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air flame stability in rectangular mesoscale combustors
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The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors Zili Yuan, Aiwu Fan* 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 16 April 2019 Received in revised form 1 May 2019 Accepted 7 May 2019 Available online xxx
The effects of aspect ratio (a ¼ 1, 2, 3 and 4) of mesoscale rectangular channels on CH4-air flame stability were numerically studied. The results show that at relatively high inlet velocity, the flame is convex (with respect to the upstream) when a 3; instead it shifts to a W-shaped appearance at a ¼ 4. In addition, the flame blowout limit exhibits a non-monotonic variation and it peaks at a ¼ 3. Our analysis reveals that when a is raised from 1 to 3, both of the heat loss ratio and hydrodynamic perturbation rate are reduced, which favors a larger blowout limit. However, for the channel with a ¼ 4, the perturbation rate of hydrodynamic instability is significantly increased at the flame tip because of the increased wave number, which results from the W-shaped flame front. Consequently, the intensified hydrodynamic instability will lead to a reduction in the flame blowout limit of the channel with a ¼ 4. © 2019 Energy Institute. Published by Elsevier Ltd. All rights reserved.
Keywords: Rectangular micro-combustor Aspect ratio Blowout limit Heat loss Hydrodynamic instability
1. Introduction Various micro-electromechanical systems such as micro-sensors, micro-engines, and micro-power generators, are emerging continuously. Compared to electrochemical batteries, hydrogen and hydrocarbon fuels have much higher energy densities and sufficient sources. Therefore, combustion-based miniature power generators have attracted extensive attention [1e3]. Micro- and meso-scale combustors has a large surface-to-volume ratio, which make them suitable to serve as heat sources for micro-thermophotovoltaic (TPV) [4] and micro thermoelectric [5] systems. Owing to the increased surface-to-volume ratio of micro- and meso-scale combustors, the interactions between flame and wall play a significant role in flame stability. Daou et al. [6] revealed that heat loss is the major factor leading to near-wall flame quenching in micro channels. Norton and Vlachos [7] numerically demonstrated that the heat-recirculation effect through channel walls is closely associated with wall thickness and material, and has an essential influence on the flame stability in micro-channels. Zhang et al. [8] numerically investigated the effects of inlet parameters on combustion characteristics in micro-channels. Maruta et al. [9] observed flames with repetitive extinction and ignition (FREI) in a micro quartz tube with controlled temperature gradient. Details of the FREI dynamics were widely scrutinized through numerical simulation by many researchers [10e14]. Stazio et al. [15] investigated the impact of external heating method on FREI, while Kishore et al. [16] and Kang et al. [17] studied the temperature gradient effect. Very recently, Xiang et al. [18] experimentally observed the FREI dynamics of non-premixed H2-air flames in a Y-shaped micro-combustor. The flame stability also exhibits a three dimensional effect in micro- and meso-scale channels. Pizza et al. [19] discovered various flame dynamics of CH4/air mixture in circular tubes based on three dimensional simulation. Pashchenko [20] found that only when the length of a micro tube is large enough compared to the diameter, can 2-D model obtain accurate results similar to those of 3-D model. Tsai [21] showed that the symmetry of CH4-air flame depends on the channel width. Benedetto et al. [22] obtained the combustible velocity ranges of C3H8/air mixture in square and circular micro channels. Anwar et al. [23] experimentally observed three flame shapes, (i.e., concave, planar, and convex flames) in mesoscale rectangular channels with different aspect ratios. However, they didn't explain the underlying physics responsible for the variation of flame shape.
* Corresponding author. 1037 Luoyu Road, Wuhan 430074, China. E-mail address: [email protected] (A. Fan). https://doi.org/10.1016/j.joei.2019.05.003 1743-9671/© 2019 Energy Institute. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Nomenclature H W L Vin Ub cp ho k T W,o T∞ Le Tb
Channel height Channel width Channel length Inlet velocity (m/s) Adiabatic flame propagation velocity (m/s) Specific heat (J/(kg$K)) Convection heat transfer coefficient (Wm2K1) Wave number (m1) Outer wall temperature (K) Ambient temperature (K) Lewis number Temperature of combustion products
Tu
Temperature of unburned mixture
Greek symbols Aspect ratio εs Surface emissivity ru Density of unburned mixture r Density (kg/m3) l Wave length (m) ε Density ratio of combustion products to unburned mixture rb Density of combustion products Thermal diffusivity (m2/s) Dth lth Thermal conductivity (W/(m$K)) s Instability disturbance rate (s1) s0 Stephan-Boltzmann constant
a
To crack the problems of flame instability under micro- and meso-scale channels, numerous approaches have been proposed. For example, thermal management methods like Swiss-roll structure were designed for premixed [24,25] and non-premixed [26] combustion. Micro-combustors with double-layered wall was developed [27], which can enhance heat recirculation and reduce heat loss simultaneously. Various flame holders, such as backward facing step [28,29], bluff body [30,31], cavity [32,33] have been demonstrated to be effective ways to anchor the flame root in the recirculation zone. Catalyst can assisted combustion [34,35] and suppress flame instability [36,37] in microchannels. A combination of these methods can achieve even better performance on flame stabilization, such as small reactor with catalyst segmentation and cavities [38], micro combustor with catalytic wall and heat recirculation channels [39], and mesoscale Swiss-roll combustor with a bluff-body [40]. Slight oxygen enrichment can also effectively improve flame stability and combustion efficiency [41]. For non-premixed combustion, Li et al. [42] found that the micro-channel with a moderate gap can obtain a highest blowout limit. Ning et al. [43] showed that the diffusion flame stability can be intensified by addition of porous media in Y-shaped meso-scale channels. It can be known from the above literature review that flame-wall coupling through heat exchange [6e18] or geometrical effect (3D effect) [19e23] has been extensively investigated. Corresponding flame stabilization methods have also been developed [24e43]. Comparatively, intrinsic flame instabilities (i.e., Darrieus-Landau and thermal-diffusive instabilities) have been seldom studied. Alipoor [44] numerically examined the significance of Darrieus-Landau (hydrodynamic) and thermal-diffusive instabilities on the appearance of asymmetric hydrogen flames in a heated micro-channel. They reported that for the flames in micro-channels, the thermal-diffusive instability plays a major role in evolution of a symmetric flame into an asymmetric one, whereas the role of hydrodynamic instability is minor. We think that this is because the fuel is hydrogen, which has a very low Lewis number. In the case of methane fuel (whose Lewis number is near unity and thus the thermal-diffusive instability is negligible), the hydrodynamic instability might have an important effect on flame stability. The rectangular channels with a large aspect ratio are frequently used for micro-thermophotovoltaics (TPV) and thermoelectric (TE) modules. Motivated by these facts, in the present work we numerically investigate the flame stability of stoichiometric CH4/air mixtures in a mesoscale channel by varying its aspect ratio while maintaining a fixed height, which can provide a guidance for the optimal design of rectangular micro-combustors using a fuel with a relatively large Lewis number like methane. 2. Numerical method The cross section of the mesoscale rectangular channel is shown in Fig. 1, where the central point of the channel entrance, “O”, is set as the origin of coordinates. X, Y and Z indicate the coordinate axis in the width, height and length directions, respectively. The channel height (H), length (L) and wall thickness are fixed at 4 mm, 40 mm and 1 mm, respectively. The aspect ratio (a ¼ W/H) takes four values of 1, 2, 3 and 4 in this work. A stoichiometric CH4/air mixture is fed into the rectangular mesoscale channels. Quartz glass is selected for the wall material. Its density, specific heat, thermal conductivity and surface emissivity are r ¼ 2650 kg/m3, cp ¼ 750 J/(kg$K), lth¼1.05 W/(m$K) and εs ¼ 0.92, respectively. As the maximal Reynolds number of the incoming cold mixture is ~400, a laminar flow, three-dimensional model was adopted. The second-order upwind scheme was used to discretize the model. The C1 mechanism [45], which evolves 18 chemical species and 58 elementary reactions, was applied to simulate the CH4/air combustion. The ideal gas assumption was used to calculate the density of the gas mixture. The specific heat, viscosity and thermal conductivity were calculated from a mass fraction weighted average of the species' properties. Thermodynamic and transport properties in CHEMKIN format [46] are imported into the CFD software. Boundary conditions are specified as follows. Uniform concentration and velocity distributions of CH4/air mixture were set at the inlet with a temperature of 300 K. A pressure boundary condition with 1 atm is given for the channel exit. At the outer surfaces of the channel, the heat loss rate is calculated through Eq. (1):
q ¼ ho TW;o T∞ þ εs s0 T 4W;o T 4∞
(1)
where ho is the convection heat transfer coefficient (20 Wm2K1) [47], T W,o is the outer wall temperature, T∞ is the ambient temperature (300 K), εs is the surface emissivity and s0 is the Stephan-Boltzmann constant (5.67 108 Wm2K4). The CFD software FLUENT 15.0 [48] was applied to solve the set of governing equations. The ‘‘SIMPLEC’’ algorithm was employed to couple the pressure and velocity. For a physically stable flame, a temperature patch (2000 K) of fluid zone was adapted to initialize the Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 1. Geometry of the rectangular mesoscale channel.
combustion reaction in the computation. Grid independency was checked by using three sets of grid system, i.e., Dx ¼ Dy ¼ Dz ¼ 0.1 mm (1440000 grids), Dx ¼ Dy ¼ 0.2 mm, Dz ¼ 0.1 mm (360000 grids) and Dx ¼ Dy ¼ Dz ¼ 0.2 mm (180000 grids). The centerline temperature profiles in the 4 4 mm2 channel under Vin ¼ 0.25 m/s are presented in Fig. 2, which demonstrates that the difference between the obtained results by using the grid systems of 360000 and 1440000 is small. Therefore, the grid system with 360000 grids was used for the final simulation. In order to evaluate the prediction accuracy of the present numerical model, a numerical simulation of an experimental case by Tang et al. [49] was carried out. The height, width and length of the channel are 3 mm, 8 mm and 18 mm, respectively. The flow rate of CH4/air mixture is 41 ml/min (Vin ¼ 0.3 m/s). The Reynolds number of the incoming mixture is ~80, which falls in the laminar regime. The predicted and measured temperature profiles along the centerline of outer wall are shown in Fig. 3. The maximum relative error comes out to be 9.89%, which confirms the reasonable accuracy of the numerical results in this paper. 3. Results and discussion 3.1. Effect of the aspect ratio on flame stability The temperature contours in the X-Z plane of the mesoscale channels with different aspect ratios are presented in Fig. 4. In each subfigure, the variation tendency of the temperature field with increasing inlet velocity is provided. It can be seen from Fig. 4 that, when the inlet velocity is relatively low (e.g., Vin ¼ 0.25 m/s), the flames are stabilized near the entrances of the four channels. For the square channel (a ¼ 1), before the occurrence of blowout, the flame still remains a stable symmetric shape. However, as the inlet velocity is slightly larger than 0.26 m/s, the flame will be blown out suddenly. For mesoscale channels with a ¼ 2 and 3, when the inlet velocity is raised up to Vin ¼ 0.3 m/s, the flame fronts are stable and slightly pushed downstream, exhibiting a convex curve with respect to upstream. In contrast, the flame front is transformed into a stable W-shaped flame at Vin ¼ 0.3 m/s in the wider channel (i.e., a ¼ 4), although it is asymmetric with respect to the centerline. As the inlet velocity is further increased to Vin ¼ 0.4 m/s, the flame fronts become inclined in the channels with a ¼ 2 and 3, but the flame is pushed farther downstream in the case of a ¼ 2. In the channel with a ¼ 4, the flame front cannot remain stable any longer as the inlet velocity is increased to Vin ¼ 0.32 m/s. It shows a continuous deformation with time, which is actually in a pulsating mode, as depicted in Fig. 5.
Fig. 2. Centerline temperature profiles in the 4 4 mm2 channel under Vin ¼ 0.25 m/s for different grid systems.
Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 3. Validation of the numerical model with the experimental data by Tang et al. [49].
Fig. 4. Evolution of temperature field in the X-Z plane with an increasing inlet velocity for the mesoscale channels with different aspect ratios.
From the variation trend of flame shape it can be expected that the flame will be finally blown out of the channels at a certain higher velocity, which is called the blowout limit herein. To compare the flame stabilization ability of the four channels with various aspect ratios, their blowout limits are plotted in Fig. 6. It is interesting to note that the blowout limit first increases as the aspect ratio is increased from 1 to 3, and then decreases with a further increase in the aspect ratio. The specific values of the blowout limits are 0.26 m/s, 0.44 m/s, 0.66 m/s and 0.33 m/s for a ¼ 1, 2, 3 and 4, respectively. Evidently, the flame blowout limit shows a non-monotonic variation with the aspect ratio, and it peaks at a ¼ 3. In the following section, the underlying mechanisms for this trend will be analyzed. 3.2. Discussion about heat loss ratio and velocity field under Vin ¼ 0.25 m/s Because the blowout limit of the channel with a ¼ 1 is only 0.26 m/s, here we chose the case of Vin ¼ 0.25 m/s to discuss about the heat loss ratio and velocity field, which can shed some light on the reasons responsible for flame stability in the channels with different aspect ratios. 3.2.1. Comparison between the heat loss ratios Here, we quantitatively compare the heat loss ratio (defined as the ratio of heat loss amount to the input enthalpy) under Vin ¼ 0.25 m/s. Table 1 tabulates the corresponding hydraulic diameter, surface to volume ratio and heat loss ratio of the four channels. It can be seen from Table 1 that with the increase of the aspect ratio, the hydraulic diameter becomes larger while the surface to volume ratio grows smaller, which leads to a reduction in the heat loss ratio. Obviously, this is beneficial to stabilize the flame in the straight mesoscale channel without a flame holder. Our calculation shows that as the aspect ratio is increased from a ¼ 1 to 2, the reduction in the heat loss ratio is 6.18%, while the reduction extent decreases to 2.54% if the aspect ratio is raised from a ¼ 2 to 3. If the aspect ratio is further increased from a ¼ 3 to 4, the reduction in the heat loss ratio is only 1.3%. These facts demonstrate that the reduction in heat loss contributes more significantly to improve flame stability when the aspect ratio is relatively small. Instead, other reasons such as flow characteristics and hydrodynamic instability should be responsible for the deterioration of flame stability in mesoscale channels with a larger aspect ratio (e.g., a ¼ 4). Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 5. Temporal evolution of temperature field (a) and contours of HCO mass fraction (b) of a pulsating flame in the X-Z plane of the mesoscale channel with a ¼ 4 at Vin ¼ 0.32 m/s.
Fig. 6. Blowout limits of the mesoscale channels with different aspect ratios.
3.2.2. Comparison between the velocity fields Although all the flames are planar in the four channels under Vin ¼ 0.25 m/s, the velocity fields differs greatly. Fig. 7 illustrates the contours of velocity field and temperature field in the X-Z plane of the mesoscale channels with a ¼ 2, 3 and 4 at Vin ¼ 0.25 m/s. It is interesting that with the increase of aspect ratio, the central high speed region shrinks (Fig. 7b) and finally splits into two located near the side walls (Fig. 7c). There are two reasons for the variation of velocity field. On the one hand, the channel width expands as the aspect ratio is increased, which leads to the reduction in the relative thickness of the velocity boundary layer. This trend can be clearly seen in Fig. 8, which shows the dimensionless velocity distribution under cold state in the width (X) direction. On the other hand, Fig. 7 also indicates that the temperature gradient close to the side walls is higher than that in the central region, and the low temperature gradient zone becomes wider with the increase of aspect ratio (or channel width). Owing to the distinct velocity field in the mesoscale channel with a ¼ 4, the W-shaped flame will appear at a sufficient high inlet velocity.
Table 1 Hydraulic diameter, surface to volume ratio, heat loss ratio of the mesoscale channels with different aspect ratios under Vin ¼ 0.25 m/s.
hydraulic diameter Surface to volume ratio heat loss ratio
4 4 mm2
4 8 mm2
4 12 mm2
4 16 mm2
4 mm 1000 m1 0.922
5.33 mm 750 m1 0.865
6 mm 666.67 m-1 0.843
6.4 mm 625 m1 0.832
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Fig. 7. Contours of velocity field (filled) and temperature field (lines) in the X-Z plane of the mesoscale channels with a ¼ 2, 3 and 4 at Vin ¼ 0.25 m/s.
Fig. 8. Dimensionless velocity distribution under cold state in the width (X) direction at Z ¼ 2 mm of the mesoscale channels with a ¼ 2, 3 and 4.
3.3. Discussion about hydrodynamic instability As has been demonstrated above, in the mesoscale channel with a ¼ 4, the flame exhibits a W-shaped appearance from Vin ¼ 0.3 m/s and starts to lose its stability from Vin ¼ 0.32 m/s. Here, the hydrodynamic instability must play a more significant role than the thermal-diffusive instability in the evolution of a stable W-shaped flame into an unstable asymmetric one because the Lewis number is close to unity. It is well known that the hydrodynamic instability [50] was first proposed by Darrieus [51] and Landau [52], and thus it is also called Darrieus-Landau instability. Fig. 9 illustrates the principle of hydrodynamic instability. Darrieus and Landau pointed out that the flow direction of the unburned mixture changes after passing through the curved flame front due to a significant volume expansion resulting from a sudden density decrease of the high temperature burnt gas. Therefore, the flame segments protruding toward the unburned gas have a tendency to move upstream, while those protruding toward the combustion product have a tendency to move downstream. 3.3.1. Analysis of flow deflection Fig. 10 shows the streamlines in the X-Z plane of the channel with a ¼ 2, 3 and 4. To illustrate the flow deflection before and after the flame front, the contours of the velocity deflection angle (defined as the angle between the velocity components in X direction and Z direction) are also drawn in Fig. 10. If q is positive (red-yellow), the streamlines points towards the upper right. In contrast, if q is negative (blue-violet), the streamlines face to the lower right. The color transition in the contours indicates the change in flow direction. It can be seen from Fig. 10 that in the near-wall region of the channels with a ¼ 2 and 3 (the flame front is convex), the gas mixture moves toward the wall before the flame front, and then towards the channel center after the flame front. In addition, velocity deflection angle is almost zero in central region of the channel with a ¼ 2 and 3, which indicates that in this region the gaseous mixture keeps moving in the Z-direction after Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 9. Schematic diagram of the hydrodynamic instability [50].
passing through the flame front. However, when the aspect ratio is a ¼ 4, the gas mixture has a velocity component in the X-direction in both of the near-wall region and central region. Therefore, when the gas mixture passes through the W-shaped flame front, flow deflection occurs in both of the near-wall and central regions. Large strain rate will result from the obvious flow deflection. For a ¼ 2 and 3, the strain rate near the wall surface has the maximum value, whereas there exists three peak values for a ¼ 4. Specifically, the maximum strain rates for a ¼ 2 and 3 are both ~6400 s1, and the counterpart for a ¼ 4 is ~6900 s1. As a result, the more intense stretch effect can weaken the stability of the W-shaped flame in the channel with a ¼ 4. 3.3.2. Analysis of the hydrodynamic instability According to Darrieus and Landau [50e52], the instability disturbance rate can be expressed as:
s ¼ U0 U b k
(2)
Fig. 10. Streamlines and contours of the velocity deflection angle in the X-Z plane of the mesoscale channels with a ¼ 2, 3 and 4.
Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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where Ub is the adiabatic flame propagation velocity, k is the wave number (k ¼ 2p/l, l is the wave length), and U0 can be calculated through Eq. (3).
U0 ¼
. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε þ ε2 ε3 ε ð1 þ εÞ
(3)
where
ε ¼ rb =ru
(4)
Here, rb and ru are the densities of combustion products and unburned mixture, respectively. According to the Darrieus-Landau theory, the hydrodynamic instability becomes stronger when the wavelength is reduced, which is inconsistent with the experimental results in follow-up studies. This is because they assumed the flame to be infinitely thin and the flame thickness is ignored in Eq. (2). However, when the wavelength is close to the flame thickness (~1 mm), the flame stretch will affect the flame speed. In order to improve the Darrieus-Landau instability theory, Markstein [53] modified the effect of flame curvature on flame velocity. Later, Sivashinsky [54] revised the formula of perturbation rate by adding a thermal diffusion term, as shown in Eqs. (5)e(7).
s ¼ U0 U b k U1 Dth k2
(5)
1=ε1 Z ε 1 ε2 ε ln εð2k þ 1 þ εÞ εð1 þ kÞðε þ kÞbð1 LeÞ lnð1 þ xÞdx U1 ¼ 2ð1 εÞ½ε þ ð1 þ εÞk x 2ð1 εÞ½ε þ ð1 þ εÞk
(6)
0
b¼
EðTb Tu Þ
(7)
RT 2b
where Dth is the thermal diffusivity of the mixture, Le is the Lewis number, and Tb and Tu are the temperatures of combustion products and unburned mixture respectively. Fig. 11 shows the density distribution on the two surfaces of the flame front. Here, the flame front is identified by the mass fraction of HCO according to Kedia and Ghoniem [55]. The flame thickness can also be reflected in this figure. Our calculation shows that the flame thickness lies within 0.5 mme0.9 mm under different aspect ratios, and the average thickness is ~0.7 mm. For the mesoscale channels with a ¼ 2, 3 and 4, their widths are about 11.4, 17.1 and 22.9 times the average flame thickness. Therefore, the influence of flame thickness cannot be ignored. Now, we apply Eq. (5) to calculate the perturbation rate. Since the Lewis number (Le) of CH4 is approximately unity, the second term on the right side of Eq. (6) can be ignored. It can be seen from Fig. 11 that for a ¼ 2 and 3, the flame front is convex and the high density ratio is located in the near-wall region. However, for a ¼ 4, the W-shaped flame has four high-density-ratio areas, including two near the wall and the other two in the channel center (actually on the sides of the flame tip). The perturbation rates at the four high-density-ratio points, marked as 1, 2, 3 and 4 in Fig. 11, are calculated to be 61.67 s1, 44.97 s1, 48.61 s1 and 104.77 s1, respectively. Based on these values, we can explain the effect of hydrodynamic instability as follows. For a ¼ 2 and 3, the channel width is the half wave length (i.e., l ¼ 2 W). Thereby, as the aspect ratio is increased from a ¼ 2 to 3, the wavelength increases which leads to a decrease in the wave number (k) and the hydrodynamic instability will be weakened. However, due to the appearance of W-shaped flame in the channel with a ¼ 4, the wave number becomes larger which results in a bigger perturbation rate. Consequently, the hydrodynamic instability will be intensified in the mesoscale channel with a ¼ 4.
Fig. 11. Density distribution on the two surfaces of the flame front in the mesoscale channels with a ¼ 2, 3 and 4.
Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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4. Conclusions Flame stability of CH4-air mixture in four mesoscale rectangular channels with different aspect ratios (a ¼ 1, 2, 3 and 4) were numerically studied. The results show that at relatively high inlet velocity, the flame is convex (with respect to the upstream) in the mesoscale channels with a 3, but shifts to a W-shaped one in the channel with a ¼ 4. Moreover, the flame blowout limit increases as a is increased from 1 to 3; however, it drops when a is further increased to 4. Namely, the blowout limit exhibits a non-monotonic variation versus the aspect ratio, and it has a maximum value of 0.66 m/s at a ¼ 3. The analysis demonstrates that as a is increased from 1 to 3, both of the heat loss ratio and the perturbation rate of the hydrodynamic instability will be reduced, which leads to an increasing blowout limit. However, for the channel with a ¼ 4, the perturbation rate of the hydrodynamic instability is greatly enlarged at the flame tip due to the increased wave number, which is a result of the W-shaped flame shape. In summary, the intensified hydrodynamic instability reduces the flame blowout limit of the mesoscale channel with a ¼ 4. Acknowledgements This work was supported by the National Natural Science Foundation of China under the Grant Number: 51576084. References [1] A.C. Fernandez-Pello, Micropower generation using combustion: issues and approaches, Proc. Combust. Inst. 29 (2002) 883e899. [2] K. Maruta, Micro and mesoscale combustion, Proc. Combust. Inst. 33 (2011) 125e150. [3] W.M. Yang, S.K. Chou, C. Shu, H. Xue, Z.W. Li, D.T. Li, J.F. Pan, Microscale combustion research for application to micro thermophotovoltaic systems, Energy Convers. Manag. 44 (2003) 2625e2634. [4] J.F. Pan, J. Huang, D.T. Li, W.M. Yang, W.X. Tang, H. 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The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors Zili Yuan, Aiwu Fan* 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 16 April 2019 Received in revised form 1 May 2019 Accepted 7 May 2019 Available online xxx
The effects of aspect ratio (a ¼ 1, 2, 3 and 4) of mesoscale rectangular channels on CH4-air flame stability were numerically studied. The results show that at relatively high inlet velocity, the flame is convex (with respect to the upstream) when a 3; instead it shifts to a W-shaped appearance at a ¼ 4. In addition, the flame blowout limit exhibits a non-monotonic variation and it peaks at a ¼ 3. Our analysis reveals that when a is raised from 1 to 3, both of the heat loss ratio and hydrodynamic perturbation rate are reduced, which favors a larger blowout limit. However, for the channel with a ¼ 4, the perturbation rate of hydrodynamic instability is significantly increased at the flame tip because of the increased wave number, which results from the W-shaped flame front. Consequently, the intensified hydrodynamic instability will lead to a reduction in the flame blowout limit of the channel with a ¼ 4. © 2019 Energy Institute. Published by Elsevier Ltd. All rights reserved.
Keywords: Rectangular micro-combustor Aspect ratio Blowout limit Heat loss Hydrodynamic instability
1. Introduction Various micro-electromechanical systems such as micro-sensors, micro-engines, and micro-power generators, are emerging continuously. Compared to electrochemical batteries, hydrogen and hydrocarbon fuels have much higher energy densities and sufficient sources. Therefore, combustion-based miniature power generators have attracted extensive attention [1e3]. Micro- and meso-scale combustors has a large surface-to-volume ratio, which make them suitable to serve as heat sources for micro-thermophotovoltaic (TPV) [4] and micro thermoelectric [5] systems. Owing to the increased surface-to-volume ratio of micro- and meso-scale combustors, the interactions between flame and wall play a significant role in flame stability. Daou et al. [6] revealed that heat loss is the major factor leading to near-wall flame quenching in micro channels. Norton and Vlachos [7] numerically demonstrated that the heat-recirculation effect through channel walls is closely associated with wall thickness and material, and has an essential influence on the flame stability in micro-channels. Zhang et al. [8] numerically investigated the effects of inlet parameters on combustion characteristics in micro-channels. Maruta et al. [9] observed flames with repetitive extinction and ignition (FREI) in a micro quartz tube with controlled temperature gradient. Details of the FREI dynamics were widely scrutinized through numerical simulation by many researchers [10e14]. Stazio et al. [15] investigated the impact of external heating method on FREI, while Kishore et al. [16] and Kang et al. [17] studied the temperature gradient effect. Very recently, Xiang et al. [18] experimentally observed the FREI dynamics of non-premixed H2-air flames in a Y-shaped micro-combustor. The flame stability also exhibits a three dimensional effect in micro- and meso-scale channels. Pizza et al. [19] discovered various flame dynamics of CH4/air mixture in circular tubes based on three dimensional simulation. Pashchenko [20] found that only when the length of a micro tube is large enough compared to the diameter, can 2-D model obtain accurate results similar to those of 3-D model. Tsai [21] showed that the symmetry of CH4-air flame depends on the channel width. Benedetto et al. [22] obtained the combustible velocity ranges of C3H8/air mixture in square and circular micro channels. Anwar et al. [23] experimentally observed three flame shapes, (i.e., concave, planar, and convex flames) in mesoscale rectangular channels with different aspect ratios. However, they didn't explain the underlying physics responsible for the variation of flame shape.
* Corresponding author. 1037 Luoyu Road, Wuhan 430074, China. E-mail address: [email protected] (A. Fan). https://doi.org/10.1016/j.joei.2019.05.003 1743-9671/© 2019 Energy Institute. Published by Elsevier Ltd. All rights reserved.
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Nomenclature H W L Vin Ub cp ho k T W,o T∞ Le Tb
Channel height Channel width Channel length Inlet velocity (m/s) Adiabatic flame propagation velocity (m/s) Specific heat (J/(kg$K)) Convection heat transfer coefficient (Wm2K1) Wave number (m1) Outer wall temperature (K) Ambient temperature (K) Lewis number Temperature of combustion products
Tu
Temperature of unburned mixture
Greek symbols Aspect ratio εs Surface emissivity ru Density of unburned mixture r Density (kg/m3) l Wave length (m) ε Density ratio of combustion products to unburned mixture rb Density of combustion products Thermal diffusivity (m2/s) Dth lth Thermal conductivity (W/(m$K)) s Instability disturbance rate (s1) s0 Stephan-Boltzmann constant
a
To crack the problems of flame instability under micro- and meso-scale channels, numerous approaches have been proposed. For example, thermal management methods like Swiss-roll structure were designed for premixed [24,25] and non-premixed [26] combustion. Micro-combustors with double-layered wall was developed [27], which can enhance heat recirculation and reduce heat loss simultaneously. Various flame holders, such as backward facing step [28,29], bluff body [30,31], cavity [32,33] have been demonstrated to be effective ways to anchor the flame root in the recirculation zone. Catalyst can assisted combustion [34,35] and suppress flame instability [36,37] in microchannels. A combination of these methods can achieve even better performance on flame stabilization, such as small reactor with catalyst segmentation and cavities [38], micro combustor with catalytic wall and heat recirculation channels [39], and mesoscale Swiss-roll combustor with a bluff-body [40]. Slight oxygen enrichment can also effectively improve flame stability and combustion efficiency [41]. For non-premixed combustion, Li et al. [42] found that the micro-channel with a moderate gap can obtain a highest blowout limit. Ning et al. [43] showed that the diffusion flame stability can be intensified by addition of porous media in Y-shaped meso-scale channels. It can be known from the above literature review that flame-wall coupling through heat exchange [6e18] or geometrical effect (3D effect) [19e23] has been extensively investigated. Corresponding flame stabilization methods have also been developed [24e43]. Comparatively, intrinsic flame instabilities (i.e., Darrieus-Landau and thermal-diffusive instabilities) have been seldom studied. Alipoor [44] numerically examined the significance of Darrieus-Landau (hydrodynamic) and thermal-diffusive instabilities on the appearance of asymmetric hydrogen flames in a heated micro-channel. They reported that for the flames in micro-channels, the thermal-diffusive instability plays a major role in evolution of a symmetric flame into an asymmetric one, whereas the role of hydrodynamic instability is minor. We think that this is because the fuel is hydrogen, which has a very low Lewis number. In the case of methane fuel (whose Lewis number is near unity and thus the thermal-diffusive instability is negligible), the hydrodynamic instability might have an important effect on flame stability. The rectangular channels with a large aspect ratio are frequently used for micro-thermophotovoltaics (TPV) and thermoelectric (TE) modules. Motivated by these facts, in the present work we numerically investigate the flame stability of stoichiometric CH4/air mixtures in a mesoscale channel by varying its aspect ratio while maintaining a fixed height, which can provide a guidance for the optimal design of rectangular micro-combustors using a fuel with a relatively large Lewis number like methane. 2. Numerical method The cross section of the mesoscale rectangular channel is shown in Fig. 1, where the central point of the channel entrance, “O”, is set as the origin of coordinates. X, Y and Z indicate the coordinate axis in the width, height and length directions, respectively. The channel height (H), length (L) and wall thickness are fixed at 4 mm, 40 mm and 1 mm, respectively. The aspect ratio (a ¼ W/H) takes four values of 1, 2, 3 and 4 in this work. A stoichiometric CH4/air mixture is fed into the rectangular mesoscale channels. Quartz glass is selected for the wall material. Its density, specific heat, thermal conductivity and surface emissivity are r ¼ 2650 kg/m3, cp ¼ 750 J/(kg$K), lth¼1.05 W/(m$K) and εs ¼ 0.92, respectively. As the maximal Reynolds number of the incoming cold mixture is ~400, a laminar flow, three-dimensional model was adopted. The second-order upwind scheme was used to discretize the model. The C1 mechanism [45], which evolves 18 chemical species and 58 elementary reactions, was applied to simulate the CH4/air combustion. The ideal gas assumption was used to calculate the density of the gas mixture. The specific heat, viscosity and thermal conductivity were calculated from a mass fraction weighted average of the species' properties. Thermodynamic and transport properties in CHEMKIN format [46] are imported into the CFD software. Boundary conditions are specified as follows. Uniform concentration and velocity distributions of CH4/air mixture were set at the inlet with a temperature of 300 K. A pressure boundary condition with 1 atm is given for the channel exit. At the outer surfaces of the channel, the heat loss rate is calculated through Eq. (1):
q ¼ ho TW;o T∞ þ εs s0 T 4W;o T 4∞
(1)
where ho is the convection heat transfer coefficient (20 Wm2K1) [47], T W,o is the outer wall temperature, T∞ is the ambient temperature (300 K), εs is the surface emissivity and s0 is the Stephan-Boltzmann constant (5.67 108 Wm2K4). The CFD software FLUENT 15.0 [48] was applied to solve the set of governing equations. The ‘‘SIMPLEC’’ algorithm was employed to couple the pressure and velocity. For a physically stable flame, a temperature patch (2000 K) of fluid zone was adapted to initialize the Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 1. Geometry of the rectangular mesoscale channel.
combustion reaction in the computation. Grid independency was checked by using three sets of grid system, i.e., Dx ¼ Dy ¼ Dz ¼ 0.1 mm (1440000 grids), Dx ¼ Dy ¼ 0.2 mm, Dz ¼ 0.1 mm (360000 grids) and Dx ¼ Dy ¼ Dz ¼ 0.2 mm (180000 grids). The centerline temperature profiles in the 4 4 mm2 channel under Vin ¼ 0.25 m/s are presented in Fig. 2, which demonstrates that the difference between the obtained results by using the grid systems of 360000 and 1440000 is small. Therefore, the grid system with 360000 grids was used for the final simulation. In order to evaluate the prediction accuracy of the present numerical model, a numerical simulation of an experimental case by Tang et al. [49] was carried out. The height, width and length of the channel are 3 mm, 8 mm and 18 mm, respectively. The flow rate of CH4/air mixture is 41 ml/min (Vin ¼ 0.3 m/s). The Reynolds number of the incoming mixture is ~80, which falls in the laminar regime. The predicted and measured temperature profiles along the centerline of outer wall are shown in Fig. 3. The maximum relative error comes out to be 9.89%, which confirms the reasonable accuracy of the numerical results in this paper. 3. Results and discussion 3.1. Effect of the aspect ratio on flame stability The temperature contours in the X-Z plane of the mesoscale channels with different aspect ratios are presented in Fig. 4. In each subfigure, the variation tendency of the temperature field with increasing inlet velocity is provided. It can be seen from Fig. 4 that, when the inlet velocity is relatively low (e.g., Vin ¼ 0.25 m/s), the flames are stabilized near the entrances of the four channels. For the square channel (a ¼ 1), before the occurrence of blowout, the flame still remains a stable symmetric shape. However, as the inlet velocity is slightly larger than 0.26 m/s, the flame will be blown out suddenly. For mesoscale channels with a ¼ 2 and 3, when the inlet velocity is raised up to Vin ¼ 0.3 m/s, the flame fronts are stable and slightly pushed downstream, exhibiting a convex curve with respect to upstream. In contrast, the flame front is transformed into a stable W-shaped flame at Vin ¼ 0.3 m/s in the wider channel (i.e., a ¼ 4), although it is asymmetric with respect to the centerline. As the inlet velocity is further increased to Vin ¼ 0.4 m/s, the flame fronts become inclined in the channels with a ¼ 2 and 3, but the flame is pushed farther downstream in the case of a ¼ 2. In the channel with a ¼ 4, the flame front cannot remain stable any longer as the inlet velocity is increased to Vin ¼ 0.32 m/s. It shows a continuous deformation with time, which is actually in a pulsating mode, as depicted in Fig. 5.
Fig. 2. Centerline temperature profiles in the 4 4 mm2 channel under Vin ¼ 0.25 m/s for different grid systems.
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Fig. 3. Validation of the numerical model with the experimental data by Tang et al. [49].
Fig. 4. Evolution of temperature field in the X-Z plane with an increasing inlet velocity for the mesoscale channels with different aspect ratios.
From the variation trend of flame shape it can be expected that the flame will be finally blown out of the channels at a certain higher velocity, which is called the blowout limit herein. To compare the flame stabilization ability of the four channels with various aspect ratios, their blowout limits are plotted in Fig. 6. It is interesting to note that the blowout limit first increases as the aspect ratio is increased from 1 to 3, and then decreases with a further increase in the aspect ratio. The specific values of the blowout limits are 0.26 m/s, 0.44 m/s, 0.66 m/s and 0.33 m/s for a ¼ 1, 2, 3 and 4, respectively. Evidently, the flame blowout limit shows a non-monotonic variation with the aspect ratio, and it peaks at a ¼ 3. In the following section, the underlying mechanisms for this trend will be analyzed. 3.2. Discussion about heat loss ratio and velocity field under Vin ¼ 0.25 m/s Because the blowout limit of the channel with a ¼ 1 is only 0.26 m/s, here we chose the case of Vin ¼ 0.25 m/s to discuss about the heat loss ratio and velocity field, which can shed some light on the reasons responsible for flame stability in the channels with different aspect ratios. 3.2.1. Comparison between the heat loss ratios Here, we quantitatively compare the heat loss ratio (defined as the ratio of heat loss amount to the input enthalpy) under Vin ¼ 0.25 m/s. Table 1 tabulates the corresponding hydraulic diameter, surface to volume ratio and heat loss ratio of the four channels. It can be seen from Table 1 that with the increase of the aspect ratio, the hydraulic diameter becomes larger while the surface to volume ratio grows smaller, which leads to a reduction in the heat loss ratio. Obviously, this is beneficial to stabilize the flame in the straight mesoscale channel without a flame holder. Our calculation shows that as the aspect ratio is increased from a ¼ 1 to 2, the reduction in the heat loss ratio is 6.18%, while the reduction extent decreases to 2.54% if the aspect ratio is raised from a ¼ 2 to 3. If the aspect ratio is further increased from a ¼ 3 to 4, the reduction in the heat loss ratio is only 1.3%. These facts demonstrate that the reduction in heat loss contributes more significantly to improve flame stability when the aspect ratio is relatively small. Instead, other reasons such as flow characteristics and hydrodynamic instability should be responsible for the deterioration of flame stability in mesoscale channels with a larger aspect ratio (e.g., a ¼ 4). Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 5. Temporal evolution of temperature field (a) and contours of HCO mass fraction (b) of a pulsating flame in the X-Z plane of the mesoscale channel with a ¼ 4 at Vin ¼ 0.32 m/s.
Fig. 6. Blowout limits of the mesoscale channels with different aspect ratios.
3.2.2. Comparison between the velocity fields Although all the flames are planar in the four channels under Vin ¼ 0.25 m/s, the velocity fields differs greatly. Fig. 7 illustrates the contours of velocity field and temperature field in the X-Z plane of the mesoscale channels with a ¼ 2, 3 and 4 at Vin ¼ 0.25 m/s. It is interesting that with the increase of aspect ratio, the central high speed region shrinks (Fig. 7b) and finally splits into two located near the side walls (Fig. 7c). There are two reasons for the variation of velocity field. On the one hand, the channel width expands as the aspect ratio is increased, which leads to the reduction in the relative thickness of the velocity boundary layer. This trend can be clearly seen in Fig. 8, which shows the dimensionless velocity distribution under cold state in the width (X) direction. On the other hand, Fig. 7 also indicates that the temperature gradient close to the side walls is higher than that in the central region, and the low temperature gradient zone becomes wider with the increase of aspect ratio (or channel width). Owing to the distinct velocity field in the mesoscale channel with a ¼ 4, the W-shaped flame will appear at a sufficient high inlet velocity.
Table 1 Hydraulic diameter, surface to volume ratio, heat loss ratio of the mesoscale channels with different aspect ratios under Vin ¼ 0.25 m/s.
hydraulic diameter Surface to volume ratio heat loss ratio
4 4 mm2
4 8 mm2
4 12 mm2
4 16 mm2
4 mm 1000 m1 0.922
5.33 mm 750 m1 0.865
6 mm 666.67 m-1 0.843
6.4 mm 625 m1 0.832
Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 7. Contours of velocity field (filled) and temperature field (lines) in the X-Z plane of the mesoscale channels with a ¼ 2, 3 and 4 at Vin ¼ 0.25 m/s.
Fig. 8. Dimensionless velocity distribution under cold state in the width (X) direction at Z ¼ 2 mm of the mesoscale channels with a ¼ 2, 3 and 4.
3.3. Discussion about hydrodynamic instability As has been demonstrated above, in the mesoscale channel with a ¼ 4, the flame exhibits a W-shaped appearance from Vin ¼ 0.3 m/s and starts to lose its stability from Vin ¼ 0.32 m/s. Here, the hydrodynamic instability must play a more significant role than the thermal-diffusive instability in the evolution of a stable W-shaped flame into an unstable asymmetric one because the Lewis number is close to unity. It is well known that the hydrodynamic instability [50] was first proposed by Darrieus [51] and Landau [52], and thus it is also called Darrieus-Landau instability. Fig. 9 illustrates the principle of hydrodynamic instability. Darrieus and Landau pointed out that the flow direction of the unburned mixture changes after passing through the curved flame front due to a significant volume expansion resulting from a sudden density decrease of the high temperature burnt gas. Therefore, the flame segments protruding toward the unburned gas have a tendency to move upstream, while those protruding toward the combustion product have a tendency to move downstream. 3.3.1. Analysis of flow deflection Fig. 10 shows the streamlines in the X-Z plane of the channel with a ¼ 2, 3 and 4. To illustrate the flow deflection before and after the flame front, the contours of the velocity deflection angle (defined as the angle between the velocity components in X direction and Z direction) are also drawn in Fig. 10. If q is positive (red-yellow), the streamlines points towards the upper right. In contrast, if q is negative (blue-violet), the streamlines face to the lower right. The color transition in the contours indicates the change in flow direction. It can be seen from Fig. 10 that in the near-wall region of the channels with a ¼ 2 and 3 (the flame front is convex), the gas mixture moves toward the wall before the flame front, and then towards the channel center after the flame front. In addition, velocity deflection angle is almost zero in central region of the channel with a ¼ 2 and 3, which indicates that in this region the gaseous mixture keeps moving in the Z-direction after Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Fig. 9. Schematic diagram of the hydrodynamic instability [50].
passing through the flame front. However, when the aspect ratio is a ¼ 4, the gas mixture has a velocity component in the X-direction in both of the near-wall region and central region. Therefore, when the gas mixture passes through the W-shaped flame front, flow deflection occurs in both of the near-wall and central regions. Large strain rate will result from the obvious flow deflection. For a ¼ 2 and 3, the strain rate near the wall surface has the maximum value, whereas there exists three peak values for a ¼ 4. Specifically, the maximum strain rates for a ¼ 2 and 3 are both ~6400 s1, and the counterpart for a ¼ 4 is ~6900 s1. As a result, the more intense stretch effect can weaken the stability of the W-shaped flame in the channel with a ¼ 4. 3.3.2. Analysis of the hydrodynamic instability According to Darrieus and Landau [50e52], the instability disturbance rate can be expressed as:
s ¼ U0 U b k
(2)
Fig. 10. Streamlines and contours of the velocity deflection angle in the X-Z plane of the mesoscale channels with a ¼ 2, 3 and 4.
Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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Z. Yuan, A. Fan / Journal of the Energy Institute xxx (xxxx) xxx
where Ub is the adiabatic flame propagation velocity, k is the wave number (k ¼ 2p/l, l is the wave length), and U0 can be calculated through Eq. (3).
U0 ¼
. pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ε þ ε2 ε3 ε ð1 þ εÞ
(3)
where
ε ¼ rb =ru
(4)
Here, rb and ru are the densities of combustion products and unburned mixture, respectively. According to the Darrieus-Landau theory, the hydrodynamic instability becomes stronger when the wavelength is reduced, which is inconsistent with the experimental results in follow-up studies. This is because they assumed the flame to be infinitely thin and the flame thickness is ignored in Eq. (2). However, when the wavelength is close to the flame thickness (~1 mm), the flame stretch will affect the flame speed. In order to improve the Darrieus-Landau instability theory, Markstein [53] modified the effect of flame curvature on flame velocity. Later, Sivashinsky [54] revised the formula of perturbation rate by adding a thermal diffusion term, as shown in Eqs. (5)e(7).
s ¼ U0 U b k U1 Dth k2
(5)
1=ε1 Z ε 1 ε2 ε ln εð2k þ 1 þ εÞ εð1 þ kÞðε þ kÞbð1 LeÞ lnð1 þ xÞdx U1 ¼ 2ð1 εÞ½ε þ ð1 þ εÞk x 2ð1 εÞ½ε þ ð1 þ εÞk
(6)
0
b¼
EðTb Tu Þ
(7)
RT 2b
where Dth is the thermal diffusivity of the mixture, Le is the Lewis number, and Tb and Tu are the temperatures of combustion products and unburned mixture respectively. Fig. 11 shows the density distribution on the two surfaces of the flame front. Here, the flame front is identified by the mass fraction of HCO according to Kedia and Ghoniem [55]. The flame thickness can also be reflected in this figure. Our calculation shows that the flame thickness lies within 0.5 mme0.9 mm under different aspect ratios, and the average thickness is ~0.7 mm. For the mesoscale channels with a ¼ 2, 3 and 4, their widths are about 11.4, 17.1 and 22.9 times the average flame thickness. Therefore, the influence of flame thickness cannot be ignored. Now, we apply Eq. (5) to calculate the perturbation rate. Since the Lewis number (Le) of CH4 is approximately unity, the second term on the right side of Eq. (6) can be ignored. It can be seen from Fig. 11 that for a ¼ 2 and 3, the flame front is convex and the high density ratio is located in the near-wall region. However, for a ¼ 4, the W-shaped flame has four high-density-ratio areas, including two near the wall and the other two in the channel center (actually on the sides of the flame tip). The perturbation rates at the four high-density-ratio points, marked as 1, 2, 3 and 4 in Fig. 11, are calculated to be 61.67 s1, 44.97 s1, 48.61 s1 and 104.77 s1, respectively. Based on these values, we can explain the effect of hydrodynamic instability as follows. For a ¼ 2 and 3, the channel width is the half wave length (i.e., l ¼ 2 W). Thereby, as the aspect ratio is increased from a ¼ 2 to 3, the wavelength increases which leads to a decrease in the wave number (k) and the hydrodynamic instability will be weakened. However, due to the appearance of W-shaped flame in the channel with a ¼ 4, the wave number becomes larger which results in a bigger perturbation rate. Consequently, the hydrodynamic instability will be intensified in the mesoscale channel with a ¼ 4.
Fig. 11. Density distribution on the two surfaces of the flame front in the mesoscale channels with a ¼ 2, 3 and 4.
Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003
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4. Conclusions Flame stability of CH4-air mixture in four mesoscale rectangular channels with different aspect ratios (a ¼ 1, 2, 3 and 4) were numerically studied. The results show that at relatively high inlet velocity, the flame is convex (with respect to the upstream) in the mesoscale channels with a 3, but shifts to a W-shaped one in the channel with a ¼ 4. Moreover, the flame blowout limit increases as a is increased from 1 to 3; however, it drops when a is further increased to 4. Namely, the blowout limit exhibits a non-monotonic variation versus the aspect ratio, and it has a maximum value of 0.66 m/s at a ¼ 3. The analysis demonstrates that as a is increased from 1 to 3, both of the heat loss ratio and the perturbation rate of the hydrodynamic instability will be reduced, which leads to an increasing blowout limit. 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Please cite this article as: Z. Yuan, A. Fan, The effects of aspect ratio on CH4/air flame stability in rectangular mesoscale combustors, Journal of the Energy Institute, https://doi.org/10.1016/j.joei.2019.05.003