Comparative Analysis of Ignition and Combustion Characteristics in Straight-Channel and U-Bend Micro Catalytic Combustors: Numerical Investigation of Inlet Velocity Effects

Abstract

This paper presents a numerical comparative study on the ignition characteristics of straight-channel and U-bend micro catalytic combustors, with particular focus on the role of inlet velocity. A two-dimensional computational fluid dynamics model with coupled gas-phase and surface catalytic reaction kinetics for propane combustion is developed using a fluid simulation program ANSYS Fluent. The catalyst coating (Pt/Al₂O₃) is modeled as a zero-thickness reaction surface, and the U-bend design features an uncoated recirculating channel to ensure identical catalyst loading between the two configurations. Simulations are conducted over an inlet velocity range of 0.25–8 m/s. Key ignition and combustion metrics including ignition temperature, ignition time, maximum combustion temperature, heterogeneous reaction contribution, and thermal/species field distributions are systematically compared. Results reveal a crossover in relative performance depending on flow regime. At low velocities (≤2 m/s), the straight-channel combustor exhibits lower ignition temperatures; at high velocities (≥4 m/s), the U-bend design achieves superior ignition performance with lower ignition temperatures (e.g., 526 K vs. 555 K at 8 m/s) and higher combustion temperatures (1726 K vs. 1474 K at 8 m/s). However, the straight-channel combustor consistently yields shorter ignition times across all velocities (25.9–108.6 s) compared to the U-bend (52.6–145.2 s). The heterogeneous reaction contribution decreases with increasing inlet velocity for both designs, with the straight-channel maintaining higher values than the U-bend. The U-bend achieves higher maximum temperatures due to enhanced heat recirculation, particularly at high flow rates. The findings suggest that the U-bend configuration is advantageous for high-flow-rate applications requiring low ignition temperatures and high combustion temperatures, whereas the straight-channel design is preferable for rapid cold-start scenarios.

1. Introduction

Micro-combustors have attracted increasing attention as core components in portable power generation systems, including thermoelectric and thermophotovoltaic devices, as well as in small-scale reformers for hydrogen production [1,2,3,4]. Their ability to release chemical energy from hydrocarbon fuels within a compact volume makes them attractive alternatives to conventional batteries. However, the miniaturized dimensions introduce severe challenges for combustion. The high surface-to-volume ratio typical of micro-combustors leads to substantial heat losses to the surroundings [5,6], while the shortened flow residence time limits the extent of chemical reactions [4]. These factors collectively influence the ignition temperature, flame stability, and overall combustion efficiency [4]. Achieving reliable ignition and maintaining sustained combustion under such confined conditions remain critical research priorities.

In the context of hydrogen production for proton exchange membrane fuel cells, some studies have addressed the thermal limitations of packed catalyst bed reactors for methanol steam reforming (MSR). Wang et al. designed and compared four reactor configurations: concentric circle (MSRC), continuous catalytic combustion (MSRR), hierarchical catalytic combustion (MSRP), and segmented catalytic combustion with fins (MSRF) [3]. The results showed that MSRF exhibited the smallest maximum temperature difference (11.3 K), a 69.8% reduction in surface temperature inhomogeneity, and a 30.7% decrease in CO concentration compared with MSRC. Moreover, MSRF achieved higher methanol conversion and effective energy absorption rates than the other designs. The effects of methanol vapor molar ratio, inlet temperature, flow rate, catalyst particle size, and catalyst bed porosity were also discussed in the study, providing valuable design guidelines for improving the performance of MSRF. To further enhance reforming temperature performance, Zheng et al. proposed a trapezoidal cavity on the reforming chamber plate of an auto-thermal methanol steam reforming micro-reactor [7]. Numerical simulations revealed that an F-type trapezoidal cavity (50 mm × 76 mm, with 0.4 mm front depth and 0.2 mm back depth) minimized the reforming temperature difference. Compared to both non-optimized designs and those with optimal multiple micro-channels, the trapezoidal cavity design yielded better comprehensive hydrogen production performance. Even when scaled up, the design maintained high methanol conversion and hydrogen yield, albeit with increased CO selectivity. These findings underscore the importance of geometric optimization of flow channels in micro-reactors.

The role of physical obstructions such as baffles and blunt bodies in catalytic micro-combustors has also been systematically investigated. Lu et al. examined hydrogen/air premixed combustion in a planar micro-combustor with platinum-coated walls and inserted baffles [8]. The baffles significantly improved the transport of bulk species to the catalytic surface by increasing gas velocity between the baffle and catalytic surface, thereby enhancing the heterogeneous reaction rate and fuel conversion ratio. Through parametric optimization of slit width, rib length, inter-row distance, and number of rows (n), the optimal parameters were identified. The improvement was especially pronounced at high inlet velocities (7 m/s), and the baffle design proved effective for both rich and lean mixtures. Similarly, a subsequent study introduced a blunt body into a micro catalytic combustor operating with premixed hydrogen/air [9]. Blockage ratios ranging from 0.2 to 0.8 were evaluated at various inlet velocities. The results showed that the hydrogen conversion ratio increased progressively with blockage ratio up to 0.6, and the average inner wall temperature was positively affected at or below a blockage ratio of 0.6 but negatively affected at 0.8. Detailed field synergy analysis indicated that the overall synergy first increased and then decreased, peaking at a blockage ratio of 0.6. These results demonstrate that well-designed flow obstructions can significantly enhance mass and heat transfer by reducing boundary layer thickness near gas–solid interfaces.

A particularly interesting phenomenon—heterogeneous/homogeneous reaction coupling—was explored in a micro-channel with segmented platinum catalyst coating [10]. The numerical simulations revealed that at high velocities, an obvious demarcation line split the channel into a heterogeneous-reaction-dominated region and a homogeneous-reaction-dominated region, with a coupling zone extending 2 mm downstream of the catalytic region. Thermal and chemical analyses indicated that heat flux into the upstream catalytic wall came primarily from the exothermic heterogeneous reaction. A small portion of heat from the homogeneous reaction was fed back via the solid wall to the inlet. The fresh gaseous mixture in the channel is preheated by the heat fluxes from the gas–solid interface, which promotes the occurrence of homogeneous reaction and further increases both the heat release rate and the kinetic reaction rate of homogeneous reaction. This mutual enhancement improved overall hydrogen conversion, demonstrating that appropriately segmented catalyst coatings can synergistically combine surface and gas-phase reactions.

Ammonia as a carbon-free fuel has also been studied in micro-combustors. One numerical investigation focused on ammonia/oxygen premixed combustion in a baffled micro-burner [11]. Compared to conventional planar micro-burners, the addition of a baffle reduced channel temperature, radiation efficiency, and NO emissions. The optimum configuration—a baffle of length 5 mm and width 0.5 mm positioned 3 mm from the inlet—reduced NO mass fraction by 24.71%. These results indicate that baffles can simultaneously improve emission performance while moderating temperature extremes, although at the cost of lower radiation efficiency.

Our research group has recently conducted systematic studies on the effects of catalytic activity on ignition characteristics in propane-fueled micro-reactors [12,13]. The simulation results indicate that, in a straight-channel Pt-catalyzed micro-reactor for SOFC preheating, the relative catalyst activity range of 0–2 was identified as highly sensitive, yielding a 541 K reduction in ignition temperature and a 50% decrease in ignition delay time. Further increasing activity from 2 to 10 produced only minor gains. The heterogeneous reaction (HTR) contribution to total heat release decreased with higher feed temperature but increased with higher catalytic activity. In a U-bend Pt-catalyzed micro-reactor, it was found that increasing the surface area factor from 0.425 to 3.4 significantly reduced the ignition temperature (from 682 K to 521 K) and ignition delay time (from 147 s to 52 s), while the HTR contribution increased from 26.1% to 65.5%. Beyond a factor of 3.4, further improvements became marginal. Temporally, catalytic reactions dominated the preheating stage, whereas gas-phase reactions became significant after ignition in both configurations. However, those two studies focused respectively on straight-channel and U-bend micro-reactors, without directly comparing their ignition and combustion characteristics under equivalent catalytic activity conditions.

While numerous studies have been conducted, most have examined each reactor configuration in isolation, offering limited comparative data under the same operating conditions. Specifically, a systematic comparison of ignition and combustion characteristics between straight-channel and U-bend micro catalytic combustors across a range of inlet velocities remains lacking. The present study addresses this gap by numerically comparing ignition behavior, including ignition temperature, ignition delay time, maximum combustion temperature, heterogeneous reaction contribution, and thermal/species field distributions, in straight-channel and U-bend Pt-catalyzed micro-combustors at various inlet velocities.

2. Results and Analysis

Steady-state simulations, with an initial feed temperature of 300 K, are first performed to determine the ignition temperatures of propane/air mixtures across a range of inlet velocities. Subsequently, transient simulations are conducted with feed temperatures set 10 K above the obtained ignition temperatures—a slight superheat that reflects the practical safety margin and preheating stage used to ensure reliable ignition.

2.1. Determination of Ignition Temperature

Figure 1 illustrates the variation of maximum temperature within straight and U-bend micro-combustors as a function of feed temperature under inlet velocities of 2 m/s and 4 m/s. A distinct thermal bifurcation is evident for each operational condition. Below a critical threshold, the maximum temperature remains little or no rise above the inlet temperature, simply tracking closely with the inlet temperature (e.g., remaining near 500 K when the feed temperature is set to 500 K). Upon reaching this critical point, the combustor’s thermal behavior undergoes a sharp transition; for instance, at 2 m/s in the U-bend microreactor, increasing the inlet temperature to 570 K triggers a dramatic surge in the maximum temperature to 1629 K. This abrupt rise signifies successful ignition. Thus, the ignition temperature is defined as the critical feed temperature below which the maximum temperature remains close to the inlet temperature, and at or above which the maximum temperature experiences a sharp rise. Furthermore, the data in the figure reveals a clear linear correlation between the maximum temperature and the inlet temperature in the post-ignition regime (i.e., for inlet temperatures at or above the ignition value). At an inlet velocity of 4 m/s, the U-bend microreactor demonstrates better performance than the straight-channel microreactor, characterized by both a reduced ignition temperature (546 K, compared to 556 K) and a higher maximum temperature (1655 K, versus 1457 K).

2.2. Comparison of Ignition Temperature Between Straight-Channel and U-Bend Microreactors at Varying Inlet Velocities

Figure 2 illustrates the ignition temperatures of straight-channel and U-bend micro-combustors as a function of inlet velocity, ranging from 0.25 m/s to 8 m/s. The blue triangles represent the straight-channel combustor, while the red squares denote the U-bend heat-recirculating design. Several key observations can be made from the figure. First, both combustors exhibit a monotonic decrease in ignition temperature as the inlet velocity increases from 0.25 to 8 m/s. This trend is attributed to the higher reactant throughput at elevated velocities, which enhances the power input and helps overcome heat losses, thereby facilitating earlier light-off. Second, and more importantly, a clear crossover in relative performance is observed depending on the flow regime. At low inlet velocities (≤2 m/s), the straight-channel combustor demonstrates a lower ignition temperature than the U-bend counterpart. For example, at 0.5 m/s, the ignition temperatures are 606 K for the straight channel and 636 K for the U-bend. Conversely, at high inlet velocities (≥4 m/s), the U-bend microreactor exhibits a distinct advantage, with consistently lower ignition temperatures compared to the straight channel. At 8 m/s, the ignition temperature of the U-bend is around 526 K, while that of the straight channel remains near 555 K. This reversal in behavior can be explained by the role of heat recirculation. At low flow rates, the reaction zone resides near the inlet, leaving little opportunity for transverse heat transfer across the dividing wall to preheat the incoming reactants. In fact, the initially cold recirculation channel may even act as a heat sink, delaying ignition in the U-bend. However, at higher flow rates, the increased axial velocity pushes the reaction zone downstream. In the straight channel, this leads to back-end ignition and a rising ignition temperature due to insufficient preheating. In contrast, the U-bend geometry benefits from enhanced heat recirculation under such conditions: the hot exhaust gases in the recirculating channel transfer heat transversely across the dividing wall, effectively preheating the incoming cold reactants. This counter-current heat exchange provides an “excess enthalpy” effect, enabling a lower thermal input for ignition. The transition from 2 m/s to 4 m/s, thus, represents a critical window in which the U-bend geometry changes from functioning as a heat sink to acting as a heat recirculator. Overall, the results demonstrate that the U-bend combustor is particularly advantageous for high-flow-rate applications, whereas the straight channel may be more suitable for low-flow conditions where simplicity outweighs the benefits of heat recirculation.

2.3. Comparison of Maximum Combustion Temperature Between Straight-Channel and U-Bend Microreactors at Varying Inlet Velocities

Figure 3 presents the variation of the maximum combustion temperature with inlet velocity for both combustor types. As the inlet velocity increases from 0.25 m/s to 8 m/s, the U-bend and straight-channel combustors exhibit the same qualitative trend: the maximum temperature rises with increasing inlet velocity. More specifically, in the straight-channel combustor, the maximum combustion temperature rises from 945 K at an inlet velocity of 0.25 m/s to 1441 K at 2 m/s, and further reaches 1474 K at 8 m/s. In the U-bend combustor, the corresponding values increase from 990 K at 0.25 m/s to 1645 K at 2 m/s, and subsequently to 1726 K at 8 m/s. Notably, the temperature rises sharply in the low-velocity range, whereas the increase becomes much more gradual at high velocities. This behavior can be explained by the fact that a higher inlet velocity corresponds to a larger mass flow rate, which delivers more reactants into the combustor. This enhanced reactant supply facilitates the accumulation of exothermic heat, making it easier to reach ignition conditions. In addition, for a given inlet velocity, the maximum combustion temperature of the U-bend combustor exceeds that of the straight-channel combustor. This is attributed to the stronger thermal recirculation in the U-bend configuration, which enhances the preheating of the fresh reactants before they enter the main reaction zone.

2.4. Comparison of Temperature Distribution Between Straight-Channel and U-Bend Microreactors

Figure 4 presents the temperature distributions within both combustors at various inlet velocities. Owing to the slender geometry of the combustors, the aspect ratio has been adjusted in the plots to enhance visual clarity. For both configurations, the combustion zone shifts progressively downstream as the inlet velocity increases. At a low inlet velocity of 0.25 m/s, the combustion zone resides near the inlet. At a high velocity of 8 m/s, however, it migrates downstream to the rear half of the channel.

This downstream shift arises because ignition requires a “hot start”. Although the incoming gas is preheated to a temperature only 10 K above the ignition threshold, this refers exclusively to its thermal state. The initial wall temperature is 300 K; thus, the fresh gas is immediately cooled upon entering the cold inlet section. To establish stable surface reactions, the wall must first be heated to its light-off temperature, and the gas must remain sufficiently hot upon reaching that location. As gas velocity increases, the residence time in the inlet region decreases. Consequently, ignition conditions cannot be satisfied near the entrance. The cold gas must travel further downstream, continuously extracting heat from the wall—which has been progressively warmed by weak reactions occurring upstream. Eventually, at a certain downstream position, the wall temperature reaches the light-off point and the local gas temperature exceeds the ignition threshold. It is at this location that the main reaction zone establishes itself.

2.5. Comparison of Propane Mass Fraction Distribution Between Straight-Channel and U-Bend Microreactors

Figure 5 shows the axial distribution of propane mass fraction in the two combustors at different inlet velocities. Both combustors exhibit the same qualitative trend. Near the inlet, the propane mass fraction remains almost unchanged and close to the inlet value, indicating the region where no ignition has occurred. Further downstream, the propane mass fraction begins to decrease sharply, marking the onset of ignition. As the inlet velocity increases, the location where propane is completely depleted shifts progressively downstream, reaching up to $x=0.02$ m at an inlet velocity of 8 m/s. At the same time, a higher inlet velocity also broadens the propane consumption zone—that is, the axial distance over which the propane mass fraction drops from 0.43 to zero becomes longer. Compared to the straight-channel combustor, the U-bend design achieves propane depletion at a location nearer to the inlet, indicating that the main combustion zone is situated further upstream.

2.6. Comparison of Ignition Delay Time Between Straight-Channel and U-Bend Microreactors at Varying Inlet Velocities

Figure 6 presents the cold-start ignition delay times for straight-channel and U-bend micro-combustors over an inlet velocity range of 0.25 to 8 m/s. Here, the ignition delay time is defined as the time from the start of cold-state operation to the moment when the fuel mass fraction at the outlet drops to 50% of that at the inlet. Evidently, the two geometries exhibit fundamentally different trends. The straight-channel combustor shows a strictly monotonic decreasing ignition time with increasing velocity, dropping from 108.6 s at 0.25 m/s to 25.9 s at 8 m/s. This trend reflects the dominant role of increased thermal power input at higher flow rates: more fuel per unit time leads to faster heat release and more rapid attainment of ignition conditions. The U-bend combustor, however, displays a non-monotonic pattern. Ignition time decreases from 145.2 s at 0.25 m/s to a minimum of 57.6 s at 2 m/s, then increases sharply to 79.0 s at 4 m/s, before decreasing again to 52.6 s at 8 m/s. The initial decrease (0.25–2 m/s) is consistent with the power-input effect observed in the straight channel. The straight channel consistently achieves lower ignition times than the U-bend across the entire velocity range, indicating that for rapid start-up applications, the simpler straight-channel design may be preferable, even if it requires a slightly higher ignition temperature at high flow rates.

2.7. Comparison of HTR Contribution Between Straight-Channel and U-Bend Microreactors at Varying Inlet Velocities

The relationship between HTR contribution and inlet velocity is illustrated in Figure 7. Here, HTR denotes the heterogeneous catalytic reaction. Its contribution ratio is defined as the amount of fuel consumed by catalytic reactions divided by the total fuel consumed. This ratio, thus, quantifies the relative importance of the catalytic pathway versus the gas-phase homogeneous pathway. In other words, it measures how dominant the catalytic route is over the gas-phase homogeneous reaction. HTR contribution is associated with the overall combustion characteristics, such as peak combustion temperature. For both combustor types, the HTR contribution decreases with increasing inlet velocity, with greater sensitivity at lower velocities—particularly between 0.25 and 1 m/s. Across the tested inlet velocity range, the straight-channel combustor shows a consistently higher HTR contribution than the U-bend design. At 8 m/s, the U-bend combustor reaches its lowest HTR contribution at about 52%, whereas the straight-channel combustor has a minimum of 69%. This difference stems from the preheating effect inherent to the U-bend geometry. Regardless of whether the inlet velocity is low or high, the U-bend combustor achieves a higher maximum temperature than the straight-channel one. This finding agrees with the principle that a greater share of catalytic reaction pathways in a coupled homogeneous–heterogeneous combustion system tends to lower the peak combustion temperature.

3. Mathematical Model

3.1. Model Description

The physical models considered in this study include a straight-channel micro-combustor and a U-bend micro-combustor, as illustrated schematically in Figure 8. Both devices share an overall length of 40 mm and a wall thickness of 0.2 mm. In each combustor, the initial 1 mm of the channel inner wall is devoid of catalyst coating, while the subsequent 39 mm is coated with Pt/Al₂O₃ catalyst. The width of the flow passage is uniformly 0.6 mm. The U-bend configuration consists of two channels that direct the flow in opposite directions. The downstream 20 mm-long channel serves as a recirculating channel. To ensure identical catalyst loading between the two combustors, the recirculating channel is left uncoated with catalyst.

It should be noted that the zero-thickness wall reaction model is justified for our configurations because the catalyst layer is very thin (typically tens of micrometers), resulting in an extremely short diffusion distance. Accordingly, the reaction operates under kinetic control, as reactants can readily access all active sites without significant intra-layer diffusion resistance, and the temperature gradient across the layer remains negligible. However, it is important to acknowledge that these assumptions may break down for thicker catalyst coatings. Therefore, the key limitation of the model lies in its inability to account for concentration or temperature gradients within an actual porous coating. Should such gradients become non-negligible, the model would over predict the apparent reaction rate and fail to capture the true utilization of the catalyst interior.

Prior to formulating the governing equations, the following assumptions are adopted:

• The width of the reaction channel is sufficiently large compared to its height such that any gradient along the width direction is negligible, thereby allowing a two-dimensional modeling approach.
• The flow in the microchannel is laminar.
• The gas mixture behaves as an ideal gas.
• Gas-phase radiation is neglected due to the small optical thickness.

The governing equations include the continuity equation, the momentum conservation equation, the energy conservation equation, and the species conservation equation.

Continuity equation:

$${\displaystyle \frac{\partial {\rho }_{\mathrm{g}}}{\partial t}}+\nabla ·\left({\rho }_{\mathrm{g}}V\right)=0$$

(1)

Momentum conservation equation:

$${\displaystyle \frac{\partial \left({\rho }_{\mathrm{g}}V\right)}{\partial t}}+\nabla ·\left({\rho }_{\mathrm{g}}VV\right)=-\nabla P+\nabla ·\mu \left[\left(\nabla V+{(\nabla V)}^T-{\displaystyle \frac{2}{3}}(\nabla ·V)I\right)\right]$$

(2)

Energy conservation equation for gas phase:

$${\displaystyle \frac{\partial \left({\rho }_{\mathrm{g}}{h}_{\mathrm{g}}\right)}{\partial t}}+\nabla ·\left({\rho }_{\mathrm{g}}{h}_{\mathrm{g}}V\right)=\nabla ·\left({\lambda }_{\mathrm{g}}\nabla T-{\displaystyle \sum _i^{n_{\mathrm{gpc}}}}{h}_i{J}_i\right)+{\displaystyle \sum _i^{n_{\mathrm{gpc}}}}{h}_i{R}_i^{\mathrm{gas}}$$

(3)

Energy conservation equation for solid phase:

$${\displaystyle \frac{\partial \left({\rho }_{\mathrm{s}}{h}_{\mathrm{s}}\right)}{\partial t}}=\nabla ·\left({\lambda }_{\mathrm{s}}\nabla T\right)$$

(4)

Species conservation equation:

$${\displaystyle \frac{\partial \left({\rho }_{\mathrm{g}}{Y}_i\right)}{\partial t}}+\nabla ·\left({\rho }_{\mathrm{g}}{Y}_{i}V+J_i\right)=R_i^{\mathrm{gas}}$$

(5)

The overall chemical equation for the oxidation reaction of propane is as follows:

$${\mathrm{C}}_3{\mathrm{H}}_8+5{\mathrm{O}}_2\to 3{\mathrm{CO}}_2+4{\mathrm{H}}_2\mathrm{O}$$

(6)

The chemical kinetic rate for the volumetric gas-phase reaction of propane is as follows [14]:

$$r_{\mathrm{homo}}=4.836\times {10}^9{\mathrm{e}}^{\left(-{\displaystyle \frac{1.256\times {10}^8}{RT}}\right)}{c}_{{\mathrm{C}}_3{\mathrm{H}}_8}^{0.1}{c}_{{\mathrm{O}}_2}^{1.65}$$

(7)

The chemical kinetic rate for the surface catalytic reaction of propane is as follows [15]:

$$r_{\mathrm{hete}}={\displaystyle \frac{\eta k_{{\mathrm{C}}_3{\mathrm{H}}_8}^{\mathrm{ads}}{X}_{{\mathrm{C}}_3{\mathrm{H}}_8}}{{\left(1+\sqrt{\frac{k_{{\mathrm{O}}_2}^{\mathrm{ads}}{X}_{{\mathrm{O}}_2}}{k_{{\mathrm{O}}_2}^{\mathrm{des}}}}\right)}^2}}$$

(8)

where $k^{\mathrm{ads}}$ and $k^{\mathrm{des}}$ are computed by the following expressions:

$$k_i^{\mathrm{ads}}={\displaystyle \frac{s_i{P}_{\mathrm{tot}}{\mathrm{e}}^{-E_{\mathrm{a},i}^{\mathrm{ads}}/RT}}{\mathrm{\Gamma }\sqrt{2\pi M_{i}RT}}}{\left({\displaystyle \frac{T}{T_{\mathrm{ref}}}}\right)}^{{\beta }_i^{\mathrm{ads}}}$$

(9)

$$k_i^{\mathrm{des}}=A_i{\mathrm{e}}^{-E_{\mathrm{a},i}^{\mathrm{des}}/RT}{\left({\displaystyle \frac{T}{T_{\mathrm{ref}}}}\right)}^{{\beta }_i^{\mathrm{des}}}$$

(10)

where $E_{{\mathrm{O}}_2}^{\mathrm{des}}$ is computed by the following polynomial:

$$E_{{\mathrm{O}}_2}^{\mathrm{des}}=0.126T_{\mathrm{r}}^4-1.849T_{\mathrm{r}}^3+9.142T_{\mathrm{r}}^2-13.253T_{\mathrm{r}}+23.903$$

(11)

where $T_{\mathrm{r}}=T/T_{\mathrm{ref}}$ denotes the temperature ratio.

A description of each symbol appearing in the above equations is provided in

Table 1. Nomenclature.

Symbol	Description
$A_i$	Pre-exponential factor
c	Molar concentration
$E_{\mathrm{a},i}^{\mathrm{ads}},E_{\mathrm{a},i}^{\mathrm{des}}$	Activation energy for adsorption/desorption
$E_{{\mathrm{O}}_2}^{\mathrm{des}}$	Activation energy of oxygen desorption
$h_{\mathrm{g}}$	Gas enthalpy
$h_{\mathrm{s}}$	Solid enthalpy
$J_i$	Diffusion flux of the i-th component
$k^{\mathrm{ads}}$	Adsorption rate constant
$k^{\mathrm{des}}$	Desorption rate constant
$M_i$	Molecular weight of species i
$n_{\mathrm{gpc}}$	Number of gas phase components
P	Pressure
R	Ideal gas constant
$R_i^{\mathrm{gas}}$	Generation rate of the i-th component
$r_{\mathrm{homo}}$	Homogeneous reaction rate
$r_{\mathrm{hete}}$	Heterogeneous reaction rate
$s_i$	Sticking coefficient
T	Temperature
$T_{\mathrm{r}}$	Temperature ratio $T/T_{\mathrm{ref}}$
$T_{\mathrm{ref}}$	Reference temperature
V	Velocity vector
X	Mole fraction
$Y_i$	Mass fraction of the i-th component
${\beta }_i^{\mathrm{ads}},{\beta }_i^{\mathrm{des}}$	Temperature exponent for adsorption/desorption
$\eta$	Surface area factor
$\mathrm{\Gamma }$	Active site density of the catalyst
${\lambda }_{\mathrm{g}}$	Gas thermal conductivity
${\lambda }_{\mathrm{s}}$	Solid thermal conductivity
$\mu$	Dynamic viscosity
${\rho }_{\mathrm{g}}$	Gas mixture density
${\rho }_{\mathrm{s}}$	Density of the solid wall

.

3.2. Meshing, Boundary Conditions, Physical Properties, and Solution Strategy

Mesh generation is performed in ANSYS ICEM CFD. The straight-channel micro-combustor features a symmetric geometry; therefore, half of it is taken as the computational domain. A uniform grid consisting of 50,000 square cells is adopted for the straight-channel configuration, and 180,000 square cells for the U-bend micro-combustor (0.02 mm cell size). Grid independence tests confirmed that such mesh density provides sufficient computational accuracy.

The computational domain is assigned the following boundary conditions. A fixed flat profile is prescribed at the inlet for the velocity, species mass fractions, and temperature. It is emphasized that, in this work, inlet velocity refers to the velocity under standard conditions. The incoming gas is a mixture of propane and air (21% O₂, 79% N₂ by volume) at an equivalence ratio of 0.7 (corresponding to a molar ratio of O₂ to C₃H₈ of 7.1). At the outlet, a pressure boundary condition of 1 atm is imposed. The outer walls are treated with a mixed thermal boundary condition that accounts for both convection (with a heat transfer coefficient of $20{\mathrm{W}/(\mathrm{m}}^2·\mathrm{K})$ and a free-stream temperature of 300 K) and radiation (with an emissivity of 0.5 and an ambient temperature of 300 K). For the inner walls, a no-slip condition is applied along with a coupled thermal boundary condition to allow conjugate heat transfer between the fluid and solid regions.

The solid wall is modeled with constant material properties. The reference case involves a low-thermal-conductivity substance (e.g., ceramics), characterized by a thermal conductivity of $k_{\mathrm{w}}=2\mathrm{W}/(\mathrm{m}·\mathrm{K})$ and a volumetric heat capacity of ${\rho }_{\mathrm{w}}{c}_{\mathrm{w}}=2800\times 900{\mathrm{J}/(\mathrm{m}}^3·\mathrm{K})$. Regarding the gas-phase mixture, thermal conductivity and viscosity are derived through mass-weighted averaging, while the transport properties (thermal conductivity, viscosity, diffusivity) of individual species are evaluated using kinetic theory. Piecewise polynomial functions are used to compute species-specific heat capacities, and a mixing law is implemented to calculate the mixture’s specific heat.

This study uses ANSYS Fluent 14.0 [16] as the CFD solver. A user-defined function (UDF) implements the heterogeneous reaction kinetics. Convection terms are discretized with a second-order upwind scheme, and pressure-velocity coupling is handled by the SIMPLE algorithm. A time-step sensitivity analysis demonstrates that a time step of 0.01 s gives sufficient accuracy. Solution convergence is confirmed through residual checks, flux balances, and monitor stability. The residual thresholds for convergence are ${10}^{-8}$ for the energy equation, and ${10}^{-4}$ for all other equations.

3.3. Model Validation

The present model is validated against the experimental data of Lu et al. [17] for a representative case with an inlet velocity of 0.3 and an equivalence ratio of 1.0. Figure 9 shows a comparison of the predicted and measured axial wall temperature distributions. The simulation reproduces the experimental trends well, particularly the location at which the peak temperature appears. The maximum absolute difference across matching points is 27 K, corresponding to a relative error of approximately 3.1%. These minor discrepancies likely arise from simplifications in the model, including a one-step global reaction scheme, which tends to overestimate flame temperatures, and the omission of porous catalyst coating geometry. Given the low error margin, the computational framework—including its chemical kinetics and physical assumptions—is considered sufficiently accurate for subsequent simulations of combustion behavior within the catalytic microreactor.

4. Conclusions

This numerical study provides a comparative analysis of the ignition and combustion characteristics in straight-channel and U-bend catalytic micro-combustors, with a particular emphasis on the role of inlet velocity. The key findings can be summarized as follows:

• The relative ignition advantage between the two configurations depends strongly on the flow regime. The straight-channel combustor exhibits lower ignition temperatures at low inlet velocities (≤2 m/s), while the U-bend design demonstrates superior ignition performance at high velocities (≥4 m/s), achieving an ignition temperature as low as 526 K at 8 m/s compared to 555 K for the straight-channel counterpart.
• Despite its higher ignition temperatures at elevated flow rates, the straight-channel combustor consistently yields shorter ignition times (25.9–108.6 s) across the entire velocity range tested, in contrast to the U-bend design (52.6–145.2 s). This suggests that the straight-channel configuration is more favorable for rapid cold-start applications where minimizing time to light-off is critical.
• The U-bend combustor achieves higher maximum combustion temperatures under high-velocity conditions (1726 K vs. 1474 K at 8 m/s), attributable to improved heat recirculation with the uncoated recirculating channel. However, this benefit is accompanied by a reduced heterogeneous reaction contribution compared to the straight-channel design across all velocities.
• The U-bend configuration is advantageous for high-flow-rate applications requiring low ignition temperatures and high sustained combustion temperatures, whereas the straight-channel design is preferable for scenarios demanding rapid ignition, such as cold-start conditions in portable power systems.

The present study is limited to a fixed set of geometric parameters and operating conditions. Future work should systematically investigate the effects of additional parameters, including the recirculation channel gap size and the equivalence ratio, to further extend the comparative findings under broader design and operating envelopes. In addition, while the current simulations were performed with propane-air mixtures, systematic variation of the oxygen concentration remains an important direction for future research to further understand the role of oxidizer composition in catalytic micro-combustion.