Investigations on flame dynamics of premixed H₂–air mixtures in microscale tubes

Abstract

Detailed numerical studies through unsteady simulations with detailed hydrogen chemistry have been reported for premixed H₂–air flames in straight microtubes to understand the role of flame-wall coupling and its effect on flame dynamics for a range of wall heat transfer conditions. Depending on the wall heat transfer conditions, and tube diameters, varying flame shapes were observed. These flame modes are represented with flame shape angles and corresponding flame shape is correlated to wall heat transfer conditions. It has been observed that an increase in wall heat transfer coefficient, h, though it increases the heat loss from a propagating flame, does not necessarily lead to a monotonic decrease in flame propagation speed. A transition regime, where the propagating flame changes its shape, has been identified. The variation of mass flux in the vicinity of the propagating flame has been used to gain a better understanding of flow-redirection and its impact on flame shape and flame propagation speed for premixed H₂–air mixtures.

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1. Introduction

Increasing demand for high intensity power sources for various miniaturized devices is receiving increased attention and interest from the combustion community. Conventional electrochemical batteries are relatively heavy due to their lower energy densities and have long recharging times.¹ Combustion based micro devices are considered to be competitive alternatives due to their improved conversion efficiency, and light weight. Compared to electrochemical batteries, combustion based devices offer higher energy densities, as well as higher heat transfer and mass transfer coefficients along with smaller recharging times.^2,3 Lower operating temperatures in micro-combustors ensure reduced pollutant emissions. However, miniaturization of these combustion devices leads to various thermal and radical quenching issues.⁴ This is mainly because of the significant role played by the wall heat transfer, flame-wall coupling and reduced residence time available for the combustion reaction. A stable combustion can be achieved through suitable thermal management and a fine balance between flow and chemical time scales.^5–9

Maruta et al.⁵ reported studies on flame stability in externally heated straight micro tubes. They observed that flame instabilities occur for moderately low velocities resulting in a FREI (flames with repetitive extinction and ignition) propagation mode. Subsequently, Fan et al.^10,11 reported the formation of various rotating and oscillating flame patterns in radial micro channels for a range of operating conditions with premixed methane–air mixtures. Khandelwal et al.⁷ and Akram and Kumar⁸ reported detailed studies on flame propagation in externally preheated diverging channels. Various stable, unstable and partially stable flame propagation modes were observed for a range of mixture flow rates and mixture equivalence ratios.

A number of studies aimed at understanding flame propagation in such micro channels with H₂–air mixtures are reported in literature.^12–26 Li et al.¹³ reported experimental studies to understand the effect of wall temperature and radiative heat flux for a series of cylindrical backward-facing step micro combustors. Cao and Xu¹⁴ suggested a stable operating regime and different methods to reduce the heat loss from micro-combustor for micro-gas turbine applications. Jianlong et al.²⁰ performed parametric studies to understand the flame blow-off limit and combustion efficiency of H₂–air mixtures in a micro channel with bluff body. Flame instabilities and effect of design parameters on extinction limits were investigated by Yuasa et al.²¹ for a possible application in MIT micro gas turbine with H₂–air and CH₄–air mixtures in a new micro combustor concept. Stabilization of lean premixed H₂–air flame in a radial micro-channel was experimentally and numerically investigated by Zamashchikov et al.²⁵ Wang et al.²⁴ carried out experimental investigations on catalyst assisted micro combustors for premixed H₂–air mixtures to understand the effect of catalyst on flame stability. Catalyst helped improving the flame stability in the micro combustors significantly.²⁶

Although various researchers have reported interesting insights on flame stability limits, flame propagation modes, effect of equivalence ratio and inlet velocities through various experimental studies, many difficulties arise while investigating flame propagation at such small scales due to smaller dimensions of these channels. Numerical studies allow better understanding through detailed analysis of flame propagation characteristics. Chen et al.¹⁶ carried out numerical investigations on combustion characteristics of hydrogen fuel in the micro combustor with multi catalyst. They also extended their studies to various flow conditions, reactor dimensions and wall materials. Effect of diameter on temperature, velocity and species profiles of micro combustors were analyzed numerically and analytically by Li et al.¹⁷ They observed that volumetric heat loss and wall shear stresses increase with a decrease in physical dimensions. Hua et al.^18,19 performed three-dimensional numerical studies to understand the effect of dynamic flow behavior on a micro gas turbine engine. They suggested an optimized design for the micro combustor through a systematic parametric analysis. Two-dimensional direct numerical simulations of Pizza et al.^22,23 with detailed chemistry for lean H₂–air mixtures in planar mesoscale channels showed the existence of various unstable flame propagation modes. This work primarily focused on understanding the flame stabilization dynamics of lean H₂–air mixtures in mesoscale channels with varying inflow velocities (0.3 < U_in < 1100 cm s⁻¹). They considered channel heights of 2, 4 and 7 mm for their study. In order to provide the physical attributes to the mesoscale combustor, a temperature profile was assigned as a wall boundary condition. Numerical studies of Baigmohammadi et al.²⁷ in a stepped micro tube combustor with inserted wire method report improvement in flame stabilization limits, temperature distribution, and combustion process by activating certain chemical reactions affecting combustion initiation reaction. Jiang et al.²⁸ conducted detailed H₂–air premixed flame simulations to analyze effects of flow velocity, mixture ratio and heat recirculation. Although these studies provide interesting insights on various issues related to flame propagation in such micro channels, they cannot be extrapolated to accurately model realistic wall thermal boundary conditions of the micro channels.

Present work is aimed at understanding flame propagation characteristics, effect of flow redirection on flame shapes and flame–flow interactions in micro-channels (1.0, 1.4 and 2.0 mm) for different wall thermal boundary conditions (0–1000 W m⁻² K⁻¹) with stoichiometric H₂–air mixtures. Straight micro-channel geometry is considered to investigate these aspects related to flame propagation with H₂–air mixtures in straight tubes.

The paper is organized as follows. Computational details such as details of computational domain, assumptions, chemical kinetics modelling details, solution methodology and boundary conditions are summarized in Section 2. Section 3 presents the results obtained in the present study. The major contributions of this work are summarized at the end.

2. Computational details

Two-dimensional transient simulations are carried out to study the flame dynamics of premixed stoichiometric H₂–air mixtures in straight micro tubes for different wall heat transfer conditions. The details of the computational domain are shown in Fig. 1. One half of the domain is modeled due to its axisymmetric nature.²⁹ The diameter and axial length of the micro tube are represented with D and L respectively. Uniform grid of square cells with Δx = Δy = 50 μm in both radial and axial directions are considered initially. This grid is further refined to Δx = Δy = 30 μm, 15 μm and 7.5 μm. Grid independence study is carried out by comparing the heat release rate (HRR) of base grid (Δx = Δy = 15 μm) and finest square grid of 7.5 μm as shown in Fig. 2a. The volumetric heat release (HRR) rate is calculated from production/destruction rate of individual species. The following formula has been adopted to determine the HRR in the present study.
where, h⁰_i, m_i and R_i are the enthalpy of formation, molecular weight and volumetric rate of formation/destruction of i^th species respectively.

Fig. 1 Schematics of the computational domain.

Fig. 2 (a) Heat release rate comparison at a flame location of 6d_q from exit plane for base grid (15 μm) and refined grid (7.5 μm) with adiabatic wall boundary condition. (b) Predicted laminar burning velocity (S_L) for different grids at a flame location of 8d_q from exit plane (c) comparison of flame structure of a laminar flame obtained from the present computations with the results of PREMIX code.

There is insignificant difference in heat release rate for both the grids considered in the present work, hence a grid of 15 μm size was considered for all numerical studies reported in this paper and a procedure similar to that of Nair et al.³⁰ and Singh et al.³¹ was considered to validate the present results. A tube diameter slightly larger than flame quenching distance (d_q) and smaller than twice the quenching distance (1d_q ≤ D ≤ 2d_q) is considered for detailed studies. Therefore, a micro tube with diameter D = 1.4 mm was chosen for the detailed investigations (0.74 mm as quenching distance obtained through detailed numerical analysis).³¹ To understand the effect of tube diameter on flame dynamics, various tubes of diameters, 1.0 mm, 1.4 mm and 2.0 mm are also studied. To validate the present model, laminar burning velocity and flame structure of H₂–air mixture is calculated by treating the upper wall as a symmetric boundary. This eliminates the wall effects and gives a flat flame in the micro-channel. Hence, the laminar burning velocity of the propagating flame can be obtained as the difference between the flame propagation speed and corresponding unburnt mixture velocity. A one-dimensional freely propagating flame model using PREMIX code is used to validate the present computational results. Laminar burning velocity is calculated for three different uniform grid sizes, 50 μm, 30 μm and 15 μm. It is found that, laminar burning velocity (∼210 cm s⁻¹) for 15 μm and 7.5 μm grid matches exactly with the PREMIX result as shown in Fig. 2b. Furthermore, the simulated flame structure for 15 μm grid depicting the variation of major species for stoichiometric hydrogen combustion provides a good agreement with the PREMIX code result as indicated in Fig. 2c.

Olm et al.³² have tested all the major hydrogen combustion mechanism that were published since 1999. Out of these mechanisms, NUIGNGM-2010, Konnov-2008 and Conaire-2004 have been shown to give an overall good performance. These mechanisms were found to predict the flame speed and ignition delay of hydrogen combustion exactly, when compared with the various experimental results. Therefore, the detailed mechanism proposed by Conaire-2004 (ref. 33) with 9 species and 21 reactions has been employed in the present study. Numerical simulations were carried out by integrating the governing equations in a physical domain using a finite-volume based general-purpose CFD code Fluent.³⁴ Transient simulations were carried out using pressure–velocity coupling algorithm, PISO.³⁵ Few initial steady state iterations with finite-volume method of SIMPLE algorithm³⁶ are carried out to prevent solution divergence at the beginning due to small domain and grid size. The flow is laminar with flow Reynolds number being equal to 218. Therefore, Arrhenius reaction based finite rate combustion model is adopted to perform H₂–air combustion studies.

The boundary conditions adopted for the present study are specified as described in Fig. 1. Stoichiometric H₂–air mixture with a flow velocity much smaller than the flame propagation velocity, 0.3 m s⁻¹ is applied at the domain inlet. A small inlet velocity of 0.3 m s⁻¹ does not affect the flame dynamics, as the flame propagation velocity is relatively much higher. This further ensures smooth convergence of numerical simulation with a small flow velocity through the channel inlet. Channel walls are considered of negligible thickness and chemically inert.^37,38 Various thermal boundary conditions are applied at the walls, through the variation of the convective heat transfer coefficients, h. The fuel–air mixture is initially ignited by providing a thin ignition patch of 2400 K near the exit plane of the channel. Many researchers^29,39,40 have reported that final solution depends on the initial flame shape.

2.1 Governing equations

Present work is carried out for stoichiometric H₂–air mixture with laminar flow in a 2-D axi-symmetric channel. Conservation equations for mass, momentum, energy and species are described below. The effects due to thermal radiation, buoyancy and surface reactions are neglected.^34,35,37,38 Low Mach number based assumption is used and ideal gas equation employed to obtain the fluid density. Based on the above assumptions, the governing equations are reduced to the following.where v⃑ = (u, v) is the velocity vector in x and y directions. p, ρ, h, μ, M_j, k and Y_j are fluid pressure, density, enthalpy, viscosity, molecular weight, thermal conductivity, and mass fraction of j^th species, respectively. is diffusion flux of j^th species due to temperature and species gradients, calculated using Stefan–Maxwell equations of multi-component diffusion. R_j represents volumetric reaction rate of j^th species, calculated from Arrhenius expressions of finite rate chemistry. Temperature dependence of thermodynamic properties is considered and hence individual species properties like viscosity, and thermal conductivity are calculated from kinetic theory relations. Specific heat is calculated using NASA piecewise polynomials and mass-fraction weighted average approach used for obtaining the mixture specific heats. Fluid thermal conductivity and viscosity are calculated from ideal gas mixing laws.

3. Results and discussion

3.1 Effect of wall heat transfer coefficient on flame shape

The normalized heat release rate contours (HRR) for a case of h = 600 W m⁻² K⁻¹ at different axial locations while flame is propagating upstream are shown in Fig. 3. Flame shape angle, θ is defined in the present work with respect to flame shape (HRR contours) as shown in the figure for various negatively and positively stretched flames. This parameter is expected to help in quantifying the extent of flame shape transition in a better way as compared to other parameters. The angle, θ made by a line passing through the flame position i.e. HRR contour tip nearly touching the wall to a perpendicular to the axis defines the flame shape angle as shown in Fig. 3. A positive or negative flame angle is decided from the flame shape being either concave or convex with respect to the incoming mixture.

Fig. 3 Normalized heat release rate contours of H₂/air flames depicting flame angle variation with (a) different d_q for h = 600 W m⁻² K⁻¹. (b) Different h values close to transition regime. (Flame at 6d_q from inlet). HRR contours normalized with 1.6 × 10¹⁰.

Fig. 3a. Shows the HRR contour at different flame positions along the axial location of the tube for h = 600 W m⁻² K⁻¹. It is observed from Fig. 3a, that the shape of the propagating flame remains similar for all the positions in the channel as it propagates upstream. Fig. 3b shows the transition of the flame shape from a concave shape to convex shaped flame and its sensitivity around h ∼ 600 W m⁻² K⁻¹. It can be observed that, for values 580 ≤ h ≥ 620 W m⁻² K⁻¹; ∂h/∂θ ≈ 0, which further implies that ∂θ/∂h → ∞ or θ is most sensitive in this regime. Therefore, the occurrence of transition in flame shape can be observed as the flame propagates upstream. The flame changes its shape from a positively stretched flame, θ > 0 to a negatively stretched flame, θ < 0 when the wall heat transfer coefficient is in 580 ≤ h ≥ 620 W m⁻² K⁻¹ range.

Fig. 4a, shows the variation of flame shape angle (θ) with wall heat transfer coefficient, h as the flame propagates upstream in the axial direction for premixed H₂–air mixtures. It can be observed from Fig. 4 that an increase in heat transfer coefficient, h results in a flame shape angle variation from θ > 0 to θ < 0, indicating a strong effect of wall heat transfer coefficient on flame shape. The flame shape changes significantly for 580 < h < 620 W m⁻² K⁻¹ wall heat transfer conditions. Fig. 4b shows the HRR contours of the propagating flame for h = 300, 600 and 700 W m⁻² K⁻¹ conditions. The flame shape angle, θ changes from 43.95° to 41.26° as h value is changed from 300 to 700 W m⁻² K⁻¹ with θ = 3.46° at h = 600 W m⁻² K⁻¹.

Fig. 4 (a) Effect of heat transfer coefficient, h on flame shape (θ) at different flame positions in the tube for H₂–air flames. d_q – quenching distance of H₂–air mixture (b) normalized heat release rate contours of H₂–air flames depicting θ variation with different h (flame at 6d_q from inlet). HRR contours normalized to 1.6 × 10¹⁰.

3.2 Variation of flame shape and propagation speed with heat transfer conditions

Fig. 5 shows the variation of flame propagation speed with wall heat transfer conditions and flame shape angle. It is to be noted that for 580 ≤ h ≤ 620 W m⁻² K⁻¹ conditions, the flame propagates with a minimum propagation velocity of S_L ∼ 200 cm s⁻¹. As the flame propagates upstream, there is a minimal change in the flame shape and flame propagation velocity. This can be confirmed from the curves corresponding to various axial position of x = 3d_q, 6d_q and 9d_q. The flame propagation velocity increases again for higher h values due to a change in the flame shape to a negatively stretched flame. For adiabatic wall boundary conditions (h = 0), the flame speed as well as θ was found to be maximum as the flame propagates upstream as shown in Fig. 5b. The flame propagation speed, S_L is observed to be minimum (∼200 cm s⁻¹) for h = 600 W m⁻² K⁻¹. For h > 600 W m⁻² K⁻¹, the flame propagation speed increases to a constant value of ∼280 cm s⁻¹ irrespective of the value of wall heat transfer coefficient as seen from Fig. 5b.

Fig. 5 Variation of flame propagation speed with (a) flame shape angle (b) wall heat transfer coefficient for d = 1.4 mm. Here d_q = 0.74 mm, quenching diameter.

3.3 Relationship between flame shape and mass flux redistribution

A detailed analysis of flow redirection for flames in microtubes was presented by Kim and Maruta³⁹ which demonstrated that flow redirection is a better parameter to understand flame propagation and its shape. Therefore, flow redirection through the analysis of mass-flux has been presented here to understand flame shape variation at different wall thermal boundary conditions.

Fig. 6a shows the variation of axial mass flux, ṁ_x (ρu), where ρ is density and u is axial velocity component at the axis. It is non-dimensionalized with mixture properties, ρ_inS^o_L (ρ_in – density of incoming mixture and S^o_L = laminar burning velocity, 2.04 m s⁻¹). Fig. 6a clearly shows that the peak value of ṁ_x occurs near the flame front and it decreases significantly with an increase in wall heat transfer coefficient, h. The change in mass-flux can also be related to a change in flame shape angle, θ due to change in wall heat transfer condition as discussed in Fig. 4a. This is due to the fact that for lower h values, higher mass flux, ṁ_x at the axis pushes the flame downwards, creating a concave shaped flame (θ > 0). For higher values of h, beyond a certain critical value, the axial mass-flux, ṁ_x values at axis decrease, resulting in a change in flame shape. This clearly explains the significant change in the mass flux distribution at the axis and transition in flame shape from θ > 0 to θ < 0 with an increase in the values of h.

Fig. 6 Non-dimensional mass-flux at various h values for H₂–air flames (a) axial variation of ṁ_x, x = 0 represents flame location (b) variation of ṁ_t in radial direction, radial variation plotted for x = 0. ‘−’ indicates upstream and ‘+’ indicates downstream of flame.

Fig. 6b presents the variation of total mass-flux (ṁ_t) variation in radial direction, defined as ṁ_t = ṁ_x + ṁ_y, where ṁ_y = ρv (product of density and radial velocity component). It can be seen from Fig. 6b that the distribution of ṁ_t becomes nearly uniform for h > 620 W m⁻² K⁻¹ values. A relatively lower value of ṁ_t is observed near the axis and the distribution of mass-flux increases towards the walls (for y/y_max > 0.9) for higher h values which can help explain the transition in flame shape from concave shape (θ > 0) to convex shape (θ < 0) as can be seen from the curve corresponding to h = 0 and 1000 W m⁻² K⁻¹.

3.4 Effect of tube diameter on flame shapes

This section describes the effect of tube diameter on the formation of a particular flame shape for micro tubes of various diameters of 1.0, 1.4 and 2 mm. Fig. 7 shows the variation of flame shape angle with wall heat transfer coefficient, h. It is interesting to note that for 1.0 mm diameter tube, a linear variation of flame shape angle has been observed as compared to a significantly different and non-linear behaviour for 1.4 mm and 2.0 mm tube diameter cases. Flame shape angle varies linearly from a positive value (θ > 0) to a negative value (θ < 0) with an increase in the heat transfer coefficient, h for 1.0 mm diameter case. However, for 1.4 and 2.0 mm cases, a specific regime of transition in flame shape can be observed. This transition occurs for large diameter tubes at 580 < h < 620 W m⁻² K⁻¹ wall heat transfer conditions. Therefore, as the tube diameter increases, the flame becomes planar for a specific range of wall heat transfer values. In other words, change in flame shape is quite gradual for smaller diameters with wall heat transfer coefficient as clear from Fig. 7. Fig. 8 shows the normalized HRR contours of H₂–air flames for different tube diameters. A relatively planar flame is observed at h = 500, 600 and 700 W m⁻² K⁻¹ for 1.0 mm tube diameter, and h = 580 and 600 W m⁻² K⁻¹ for 1.4 mm tube diameter. Similarly, it was observed that for 2.0 mm case, a planar flame was observed to form for h = 655 W m⁻² K⁻¹ wall heat transfer condition.

Fig. 7 Variation of flame shape angle with wall heat transfer coefficient for 1.0 mm, 1.4 mm and 2.0 mm tube diameters. (Data plotted at 6d_q from inlet).

Fig. 8 Normalized HRR contours of H₂–air flames in different tube diameters. Contours normalized to 1.6 × 10¹⁰.

Fig. 9 shows the effect of tube diameter on flame propagating speed with respect to various heat transfer conditions. For 1.4 mm and 2.0 mm diameter cases, flame speed is observed to be maximum for adiabatic conditions and minimum for wall heat transfer conditions, where flame shape changes from θ > 0 to θ < 0. It is to be noted that for 1.0 mm diameter case, the flame propagation speed shows a random behavior perhaps due to the reason that flame shape change is insignificant with wall heat transfer coefficient. Flame thermal wall coupling plays an important role in determining the flame dynamics for channels with dimensions close the flame quenching distance (i.e. 1.0 mm diameter case in present work). A two-dimensional analytical model considering conjugate heat transfer developed by Veeraragavan^41,42 endorses the effect of thermal wall coupling on the flame speed. Due to this, perhaps a peculiar behavior on the variation of flame speed with heat transfer coefficient has been observed in the present work for 1.0 mm case. Fig. 9b shows the variation of normalized flame propagation speed with normalized wall heat transfer coefficient. Both the variables are normalized using following relations.

Fig. 9 Effect of tube diameter on (a) flame propagation speed with wall heat transfer coefficient. (b) normalized speed with heat transfer coefficient.

It is interesting to note that for h_norm < 1, the values of flame propagation speed almost fall into a single line indicating that flame propagation behavior is independent of tube diameter. For h_norm > 1, the value of flame propagation speed for 1.4 mm and 2.0 mm diameter fall into single line indicating a similarity in flame propagation behavior. However, it is interesting to note that for 1.0 mm diameter tube, the flame propagation speeds remain relatively much smaller for higher values of wall heat transfer coefficient, h. This phenomena of lower flame propagation speeds for 1.0 mm diameter tube can also be observed from Fig. 9a and could be attributed to very small change in flame shape angle with wall heat transfer coefficient, h.

Fig. 10 and 11 show the variation of the velocity angle (tan⁻¹(v/u)) to understand the extent of flow redirection near the flame zone. The velocity angle is plotted for tube diameters of 1.0 mm and 2.0 mm cases with adiabatic wall conditions and h = 600 and 655 W m⁻² K⁻¹ conditions which correspond to lowest flame propagation velocity in 1.0 and 2.0 mm cases. A significant difference in flow redirection for adiabatic wall conditions can be observed from Fig. 10a and 11a due to the effect of tube diameter (1.0 and 2.0 mm). For smaller tube diameters, the effect of flow redirection becomes pronounced near the flame front location (1d_q) as compared to large tube diameters (2d_q). For instance, the point of maximum flow redirection moves from 2d_q to 1d_q as the tube diameter decreases from 2.0 mm to 1.0 mm. The effect of flow redirection continues to be there in larger tube diameters even at the flame stabilization point (x = 0) as clear for 2.0 mm diameter case shown in Fig. 10a. A similar comparison of flow redirection for transition conditions (h_min) shows that the flow redirection continues to be more prominent for larger tube diameters. The comparison of Fig. 10b and 11b shows that maximum flow redirection occurs for 1.0 mm diameter case at the flame location. However, the point of maximum flow redirection gets shifted upstream to 0.5d_q as tube diameter is increased to 2.0 mm. An overall comparison shows that an increase in wall heat transfer coefficient pushes the point of flow redirection towards the location of the flame front and increase in tube diameter also increases the extent of flow redirection and pushes it in the upstream direction.

Fig. 10 Variation of velocity angles for H₂–air flame in a 2.0 mm channel (a) h = 0 (b) h = 655 W m⁻² K⁻¹.

Fig. 11 Variation of velocity angles for 1.0 mm channel (a) h = 0 (b) h = 600 W m⁻² K⁻¹.

4. Conclusions

Unsteady numerical studies have been presented in this paper to understand the flame dynamics and flame propagation studies of stoichiometric H₂/air mixtures in straight microtubes. The flame propagation behavior has been studied for a range of wall thermal boundary conditions varying between adiabatic to isothermal wall boundary conditions. It was observed that for the range of thermal boundary conditions investigated in the present work, the flame shape angle is very sensitive to wall heat transfer conditions and tube diameter. The flame behavior changes significantly in this range of h and corresponds to the transition regime in which the flame shape angle varies from positive to negative. The variation of flame propagation speed with heat-loss is non-monotonic and a minimum value is observed for a particular thermal boundary condition due to flame shape transition for 1.4 and 2.0 mm tube diameter. However, for 1.0 mm tube diameter, a gradual variation in the flame shape angle has been observed and behavior is markedly different from that of higher tube diameters. The trends of variation of the normalized flame propagation speed with normalized convective heat transfer coefficient have been observed to be independent of the tube diameter for lower wall heat transfer coefficient (h ≤ h_min). For h > h_min, the flame propagation speeds in 1.0 mm tube diameter are much smaller as compared to larger (1.4 and 2.0 mm) tube diameters. Normalized mass-fluxes and velocity angles (tan⁻¹(v/u)) have been used to explain the formation of different flame shapes at different thermal boundary conditions. The flame interacts with the flow in a way, which induces significant radial component in the upstream region of the flow. A higher isothermal wall temperature helps suppress the induced radial components near the flame front.

Nomenclature

D	Tube diameter (mm)
L	Axial distance (mm)
dq	Quenching distance or its numerical value (mm)
θ	Flame shape angle (degrees)
h	Wall heat transfer coefficient (W m^−2 K^−1)
hmin	h corresponding to minimum flame propagating speed (W m^−2 K^−1)
HRR	Heat release rate
SL	Flame propagating speed (cm s^−1)
u	Axial velocity component (m s^−1)
v	Radial velocity component (m s^−1)
ρ	Density (kg m^−3)
ṁt	Total mass flux (kg m^−2 s^−1)
ṁx	Axial mass flux (kg m^−2 s^−1)
Yi	Species mass fraction
SL	Laminar flame velocity
SL,norm	Normalized flame propagating speed
hnorm	Normalized wall heat transfer coefficient

Acknowledgements

This work was supported by the DST, Govt. of India under joint Indo-Russian grant no. INT/RFBR/P-179. Partial support for this work from FEFU through project No. 13-06-0223 and RFBR project No. 14-08-92695 is acknowledged. Partially, this work was supported by Advanced Research Center Program (NRF-2013R1A5A1073861) through the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) contracted through Advanced Space Propulsion Research Center at Seoul National University.

References

1. D. Dunn-Rankin, E. M. Leal and D. C. Walther, Personal power systems, Prog. Energy Combust. Sci., 2005, 31(5), 422–465.
2. N. S. Kaisare and D. G. Vlachos, A review on microcombustion: Fundamentals, devices and applications, Prog. Energy Combust. Sci., 2012, 38(3), 321–359.
3. A. H. Epstein, S. A. Jacobson, J. M. Protz and L. G. Frechette, Shirtbutton-sized gas turbines: the engineering challenges of micro high speed rotating machinery, in Proceedings, 8th Int'l Symposium on Transport Phenomena and Dynamics of Rotating Machinery, Honolulu, HI, 2000.
4. D. C. Walther and J. Ahn, Advances and challenges in the development of power-generation systems at small scales, Prog. Energy Combust. Sci., 2011, 37(5), 583–610.
5. K. Maruta, J. Parc, K. Oh, T. Fujimori, S. Minaev and R. Fursenko, Characteristics of microscale combustion in a narrow heated channel, Combust., Explos. Shock Waves, 2004, 40(5), 516–523.
6. K. Lee, Y. Hong, K. Kim and O. Kwon, Stability limits of premixed microflames at elevated temperatures for portable fuel processing devices, Int. J. Hydrogen Energy, 2008, 33(1), 232–239.
7. B. Khandelwal and S. Kumar, Experimental investigations on flame stabilization behavior in a diverging micro channel with premixed methane–air mixtures, Appl. Therm. Eng., 2010, 30(17), 2718–2723.
8. M. Akram and S. Kumar, Experimental studies on dynamics of methane–air premixed flame in meso-scale diverging channels, Combust. Flame, 2011, 158(5), 915–924.
9. L. Sitzki, K. Borer, E. Schuster, P. D. Ronney and S. Wussow, Combustion in microscale heat-recirculating burners, in The Third Asia-Pacific Conference on Combustion, Seoul, Korea, 2001.
10. A. Fan, S. Minaev, S. Kumar, W. Liu and K. Maruta, Experimental study on flame pattern formation and combustion completeness in a radial microchannel, J. Micromech. Microeng., 2007, 17(12), 2398.
11. A. Fan, S. Minaev, E. Sereshchenko, R. Fursenko, S. Kumar, W. Liu and K. Maruta, Experimental and numerical investigations of flame pattern formations in a radial microchannel, Proc. Combust. Inst., 2009, 32(2), 3059–3066.
12. J. Lee, G. Do, H. Moon and O. Kwon, An annulus-type micro reforming system integrated with a two-staged micro-combustor, Int. J. Hydrogen Energy, 2010, 35(4), 1819–1828.
13. J. Li, S. Chou, G. Huang, W. Yang and Z. Li, Study on premixed combustion in cylindrical micro combustors: transient flame behavior and wall heat flux, Exp. Therm. Fluid Sci., 2009, 33(4), 764–773.
14. H. Cao and J. Xu, Thermal performance of a micro-combustor for micro-gas turbine system, Energy Convers. Manage., 2007, 48(5), 1569–1578.
15. J. Li, S. Chou, Z. Li and W. Yang, Characterization of wall temperature and radiation power through cylindrical dump micro-combustors, Combust. Flame, 2009, 156(8), 1587–1593.
16. G.-B. Chen, Y.-C. Chao and C.-P. Chen, Enhancement of hydrogen reaction in a micro-channel by catalyst segmentation, Int. J. Hydrogen Energy, 2008, 33(10), 2586–2595.
17. Z. Li, S. Chou, C. Shu, H. Xue and W. Yang, Characteristics of premixed flame in microcombustors with different diameters, Appl. Therm. Eng., 2005, 25(2), 271–281.
18. J. Hua, M. Wu and K. Kumar, Numerical simulation of the combustion of hydrogen–air mixture in micro-scaled chambers. Part I: Fundamental study, Chem. Eng. Sci., 2005, 60(13), 3497–3506.
19. J. Hua, M. Wu and K. Kumar, Numerical simulation of the combustion of hydrogen–air mixture in micro-scaled chambers Part II: CFD analysis for a micro-combustor, Chem. Eng. Sci., 2005, 60(13), 3507–3515.
20. J. L. Wan, A. W. Fan, K. Maruta, H. Yao and W. Liu, Experimental and numerical investigation on combustion characteristics of premixed hydrogen/air flame in a micro-combustor with a bluff body, Int. J. Hydrogen Energy, 2012, 37(24), 19190–19197.
21. S. Yuasa, K. Oshimi, H. Nose and Y. Tennichi, Concept and combustion characteristics of ultra-micro combustors with premixed flame, Proc. Combust. Inst., 2005, 30(2), 2455–2462.
22. G. Pizza, C. E. Frouzakis, J. Mantzaras, A. G. Tomboulides and K. Boulouchos, Dynamics of premixed hydrogen/air flames in mesoscale channels, Combust. Flame, 2008, 155(1), 2–20.
23. G. Pizza, C. E. Frouzakis, J. Mantzaras, A. G. Tomboulides and K. Boulouchos, Dynamics of premixed hydrogen/air flames in microchannels, Combust. Flame, 2008, 152(3), 433–450.
24. Y. Wang, Z. Zhou, W. Yang, J. Zhou, J. Liu, Z. Wang and K. Cen, Combustion of hydrogen–air in micro combustors with catalytic Pt layer, Energy Convers. Manage., 2010, 51(6), 1127–1133.
25. V. Zamashchikov and E. Tikhomolov, Sub-critical stable hydrogen–air premixed laminar flames in micro gaps, Int. J. Hydrogen Energy, 2011, 36(14), 8583–8594.
26. W. Choi, S. Kwon and H. D. Shin, Combustion characteristics of hydrogen–air premixed gas in a sub-millimeter scale catalytic combustor, Int. J. Hydrogen Energy, 2008, 33(9), 2400–2408.
27. M. Baigmohammadi, S. S. Sadeghi, S. Tabejamaat and J. Zarvandi, Numerical study of the effects of wire insertion on CH₄ (methane)/AIR pre-mixed flame in a micro combustor, Energy, 2013, 54, 271–284.
28. D. Jiang, W. Yang and K. J. Chua, Entropy generation analysis of H₂/air premixed flame in micro-combustors with heat recuperation, Chem. Eng. Sci., 2013, 98, 265–272.
29. A. Gutkowski, Numerical analysis of effect of ignition methods on flame behavior during passing through a sudden contraction near the quenching conditions, Appl. Therm. Eng., 2013, 54(1), 202–211.
30. A. Nair, V. R. Kishore and S. Kumar, Dynamics of Premixed Hydrogen–Air Flames in Microchannels with a Wall Temperature Gradient, Combust. Sci. Technol., 2015, 187(10), 1620–1637.
31. A. P. Singh, V. RatnaKishore, S. Minaev and S. Kumar, Numerical investigations of unsteady flame propagation in stepped microtubes, RSC Adv., 2015, 5(122), 100879–100890.
32. C. Olm, I. G. Zsély, R. Pálvölgyi, T. Varga, T. Nagy, H. J. Curran and T. Turányi, Comparison of the performance of several recent hydrogen combustion mechanisms, Combust. Flame, 2014, 161(9), 2219–2234.
33. M. Ó. Conaire, H. J. Curran, J. M. Simmie, W. J. Pitz and C. K. Westbrook, A comprehensive modeling study of hydrogen oxidation, Int. J. Chem. Kinet., 2004, 36(11), 603–622.
34. A. Fluent, 14.5, Theory Guide, ANSYS. Inc., Canonsburg, PA, 2012.
35. R. Issa, B. Ahmadi-Befrui, K. Beshay and A. Gosman, Solution of the implicitly discretised reacting flow equations by operator-splitting, J. Comput. Phys., 1991, 93(2), 388–410.
36. S. Patankar, Numerical Heat Transfer and Fluid Flow, McGraw-Hill, New York, 1980.
37. K. Maruta, T. Kataoka, N. I. Kim, S. Minaev and R. Fursenko, Characteristics of combustion in a narrow channel with a temperature gradient, Proc. Combust. Inst., 2005, 30(2), 2429–2436.
38. C. M. Miesse, R. I. Masel, C. D. Jensen, M. A. Shannon and M. Short, Submillimeter-scale combustion, AIChE J., 2004, 50(12), 3206–3214.
39. N. I. Kim and K. Maruta, A numerical study on propagation of premixed flames in small tubes, Combust. Flame, 2006, 146(1), 283–301.
40. S. T. Lee and C. H. Tsai, Numerical investigation of steady laminar flame propagation in a circular tube, Combust. Flame, 1994, 99(3), 484–490.
41. A. Veeraragavan, On flame propagation in narrow channels with enhanced wall thermal conduction, Energy, 2015, 93, 631–640.
42. A. Veeraragavan and C. P. Cadou, Flame speed predictions in planar micro/mesoscale combustors with conjugate heat transfer, Combust. Flame, 2011, 158(11), 2178–2187.

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