Dynamics of Premixed Hydrogen-Air Flames in Microchannels with a Wall Temperature Gradient

Transcription

1 Combustion Science and Technology ISSN: (Print) X (Online) Journal homepage: Dynamics of Premixed Hydrogen-Air Flames in Microchannels with a Wall Temperature Gradient Aswathy Nair, V. Ratna Kishore & Sudarshan Kumar To cite this article: Aswathy Nair, V. Ratna Kishore & Sudarshan Kumar (2015) Dynamics of Premixed Hydrogen-Air Flames in Microchannels with a Wall Temperature Gradient, Combustion Science and Technology, 187:10, , DOI: / To link to this article: View supplementary material Accepted author version posted online: 11 Jun Submit your article to this journal Article views: 149 View related articles View Crossmark data Citing articles: 1 View citing articles Full Terms & Conditions of access and use can be found at Download by: [Aswathy Nair] Date: 23 January 2016, At: 02:37

2 Combust. Sci. Technol., 187: , 2015 Copyright Taylor & Francis Group, LLC ISSN: print / X online DOI: / DYNAMICS OF PREMIXED HYDROGEN-AIR FLAMES IN MICROCHANNELS WITH A WALL TEMPERATURE GRADIENT Aswathy Nair, 1 V. Ratna Kishore, 1 and Sudarshan Kumar 2 1 Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, India 2 Department of Aerospace Engineering, Indian Institute of Technology Bombay, Powai, Mumbai, India Two-dimensional numerical investigations on flame dynamics in a microchannel have been carried out for premixed hydrogen-air mixtures with detailed chemistry. Detailed studies on the formation of flames with repetitive extinction and ignition (FREI) mode have been carried out for a 0.75-mm diameter tube with fixed conditions of flow velocity of 10 cm/s and Φ = with wall temperature linearly varying from 300 K to 960 K. An unsteady flame propagation behavior similar to FREI has been observed to appear for a range of mixture equivalence ratios and channel diameters. FREI was observed to occur for 0.5 < Ф < 0.8 for 0.75-mm diameter channel and disappears for higher mixture equivalence ratios. The effect of tube diameter has also been analyzed for 10 cm/s inlet velocity of mixture at K wall temperature for diameters of 0.6 mm, 0.75 mm, and 1.0 mm. As the tube diameter increased, the frequency of the FREI process decreased, which hints to the contribution of disappearance of FREI phenomenon. Keywords: Flame repetitive extinction and ignition; Hydrogen; Microchannel; Microscale combustion INTRODUCTION An increasing trend towards the development and miniaturization of various mechanical and electromechanical systems has been observed recently. The miniaturization of many of these devices, such as micro-robots, micro-airplanes, and micro-pumps, is limited due to the higher weight of electrochemical batteries (Fernandez-Pello, 2002; Ju and Maruta, 2011; Maruta, 2011). Combustion-based devices for power generation have been proposed recently due to higher (20 50 times) power density of hydrogen and hydrocarbon fuels as compared to electrochemical batteries. Despite all of the advantages, the flame propagation and its dynamics for various premixed fuel-air mixtures in meso/ microscale channels and ducts are not fully understood. Due to increased surface area-tovolume ratio, the flame wall coupling increases, which leads to the phenomena of wave propagation, pattern formation, and flame front instabilities (Fan et al., 2008, 2009a, 2009b; Ju and Maruta, 2011; Kumar, 2011; Kumar et al., 2007, 2008; Maruta, 2011; Received 2 May 2014; revised 21 March 2015; accepted 3 June Address correspondence to V. Ratna Kishore, Department of Mechanical Engineering, Amrita Vishwa Vidyapeetham, Ettimadai, Coimbatore, Tamil Nadu , India. ratnavk@gmail.com, v_ratnakishore@cb.amrita.edu 1620

3 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1621 Maruta et al., 2005; Minaev et al., 2009; Nakamura et al., 2011; Pizza et al., 2008a; Richecoeur and Kyritsis, 2005). Understanding these phenomena becomes more difficult as the combustion process in these microscale systems is governed by nonlinear coupling of chemical reactions, fluid dynamics, and heat and mass transfer properties of the premixed fuel-air mixtures (Fan et al., 2008, 2009a, 2009b; Kumar, 2011; Kumar et al., 2007, 2008; Maruta et al., 2005; Minaev et al., 2009; Pizza et al., 2008a; Richecoeur and Kyritsis, 2005; Veeraragavan and Cadou, 2008, 2011). A large range of rich flame dynamics has been observed by various researchers both experimentally as well as numerically (Fan et al., 2008, 2009a, 2009b; Kumar et al,, 2008; Maruta et al., 2005; Pizza et al., 2008a, 2008b; Richecoeur and Kyritsis, 2005). Maruta et al. (2005) has experimentally studied the flame propagation characteristics of premixed methane-air mixtures in a 2.0-mm diameter straight quartz channel with a positive temperature gradient along the direction of flow. This is a simple 1D configuration to study flame propagation characteristics in micro-/mesoscale channels resembling a system with heat recirculation through channel walls. Experimental studies showed that steady premixed flames existed for high and extremely low mixture velocities. Various unstable flame propagation modes were observed to exist at intermediate mixture velocities and referred to as flame repetitive extinction and ignition by the authors. Many experimental observations on flame instabilities were reported in straight tubes by Maruta and others (Fan et al., 2009b; Kim et al., 2005; Maruta et al., 2005; Minaev et al, 2009; Nakamura et al., 2011), curved ducts by Richecoeur and Kyritsis (2005), and radial microchannels (Fan et al., 2008, 2009a, 2010; Kumar,2011; Kumar et al., 2007, 2008). Theoretical investigations of Nakamura et al. (2011) and Minaev et al. (2009) showed the existence of a bifurcation and splitting phenomenon of flames in microchannels with a wall temperature gradient. These observations were further confirmed by Fan et al. (2009a). Pizza et al. (2008a) have carried out numerical simulations with detailed chemistry for understanding the flame dynamics of lean premixed (Ф =0.5)hydrogen-air mixtures for a heated planar microchannel with their height varying from mm and mixture velocity (4 cm/s to 400 cm/s). They observed that a stable combustion regime exists for very small mixture flow rate limits. For narrow channels, they further observed that some of the flame modes are suppressed. The frequency of ignition and extinction is faster in narrow channels due to the short distance of the ignition location from the inlet side and increased flame-wall coupling. Different flame structures were observed for a wide array of mixture velocities. For lower mixture velocity range (4 cm/s to 18 cm/s), periodic extinction and ignition was observed with 1.0-mm channel height. As the inlet velocity is increased from 18 cm/s to 75.5 cm/s and above 77 cm/s to 113 cm/s, V-shaped stable flame and oscillating flames were respectively observed. An asymmetric stable flame was observed for 77 cm/s to 77.2 cm/s for the same channel dimensions. For a channel height of mm, all of the above-mentioned flame modes were observed except oscillating flames for higher mixture velocities. For mm channel height, only periodic extinction-ignition and V-shaped flame structures were observed. A 3D simulation for lean (Ф = 0.5) hydrogen-air mixtures in microtubes with diameters of mm have been reported by Pizza et al. (2008b). Three axisymmetric combustion modes were observed for narrow tubes, i.e., steady mild combustion, oscillatory extinction and ignition, and steady flames in the mixture velocity range of 0.5 cm/s to 500 cm/s. For wider tubes, rich flame dynamics, such as steady mild

4 1622 A. NAIR ET AL. combustion, oscillatory extinction/ignition, steady closed and open axi-symmetric, steady non-axi-symmetric flames, and azimuthally spinning flames were observed for mixture velocities varying from 0.5 cm/s to 600 cm/s. Jejurkar and Mishra (2011) carried out numerical studies on flame stability of hydrogen-air mixtures in an annular microcombustor. The results show that the flame stabilization could be achieved without any need of catalytic action, which simplifies the combustor design. Hua et al. (2005) have performed simulations to study the combustion of premixed hydrogen-air mixtures in a number of microscaled cylindrical chambers by scaling down the chamber dimensions from millimeter level to micrometer level. The effects of heat conduction within wall chambers and heat loss through the walls on combustion characteristics are investigated. Although a significant amount of work has been reported in the literature on flame stabilization in micro- and mesoscale channels, all of these studies are focused on limited conditions of mixture equivalence ratios and channel dimensions. No significant studies focusing on the flame dynamics under flames with repetitive extinction and ignition (FREI) conditions are available for hydrogen-air mixtures. Therefore, there is a serious need of understanding the effect of mixture equivalence ratio on the formation of FREI flame modes in mesoscale channels with hydrogen-air mixtures, as mixture equivalence ratio is one of the five important parameters (channel dimension, temperature gradient, inlet velocity, and mixture combination) on which the dynamics of the FREI flames depend. In the present work, 2D axisymmetric numerical simulations have been carried out for premixed hydrogen-air flames in a straight microtube with a temperature gradient along the direction of fluid flow to analyze the formation of FREI phenomenon for a range of mixture equivalence ratios. The effect of equivalence ratio, effect of tube diameter, and mixture velocity on FREI characteristics has been discussed in detail. COMPUTATIONAL DETAILS Computation Domain Figure 1a shows details of the computational domain and the grid employed for the present work. A 2D axi-symmetric domain for a 0.75-mm diameter tube is considered. The domain is drawn along the center line of the cylindrical tube and the units of axial and radial distance (m) are shown in the figure. The choice of a 2D domain is considered in the present work as it can give sufficient information on the interaction of the propagating flame with solid walls as demonstrated by Pizza et al. (2008a). Studies are also extended for other tube diameters, such as 0.6 mm and 1.0 mm. The mesh is generated using GAMBIT and the initial grid size used for the present work is Δx =30μm, Δy =18.75μm. The grid resolution is expected to be sufficient for a typical flame with a thickness of δ f =0.39mm,δ f / Δx =13 indicating that sufficient number of grid points are available within the flame zone. Similar Figure 1(a) Computational domain and grid (dimensions in m).

5 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1623 Figure 1(b) HRR plot for Δx =30μm and Δx =15μm at point of ignition along the axis. sized grids were used in the literature by Pizza et al. (2008a) and Kim and Maruta (2006). The grid independence test has been performed for ϕ = 0.5, 0.75-mm tube diameter, and mixture velocity of 10 cm/s. The computed results of heat release rate along the axis for a refined grid of size Δx =15μm and coarse grid of size Δx =30μm are shown in Figure 1b. It is clear from the figure that the results for both of the grids compare well and indicate that a grid with Δx = 30 μm is sufficient to resolve all the details of FREI dynamics in the present work. Also, the sensitivity of the time step to these unsteady simulations was confirmed for ϕ = 0.6, 0.75-mm tube diameter, and mixture velocity of 100 cm/s. Figure 1c shows the variation of heat release rate along the axis for 10 μs and 1 μs time step and results for both time steps compare well showing that a time step of 10 μs is sufficient for present work. Chemical Reaction Modeling For investigating the FREI phenomenon in microchannels, numerical simulations have been carried out for premixed hydrogen-air mixtures. The H 2 -O 2 detailed mechanism proposed by Li et al. (2003) has been employed in the present work. The mechanism consists of 9 species and 19 reactions. This mechanism has been updated with the mechanism used by many researchers (Kee et al., 1996a, 1996b; Pizza et al., 2008a; Yetter et al., 1991) in their work. This reaction mechanism of Li et al. (2003) has been shown to work well for a wide range of conditions (temperature range from K, pressure range of atm, and Ф = ). A multicomponent diffusion-based transport model is used, which uses the CHEMKIN transport database for calculating the various transport properties (Kee et al., 1996a). Thermal diffusion is taken into consideration. Chemical reaction rates are evaluated using the stiff kinetic chemistry solver. The stiff chemistry solver approximates the reactions rates R i in the species

6 1624 A. NAIR ET AL. Figure 1(c) Effect of time-step on the variation of heat release rate for ϕ = 0.6, tube diameter of 0.75 mm, and mixture flow velocity of 102 cm/s. ð τ transport equation as R i ¼ 1 τ R i dt. Here, the default value of τ is set to one-tenth of the o minimum convective or diffusive time scale in the cell. The contributions of five reactive species, i.e., H 2,O 2, H, OH, and HO 2 on the hydrogen combustion during FREI cycle have been brought out in the work. Boundary Conditions The system of highly nonlinear and coupled systems of governing equations has been solved by subjecting it to a set of boundary conditions. The following boundary conditions are applied: 1. Channel inlet section: Uniform axial velocity varying from cm/s. 2. Outlet section: Pressure outlet with ambient pressure conditions (P atm = 101,325 Pa). 3. A linearly varying wall temperature profilefrom300kto960k(referredtoas T 1 profile) is applied for most of the studies. A different temperature profile with higher peak temperatures of K (referred to as T 2 profile) is applied to understand the effect of diameter and wall temperature gradient on FREI. A temperature of 960 K was chosen to ensure a boundary condition similar to the work of Pizza et al. (2008a) on flame dynamics for hydrogen-air mixtures in micro- and mesoscale channels. The authors found that both T 1 (300 to 960 K) and T 2 (300 to 1050 K) temperature profiles did not result in much difference in frequency of FREI cycle. No-slip wall condition is applied at the channel walls. The variation of the wall temperature profile for different boundary conditions is shown in Figure 2.

7 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1625 Figure 2 Wall temperatures provided to the channel along the axial distance. 4. An axis boundary condition (axi-symmetric condition) along the center line (axis) of the channel is applied. Initial Conditions and Numerical Solution Approach A general purpose CFD code, Fluent 13.0, is used for solving the governing equations of mass, momentum, energy, and species conservation for unsteady reacting flow. Parallel computations were carried out to reduce the computational time. Second-order accurate schemes are used for discretizing the various terms in the governing equations. The solution was allowed to converge at every time step until the convergence criteria were satisfied. The convergence limit of the RSM residuals is set to 10 6 for all of the equations. Initially, cold flows in the computational domain is solved at steady state and after some iterations, the transient solver is initiated with second-order implicit transient formulation. A pressure-based solver with absolute velocity formulation is used in this computational study. Pressure velocity coupling is achieved using the PISO algorithm. This algorithm, an extension of SIMPLE algorithm, is originally developed for noniterative computation of unsteady compressible flow. Also, it is adapted successfully for steadystate problems. The results of FREI for the second cycle onwards are considered to be of our interest in the present computations and the results from the third cycle onwards have been observed to quantitatively agree with the results of the second cycle. Results from the first cycle are not considered because the initial conditions are expected to influence the results during the first cycle of FREI propagation.

8 1626 A. NAIR ET AL. RESULTS AND DISCUSSION Figure 3 shows the regime diagram for the existence of various flame propagation modes in a 0.75-mm diameter tube for a range of mixture flow velocities and equivalence ratios with T 1 temperature profile. The FREI phenomenon depends on mixture inlet velocity, temperature gradient, equivalence ratio, tube diameter, and mixture combination (hydrogen-air in the present case). The unsteady flame propagation mode of FREI is observed for moderate flow velocity range and higher temperatures as discussed in Nakamura et al. (2011). Two steady flame propagation modes, namely, weak flame and normal or strong flame modes, are observed to exist for very low and high mixture flow rates as shown in Figure 3. Variation of FREI Frequency Figures 4a and 4b show the graph for variation of FREI frequency with different equivalence ratios and variation of frequency with inlet velocity for Ф =0.6for0.75- mm diameter channel. As the Ф increases ( ) for the same channel diameter (0.75 mm), the frequency of the FREI cycle decreases as shown in Figure 4a. The observed frequencies are Hz, Hz, Hz, and 6.68 Hz for Ф = 0.5, 0.6, 0.7, and 0.8, respectively. It was observed that for 0.75-mm diameter channel, beyond Ф = 0.8, the FREI phenomenon disappears and flashback was observed for higher equivalence ratios (Ф = 0.9 onwards). Thus, it may be concluded that for higher Ф value, the chances of appearance of FREI propagation mode disappear due to an increase in the heat release rate from increased fuel concentration in the fuel-air mixtures. Also, it is seen from Figure 4b that for 0.75-mm diameter channel, with Ф = 0.6, as the inlet velocity increased ( cm/s), the frequency of the FREI Figure 3 Regime diagram for various flame modes in a 0.75-mm channel for different flow velocities and mixture equivalence ratios with T 1 temperature profile.

9 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1627 Figure 4(a) Variation of FREI frequency with mixture equivalence ratio for 0.75-mm-diameter channel and a flow velocity of 10 cm/s. Figure 4(b) Variation of the FREI frequency with mixture inlet velocity for Ф = 0.6 and 0.75-mm tube diameter. propagation cycle correspondingly increases from 18 Hz to 112 Hz. For higher inlet velocity (i.e., beyond 102 cm/s), FREI disappears and normal flame is observed to exist. From smaller mixture velocities (v < 10 cm/s), weak flames were observed to

10 1628 A. NAIR ET AL. appear in the channel with their characteristics similar to those reported by Nakamura et al. (2011). These observations are similar to the experimental observations of Nakamura et al. (2011), where stable flames are observed to exist for very low and high mixture flow rate conditions. FREI Propagation Details Figure 5 shows the contour plots for H 2 fuel species, temperature, OH species, and HRR (heat release rate) during the different phases of a FREI cycle: (i) initiation, 0 ms; (ii) ignition, 7 ms; (iii) propagation, 22 ms; and (iv) weak reaction phase, 42.5 ms. The contour plots of nondimensional values scaled to maximum values for each Figure 5 Contours of H 2, temperature, OH species, and HRR for different phases in a FREI cycle for Ф = 0.5 and a flow velocity of 10 cm/s. Minimum values for species and HRR are 0 and T min = 300 K. Contour levels for temperature and H 2 mole fraction are the same for all of the time instants.

11 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1629 parameter (H 2, temperature, OH, HRR) at different time intervals are shown in Figure 5. The values corresponding to various colors are shown in Figure 5. Various details related to different processes for the entire FREI cycle with each phase are explained in the next section. At t = 0 ms, near the downstream side, the overall heat release rate is relatively small. This is because the unburned mixture remaining from a previous cycle of FREI gets carried on to the next cycle as reported by Nakamura et al. (2011). This mixture starts reacting and thus releases very small heat. At t =7ms, ignition occurs at a downstream location of the channel. The maximum value of HRR is observed at t = 22 ms. The flame slowly moves towards the upstream direction and its position at t = 22 ms and 42.5 ms is shown in Figure 5. Aftert =42.5ms,theflame propagation rate slows down at an upstream location, however, the weak reaction phase continues and the entire fuel is consumed. Flame Dynamics in FREI Propagation Mode In this section, the overall dynamics of flame propagation in FREI mode is explained for 0.75-mm diameter tube with Ф = 0.5, a flow velocity of 10 cm/s, and T 1 ( K) wall temperature profile. The entire FREI cycle has been divided into five regions: (i) initiation phase, (ii) ignition phase, (iii) propagation phase, (iv) weak reaction phase, and (v) flowing phase as discussed in Nakamura et al. (2011). Similar results for FREI propagation were also observed for Ф = range. Figure 6a shows the profiles of temperature and H 2 mole fraction for the entire FREI cycle starting from t = 0 ms (initiation phase) to t = 57 ms (flowing phase). The profiles at intermediate time steps, t = 7 ms, t = 22 ms, and t = 42.5 ms, correspond to ignition phase, propagation phase, and weak reaction phase, respectively. Figure 6b shows the corresponding heat release rate profiles (HRR) along the axis for the above-mentioned phases of a typical FREI cycle. P 1,P 2, and P 3 are the second peaks of HRR observed during the Figure 6(a) Temperature and H 2 mole fraction profiles for different instances of FREI propagation cycle along the axis.

12 1630 A. NAIR ET AL. Figure 6(b) Profiles of heat release rate (HRR) for different instances of FREI propagation cycle along the axis. propagation phase, weak reaction phase, and flowing phase, respectively, as shown in Figure 4b. It should be noted that log scale is used for HRR graph due to the large variation in the range of HRR values for different FREI phases. Figure 6c shows the mole fraction of hydrogen at different instances during the propagation phase to the flowing Figure 6(c) H 2 mole fraction profiles for different instances of FREI propagation cycle to understand bifurcation of flame for Ф = 0.5 and a flow velocity of 10 cm/s.

13 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1631 Figure 6(d) Contours of H 2 mole fraction and HRR showing the bifurcation of flame during ignition phase for Ф = 0.5 and a flow velocity of 10 cm/s. phase along the axis. Figure 6d shows the contours of H 2 mole fraction and HRR, which clearly show the existence of a flame bifurcation during ignition phase. The leading flame moves in the upstream direction and the trailing flame moves in the downstream direction and its intensity decreases with time. Initiation phase. During the initiation phase, the wall temperature and axis temperature (overlaps with t = 57 ms temperature profile) remains almost the same and negligible consumption of H 2 species is observed as reported by Nakamura et al. (2011). In this case, the wall temperature profile and axis temperature profile coincides and, therefore, wall temperature profile is not shown in the figure. Two peaks of HRR corresponding for this phase can be seen in Figure 6b at x = m and m along the direction of fluid flow. The smaller peak at m location is due to the result of a previous cycle of FREI and will be discussed later. The second peak corresponds to initiation of the reaction at a downstream location, which later leads to ignition of the mixture. Ignition phase. The premixed fuel-air mixture continuously gets heated in the tube along the length of the channel and ignition occurs after some time delay. The ignition temperature for this mixture at Ф = 0.5 was observed to be 960 K. Therefore, a maximum temperature of 960 K was considered as a boundary condition for T 1 temperature profile. During the ignition phase, the consumption of fuel species, H 2 is relatively small. The mixture is considered to be ignited when T g -T w = 50 K. During this phase, OH mole fraction increases slightly. However, the value of HRR increases significantly at ignition phase as compared with initiation phase as seen in Figure 6b for the case of t = 7 ms.

14 1632 A. NAIR ET AL. Propagation phase. During the propagation phase, a significant consumption of fuel can be observed from the curves corresponding to t =22msshowninFigures 6a and 6b. As seen in Figure 6b, anotherpeak(p 1 )ofhrrisobservedat0.038m location. Additionally, it is interesting to note that two peaks of H 2 mole fraction can be seen to exist at different locations along the direction of the fluid flow. The smaller peak of H 2 mole fraction at around 0.04 m is due to the presence of unburned mixture at a downstream location of the channel as shown in Figure 6a. Thepresenceofthe unburned mixture at different instances from propagation phase to the flowing phase is shown in Figure 6c. This is due to the bifurcation of the flame as ignition happens at an axial distance of m. In order to understand this bifurcation phenomenon, contours of H 2 mole fraction and HRR are plotted in Figure 6d. It can be seen that bifurcation of a flame occurs in the ignition phase and a weak flame propagates towards the downstream direction as clearly shown in Figure 6d. A similar phenomenon of flame bifurcation has also been reported by Nakamura et al. (2011) for premixed methane-air mixtures. A peak temperature value of 1500 K has been observed for this phase. The heat release rate increases suddenly for this case from a value of 1e-7 kj/m 3 -s in initiation phase to 1e-4 kj/m 3 -s in propagation phase. This phase starts at t = 20 ms and continues until t =41ms. Weak reaction phase. Once the propagation phase comes towards an end at t = 41 ms, the overall reaction rate drops to very low values as the flame reaches an upstream location, x = m, where the temperature of fresh incoming mixture is very low. As seen from the curve corresponding to t =42.5ms,thepeaktemperature lowers suddenly, due to which the heat release rate drops approximately by six orders of magnitude. The magnitude of the second peak of H 2 mole fraction at a position of 0.04 m reduces comparatively due to dilution of the stream with hot combustion products. Further, it can be seen in Figure 6b that the position of peak HRR shifts to the upstream location. Two peaks of HRR observed during this mode of FREI propagation: (i) at upstream location and (ii) at a downstream location. The P 2 point represents the second peak of HRR for this phase as seen in Figure 6b. The peak value of HRR lowers suddenly to around 5e-9 kj/m 3 -s. The other peak of HRR is seen at around 0.04 m location along the x-axis with a typical value of 1e-8kJ/m 3 -s. Flowing phase. During this propagation mode, the temperature profile appears almost similar to that of the initiation phase as shown in Figure 6a. In this phase, the primary reaction zone weakens further and the secondary reaction zone at a downstream location becomes more significant as is clear from Figure 6b. After a small delay, again the FREI cycle starts followed by initiation and ignition. The smaller peak (P 3 ) of HRR is carried to the next cycle of FREI, which states the presence of unburned mixture still remaining even after ignition near the downstream side of the channel. Effect of Mixture Equivalence Ratio on FREI Propagation The effect of mixture equivalence ratio on FREI propagation is explored for Ф = 0.5 to 0.8 at a mixture velocity of 10 cm/s. The T 1 wall temperature profile was applied on the wall and diameter tube was 0.75 mm. Figure 7 shows the variation of the temperature profile at a time of 20 ms, 22 ms,30ms,and52msforф = 0.5, 0.6, 0.7, and 0.8, respectively, along the axis. This

15 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1633 Figure 7 Variation of temperatures at [0.35(Δt cycle )] ms at different equivalence ratios along the axis for mm diameter channel and a flow velocity of 10 cm/s. corresponds to approximately 0.35Δt of the complete FREI cycle. Further, 0.35Δt cycle has been considered in the present case for comparison purposes to understand the effect of mixture equivalence ratio on FREI propagation mode. The case of Ф =0.9 was not considered as FREI disappeared for a mixture with Φ 0.8, as a tube of mm diameter is not sufficient to quench the flame at an upstream location. (Quenching distance is a function of mixture equivalence ratio.) The entire time periods for each Ф ( )are57ms,63ms,85.5ms,and149.5ms(asshowninFigure4,frequency decreases with an increase in mixture equivalence ratio). It can be observed from Figure 7 that for the same mixture velocity and wall temperature gradient, the peak temperature increases with mixture equivalence ratio. A minimum temperature value of 1490 K is observed for Ф = 0.5 and this value increases to 1800 K for Ф =0.8.The increase in peak temperature value during the propagation phase of FREI also hints at its contribution towards the disappearance of FREI for higher equivalence ratio mixtures. The mole fraction of two minor species H and OH at the ignition point for different mixture equivalence ratios along the axis are shown in Figures 8a and 8b. As the value of Ф increases from 0.5 to 0.8, the mole fraction of both of the species, H and OH, also increases. The mole fraction of H is at Ф = 0.5 and it increases to at Ф = 0.8. The mole fraction of OH increases from at Ф = 0.5 to at Ф = 0.8. A sudden increase in the value of OH mole fraction can be observed as Ф increases from 0.7 to 0.8, even though the increase in the mole fraction of H is relatively much smaller. This is due to the reason that reaction rate of H to OH with the primary reaction H + O 2 OH + O for Ф = 0.8 becomes much faster as compared to Ф = 0.5, resulting in an increase in the unburned mixture for higher Ф value.

16 1634 A. NAIR ET AL. Figure 8 Mole fraction of H and OH at point of ignition for different equivalence ratios along the axis for mm diameter channel and a flow velocity of 10 cm/s. Effect of Tube Diameter on FREI To understand the effect of tube diameter on FREI propagation, computations are carried out for various tube diameters of 0.6, 0.75, and 1.0 mm with an incoming flow velocity of 10 cm/s and mixture equivalence ratio of Φ = 0.5.

17 PREMIXED H 2 -AIR FLAMES IN MICROCHANNELS 1635 Figure 9 shows the variation of heat release rate (HRR) and OH mole fraction along the axial direction of the tube for different tube diameters along the axis. A wall temperature profile T 2 ( K) is considered in the present work. It is clear from Figure 9a that the value of HRR increases with an increase in the tube diameter from 0.6 mm to 1.0 mm. From Figure 9b, it can be seen that for increasing tube diameter, the mole fraction of OH decreases. This is because the OH Figure 9 HRR profile and mole fraction of OH at the point of ignition for different diameters along the axis for Ф = 0.5 and a flow velocity of 10 cm/s.

18 1636 A. NAIR ET AL. production rate from the reaction of H + O 2 O + OH becomes slower as the diameter of the channel decreases. It has been observed that the ignition temperatures for tube of diameters 0.6 mm, 0.75 mm, and 1.0 mm have been observed to increase with an increase in the tube diameter. The ignition temperatures observed are 1050 K, 1060 K, and 1065 K for diameters 0.6 mm, 0.75 mm, and 1.0 mm tube diameters, respectively. This substantiates the fact that for larger tube diameters, the fuel-air mixture needs to travel a longer distance to achieve the autoignition temperature condition within the given channel length. The frequencies of the FREI process observed were Hz, Hz, and Hz for the diameters of 0.6 mm, 0.75 mm, and 1.0 mm, respectively. For increasing channel diameter, the frequency of the FREI process decreases, which has been already reported by Pizza et al. (2008b). From their observations, it was found that as the diameter of the channel increases, the time needed to heat up the fresh incoming fuel/air mixture until it ignites increases. Hence, distance of ignition location from the inlet section of the channel is farther and frequency of the process decreased. Thus, this decrease in frequency of FREI cycle for increasing tube diameters may hint to the contribution of disappearance of FREI inside the channel. CONCLUSIONS The dynamics of flame propagation in FREI mode has been numerically investigated for premixed hydrogen/air mixtures with detailed chemistry. The effect of two important parameters, mixture equivalence ratio and tube diameter, on the formation of FREI mode has been investigated in detail. Numerical studies for a range of mixture velocities and equivalence ratios show that the FREI occurs within a range of cm/s of flow velocity and for Ф = range. For smaller equivalence ratios, i.e., Ф = 0.2 and 0.3, the FREI occurs for an inlet velocity range of cm/s. An increase in mixture equivalence ratio results in increased values of HRR and temperatures for the same diameter tubes. Two peaks for species H and OH appear for mixtures with Ф = 0.8 indicating the appearance of flame bifurcations. It has been observed that for an increased value of Ф > 0.8, the flame propagates throughout the channel and flame flashback occurs and FREI disappears for increased Ф value beyond Ф = 0.8. Also, for increasing tube diameters beyond 1.0 mm, the frequency of the FREI cycle decreases, which may hint to contribute to the disappearance of FREI and a weak flame will be observed. SUPPLEMENTAL MATERIAL Supplemental data for this article can be accessed on the publisher s website. REFERENCES Fan, A.W., Maruta, K., Nakamura, H., Kumar, S., and Liu, W Experimental investigation on flame pattern formations of DME air mixtures in a radial microchannel. Combust. Flame, 157 (9), Fan, A.W., Minaev, S., Kumar, S., Liu, W., and Maruta, K Regime diagrams and characteristics of flame patterns in radial microchannels. Combust. Flame, 153, Fan, A.W., Minaev, S., Sereshchenko, E., Fursenko, R., Kumar, S., Liu, W., and Maruta, K. 2009a. Experimental and numerical investigations of flame pattern formations in a radial microchannel. Proc. Combust. Inst., 32,

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