A 3D CFD study of homogeneous-catalytic combustion of hydrogen in a spiral microreactor

Combustion and Flame 206 (2019) 441–450

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A 3D CFD study of homogeneous-catalytic combustion of hydrogen in a spiral microreactor Neha Yedala, Aswathy K. Raghu, Niket S. Kaisare∗ Department of Chemical Engineering, Indian Institute of Technology Madras, Chennai 600036, India

a r t i c l e

i n f o

Article history: Received 19 September 2018 Revised 26 November 2018 Accepted 15 May 2019

Keywords: Spiral microreactor Pt catalyst Homogeneous-catalytic combustion Hydrogen–air Co-current heat recirculation

a b s t r a c t A spiral microreactor is analyzed for combustion of hydrogen on Pt catalyst using 3D computational fluid dynamics (CFD) simulations with detailed mechanisms for both catalytic and gas phase reactions. A spiral microreactor comprises of a single channel that is curled-up in a spiral, starting at the center and spiraling outwards. A comparison of the spiral with a conventional straight-channel reactor is presented. Maximum temperature attained in the spiral microreactor, investigated for equivalence ratios within the range of 0.3 to 0.65 under non-adiabatic conditions (with heat losses by convection and radiation), is found to be greater than the adiabatic flame temperatures. Comparison with a straight-channel reactor of equivalent dimensions shows higher temperature and higher contribution of homogeneous chemistry in the spiral microreactor. The nature of homogeneous reactions in the presence of catalytic micro reactor is presented. Combustion characteristics presented herein indicate that the preheating of reactants and protection of reaction zone in the spiral reactor make it superior to the straight channel reactor. The effect of inlet velocity is presented and the effect of heat recirculation on homo-catalytic interactions is analyzed. © 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

1. Introduction Combustion of high energy density fuels, such as hydrogen and hydrocarbon, in micro-scaled devices gained importance due to their potential application in portable and light-weight devices in niche areas [1–3]. Recent reviews highlight certain theoretical and practical challenges in micro-combustion [1–3]. Being subjected to thermal and radical quenching, homogeneous combustion is difficult to sustain in micro-channels. Thermal quenching occurs due to high heat dissipation and radical quenching due to recombination of active combustion carriers at the micro-channel walls. Catalytic combustion in micro-channels, on the other hand, is promoted due to higher surface area and shows broader stability limits [4], ignition at lower temperatures [5], suppression of the flame instabilities [6] and a few more [7,8]. Indeed, catalyst can also aid flame stabilization in channels and, hence, sustain combustion even in presence of higher heat losses [9,4]. It is well-known that microreactor walls play a dual role: they are major heat loss components in straight channels, but are also useful in stabilizing combustion since heat gets transferred to the preheating zone due to conduction through the walls [4,10– 12]. Ronney [13] used a simplified model to demonstrate the im-

∗

Corresponding author. E-mail address: [email protected] (N.S. Kaisare).

portance of walls in stabilizing combustion. Schoegl and Ellzey [14] showed that in co-current geometry (with multiple channels), axial heat transfer through the walls is responsible for stabilizing combustion. However, heat loss through the walls also makes straight channel microreactors susceptible to quenching under certain conditions, such as low/high flowrates or fuel lean operation. Some approaches for improving combustion characteristics of the straight-channel microreactor further include: better heat recirculation, protecting the reaction zone from heat losses, and promoting combustion chemistry [1,2]. Heat recirculation refers to utilizing the “excess enthalpy” of the combustion products by heat transfer to preheat the incoming feed in an adjacent channel [15– 18]. In some of the heat recirculating geometries, such as Swiss roll [17] and serpentine [19], the peripheral channels protect the inner reaction zone from heat losses. Catalyst can be selectively placed in some of the channels of a multi-channel catalytic monolith, thereby protecting the central channels from heat losses [20,21]. A transient analysis revealed that high temperatures can be limited to inner non-catalytic channels of a partially-coated monolith by confining homogeneous ignition [21]. In another simulation study, using channels with square cross-section was shown to delay blowout [22], which was attributed to accumulation of heat in the corners due to the recirculation zones formed in these channels. Finally, new catalysts can alter the catalytic chemistry [20,23], whereas interaction between homo-/catalytic mechanisms

https://doi.org/10.1016/j.combustflame.2019.05.022 0010-2180/© 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.

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Fig. 1. Schematic of the three-turn spiral microreactor simulated in this work. The fluids enter at the center, normal to the circular face of the microreactor and spiral towards the outlet at the periphery of the microreactor. The dark shade traces the fluid path, light shade depicts the sold wall and arrows indicate the flow direction.

has been exploited to improve combustion behavior, such as selective catalyst placement, catalytically stabilized combustion [24] and catalyst segmentation [25,26]. Jones et al. [16] proposed several geometries for combustion in heat exchangers, for conventional (large-sized) systems. Many heat recirculating geometries have been investigated in microreactors, such as Swiss roll [17], U-bend [18,19], serpentine [19], etc., as well as heat recuperative reverse-flow micro-reactor [27], have been analyzed. Federici and Vlachos [28] showed that a heat recirculation reactor, where the product gases are circulated on either side of the combustion channel, could sustain combustion with higher critical heat transfer coefficients. Taywade et al. [29] used a similar concept for heat recirculation, within a stepped microreactor. Ronney [13] compared stability of a 2D counter current reactor with a conductive tube having the reaction zone at the exit of the reactor. Wall acts as heat recirculating element in the conductive tube whereas the exit channel aids heat recirculation in counter current reactor. Swiss roll (micro-)reactor has been extensively studied [48,30,31]. Maruta and coworkers [30,31] showed that the number of turns of a Swiss roll can be varied to manipulate heat recirculation independent of the combustion zone. Ronney [48] showed that a Swiss roll may be considered as a sequence of U-bend reactors, with central combustion zone. The transfer of excess enthalpy in all the above reactors occurs between adjacent channels with counter-current flow. In our recent work, a novel spiral geometry was analyzed for catalytic combustion of propane using 2D CFD simulations [32]. Unlike Swiss roll (which is a double spiral geometry), the focus of this work is a single spiral geometry. The spiral micro-reactor may be imagined as a straight channel that is curled up to form a spiral, with reactants entering at the center of the spiral, flowing outwards in one direction and exiting from the periphery (see the single spiral geometry in Fig. 1). Schoegl and Ellzey [14] argue that unlike counter-current U-bend or Swiss roll geometries, heat recirculation in co-current flow geometry is only possible due to heat conduction via the walls. Similar observations were made by Zuo et al. [33] as well. While counter-current heat exchangers are more efficient in excess enthalpy combustion, Weinberg and coworkers [16] proposed several co-current excess enthalpy geometries for large-sized combustors. The single-spiral is perhaps one of the unique microreactor geometries since heat recirculation is achieved with co-current heat exchange between adjacent channels. We showed in [32] that

for propane/air combustion considering purely catalytic chemistry (ignoring homogeneous reactions), spiral microreactor is more stable towards blowout and extinction than the conventional straightchannel setup for lean propane-air combustion, for a wide range of operating parameters examined. Our previous work on spiral microreactor used 2D CFD simulations with single-step catalytic chemistry of propane. But, combustor performance and stability is dependent on out of plane heat losses as well. Hence, heat losses in the third dimension (i.e., top and bottom cover-plates of the microreactor) should also be included. Although empirical equations have been used to model out of plane heat loss in 2D simulations of Swiss roll microburners [34], a fully 3D model [35] more reliable captures the effect of the third dimension. Hence, in this work, we model the full 3D single-spiral microreactor geometry. Furthermore, since the gap size of the channel is 1 mm and the microreactor is expected to reach high temperatures, homogeneous chemistry should also be included [36,37]. Homogeneous and catalytic chemistries for hydrogen–air combustion have been well-investigated [6,9,24,25], including for multi-fuel case [7,38,39] and ignition [40]. Therefore, the spiral geometry has been modeled in 3D (with top and bottom covers in the Z direction) and compared with straight channel to understand the combustion characteristics of fuel lean hydrogen– air mixtures, with detailed homogeneous and catalytic chemistries. The features of combustion in a spiral microreactor at various inlet velocities and equivalence ratios are compared with an equivalent straight channel microreactor. 2. Methodology A spiral microreactor is modeled using 3D CFD, with detailed gas-phase and catalytic combustion chemistry, for fuel-lean combustion of hydrogen. The spiral microreactor consists of a single channel with internal walls coated with Pt catalyst, with inlet at the center and the flow channel spiraling outward into turns, as shown in Fig. 1. It is covered by top and bottom plates (not marked in the schematic) on either side in the third dimension. Premixed hydrogen–air mixture enters the reactor at the center vertically and spirals outward exiting the reactor through the outer turn tangentially. As indicated by curved arrows in Fig. 1, the flow in the adjacent channels occurs in co-current direction. The inlet section is non-catalytic; flow straighteners present in this region prevent occurrence of homogeneous reactions as well. The spiral channel itself is of a rectangular cross-section of 1-mm × 4-mm dimension. The total axial length of the three-turn spiral reactor, as measured at the centerline, is 48.3 mm. All solid walls are 0.5 mm thick, including the top and bottom cover-plates. For comparison, an equivalent straight-channel microreactor (with 1 mm gap-size, 4 mm deep and 48.3 mm long), consisting of two Pt-coated parallel plates, is also simulated. The flow channel in this case also has a rectangular cross-section of 1 mm × 4 mm. One half of the straight channel is modeled due to the symmetry about the longitudinal plane. The inlet flowrate of the fuel mixture is maintained same for both the geometries for a fair comparison. The three-turn spiral geometry was created in FLUENT and meshed into structured grid with 3D hexahedrons all over the computational domain that includes fluid, walls and covers. Steady-state mass, momentum, energy and species conservation equations are solved in 3D using ANSYS FLUENT 17.2 with SIMPLE algorithm, with uniform mesh spacing and second-order upwind discretization. We verified grid independence of solutions for both spiral and straight-channel geometries for certain representative conditions, as shown in Appendix C. The fluid is modeled as an ideal gas, and the multi-component and Soret diffusion effects are included. The mixture properties, such as thermal conductivity and viscosity, are computed as mass averaged; thermal

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conductivity, viscosity and diffusivity coefficients of each species are estimated by kinetic theory; piecewise polynomials are used to calculate species specific heats; and mixing law is employed to calculate specific heat of the mixture. Thermal conductivity of the solid is assumed to be constant and is taken as 1 W/m/K, which is of the order of ceramics. Since heat recirculation benefits more at lower wall thermal conductivities [28,34], this value of conductivity is chosen to facilitate a comparison and better highlight the significance of transverse heat transfer in spiral microreactor for this investigation. Detailed kinetic mechanisms are employed for gas and surface reactions. The gas phase mechanism of hydrogen combustion of Chattopadhyay and Veser [41] (which is a subset of GRIMech 3.0 mechanism) and the surface reaction mechanism on Pt of Deutschmann et al. [42], written in CHEMKIN formats are imported to the solver to simulate the reacting flows. The detailed mechanisms are summarized in Appendix A. The inlet flowrates considered in this study, 0.048–2.4 standard liters per minute (slpm), are in the laminar range. This corresponds to inlet velocity in the range 0.2–10 m/s in the straight-channel geometry. In order to aid comparison with prior work in the literature, results are presented in terms of inlet velocity of the corresponding straight-channel reactor [4,10,43–45]. The reactants enter the reactor with a flat velocity profile, at appropriate inlet velocity, hydrogen–air equivalence ratio (in the range 0.3–0.75) and uniform temperature of 300 K. The reactor outlet is at 1 bar pressure. No slip is applied on the solid–fluid interface. The outer walls (including top and bottom covers) lose heat to the ambient by convection (heat loss coefficient, h∞ = 15 W/m2 K) and radiation (ε = 0.5). The governing equations, along with the boundary conditions, are solved until the residuals fall below 10–6 , mass-weighted average temperature and OH mass fraction at different planes in the geometry remain constant over several thousand iterations and overall mass and energy fluxes converge within 0.1% of the lowest flux. This procedure is applied to both spiral and straight-channel geometries. Prior to further simulations, grid-independence of the solutions was ensured for several cases of interest. 3. Results and discussions In the sections that follow, homogeneous-catalytic combustion of hydrogen/air mixtures in a spiral microreactor is analyzed. We investigate the homo-hetero reactions in the presence of heat recirculation in the spiral microreactor and compare it with the straight channel reactor which does not exhibit heat recirculation in transverse direction. 3.1. Comparison with straight channel Figure 2 shows the temperature of the inner wall vs. dimensionless axial distance for the spiral and straight-channel micro-reactors for equivalence ratio of 0.65 and inlet flowrate of 0.48 slpm (corresponds to an inlet velocity of 2 m/s in the straight channel). Figure 2 is plotted for middle plane in the 3D geometry, though the results are similar for other planes as well. The vertical lines in the figure demarcate each turn in the spiral microreactor. The reaction zone is located close to the inlet for both the geometries, as is expected at this moderate velocity. The maximum temperature occurs in the gas-phase close to the inner wall for homo-catalytic case, which is due to the synergy provided by catalytic reactions to homogeneous combustion. Clearly, temperatures attained in the spiral microreactor are greater than that in the straight channel reactor. The higher temperature in the spiral may be attributed to better protection of the reaction zone from heat losses by the peripheral channels and improved preheating of the cold inlet due to transfer of excess enthalpy from adjacent

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Fig. 2. Axial profile of temperature along the wall on the center-plane of spiral (solid line) and straight-channel (dashed line) micro-reactors for φ = 0.65 and inlet flowrate of 0.48 slpm. This corresponds to inlet velocity of 2 m/s in straight channel.

Fig. 3. Comparison of maximum temperatures (filled triangles) and OH mass fraction (filled circles) of spiral (solid lines) and straight-channel (dashed lines) for varying equivalence ratio, with other parameters as in Fig. 2.

channels. Analysis of the spiral geometry will be discussed in the subsequent sections. With other parameters kept constant, the equivalence ratio is varied in both geometries from 0.3 to 0.75. Figure 3 compares the maximum reactor temperatures attained (filled triangles) and the corresponding maximum in OH mass fractions (filled circles) at various equivalence ratios for the same inlet velocity of 2 m/s. The maximum temperature as well as OH radical concentrations are higher in the spiral microreactor than the straight-channel. Here we use OH mass fraction as a convenient indicator of the relative contribution of homogeneous chemistry, since it has been used as a sign of homogeneous ignition and combustion in the literature [24,46,47]. We have also evaluated the contribution of homogeneous chemistry using reaction path analysis in Appendix B, where a comparison with peak OH concentrations at various inlet velocities for a straight channel indicates that maximum value of the OH concentration is useful, albeit a qualitative measure of the relative homogeneous contribution. As seen in Fig. 3, higher value of OH mass fraction indicates that the relative contribution of homogeneous chemistry towards conversion of hydrogen is higher in the spiral microreactor. From the OH mass fraction trends, it is interesting to observe that in the straight-channel, homogeneous chemistry is relatively negligible and catalytic chemistry primarily accounts for hydrogen combustion for equivalence ratios less than φ = 0.45. In contrast, both homogeneous and catalytic mechanisms are active in the spiral microreactor for all the cases shown in the figure. Furthermore, the spiral microreactor possesses higher maximum temperatures than straight-channel at all the conditions investigated in our work. Due to the compact nature of the spiral geometry, the central reaction channel is better protected from heat losses than the straight-channel. While axial conduction of heat

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Fig. 4. Contours of temperature and OH concentration taken at central plane for φ = 0.65 and inlet velocity of 5 m/s, with all the other parameters at their nominal values. The cold inlet feed results in low temperatures near the center-line, whereas gas close to the walls shows maximum temperature and high OH mass fraction. Lines 1 and 2 are drawn to facilitate discussion on the transverse temperature profiles in Fig. 6, whereas the non-catalytic walls at the inlet of the spiral microreactor are indicated with black or white thick-dotted-lines.

along the wall is the primary mode of preheating the cold inlet in the straight-channel geometry, the incoming cold feed is additionally preheated in the spiral microreactor via transverse transfer of excess enthalpy from the hot product stream in the second turn of the spiral. In fact, the maximum temperatures in the spiral (solid lines in Fig. 3) exceed the adiabatic flame temperature for the corresponding equivalence ratio by 250 K–400 K; for instance, at equivalence ratio of 0.65, maximum temperature of spiral is 2147 K (for conditions maintained in Fig. 2), which is 219 K above the adiabatic flame temperature of 1928 K; this in spite of heat losses to the ambient via convection and radiation from all surfaces in the 3D geometry. These high temperatures would indeed be detrimental for the catalyst and induce thermal stresses in the walls of reactor; however, this study presents the proof of concept of combustion behavior in a single-spiral microreactor. With improved combustion behavior, the spiral microreactor is expected to be more advantageous at lean and low fuel input rates where the temperatures are expected to be lower, as well as for other fuels. 3.2. Combustion characteristics 3.2.1. Temperature and reaction The temperature and OH contours at a plane in the middle of the spiral microreactor is depicted in Fig. 4 for inlet flowrate of 1.2 slpm (i.e., equivalent to inlet velocity of 5 m/s in straightchannel case), equivalence ratio φ = 0.65 and other parameters at their nominal values. The corresponding contours of mid plane of straight channel are also depicted for comparison. Propagation of the flame in the channels is qualitatively similar in spiral and straight-channel microreactors for the operating conditions in this figure. In both the geometries, the region of maximum temperature coincides with the maximum in OH mass fraction, and is located in the gas-phase close to the microreactor walls. The curvature effect and asymmetry across the centerline in spiral geometry results is reflected in the OH mass fraction contours in the spiral microreactor. These results are qualitatively similar in other cutting planes in the 3D geometry as well (only the middle plane is shown for brevity), although the extent of the cold central region shrinks as we move towards the bottom plate in the 3D spiral geometry. This central region is cold due to the cold inlet feed. There is no catalyst in this inlet region and homogeneous reaction is turned off.

Fig. 5. Mass-weighted averages of temperature (solid line) and hydrogen mass fraction (dashed line) in the bulk along the axial length, for the conditions in Fig. 4 (i.e., φ = 0.65 and inlet velocity 5 m/s).

Figure 5 shows the axial profiles of mass-weighted temperature and hydrogen mass fraction along the dimensionless axial length in the spiral microreactor, for same conditions. Majority of conversion takes place and the maximum temperature is also reached in the first turn of the spiral, under these conditions. The temperature and hydrogen conversion are low initially and rise rapidly, and most of hydrogen conversion is observed within the first turn. As seen in Fig. 4, the cold incoming fluid enters the reactor and attains fully developed flow in second half of the turn-1. The fluid close to the walls of the inlet region is hotter than that at the center of the channel, where it moves with a higher velocity and gets replenished by the entering cold stream. The fluid in the inlet region gets heated up owing to transverse heat transfer of excess enthalpy from the fluid in turn-2 as well as through catalytic side of the wall in turn-1, where the reaction is occurring. To demonstrate this, two lines are marked diagonally across the plane of the spiral in Fig. 4: While line-2 starts at the center of the spiral and crosses the second-half of the three turns of the spiral, line-1 crosses the inlet region. Transverse temperature profiles along these lines in the spiral microreactor are shown in Fig. 6. The shaded regions indicate the 500-μm-thick solid walls of the microreactor that separate each turn of the spiral reactor in the radial direction, whereas dash-dot lines indicate center of the channels. The arrows indicate the direction of heat transfer across the first solid wall. Along line-1, as indicated by the solid-red curve in Fig. 6, temperature

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Fig. 6. Temperature in the microreactor vs. dimensionless radial distance, starting from center of the microreactor, along Line-1 (solid red curve) and Line-2 (dashed blue curve). Lines-1 and 2 are depicted in Fig. 4. The shaded region represents solid walls, dash-dot line is the center of each channel, and the block arrows indicate the direction of heat transfer from the first wall to the adjacent channels. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7. Total heat lost (a) from the entire microreactor, and (b) from the top/bottom faces of the microreactor, calculated at various inlet velocities for both straight channel (squares) and spiral (diamonds). The schematic in panel (b) is indicates the outer faces of the top and bottom plates on the 3D microreactor geometry.

external surface area, and is calculated as:

 Qloss =

is higher in turn-2. Consequently, the direction of heat transfer is from turn-2 to turn-1, with the flow in both channels being in the same direction. This explains the heat recirculation between cocurrent flowing fluids in the inlet region of the spiral microreactor. This kind of transverse heat transfer is not observed in a straightchannel microreactor, the spiral geometry is perhaps unique in displaying transfer of excess enthalpy between co-current flowing fluids. On the other hand, along Line-2, the solid wall separating turn-1 and turn-2 is hot due to the hot reaction zone being located close to the wall and the direction of heat transfer is from the wall to the center of either channels. Thus, in the inlet region of turn-1, cold feed is heated by transverse heat transfer from turn2; whereas, in the latter half of turn-1, the direction of heat transfer is from the inner turns to the outer periphery. Heat loss to the surroundings takes place only through the third wall, and not the first two. Finally, we performed simulations under adiabatic conditions, with other parameters same as Fig. 4. Even without heat losses, the maximum temperature of 2567 K in the spiral geometry exceeded that in the straight-channel geometry (i.e., 2300 K for same conditions), indicating the role of both transverse heat transfer and lower heat losses in the spiral microreactor. The high temperatures (exceeding 20 0 0 K) at these conditions would be detrimental to the microreactor. However, as we shall discuss in Section 3.3, it is feasible to operate the spiral microreactor under very lean and low-flow conditions, where stable operation with much lower temperatures can be obtained. In summary, preheating of reactants at the inlet region due to heat recirculation, transverse heat transfer and protection of reaction zone contribute to higher maximum temperatures, OH mass fraction and homogeneous contribution in the spiral geometry. While several heat recirculating geometries, such as u-bend, serpentine or double-spiral (Swiss roll), have been considered in the literature, they involve heat transfer between channels with flow in counter-current direction. In contrast, the (single-)spiral geometry is perhaps unique in displaying transfer of excess enthalpy between co-current flowing fluids.

3.2.2. Analysis of heat losses Figure 7 shows the heat loss, calculated under non-adiabatic conditions, with the heat loss coefficient of h∞ = 15 W/m2 K and emissivity ε = 0.5, at different velocities. The equivalence ratio and wall thermal conductivity are taken as φ = 0.65 and ks = 1 W/m/K. The heat lost at steady state depends on surface temperature and

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0

A





4 h∞ (T − T∞ ) + εσ T 4 − T∞



.dA

where, the external area represents the periphery of the spiral section and the outer surfaces of the top and bottom plates. Figure 7(a) shows the total heat loss, whereas Fig. 7(b) shows the heat lost through the top and bottom surfaces (indicated in the schematic for clarity). As can be expected from the discussion in the previous section, the outer surface temperatures are higher in the spiral microreactor compared to the straight-channel. Consequently, as seen in Fig. 7(b), the net heat lost from the top and bottom plates is higher. However, since the spiral microreactor is a more compact device, the total surface area (of all the external surfaces) and hence the net heat losses from a spiral microreactor is lower than the straight-channel case. It is also interesting to note that heat lost from the top and bottom surfaces accounts for about 50% or more of the net heat loss in the spiral microreactor, whereas it accounts for only 20% in the straight-channel microreactor. This is an important observation because an integrated device (such as thermoelectric unit or endothermic reaction channels) will often be coupled on the top/bottom surfaces of the micro-combustor. While a 2D model is useful for analysis of microreactor behavior, a full 3D model provides further insights for thermal coupling and thermal management by capturing key features in the third dimension. Finally, these results also indicate that combustion can be better sustained in the spiral microreactor than the straight-channel, with high temperatures and high OH concentrations, since the former is shielded better from heat loss and the preheated inlet that’s receiving heat from by the transverse heat transfer from outer turns. 3.2.3. Analysis of homogeneous reactions We further compared the homo-catalytic combustion mode with a purely homogeneous mode (contours not shown) in the spiral microreactor, keeping all other conditions same. The OH concentration is higher in purely homogeneous case than the homo-/catalytic case. The region of maximum temperature is in the gas phase, close to a wall, in the homogeneous case. However, the region of maximum OH concentration remains anchored to the walls in homo-catalytic case for all conditions examined. The catalyst plays a dual role: Depletion of reactants which hinders homogeneous chemistry and catalytic heat release that increases temperature and promotes homogeneous reaction. Comparison with homogeneous-only case shows that the former effect causes slightly lower OH concentrations, whereas the latter results in more intense temperature region near the catalytic walls in the homo-catalytic case.

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Fig. 8. Contours of temperature and OH concentration taken at central plane in the spiral (top panels) and straight-channel (bottom panels) microreactors for φ = 1 and inlet velocity of 5 m/s, with all the other parameters kept constant.

As fluid turns into the spiral channel past this inlet region, both catalytic and homogeneous reactions commence. OH contours depict regions of intense homogeneous reactions located near the walls in turn-1 (Fig. 3). This is due to the effect of the Lewis number of the deficient fuel Hydrogen. Since the Lewis number of Hydrogen is less than 1, the region of intense homogeneous reactions is closer to the catalytic walls [24]. The rate at which fuel diffuses towards the catalytic walls due to concentration gradient is faster than heat diffusion due to temperature gradient. Due to the higher concentration of fuel near the catalytic wall and high heat release due to the catalytic reaction, homogeneous reaction is also close to the walls. This region of intense homogeneous reaction was close to the walls in the straight channel as well. Finally, to decouple the effect of geometry and nature of the fuel, we have simulated for the equivalence ratio of 1 with rest of the conditions maintained constant (h∞ = 15 W/m2 K, ε = 0.5, k = 1 W/m K, uin - 5 m/s). The temperature and OH contours for spiral and straight-channel microreactors are shown in Fig. 8. From the OH contour, it can be observed that the reaction zone starts right from the inlet, but the region of maximum OH concentration shifts to the centerline of the reactor. This is because of the increase in the Lewis number as the fuel becomes richer. This observation is also consistent with the straight channel. The turning effect of the fluid just past the inlet and initiation of homogeneous reaction right at the commencement of the catalytic length of the reactor are solely the effects of single spiral co-current geometry. The maximum temperature reached by the spiral geometry under the conditions of Fig. 8 is 2705 K, which is well above the adiabatic flame temperature of stoichiometric mixture of hydrogen–air. In contrast, since hydrogen is no longer the limiting reactant, subadiabatic temperatures are observed in straight-channel geometry [24]. To summarize, the temperatures higher than adiabatic flame temperatures is not only due to the Lewis number effect of hydrogen, but also because of the virtue of the geometry. 3.3. Effect of inlet velocity The inlet velocity of the fuel mixture is varied from 0.2 m/s to 10 m/s (i.e., 0.048–2.4 slpm) at equivalence ratio of φ = 0.3 to study the effect of velocity on interactions between homogeneous and catalytic chemistries in the spiral microreactor. The corresponding results for straight-channel microreactor are also contrasted in this section. Figure 9 shows that the maximum temperatures in spiral microreactor (solid lines) are higher than in the

Fig. 9. Maximum temperatures (triangles) and OH concentrations (filled circles) of the spiral (straight line) and straight-channel (dashed line) microreactors for homocatalytic mode of operation at equivalence ratio of 0.3. For comparison, the OH mass fractions in the spiral geometry for homogeneous case (with catalytic reaction turned off) is shown as solid lines with open triangles for φ = 0.3.

straight-channel reactor (dashed lines) at all conditions, which is attributed to better heat recirculation between the adjacent channels of the spiral. Likewise, OH mass fractions are also higher in the spiral microreactor owing to an increase in power input and resultant increase in reaction rates. Figure 9 shows that for these lean conditions (i.e., φ = 0.3), OH mass fraction is negligible in straight-channel for all the velocities considered, indicating that the contribution of homogeneous chemistry is very low and hydrogen conversion is primarily due to catalytic reactions. On the other hand, homogeneous reactions are sustained for higher velocities in spiral microreactor, marked by the rise in the peak OH mass fraction. The peak OH mass fractions decrease with decreasing velocity in the spiral geometry. While contributions of homogeneous and catalytic chemistries are comparable at higher velocities, below 1.5 m/s catalytic chemistry becomes the primary mode of hydrogen conversion and the homogeneous contribution is only minor. We further investigated this by comparing these results with purely homogeneous case in spiral microreactor. The open circles in Fig. 9 indicate the OH mass fractions for the spiral microreactor operated in homogeneous mode (catalytic reactions turned off). Homogeneous combustion is not sustained below 2.1 m/s and the reactor quenches. In other words, at φ = 0.3, for velocities lower than 2.1 m/s, homogeneous combustion requires catalyst for

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Fig. 11. Comparison of mass-weighted OH mass fraction vs. dimensionless axial distance in the spiral (top) and straight-channel microreactors (bottom) for various inlet velocities.

Fig. 10. Contours of OH (left) and temperature (right) at φ = 0.3 and inlet velocities of 2 m/s (top-panel), 5 m/s (middle-panel) and 10 m/s (bottom-panel) in the central plane.

its sustenance. It is interesting to note that the homogeneous OH mass fraction starts to rise from 1.3 m/s in homo-catalytic mode (filled circles with solid line) substantiating the role of the catalyst in stabilizing homogeneous chemistry. The effect of velocity on the spiral microreactor is further analyzed in Fig. 10 using contours depicting the OH mass fraction and temperatures for different inlet velocities. The contours belong to the central plane with the legends representing the range of global minima and maxima of OH mass fractions and temperatures in the spiral reactor for each case. As described in the previous section, the reaction zone (indicated by high OH mass fraction) is anchored close to the spiral walls, where the catalyst commences in all the three cases shown. The region of higher temperature occurs in the gas-phase close to the wall, where both catalytic and homogeneous reactions occur at the same axial location close to each other. At lower velocity of 2 m/s (top panels), the OH concentration and homogeneous reaction rate is highest in turn-1 near the inner wall of the spiral. The residence time is moderate and both homogeneous and catalytic reactions occur close to the inlet, which is also the location of maximum wall temperature. When the inlet velocity increases to 5 m/s, the amount of homogeneous reaction increases, thereby yielding temperatures higher than that of 2 m/s. The reaction zone is more diffuse, as indicated by OH contours; however, most of the reaction still takes place in turn-1. The maximum temperature as well as OH concentration increase from 2 m/s to 5 m/s for both spiral and straight-channel microreactors. When the ve-

locity is further increased to 10 m/s (bottom panel in Fig. 10), the flame still remains anchored near the start of the catalyst owing to the flow patterns in the turns of the spiral channel and transverse heat transfer from adjacent channels, though the flame becomes more diffused since higher flows pushes it downstream, and the OH concentration extends into the first half of turn-2. Figure 11 compares the mass-weighted values of OH mass fractions in the spiral (top) and straight (bottom) channels at various inlet velocities and equivalence ratio of φ = 0.65. This equivalence ratio is chosen because homogeneous combustion is sustained in straight-channel for a reasonable range of velocities to facilitate comparison with the spiral. At low inlet velocities, the location of homogeneous reaction is close to the inlet for both the geometries. The bottom panel (spiral) shows that although the maxima in OH profile shift downstream with increasing velocity, homogeneous reaction starts just after the inert inlet and expands into the outer turns. In contrast, the OH profile in straight-channel (top panel) shifts downstream with the increase in velocity. It should be noted that homogeneous reaction is not significant for straight-channel at 0.5 m/s and the catalytic chemistry primarily accounts for conversion of hydrogen. The contribution of homogeneous chemistry to overall conversion in straight-channel microreactor is high only for the middle range of velocities. As a result of preheating that is caused by the virtue of the geometry of spiral reactor, homogeneous contribution remains high for the velocities considered. These results corroborate the preceding observation that the maxima in OH mass fractions increase and shift downstream, and the reaction zone gets more spread-out with increasing inlet velocity in the spiral microreactor. 4. Conclusions Homogeneous/catalytic combustion of lean hydrogen–air mixture in a novel single-spiral microreactor, which is a curled-up form of straight-channel geometry, was analyzed using 3D CFD simulations in this work. The reactions in bulk gas and catalyst surface were modeled using detailed microkinetic models. The

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spiral microreactor showed higher temperature and higher contribution from homogeneous chemistry than the conventional straight-channel microreactor of equivalent dimension. The maximum temperature in spiral microreactor exceeded the adiabatic flame temperature and the straight-channel maximum temperature by 250–400 K. These higher temperatures were attributed to transverse heat transfer to the catalytic combustion from the hot product gases in the adjacent channels, and better protection of the central combustion zone. This transfer of excess enthalpy took place between adjacent channels with co-current flow of gases. Analysis of heat losses indicated that while the net heat loss was lower in spiral geometry, more heat was available for transfer from the top and bottom face-plates. These results have practical interest as the single-spiral geometry could potentially provide an alternative design for improved thermal management and stability of catalytic microreactors. The effect of equivalence ratio and inlet velocity on combustion in the spiral microreactor was also analyzed. Homogeneous chemistry was sustained in the spiral microreactor in presence of catalyst for a wider range of conditions than purely homogeneous combustion. For the entire range of inlet velocity and equivalence ratio considered, the reaction zone remained near the start of the catalytic section in the spiral microreactor. At low values of equivalence ratio and inlet velocity, homogeneous chemistry was not significant and catalytic reactions were primarily observed. The role of homogeneous chemistry, as indicated by OH mass fractions, increased as the velocity was increased. Due to the low Lewis number, the maximum OH mass fraction was often located close to the walls of the micro-channels. While the reaction zone was pushed downstream at higher velocity in straight-channel microreactors, the reaction started close to the inlet in spiral microreactor, though the region of homo and catalytic reactions broadened at higher velocity. The promising results in this work motivate further analysis of combustion in the spiral geometry, including setting up a practical prototype to demonstrate the features observed in the simulation study. Acknowledgment NSK gratefully acknowledges financial support from the Startup Grant #16-17/672/NFSC from IIT Madras. Appendix A. Kinetics of hydrogen combustion The gas-phase kinetics for hydrogen–air combustion of Chattopadhyay and Veser [41] is summarized below. No.

Reaction

1 2 3 4 5

H + O2 ↔ O + OH H2 + O ↔ H + OH H2 + OH ↔ H2 O + H OH + OH ↔ H2 O + O H + OH + M ↔ H2 O + M H2 O /20.0/ O2 + M ↔ O + O + M H2 + M ↔ H + H + M H2 O/6.0/ H/2.0/ H2 /3.0/ H2 + O2 ↔ OH + OH H + O2 + M ↔ HO2 + M H2 O/21.0/ H2 /3.3/ H + O2 + O2 ↔ HO2 + O2 H + O2 + N2 ↔ HO2 + N2 HO2 + H ↔ H2 + O2 HO2 + H ↔ OH + OH HO2 + O ↔ OH + O2 HO2 + OH ↔ H2 O + O2 HO2 + HO2 ↔ H2 O2 + O2 H2 O2 + M ↔ OH + OH + M H2 O2 + H ↔ HO2 + H2 H2 O2 + OH ↔ H2 O + HO2

6 7 8 9 10 11 12 13 14 15 16 17 18 19

k0 (mol, cm, s)

β (–)

E (kJ/mol)

5.13 × 1016 1.80 × 1010 1.20 × 10°9 6.00 × 10°8 7.50 × 1023

−0.82 1.0 1.3 1.3 −2.6

69.1 37.0 15.2 0.0 0.0

1.90 × 1011 2.20 × 1012

0.5 0.5

400.1 387.7

1.701 × 1013 2.10 × 1018

0.0 −1.0

200.0 0.0

6.70 × 1019 6.70 × 1019 2.50 × 1013 2.50 × 1014 4.80 × 1013 5.00 × 1013 2.00 × 1012 1.30 × 1017 1.70 × 1012 1.00 × 1013

−1.42 −1.42 0.00 0.0 0.0 0.0 0.0 0.0 0.0 0.0

0.0 0.0 2.93 7.9 4.2 4.2 0.0 190.5 15.9 7.5

The microkinetic model for catalytic oxidation of hydrogen/air mixtures, taken from Deutschmann et al. [42], is listed in the table below. ∗ Sticking coefficient of O2 (Reaction 3) is temperaturedependent and is given by s = 0.07( TT )β with T0 = 300 K. 0

No.

Reaction

1 2

H2 + 2Pt(S) → 2H(S) 2H(S) → H2 + 2Pt(S) COV /H(S) O2 + 2Pt(S) → 2O(S) 2O(S) → O2 + 2Pt(S) COV /O(S) H + Pt(S) → H(S) O + Pt(S) → O(S) H2 O + Pt(S) → H2 O(S) H2 O(S) → H2 O + Pt(S) OH + Pt(S) → OH(S) OH(S) → OH + Pt(S) H(S) + O(S) ↔ OH(S) + Pt(S) H(S) + OH(S) ↔ H2 O(S) + Pt(S) 2OH(S) ↔ H2 O(S)+ O(S)

3 4 5 6 7 8 9 10 11 12 13

s (–) or A (mol, cm, s)

β (–)

E (kJ/mol)

0.046 3.70 × 1021

0 0

0.0 67.4−6.0

21∗ 3.70 × 1021

−1.0 0

0.0 213.20−60.0

1.0 1.0 0.75 1 × 1013 1.0 1 × 1013 3.70 × 1021 3.70 × 1021

0 0 0 0 0 0 0 0

0.0 0.0 0.0 40.3 0.0 192.8 11.5 17.4

3.70 × 1021

0

48.2

Appendix B. Contribution of homogeneous chemistry The peak value of OH mass fraction is used as an indicator of homogeneous contribution. Analysis of OH mass fraction and the relative contribution of homogeneous combustion is presented in Fig. 12. The relative contribution of homogeneous chemistry is calculated as:





−rHhomo dV 2  homo −rH2 dV + −rHsurf dS 2

where rH2 represents the rate of consumption of hydrogen per unit volume and is the sum of all elementary steps in the microkinetic model involving hydrogen in gas-phase and catalyst surface (indicated by superscripts homo and surf). The peak OH mass fraction and corresponding homogeneous contributions are plotted on the left and right ordinate, respectively, at various inlet velocities for straight channel at the equivalence ratio of 0.65. This equivalence ratio is chosen because unlike equivalence ratio of 0.3, straight channels show good variation in OH mass fraction over the range of velocity. This figure indicates that qualitative trends of peak OH mass fraction and the relative homogeneous contribution follow similar trend. In the equation above, the homogeneous contribution is calculated by integrating the reaction rates over entire volume or surface. It should be noted that the peak value of OH mass fraction may vary depending on the location and spread of the reaction zone. Hence, it is not a quantitative measure of the overall homogeneous reaction rate. Indeed, low values of peak OH mass

Fig. 12. Plot depicting the OH mass fractions (solid line) and percentage homogeneous contribution (dashed line) vs. inlet velocity for straight channel microreactor at equivalence ratio of 0.65 with rest of the parameters kept constant.

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449

Fig. 13. Inner wall temperature in the central planes, along the length of the spiral (left panel) and the straight-channel microreactors, at equivalence ratio of φ = 0.65, inlet velocity uin = 5 m/s, h∞ = 15 Wm−2 K−1 , ε = 0.5 and k = 1 Wm−1 K−1 .

fractions do not indicate absence of homogeneous combustion. Instead, the relative contribution of homogeneous reaction follows similar qualitative trend as peak OH mass fraction. Such observations were valid at other conditions as well. Appendix C. Grid independence for spiral and straight-channel microreactors Figure 13 shows the results of grid independence study undertaken for conditions in Fig. 4. A grid with 1,056,057 nodes was chosen as grid independent for spiral and 365,904 for straight-channel microreactors, as described here. For grid independence of straight channel reactor, three meshes were chosen based on prior experience and initial simulations. These included a mesh with 1,079,172 nodes consisting of 966 axial divisions, 35 radial divisions and 10 divisions in the z-direction. The number of axial and radial nodes were varied independently to obtain two more grids with 518,364 nodes (483 axial, 45 radial and 10 z-dimensional divisions) and 365,904 nodes (483 axial, 30 radial and 10 z-dimensional divisions) were considered. Figure 13b shows the temperature profile along the length of the reactor. The hydrogen mass fraction were also plotted, and this was repeated for cases in Fig. 3 (results not shown for brevity). The results were qualitatively similar for all conditions. Based on these results, the mesh with 365,904 nodes is found to be grid independent. In a similar manner, the baseline case for spiral microreactor consisted of 200,449 nodes (60 circumferential and 25 radial divisions for each turn and 30 divisions in z-direction). The mesh in the three directions were varied independently, which revealed that the results were mainly sensitive to the grid in the first halfturn of the spiral geometry. To demonstrate grid independence of solutions, results from two other meshes with 334,806 nodes (100 circumferential and 25 radial divisions for each turn, and 30 divisions in Z-direction) and 1,365,401 nodes (120 circumferential and 50 radial divisions for each turn, and 60 divisions in Z direction) are plotted in Fig. 13a. Since the difference in the profiles were observed only in the left-half of the spiral, a new mesh with 1,056,057 nodes (80 circumferential divisions on the left half of spiral and 50 circumferential divisions in the right half of spiral, 50 radial divisions and 30 divisions in Z direction) was chosen. Consequently, the final mesh with nearly 1 million nodes was chosen for further simulations in this work. References [1] A.C. Fernandez-Pello, Micropower generation using combustion: issues and approaches, Proc. Combust. Inst. 29 (2002) 883–899. [2] N.S. Kaisare, D.G. Vlachos, A review on microcombustion: fundamentals, devices and applications, Prog. Energy Combust. Sci. 38 (2012) 321–359.

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