Effects of non-catalytic surface reactions on the CH₄–air premixed flame within micro-channels

Abstract

The non-catalytic surface of a micro-combustor plays a significant role in flame propagation. For the purpose of investigating the effects of surface reactions on the combustion process, this paper presents a numerical 2D simulation of a CH₄–air premixed flame within a micro planar channel with detailed gas-phase and non-catalytic surface reaction mechanisms. In this paper, we focus on numerically examining the effects of surface reactions on the flame structure. The simulation results show that surface reactions affect the temperature distribution in three controlling regimes, distinguished according to the inlet velocity. Besides, radicals suffer sharper declines near the active surface than those near the inert surface due to the radical removing effect. Moreover, as the temperature increases, the difference will become more remarkable especially in the vicinity of the wall. Among the radicals, the mass fractions of H, O, and OH & CH₃ near the surface experience the largest, mediate and smallest decay, respectively, when changing the inert surface to the active surface. The adsorption of H should be of the greatest concern. The OH radical has a similar distribution profile to the O radical for both kinds of surfaces.

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1 Introduction

With the advances in the fabrication technologies for micro-electromechanical systems (MEMS), micro-burners of millimeter scale have been widely developed and applied for various micro-thrusters,^1–3 micro-engines^4–6 and micro-reactors^7–10 in the past few decades. These applications were mainly due to the fact that hydrocarbon fuel based micro-burners show a higher energy density, compared with the most advanced currently available lithium ion batteries.¹¹ However, with the decrease of the combustor size, the combustor surface to volume ratio increases dramatically, creating a strong flame–wall interaction and the flame can be quenched.¹² The quenching mechanisms mainly consist of thermal and kinetic mechanisms, i.e., heat loss to the wall and radical adsorption on the surface.^13–15 Thus, the surface of the micro-combustor plays a significant role in flame propagation.

In the past few decades, many efforts have been made to deduce the kinetic mechanism especially with the catalytically active surfaces.^16–22 However, the kinetic mechanism on non-catalytic surfaces (such as quartz and chromium surfaces) has not drawn much attention and its effects within micro-burners are not well understood. Vlachos et al. investigated the radical quenching mechanism, i.e., the kinetic mechanism of the ignition and extinction of flames for premixed hydrogen–air near surfaces with a detailed gas-phase mechanism and they treated the wall as a sink of radicals.^23,24 Raimondeau et al. conducted 2D simulations of the flame propagation of methane–air and the gas-surface interaction, using a detailed gas-phase mechanism and a radical quenching mechanism.¹⁵ They showed that the flames could propagate within the micro-channels by preheating and insulation, and the near-entrance heat loss and radical quenching at the wall are the two key issues for flame propagation in micro-channels. Aghalayam et al. investigated the role of radical quenching in flame stability of hydrogen–air mixtures and wall heat flux.²⁵ They claimed that the ignition is retarded solely by the kinetics of surface reactions, while the extinction is controlled by both the kinetics and thermal feedback from radical recombination on the wall. The combustion of methane was studied by Rahmat Sotudeh-Gharebagh et al. in a fixed bed reactor to determine the effect of inert particles at distinct temperature intervals.²⁶ They found that sand particles might act as catalysts to increase the conversion at low temperature (∼750 °C) but with quite a small contribution. Besides, wall surfaces inhibited homogeneous combustion by reducing the free radical concentrations at moderately high temperatures (750–850 °C), and the inhibition effects became less significant and could be neglected compared with the rapid homogeneous reactions at high temperatures (above 875–900 °C). Miesse et al. experimentally studied the effects of wall temperature and materials on radical quenching.²⁷ They found that the thermal quenching dominates at a colder surface (near 500 K) since the quenching lengths were relatively independent of wall materials, whilst they strongly depend on wall material at higher temperatures (near 1273 K) with radical quenching controlling the process. Kim et al. experimentally examined the significance of the two quenching mechanisms.¹⁴ Three distinct controlling regimes occurred during the quenching behaviors, representing the thermal regime (100–350 °C), the heterogeneous reaction regime (400–600 °C), and the gas-phase reaction regime (above 600 °C), respectively. Saiki et al. combined OH-PLIF/micro-OH-PLIF and numerical simulation to estimate the initial sticking coefficients associated with radical adsorption, and the results confirmed that a radical quenching effect should exist for the quartz surface.²⁸ Bai et al. proposed an analytical model to provide the ability to theoretically analyze flame propagation with both thermal and radical quenching mechanisms, using a model with two gaseous chain-branching reactions and a one step surface reaction.¹³ Even though previous studies have experimentally and numerically investigated the dependence of quenching distances on materials, there is little research conducted to directly reflect the kinetic effects especially with detailed gas-phase and surface reaction mechanisms. Thus we still do not have a deeper insight into the effects of radical quenching on combustion characteristics. Fortunately, simulation might give access to a fundamental understanding of the radical quenching effects.

Obviously, the surface reactions initially affect the radical distribution especially near the wall, which further impacts the reaction rates and heat release, and subsequently influences the temperature profiles. In this work, the emphasis is imposed on numerically examining the effects of non-catalytic wall surface reactions, i.e., radical-removing effects, on the flame structure, since it is significant to characterize the combustion process. In case of misunderstanding, the surfaces discussed hereafter are non-catalytic surfaces instead of traditionally catalytic ones. In this paper, the “active surface” and “inert surface” refer to the non-catalytic (radical-removing) surface and the completely inert surface, respectively.

2 Model description

2.1 Physical model

The 2D cross-sectional view (5 × 1 mm²) of the reactor is shown in Fig. 1. The micro-burner consists of two parallel, infinitely wide plates. The combustion within micro-burners is normally accompanied with complex radical and thermal effects, meaning that these reactors are quite different from the classic CSTR (Continuous Stirred Tank Reactor) and PFR (Plug Flow Reactor). In this paper, our primary focus is on understanding the effects of wall surface reactions within the micro-reactor, instead of the thermal effects. Thus, the thickness of the wall is set as zero, to remove the wall heat conduction effects. Besides, the plates are set as isothermal and thereby heat recirculation is not necessarily considered in the present model. Since the premixed, preheated CH₄–air mixture enters into the gap of two parallel plates, meaning a symmetrical flow with respect to the centerline, only half of the reactor is taken as the computational domain for time saving.

Fig. 1 Schematic diagram of the 2D reactor with a 5 mm length (L) and 1 mm height (H).

2.2 Numerical model

Based on the above descriptions and assumptions, the governing conservation equations of mass, momentum, and species as well as the ideal gas law are listed as follows:where ρ is the fluid density (kg m⁻³), t is the time (s), ∇ is the spatial gradient operator, · is the vector dot product, and U is the absolute velocity (m s⁻¹).where P is the absolute pressure (Pa), and μ is the dynamic viscosity (N s m⁻²). x and y indicate the axial and transverse positions (mm), respectively. u and v represent the axial and transverse velocities (m s⁻¹), respectively.where Y_i is the mass fraction of the ith species, D_i,m is the diffusivity of species i (m² s⁻¹), R_i is the production rate of the ith species (kg m⁻³ s⁻¹).where c_p is the constant pressure specific heat (J K⁻¹ mol⁻¹), T is the temperature (K), λ is the thermal conductivity (W m⁻¹ K⁻¹), h_i is the specific enthalpy of species i (J kg⁻¹), and N is the number of gas-phase species.where R is the universal gas constant (J mol⁻¹ K⁻¹), and M_i is the molar mass of species i (kg mol⁻¹).

The idea used to calculate the rates of the surface reactions is shown by eqn (7)–(10):²⁹

[X_j] = Γθ_j, (j = 1,…, N_s) (10)

where υ_ik is the stoichiometric coefficient of species i in the kth reaction, k_fk is the forward rate constant of the kth reaction (kg mol⁻¹ s), and [X_j] is the molar concentration of the jth surface species (mol m⁻²). N_g and N_s indicate the number of species in the gaseous phase and wall surface, respectively. S_0,i is the sticking coefficient of species i. The surface site densities (Γ) of chromium (3.170 × 10⁻⁹ mol cm⁻²) and γ-Al₂O₃ (1.360 × 10⁻⁹ mol cm⁻²) are estimated via the distance between the atoms of the lattice.²⁸ The superscript τ is the number of sites occupied by the reactant species. The subscript a and s represent the adsorption and surface reaction, respectively. θ is the surface coverage.

2.3 Reaction mechanisms

The gas-phase mechanism of CH₄–air includes 50 species and 309 reactions (GRI-mech 3.0 (ref. 30) excluding Ar, C₃H₈ and C₃H₇ species and their associated reactions). The heterogeneous mechanism shown in Table 1 is the same as in ref. 15 and 28, containing 5 surface species and 10 elementary surface reactions along with the corresponding kinetic parameters. Previous work³¹ has analyzed the sensitivity of homogeneous ignition and extinction to radical quenching by examining the difference in ignition and extinction temperatures respectively for adsorptive surfaces (where an intermediate species (CH₃O, HCO, OH, O, HO₂, H or CH₃) is selectively removed) and inert surfaces (no adsorption). The sensitivity analysis showed that CH₃/H and H/OH/O radicals (shown in Table 1) have a significant effect on the ignition and extinction near the surfaces, respectively. The heterogeneous mechanism takes radical adsorption, recombination on the surface, and stable gas-phase species desorption into account.

Table 1 Heterogeneous mechanism and kinetic parameters^a15,28

No.	Reactions	S0 or A (s^−1)	β	E (kJ mol^−1)
a * refers to the surface site in which the radicals are adsorbed; ^* represents the adsorbed surface species; S0 indicates the initial sticking coefficient or sticking probability; A is the pre-exponential factor (s^−1); β shows the temperature exponent; E is the activation energy (kJ mol^−1).
1	CH3 + * ⇒ CH^*3	1	—	—
2	H + * ⇒ H^*	1	—	—
3	O + * ⇒ O^*	1	—	—
4	OH + * ⇒ OH^*	1	—	—
5	2CH^*3 ⇒ C2H6 + 2*	10^13	0	0
6	CH^*3 + H^* ⇒ CH4 + 2*	10^13	0	0
7	2H^* ⇒ H2 + 2*	10^13	0	0
8	2OH^* ⇒ H2O + O* + *	10^13	0	0
9	2O^* ⇒ O2 + 2*	10^13	0	0
10	OH^* + H^* ⇒ H2O + 2*	10^13	0	0

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It is necessary to discuss the uncertainties of the parameters in Table 1 and the sensitivity of the results to them as follows:

The initial sticking coefficient (S₀) of each radical adsorption on the non-catalytic and inert surfaces is set as one (the strongest quenching affinity) and zero (the weakest quenching affinity), respectively.^15,28 S₀ depends on the binding energy of the adsorbate to metals, since higher binding energy leads to easier adsorption on the surface. From the d-band theory, the bond strength of the adsorbate-surface relies on the metal d-band center relative to the Fermi level.^32,33 The d-band center is a function of the filling of the anti-bonding states (d-band) of the adsorbates on transition metals.³² As we move left in the periodic table, the anti-bonding states will move up in energy and become less filled, resulting in the d-band center moving up relative to the Fermi level, hence the stronger bonding. Thus, it is reasonable to approximately set S₀ as one for chromium, since S₀ = 1 in precious Pt and Pd cases³⁴ which have more filled anti-bonding states than chromium (generally non-catalytic for methane combustion). The zero sticking coefficient could be related to the γ-Al₂O₃ surface usually treated as an inert surface.²⁸

The pre-exponential factor of each radical recombination is set as 10¹³ s⁻¹, roughly calculated via transition theory.³² When a molecule adsorbs on the surface, it will lose the major part of its gas-phase entropy, since its translational and rotational degrees of freedom typically become constrained.³⁵ Therefore, the major contribution to adsorbed molecule entropy is the small vibrational component. For adsorbed atoms, the residual entropy from electronic contribution is so small that it can be ignored. Given the above, the entropic change for the radical recombination is quite small and could even be ignored.³⁵ Therefore, in the absence of large entropic effects, it is reasonable to approximate the pre-exponential factor by k_BT/h, ∼10¹³ s⁻¹. k_B and h are the Boltzmann constant and the Planck constant, respectively.

We treat the surface recombination as non-activated^15,28 based on two reasons. Firstly, even though we can not experimentally measure the activation barrier for each elementary reaction, we can estimate them by the principle of microscopic reversibility³⁶ and the Brønsted–Evans–Polanyi (BEP) relation³⁷ between activation energy and dissociative chemisorption energy. Based on many experiments and DFT calculations, Nørskov et al. realized that for dissociative adsorption processes involving simple diatomic molecules, the slope of the BEP equation is often close to 1, implying that the transition state energy is similar to that of the final state.³² Combining this rule of thumb with the principle of microscopic reversibility,³⁶ one could estimate that the activation barrier of the reversible reaction (surface recombination) of the surface dissociative reaction is close to 0. Secondly, the activation energy does not play an important role in the total rate of the surface reaction, since the radical quenching is adsorption-limited. Even though the real activation barrier might be non-zero, even quite large, assuming it is in the order of 100 kJ mol⁻¹, the rate of the surface combination is about 10⁸ s⁻¹, still three orders of magnitude larger than that of the adsorption (in the order of 10⁵ s⁻¹). Thus, our non-activated assumption makes no or quite a small difference to the results.

The most critical value for the results is the initial sticking coefficient. The rates of radical adsorption and surface recombination estimated from eqn (7) and (8) are on the order of 10⁵ and 10¹³ s⁻¹, respectively. Thus, we can suppose that the rate-determining step for radical quenching is the radical adsorption process. In order to validate that, we also performed a sensitivity analysis in our preliminary calculations by examining how the flame structure changes as the pre-exponential factor varies from 10⁸ to 10¹³ s⁻¹. The results showed that the flame structure remained unchanged for all the tested pre-exponential factors. Therefore, the most crucial value for radical quenching effects is S₀, completely the same as in ref. 28.

We expected to use the CHEMKIN thermodynamic and transport database.³⁸ Unfortunately, to the authors’ knowledge, there is no thermodynamic data of surface species for the common experimental materials (chromium, γ-Al₂O₃, quartz, etc.) except for catalysts (Pt, Pd, etc.). Therefore, isothermal boundary condition is imposed on the wall, so that we do not have to obtain the thermodynamic data of surface adsorbed species or calculate the heat released by the surface reactions.

2.4 Boundary conditions and initial conditions

Inlet: (Y_i)_x=0 = Y_i,in(Φ), (T)_x=0 = T_s, u = u₀, v = 0

Initialization: T(x) = 1800 K, T_s = T_in, Y_i(x) = Y_i,in

where the subscript s and in represent the wall surface and the combustor inlet, respectively. Φ is the equivalence ratio, and Ψ is the collection of the parameters.

2.5 Adaptability of the model

The governing equations were made discrete by a finite-volume method and solved by Fluent Release 6.3.26. Unsteady simulations were conducted unless otherwise stated. A first-order upwind scheme was introduced to make the governing equations discrete and the SIMPLE algorithm was used to solve the pressure–velocity coupling. To solve the governing equations implicitly, a 2D segregated solution solver was used with an under-relaxation method. The convergence criteria for residuals of the governing equations were set to be 1 × 10⁻⁵ for continuity, 1 × 10⁻⁵ for velocity, 1 × 10⁻⁶ for energy and 1 × 10⁻⁵ for species concentration. The residuals were monitored throughout the simulation process. The density was calculated using the impressible-ideal-gas-law. The gas specific heat, thermal conductivity and viscosity of the gas mixture were calculated by the mass fraction-weighted-mixing-law, and the species specific heat was obtained by the piecewise polynomial fit of temperature.

In the simulations, the mesh was non-uniformly accumulated at the reaction zone and near the wall surface. In order to determine the optimal mesh density for the solutions, four cases with different numbers of grid points (2000, 3200, 5000, 8400) were conducted. Fig. 2 illustrates the centerline temperature profiles for all the tested cases. The case with 2000 cells, the coarsest case, fails to depict the maximum temperature. However, as the mesh number increases to 5000 cells, the solutions come to a convergence, giving the desired accuracy. A larger mesh number, up to 8400 cells, yields no obvious advantage. Therefore, the case with 5000 cells and a time step of 10⁻⁵ s was adopted hereafter, considering both the accuracy and the computing time.

Fig. 2 The centerline temperature profiles for cases with different grid numbers. The inset shows the partial enlarged detail of the temperature profiles around the respective maxima. A case is casually selected among all the computed cases for mesh validation, with the parameters u₀ = 1.4 m s⁻¹, v₀ = 0 m s⁻¹, T_in = T_s = 1273 K, P = 1 atm, Φ = 0.95.

3 Results and discussion

3.1 Temperature distribution

Fig. 3 shows that two regions, i.e., the combustion region (A) and the post-combustion region (B), could be obviously distinguished in all cases. Almost no preheating zone exists since the high inlet temperature approaches the ignition temperature. Since the isothermal wall has been introduced and it is as hot as the inlet gas, no wall thermal conductivity, namely heat recirculation, prevails throughout. Thus the upstream conductive heat flux through the fluid mixture is the only pathway for the flammable mixture to warm up and ignite at the very front end of region A. This heat flux is initially conducted from the combustion zone, where the fluid mixture is the hottest. On account of the hottest position being located at the centerline, and thus the mixture warming up from the centerline to the wall, ignition occurs and then the flame stabilizes both at the centerline instead of in the vicinity of the wall, consistent with the case in ref. 15.

Fig. 3 The centerline temperature profiles for cases with inert or active surfaces. The inset shows the partial enlarged detail of the temperature profiles around their respective maxima. The parameters are u₀ = 0.6 m s⁻¹, v₀ = 0 m s⁻¹, T_in = T_s = 1123 K, P = 1 atm, Φ = 0.95. For convenience, hereafter the active and inert surfaces refer to the surfaces with and without surface reactions, respectively.

Firstly, we examined the effects of surface reactions on flame temperature, usually defined as the maximum of fluid temperature.³⁹ It should be noted that in Fig. 3 the flame temperature with the active surface is approximately 10 K lower than that with the inert surface. Moreover, the flame with the effects of surface reactions is less stretched especially in region B, and the position of flame temperature moves downstream slightly meaning that the flame propagation velocity slightly decreases. In order to understand the above effects of surface reactions on the flame structure, further discussion is conducted as follows.

As shown in Fig. 4, the flame temperature increases with improving T_in and T_s and eventually tends to level off, but is still generally lower than the adiabatic flame temperature. This is because the rate of transverse heat transfer within the fluid is comparable with that of heat release on such small scales, and besides there is no wall upstream thermal conductivity, i.e., the significant approach for preheating the mixture.^40–43 However, a super-adiabatic flame temperature could be obtained as the inlet velocity exceeds 2.2 m s⁻¹ (1273 K), which is similar to the results of ref. 43, but this results in more heat release as well as quite hot T_in and T_s instead of heat recirculation through the wall. Under the same inlet velocity, higher T_in and T_s yield a higher flame temperature for both kinds of surfaces, moreover, with the flame temperature over the active surface much lower than that over the inert one. As the inlet velocity increases, the difference between the flame temperatures for both kinds of surfaces tends to diminish and even disappear (at 3.0 m s⁻¹), with its maximum emerging at the lowest inlet velocity (0.6 m s⁻¹). Interestingly, the flame temperature increases linearly with T_in and T_s at the same inlet velocity as shown in Fig. 5. It also illustrates that surface reactions have no effects on flame temperature at a higher inlet velocity, but the differences could still exist at lower velocities regardless of the inlet and wall temperatures. For methane, its thermal diffusivity is similar to the diffusion coefficient since its Le (Lewis number) is approximately unity.³⁹ Thus to understand these results, the Pe (Peclet number) could be used to represent the relative significance of radical diffusion to axial convection, defined as eqn (11). x indicates the axial position from the inlet. Sc (0.714), Schmidt number, is taken from ref. 45 and Re_in is evacuated at the combustor inlet.

where τ_C and τ_D represent the time (s) of axial convection and transverse diffusion, respectively. ν is the kinematic viscosity (m² s⁻¹).

Fig. 4 The effects of inlet velocity on flame temperature for cases with inert or active surfaces at distinct temperatures (1123, 1173 and 1273 K). Other parameters are v₀ = 0 m s⁻¹, P = 1 atm, Φ = 0.95. The dashed purple line represents the adiabatic flame temperature (∼2226 K (ref. 44)). Note that blowout or extinction tend to occur, especially for the case with 1123 K, when v₀ is above 3.0 m s⁻¹ or below 0.6 m s⁻¹. Thus we take the intersection of inlet velocities (0.6–3.0 m s⁻¹) among the involved cases.

Fig. 5 The effects of T_in and T_s on flame temperature for cases with inert or active surfaces at distinct inlet velocities (1.0, 2.2 and 3.0 m s⁻¹). Other parameters are v₀ = 0 m s⁻¹, P = 1 atm, Φ = 0.95.

The convection time scale of flow to reach the same axial position (x) could be shortened with faster inlet velocity, i.e., higher Re₀, yielding a higher Pe. Thus fewer radicals could arrive at the wall surface. Besides, higher u₀ will give a higher flame temperature to boost the rates of heat release and radical generation and then compensate the heat and radical loss towards the wall to some extent. So the difference in flame temperatures between both kinds of surfaces tends to diminish at higher Pe.

Secondly, we investigated the effects of surface reactions on the post-combustion region. As shown in Fig. 6, there are significant axial and transverse temperature gradients in region A, since drastic gas-phase reactions occur, releasing heat and then resulting in a sharp rise in fluid temperature. In the post-combustion region B where no drastic reactions occur because the reactants have been depleted, the fluid mixture cools down towards the wall temperature. Obviously, there are no significant axial and transverse gradients within region B. The sizes of the two regions vary with the operating conditions.

Fig. 6 The temperature contours of the micro flame with inert (upper) or active surfaces (lower) with distinct inlet velocities (u₀ = (a) 1.0, (b) 2.2, (c) 3.4, (d) 4.2 m s⁻¹). Other parameters are v₀ = 0 m s⁻¹, T_i = T_s = 1273 K, P = 1 atm, Φ = 0.95.

As illustrated in Fig. 6 and 7, the sizes of region A and region B broaden and narrow respectively with increasing u₀ despite whether it is with an inert or active surface. It is noticeable that a bifurcation appears in the centerline temperature profiles for both kinds of surfaces, but it could disappear before the exit at low u₀ values, since reactants could be completely consumed within the reactor. Moderate u₀ values allow the bifurcation to emerge later and remain until the exit, meaning incomplete conversion. When u₀ surpasses a critical value, the temperature curves for both kinds of surfaces become entirely identical. The above results could also be explained and divided by Pe into three regimes, but x should be replaced by L (length of the reactor): low and moderate u₀ values, i.e., low and moderate Pe values, imply transverse diffusion outperforming or being comparable to axial convection, which causes large quantities of radicals to be quenched by the active surface which then leaves less radicals to react at the centerline. Consequently, the centerline temperature with an active surface is lower than that with an inert surface. In addition, the flame is less stretched by surface reactions. Quite high u₀ (high Pe) values enhance the axial convection, signifying that quite a few radicals diffuse towards the wall surface during the residence, thus they could be identified. Overall, radical quenching should draw particular attention especially at low inlet velocity.

Fig. 7 The centerline temperature profiles for cases with inert or active surfaces at distinct inlet velocities. The parameters are the same as those in Fig. 6.

3.2 Radical distribution

Actually, the differences in temperature distribution between the inert and active surfaces essentially result from the effects of surface reactions on radical distribution, thus it is necessary to have further discussion below. Fig. 8 demonstrates the simulation results for the mass fraction distributions of H, O, OH and CH₃ (ref. 31) which are important for flame propagation and stabilization. With the inert surface, the mass fractions of all the radicals, especially H, show a mild transverse gradient, identical to the negligible radical gradients in the micro-channels (R ≤ 1 mm).¹⁵ Therefore, for the sake of simplification, PFR models might be adequate for future investigations on the micro-reactor. However, for the active surface, it should be noted that the ratios of the radicals decrease to some extent in the combustion region and large quantities of radicals are adsorbed near the wall surface, showing a significant transverse radical concentration gradient. Thus, obvious radical gradients will still prevail in the micro-channels with the active surfaces.

Fig. 8 Mass fraction contours of (a) H, (b) O, (c) OH and (d) CH₃ radicals with inert (upper) or active surfaces (lower). The parameters are the same as those in Fig. 3.

To better understand the effects of surface reactions on the flame structure, we focus on the mass fraction distribution near the wall and at the centerline as illustrated in Fig. 9. In the combustion region, OH accounts for the most mass fraction among the radicals, followed by O, H and CH₃ in descending order. They peak almost at the same axial positions except for CH₃. Dehydrogenation of methane is the origin of the chain branching process, thus the mass fraction of CH₃ achieves its maximum earlier in the axial direction. Near the wall, in contrast with the radical mass fractions with the inert surface, their counterparts with the active surface are all significantly reduced (even above 60%) by surface reactions especially in the combustion region. On the contrary, there is no significant difference between the two cases around the centerline in region A, though the radical mass fractions with surface reactions are slightly smaller than their equivalents with the inert surface. But the difference appears obviously in region B due to the effects of low Pe discussed above in Section 3.1.

Fig. 9 The mass fraction plots of H, O, OH and CH₃ radicals (a) near the wall and (b) at the centerline. The parameters are the same as those in Fig. 3. The inset in (b) shows the partial enlarged detail of Y_H and Y_CH3 distributions. Letters A and B represent the combustion region and post-combustion region, respectively.

Fig. 10 demonstrates the normalized radical mass fraction [Y_i] distributions in the transverse direction. For both kinds of surface, [Y_H] undergoes the mildest decline from the centerline to the wall. This might be due to its higher diffusion coefficient (1.21–3.16 × 10⁻³ m² s⁻¹). [Y_O] and [Y_OH] present an identical tendency for both kinds of surface since they have similar diffusion coefficients (3.12–8.15 × 10⁻⁴ m² s⁻¹ and 3.07–8.01 × 10⁻⁴ m² s⁻¹, respectively). [Y_CH3] encounters a peak in the transverse direction with the inert surface due to its smaller diffusion coefficient (2.24–5.83 × 10⁻⁴ m² s⁻¹). The mass fraction of each radical (H, O, OH, CH₃) near the surface has a sharper decrease when changing the inert surface to the active surface. In detail, H suffers the largest decay (81.82%), O undergoes a smaller decrease (65.52%), and OH and CH₃ enjoy the smallest reductions (55.56% and 52.38%, respectively). Since we have validated that the radical quenching process is adsorption-limited, the role of each radical adsorption in radical quenching could be arranged as reactions 2, 3, 4 and 1 in descending order (Table 1). In general, surface reactions affect radical distributions by transverse diffusion and subsequent adsorption, and its effects decrease from the vicinity of the wall to the centerline. One should also infer that the surface reactions will more largely affect the radical distributions even at the centerline if the channel becomes narrower.

Fig. 10 The wall-normal mass fraction plots of radicals (normalized by their respective maxima) in the transverse direction. The axial positions are anchored at the respective maxima of the radical mass fractions. The parameters are the same as those in Fig. 3.

The OH radical is chosen as an example to further illustrate the effects of surface reactions on radical distribution since it enjoys the highest mass fraction among the four significant radicals. Additionally, it is traditionally considered as the crucial trigger for chain branching and propagation.⁴⁴ Fig. 11 shows the wall-normal mass fraction profiles of the OH radical for both kinds of surfaces at x = 0.30, 0.29 and 0.26 mm where the respective axial maxima are achieved for distinct T_in and T_s values (1123, 1173 and 1273 K, respectively). It should be noticed that, as the T_in and T_s increase, the Y_OH curve peaks earlier in the axial direction and decreases more slowly for both kinds of surfaces, resulting from the promotion of the diffusion coefficient with increasing temperatures. However, Y_OH with the active surface still experiences a larger decline in the wall-normal direction than its counterpart with the inert surface. Moreover, this difference becomes more obvious especially near the wall as the temperature increases. This is due to the fact that higher temperatures can promote the radical adsorption process as implied by eqn (8).²⁹

Fig. 11 The wall-normal mass fraction plots of the OH radical (normalized by their respective maxima) in the transverse direction. Note that Y_OH peaks at axial positions (0.30, 0.29 and 0.26 mm) for distinct T_in and T_s values (1123, 1173 and 1273 K, respectively). The other parameters are the same as those in Fig. 3.

4 Conclusions

The effects of surface reactions on the CH₄–air premixed flame within a micro-channel has been numerically investigated with detailed gas-phase and non-catalytic surface reaction mechanisms. The results show that the surface reactions change the flame structure and the conclusions are summarized as follows:

The effects of surface reactions on the temperature distribution could be divided into three controlling regimes by the inlet velocity: at low u₀ values, the flame temperature is reduced and appears lower and besides the flame structure is less stretched; at moderate u₀ values, the flame temperature approaches that with inert surface but the flame shows an obvious contraction in the axial direction especially in the post-combustion region; at high u₀ values, there is no difference between the temperature distributions for both kinds of surfaces, namely surface radical removal no longer having an inhibitory effect on the temperature distribution.

Radicals show great transverse gradients from the centerline to both kinds of surfaces in the micro-channels, but suffer sharper declines near the active surface than those near the inert surface due to radical removal. Furthermore, the difference becomes more pronounced especially in the vicinity of the surface as the temperature increases, owing to the promotion of diffusion coefficients with higher temperatures. Among the radicals, the mass fractions of H, O, and OH & CH₃ near the wall suffer the largest, intermediate and smallest decreases, respectively, when changing from the inert surface to the active surface. The adsorption of H should be of the greatest concern. OH and O have similar distribution profiles for both kinds of surfaces. The inhibition of surface radical removal would be more pronounced within narrower micro-reactors.

Since the effects of surface reactions on flame structure are inclined to be weakened and even negligible as the inlet velocity exceeds a certain level, this would make it feasible to improve the micro-combustion by properly organizing the flow field to promote the axial and inhibit the transverse diffusion and conduction.

Acknowledgements

The authors thank the financial support of the National Natural Science Foundation of China with Project no. 51206200, and the Fundamental Research Funds for the Central Universities with Project no. CDJZR12140031.

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