged at a higher pressure. This leads to more intense stretching effect, which is detrimental for flame stability. Therefore, the flame blow-off limit depends on the competition between the positive and negative sides. When the pressure is increased from 1 atm to 2 atm, the enhancement of anchoring ability in the cavity overwhelms the augmentation of stretching effect, which leads to an increase in flame blow-off limit. However, as the pressure is further raised from 2 atm to 3 atm, the stretching effect becomes the dominated side, which results in a decrease in flame blow-off limit. In summary, these complicated interactions determine that the flame blow-off limit is a non-monotonic function of the pressure. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Mesoscale combustor Cavity Elevated pressure Blow-off limit Reaction rate Stretching effect
1. Introduction With the rapid development of MEMS (micro-electro-mechanical systems) technology, the demand for micro power generation devices becomes more and more urgent. Currently, the primary power sources for portable electronics are conventional electrochemical batteries. However, the batteries have disadvantages including a short life span, a long recharging period and a low energy density. Micro-power-MEMS are considered to be promising alternatives due to their much higher energy densities [1,2]. However, there exist some challenges to maintain a stable combustion in micro- and meso-scale combustors. First, the large surface-area-to-volume ratio leads to a considerable increase in the heat-loss ratio as the combustor is scaled down. Moreover, the residence time of the gaseous mixture flowing through the combustor is very short, which sometimes makes it hard to achieve a complete combustion for the fuel [2]. Due to those problems, various unstable flames occur in small combustors [3e5]. Hence, it
* Corresponding author. 1037 Luoyu Road, Wuhan 430074, China. Tel.: þ86 27 87542618; fax: þ86 27 87540724. E-mail addresses: [email protected], [email protected] (A. Fan). http://dx.doi.org/10.1016/j.energy.2015.08.026 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
is vital to develop flame stabilization technologies for those miniature combustors. By far, many methods have been used to promote the flame stability in micro- and meso-scale combustors. Heat management is a frequently applied strategy [6e11]. To name a few, Kuo and Ronney [9] studied the combustion characteristics in micro “Swissroll” combustors, and the results showed that a better heat recirculation effect can extend the operational limit of inlet velocity more effectively. Jiang et al. [10] proposed a miniature combustor with a porous wall that can enhance the flame stability by reducing the heat loss and the preheating effect on the fresh mixture. Wang et al. [11] pointed out that the inert porous media can significantly extend the operating range of gas flow rate and equivalence ratio of CH4/air mixture. Moreover, the catalytic combustion is a good way to stabilize flame under small scales. Chen et al. [12] investigated the catalytic combustion of H2/air mixture in a micro combustor, which demonstrated that the flame stability can be significantly improved by the catalyst. Choi et al. [13] confirmed that combustion can occur in a catalytic combustor of sub-millimeter scale. Baigmohammadi et al. [14,15] numerically studied the impacts of wire insertion on premixed CH4/air flame and catalytic segmented bluff body on CH4/H2/air flame in a micro combustor, respectively. Their results show that the inserted wire and catalytic segmented
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bluff body have significant effects on flame stabilization and can also modify the flame location within the micro combustor. Forming a recirculation zone or low-velocity zone in the flow field is another effective way to stabilize the flame in microcombustors. Yang et al. [16] investigated the flame stability in micro combustors with one backward facing step. They found that the flame can remain stable in different combustor configurations over wide ranges of inlet velocity and equivalence ratio. Khandelwal et al. [17] experimentally studied the flame stabilization in a micro combustor with three steps, and the flame can be anchored with improved flammability limits. Wan et al. [18] and Fan et al. [19] developed micro bluff-body combustors that can expand the blow-off limit by several times compared with the straight channel. Recently, Wan et al. [20e22] and Yang et al. [23] studied the combustion characteristics of H2/air mixtures in micro combustors with wall cavities. They found that although the flame blow-off is greatly extended by the cavity, the “flame tip opening phenomenon” occurred at relatively high velocity which leads to a sharp drop in the combustion efficiency. Very recently, Wan et al. [24] investigated the flame behaviors of CH4/air flames in a mesoscale channel with cavities experimentally and numerically. The flame blow-off limits of this cavity-combustor are several times the corresponding burning velocities of incoming mixtures, indicating that the cavities have a strong ability to extend the operational range of inlet velocity. They also investigated the effect of channel gap distance on the flame blow-off limit [25] and a monotonic dependence was found. Moreover, the impact of wall thermal conductivity was examined and they revealed a nonmonotonic tendency [26]. Those findings provide a guideline for an optimum design of this type of micro- and meso-scale combustor. It is well known that the pressure has a significant effect on combustion characteristics. In the present work, we numerically investigated the flame blow-off limits of a mesoscale cavity-combustor at normal and elevated pressures. A nonmonotonic variation trend of the flame blow-off limit versus the pressure was found and analyzed.
20 mm, 4 mm and 70 mm respectively, while the wall thickness (W3) is 3 mm. The cavity length (L2) and depth (W2) are 4.5 mm and 1.5 mm, respectively. The angle of the ramped cavity wall (q) is set as 45 . The distance from the combustor entrance to the vertical cavity wall (L1) is 10 mm. The solid material of combustor walls is quartz glass.
2.2. Mathematical model First, the value of the Knudsen number, Kn ¼ Lg/Lc, was estimated, where Lg is the mean free path of gas and Lc is the characteristic scale of the combustor. The calculation shows that the order of magnitude of Kn is 105 for CH4 and O2, which is much less than the criterion of 103. Thus, the mixture can be reasonably regarded as a continuum and the NaviereStokes equations are suitable for the present study [27]. As the largest Reynolds number of the incoming mixture is approximately 1,750, a three-dimensional, unsteady laminar model was adopted. The governing equations for the mixture are shown below, Continuity:
vr v v v þ ðrvx Þ þ rvy þ ðrvz Þ ¼ 0 vt vx vy vz
(1)
Momentum:
X direction :
vðrvx Þ vðrvx vx Þ v rvx vy vðrvx vz Þ vp ¼ þ þ vt vx vz vx vy vtxx vtxy vtxz þ þ þ vx vy vz (2)
Y direction :
2. Numerical method 2.1. Geometric model
103
Z direction :
Fig. 1 shows the schematic of the mesoscale combustor with cavities. The width (W0), height (W1) and length (L0) of the channel are
v rvy v rvy vx v rvy vy v rvy vz vp ¼ þ þ vy vt vx vy vz vtyx vtyy vtyz þ þ þ vx vy vz (3) vðrvz Þ vðrvz vx Þ v rvz vy vðrvz vz Þ vp ¼ þ þ vt vx vz vz vy vtzx vtzy vtzz þ þ þ vx vy vz (4)
Energy:
v rcp T v rvx cp T v rvy Cp T v rvz cp T þ þ þ vt vx vy vz v lf vT v lf vT v lf vT X v vYi rc ¼ þ þ þ TD p;i m;i vx vx vx2 vy2 vz2 i X v vY v vY þ rcp;i TDm;i i þ rcp;i TDm;i i þ hi Ri vy vz vy vz i (5) Species:
Fig. 1. Schematic of the mesoscale combustor with cavities: (a) longitudinal cross section, (b) vertical cross section. The origin of coordinates is located at the center of the combustor.
vðrYi Þ vðrYi vx Þ v rYi vy vðrYi vz Þ þ þ þ vt vx vz vy v vYi v vYi v vY rDm;i rDm;i rDm;i i þ Ri þ þ ¼ vx vy vz vx vy vz
(6)
104
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where Yi, Ri, Cp,i and hi denote the mass fraction, generation or consumption rate, specific heat capacity and formation enthalpy of species i, respectively. lf is the thermal conductivity of the fluid. It has been widely confirmed that the heat conduction in the solid walls affects the micro- and meso-scale combustion significantly [19]. Therefore, heat transfer in the combustor walls was considered in our computation. The energy equation for the solid walls is given as
v rw cp;w Tw v vTw v vTw v vTw ls ls ls ¼ þ þ vx vy vz vt vx vy vz
(7)
where ls, rw and cp,w are the thermal conductivity, density, and specific heat of the solid wall, respectively.
overlapped with each other. Therefore, the cell size of Dx ¼ Dy ¼ Dz ¼ 200 mm is sufficiently fine to capture the flame structure. Further refinement of the meshes near the local region of cavities was conducted and a non-uniform grid system with 1,576,960 cells was applied in final computations, as presented in Fig. 3. A time step of 105 s was adopted for the iterations. The convergence of the CFD simulation was judged based on the residuals of all governing equations to be less than 1.0 106. The blow-off limit is defined as the largest combustible velocity over which the flame is blown out of the combustion chamber. Under small inlet velocity, the flame can be stabilized in the cavities. Then, we increase the inlet velocity step by step with a small interval (e.g., 0.05 m/s or even less). When the flame blow-off occurs, there is no flame in the combustor and the whole temperature field is uniform with a same value as the incoming mixture (i.e., 300 K).
2.3. Computation schemes
2.4. Model validation
The density of gaseous mixture was calculated using the ideal gas assumption, while the viscosity, specific heat and thermal conductivity were calculated based on a mass-fraction-weighted average of the species’ properties [28]. The detailed chemistry, C1 mechanism, which includes 18 species and 58 elementary reactions, was applied to simulate the premixed CH4/air combustion. The thermodynamic and transport properties of the species were taken from the CHEMKIN databases [29,30]. As the combustor was specially processed (e.g., annealed in oxygen atmosphere) and the interior surfaces was made chemically inert, the surface reactions were not considered in the computation. The density, specific heat and thermal conductivity of the quartz material at 300 K are 2650 kg/m3, 750 J/(kg$K) and 1.05 W/(m,K), respectively. Temperature dependences of the specific heat and thermal conductivity of the solid wall were incorporated using polynomial functions based on the handbook [31]. The boundary conditions are specified as follows. Uniform velocity distributions and concentration of CH4/air mixture were set at the entrance with a temperature of 300 K. A Neumann boundary condition was given at the exit of combustor. The DO (discrete ordinates) model was adopted to consider the effect of interior surface radiation. Temperature continuity at the interface was applied to link the solid and fluid phases. In addition, a non-slip boundary condition was considered for the inner wall. The heat-loss rate from the outer wall surfaces of the combustor was calculated through Eq. (8):
The accuracy of the present numerical model has been evaluated in our recent paper [24], where we conducted experimental and numerical investigation in the blow-off limits of CH4/air flames at atmospheric pressure, as shown in Fig. 4. The maximum relative deviation is 6.25% which demonstrates that the predictions agree well with experimental data. This confirms the reasonable accuracy of the numerical model adopted in the current work.
4 4 q ¼ hs TW;O T∞ þ εs s TW;O T∞
(8)
where hs is the natural convection heat transfer coefficient (20 W m2 K1) [32], T∞ is the ambient temperature (300 K), Tw,o is the outer wall temperature, εs is the emissivity of the quartz glass (0.92), and s is the StefaneBoltzmann constant, 5.67 108 W m2 K4. The mass, energy, momentum, and species conservation equations, together with the conjugated heat conduction in solid walls, were solved by the CFD (computational fluid dynamics) software, FLUENT 6.3 [28]. A “temperature patch (2000 K)” near the exit of combustor was set to initiate the combustion reaction in the computation. Additionally, the “SIMPLE” algorithm was employed to decouple the velocity and pressure. The convection and diffusion terms are discretized using the second-order upwind scheme. The grid independency was checked by using three sets of grid system, i.e., Dx ¼ Dy ¼ Dz ¼ 200, 100 and 50 mm, respectively. The mass fraction profiles of two key radicals (HCO and OH) along the centerline of the yz plane are shown in Fig. 2. This figure illustrates that the results obtained by these three grid systems were almost
3. Results and discussion 3.1. Flame blow-off limits under various pressures Fig. 5 shows the blow-off limits of the mesoscale cavitycombustor for premixed CH4/air flames under different pressures and equivalence ratios. This figure demonstrates that for a same pressure, the flame blow-off limit increases with the increase of mixture equivalence ratio. For instance, when P ¼ 2 atm, the blowoff limits of f ¼ 0.8, 0.9 and 1.0 are 3.0, 3.7 and 4.1 m/s, respectively, which are ~15 times larger than the corresponding laminar burning velocities of the incoming CH4/air mixtures, whose values are 0.21 m/s, 0.24 m/s and 0.28 m/s, respectively [33]. Moreover, it is interesting to see from Fig. 4 that the flame blow-off limit exhibits a non-monotonic trend versus the pressure. To be more specific, when the pressure is lower than 2 atm, the flame blow-off limit increases as the pressure is increased, and reaches a peak at P ¼ 2 atm; then it decreases with the further increase in the pressure. In the following section we will discuss the reasons for this non-monotonic variation. 3.2. Discussion It is expected that the flame-anchoring ability in the mesoscale cavity-combustor depends mainly upon two competitive aspects. The first one is the stabilization of the flame root, which is affected by both the reaction intensity in the cavity and the heat recirculation via the upstream walls; while the other aspect is the stretching effect on the flame front, especially for the flame tip. The former is considered to be positive whereas the latter is detrimental for flame stabilization. Therefore, the flame blow-off limit relies on the competition between these two sides. 3.2.1. Effect of pressure on the heat recirculation via upstream wall Because the preheating effect via the upstream wall can affect the combustion intensity in the wall cavity, we study the effect of pressure on the heat recirculation in this section as a first step. It is easy understanding that the heat release amount at a higher pressure is larger than that at a lower one. The first reason is that
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Fig. 2. Local profiles of the mass fractions of HCO and OH for different grid resolutions along the centerline of the yz plane under the condition of f ¼ 1.0, Vin ¼ 0.5 m/s.
Fig. 3. The mesh generation near (30 mm < y < 0 mm, 5 mm < z < 5 mm) in the yz plane.
the
cavities
Fig. 5. Blow-off limits of premixed CH4/air flames in the mesoscale cavity-combustor under different pressures and equivalence ratios.
Fig. 4. Experimental and numerical flame blow-off limits of the mesoscale combustor with cavities for different equivalence ratios [24].
the reaction rate in the cavity is increased with the increase of the pressure. The second reason is that the mass flow rate is proportional to the density of the gaseous mixture which has a linear relationship with the pressure according to the ideal gas state equation (r ¼ P/RT). As a result, the temperature level in the
mesoscale cavity-combustor increases with the pressure. To verify this, Fig. 6 shows the temperature fields of the whole combustor at different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9. It is known from this figure that the maximum temperatures for P ¼ 1 atm, 2 atm and 3 atm are 1929.4 K, 2095.5 K and 2174.6 K, respectively. Fig. 7 depicts the gas temperature profiles in the vicinity of the upstream inner wall (z ¼ 1.975 mm), and in the cross-section at the cavity entrance (y ¼ 25 mm) under the same condition (Vin ¼ 1.0 m/s, f ¼ 0.9). From Fig. 7a, it is seen that for a larger pressure (i.e., P ¼ 2 atm and 3 atm), the gas temperature near the upstream inner wall rises up to a higher level. This is because that, at a larger pressure, more heat energy is released in the cavity and transferred to the upstream solid wall. However, it is also obviously noted from Fig. 7b that, the gas temperature level far from the wall (i.e., mainstream temperature) is comparatively lower for a larger pressure. This is mainly because the mass flow rate is larger at a higher pressure. These distinct temperature patterns have essential influences on the flame shapes (both the locations of flame root and flame tip) at different pressures.
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Fig. 6. Temperature fields of the mesoscale cavity-combustor at different pressures under the condition of Vin ¼ 1.0 m/s, f ¼ 0.9.
Fig. 7. Gas temperature profiles at different locations under the same condition of Vin ¼ 1.0 m/s, f ¼ 0.9: (a) in the vicinity of upstream inner wall (z ¼ 1.975 mm); (b) in the crosssection at the cavity entrance (y ¼ 25 mm).
3.2.2. Effect of pressure on the reaction intensity in the cavity Nikolaou and Swaminathan [34] indicated that for near stoichiometric CH4/air flames, the reaction rate of H þ CH2O ¼ HCO þ H2 (hereafter referred as R-1) serves as a good marker of the heat release rate. Our previous study [24,25] reveals that the flame root is anchored by the vertical cavity wall. Thus, we show the Arrhenius rate of R-1 in the vicinity of the vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) in Fig. 8. It is evident
from Fig. 8 that the reaction rate of R-1 increases drastically from P ¼ 1 atm to P ¼ 2 atm and then slows down from P ¼ 2 atm to P ¼ 3 atm. The maximum reaction rates for P ¼ 1 atm, 2 atm and 3 atm are 0.14 kgmol/m3s, 1.02 kgmol/m3s and 1.38 kgmol/m3s, respectively. Hassan et al. [33] pointed that the chemical reactions exhibit the similar largest sensitivities at low and high pressures. For C1 mechanism, the main chain propagation reactions are R-2
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Fig. 8. Arrhenius rate profiles of R1(H þ CH2O ¼ HCO þ H2) in the vicinity of the vertical cavity wall (y ¼ 24.975 mm) for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
Fig. 10. Gas temperature profiles in the vicinity of vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
(OH þ CO ¼ H þ CO2) and R-3 (H þ O2 ¼ O þ OH). Fig. 9 depicts the Arrhenius rate profiles of R-2 and R-3 in the vicinity of vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) at different pressures, which exhibits similar variation tendencies with that of R-1. As a result, the gas temperature level near the vertical cavity wall is much higher at P ¼ 2, 3 atm compared with that at P ¼ 1 atm, as shown in Fig. 10. The peak values of these three curves are 879.46 K, 1017.09 K and 1073.96 K for P ¼ 1 atm, 2 atm and 3 atm, respectively. It is well known that the radical HCO can be used to identify the flame front [35]. Here, we show the mass fraction profiles of HCO in the vicinity of the vertical cavity wall for different pressures in Fig. 11. The peak of HCO mass fraction is indicated by a dashed line, which can be used to identify the location of flame root. It is noted from Fig. 11 that the maximum mass fraction of HCO decreases with the increase of pressure. This is because that the rates of the chemical reactions that consume HCO increase with an increasing pressure [36]. Furthermore, Fig. 11 demonstrates that the location of the flame root shifts towards the combustor center
(corresponding to a smaller z value) as the pressure is increased. To be more specific, the distance between the flame root and the combustor center at P ¼ 1 atm, 2 atm and 3 atm are 2.76 mm, 2.72 mm and 2.53 mm, respectively. In conclusion, a higher pressure leads to larger reaction rate and larger heat release rate in the cavity, which is beneficial for anchoring the flame root near the vertical cavity wall. In other words, this is a positive factor for a larger flame blow-off limit.
3.2.3. Effect of pressure on the flame stretch The mass fraction profiles of HCO along the combustor centerline are shown in Fig. 12. The peak of HCO is used to mark the location of flame tip. Meanwhile, the flame shapes under different pressures are schematically shown in Fig. 13, which are drawn based on the locations of both flame root and flame tip. Here, we define the flame height as the distance between the flame tip and the vertical cavity wall (i.e., flame root). It turns out that the flame heights are around 7.1 mm, 9.2 mm and 10.1 mm for P ¼ 1 atm, 2 atm and 3 atm, respectively. Accordingly, the ratios of flame
Fig. 9. Arrhenius rate profiles of R-2 (OH þ CO ¼ H þ CO2) and R-3 (H þ O2 ¼ O þ OH) in the vicinity of vertical cavity wall (y ¼ 24.975 mm, 2.0 mm z 3.5 mm) at different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
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reflects the maximum stretching effect along the flame surface, is augmented as the pressure is increased. 3.3. Brief summary
Fig. 11. Mass fraction profiles of HCO in the vicinity of the vertical cavity wall (y ¼ 24.975 mm) for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
From the above discussion, the flame stabilization ability depends mainly on the anchoring ability of the flame root and the stretching effect of flame front. The former is a positive factor while the latter is a negative one for flame stabilization. Therefore, the flame blow-off limit is a result of the competition between these two sides. As have been shown in Fig. 8 that the reaction rate increases significantly with the increase of pressure. A larger reaction rate results in a stronger flame root, which is beneficial for flame stabilization. Thus, when the pressure is increased from 1 atm to 2 atm, the anchoring ability of the flame root overwhelms the stretching effect, which leads to an increase in the flame blow-off limit. However, as the pressure is raised from 2 atm to 3 atm, the stretching effect becomes the dominated factor, which results in a decrease in the flame blow-off limit. In summary, the flame blowoff limit is a non-monotonic function of the pressure. 4. Conclusions
Fig. 12. Mass fraction profiles of HCO along the centerline of the combustor for different pressures under Vin ¼ 1.0 m/s, f ¼ 0.9.
height to flame width are 1.29, 1.69 and 2.0 for the three cases. These values illustrate that the flame inclination angle (a) decreases with the increase of pressure, which means that the curvature of the flame tip increases with the increase of pressure. Moreover, the strain rates at the flame tips for P ¼ 1 atm, 2 atm, and 3 atm are 2845.3 s1, 3758.6 s1 and 4149.5 s1, respectively. As the flame stretch depends on both the curvature and strain rate [37], it can be deduced that the stretching effect on the flame tip, which
The blow-off limits of premixed CH4/air flames in a mesoscale cavity-combustor were investigated numerically under atmospheric and elevated pressures. The results show that the flame blow-off limit exhibits a non-monotonic variation versus the pressure and it achieves a maximum at a moderate pressure. Three typical pressures (i.e., P ¼ 1 atm, 2 atm, 3 atm) are adopted to analyze the influence of pressure on the flame blow-off limit in terms of heat recirculation, chemical reaction near the flame root (i.e., in the cavity) and flame stretch. The former two aspects are considered to be positive functions for flame-anchoring, whereas the latter is detrimental for flame stabilization. Therefore, the flame blow-off limit relies on the competition between the positive and negative sides. Analysis demonstrates that the heat recirculation via the upstream wall and the reaction intensity of the flame root are enhanced as the pressure is raised. However, the stretching effect is also strengthened at a higher pressure. When the pressure is increased from 1 atm to 2 atm, the anchoring ability of the flame root overwhelms the stretching effect, which leads to an increase in the flame blow-off limit. However, as the pressure is further raised from 2 atm to 3 atm, the stretching effect becomes the dominated factor, which results in a decrease in the flame blow-off limit. In summary, the flame blow-off limit is a non-monotonic function of the pressure. Acknowledgements This work was supported by the Natural Science Foundation of China (Grant No.51576084) and the Foundation of State Key Laboratory of Coal Combustion, China (Grant No. FSKLCCA1503). References
Fig. 13. Schematic of the flame shapes under different pressures. The numbers 1, 2 and 3 indicate the flame fronts at P ¼ 1 atm, 2 atm and 3 atm, respectively.
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