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Steady-State Multiplicity in Catalytic Microcombustors Almerinda Di Benedetto* and Valeria Di Sarli Istituto di Ricerche sulla Combustione, Consiglio Nazionale delle Ricerche (CNR), Via Diocleziano 328, 80124 Naples, Italy
In this work, two-dimensional computational fluid dynamics (CFD) simulations were run to investigate the possibility of a link between the initial conditions and the occurrence of blowout for a parallel-plate catalytic microcombustor. The results show that steady-state multiplicity occurs: Depending on the initial conditions, the range of inlet gas velocities at which stable operation is attained can be enlarged to avoid blowout. It is concluded that investigations into the thermal behavior of catalytic microcombustors have to deal with appropriate and aware choices of the initial conditions. 1. Introduction Catalytic microcombustors exhibit wider operating maps than homogeneous microcombustors.1,2 The catalysts in such reactors allow chemical reactions to be sustained at lower temperatures and in the presence of higher heat losses, thus reducing the impact of thermal quenching. The challenge for catalytic microcombustors for applications in microelectromechanical systems (MEMS) is to attain stable steady-state conditions at high inlet gas velocities and, thus, high input power densities. Literature results have shown that the range of operability for catalytic microcombustors is limited by extinction at low inlet velocities (∼0.1 m/s) and blowout at relatively high inlet velocities (∼10 m/s).1-5 At extinction, the flame quenches because the heat released by combustion is not sufficient to counterbalance heat losses. At blowout, the reaction front is swept out of the reactor owing to the low residence time. By means of computational fluid dynamics (CFD) simulations, we have shown that it is possible to operate a catalytic microcombustor at high inlet gas velocities (i.e., up to the velocity value limiting the laminar regime for the incoming flow) without encountering blowout.6,7 These apparently contradictory results can be explained by studying the opportunity for the occurrence of steady-state multiplicity for catalytic microcombustors. In the literature, steady-state multiplicity has been found for both meso and macrocatalytic combustors.8,9 In the present work, we aimed to investigate the possibility of a link between the operating and initial conditions and the occurrence of blowout and steady-state multiplicity for catalytic microcombustors. To this end, we performed a continuation analysis by means of direct (CFD) simulations of a parallel-plate catalytic microreactor. We ran simulations starting from different initial conditions (different gas velocities). We then continued the solution branch changing the inlet gas velocity, eventually building the entire operating map for the catalytic microcombustor.
gas-solid interface and in the gas phase for combustion of a lean propane/air mixture. In Figure 1, the scheme of the catalytic microcombustor is shown, which consists of two parallel (infinitely wide) plates with a gap distance of d ) 600 µm, a wall thickness of dw ) 200 µm and a length of L ) 10 mm. The model solves the mass, momentum, chemical species, and energy conservation equations in the fluid along with the energy equation in the solid wall. Steady-state simulations were carried out. The conservation equations in the fluid are as follows (conventional notation is adopted): Continuity Vx
(
)
∂Vy ∂Vx ∂F ∂F + Vy +F + )0 ∂x ∂y ∂x ∂y
(1)
Momentum ∂F VxVx ∂τxx ∂τyx ∂F VxVy ∂p )+ + + ∂x ∂y ∂x ∂x ∂y
(2)
∂F VxVy ∂τxy ∂τyy ∂F VyVy ∂p )+ + + ∂x ∂y ∂y ∂x ∂y
(3)
Species (i ) 1, ..., Ns - 1, where Ns is the number of species) ∂F VxYi ∂x
+
(
) (
)
∂F VyYi ∂Yi ∂Yi ∂ ∂ ) FDi,m + FDi,m + Rhom,i ∂y ∂x ∂x ∂y ∂y
(4)
2. The Model A two-dimensional CFD model was developed to simulate the coupling of the fluid flow and the chemical processes at the * To whom correspondence should be addressed. Tel.: +39 0817622673. Fax: +39 0817622915. E-mail: almerinda.dibenedetto@ irc.cnr.it.
Figure 1. Scheme of the catalytic microcombustor (parallel-plate reactor). The dashed line is the axis of symmetry.
10.1021/ie901615d 2010 American Chemical Society Published on Web 02/02/2010
Ind. Eng. Chem. Res., Vol. 49, No. 5, 2010
Energy
Table 1. Operating Conditions for Simulations
∂F Vxh ∂F Vyh ∂ ∂T ∂ ∂T ) + λ + λ + ∂x ∂y ∂x ∂x ∂y ∂y ∂Yi ∂Yi Ns ∂ h FD ∂ hiFDi,m i i,m ∂x ∂y + ∂x ∂y i)1
∑
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( )
((
( )
))
) (
Ns
∑hR
i hom,i
(5)
i)1
Equations 1-5 are coupled to the ideal-gas equation pWmix F) RT
(
∂2Tw ∂x2
+
(6)
∂2Tw ∂y2
)
(7)
where λw is the solid thermal conductivity. At the inlet of the microcombustor, a fixed flat velocity profile was assumed. For the species and energy equations, Danckwerts boundary conditions were used. At the exit, a static pressure equal to the atmospheric pressure was imposed, and far-field conditions were specified for the remaining variables. At the fluid-wall interface, no-slip boundary conditions were assigned (so that the fluid had zero velocity relative to the boundary) and coupled to the species balances (so that the mass flux of each species, FJi, was equal to the corresponding rate of production/consumption, ωy,i) FJi ) ωy,i
(8)
Further, the energy balance was expressed as λ
∂Tw ∂T ) λw + ωh ∂y ∂y
(9)
where ωh is the heat surface production rate. Heat losses from the ends of the microcombustor were not considered (insulated ends), and Newton’s law of convection was used at the outer surface of the wall q ) h(Tw,ext - Ta,ext)
(10)
where h is the exterior convective heat-transfer coefficient, Tw,ext is the temperature at the exterior wall surface, and Ta,ext is the external temperature () 300 K). The reaction rate for homogeneous propane combustion was calculated according to the single-step reaction rate expression of Westbrook and Dryer10 Rhom ) 4.836E + 9 exp
+8 ( -1.256E )(C RT
0.1 1.65 C3H8) (CO2)
[ ] kmol (m3 s)
(11)
with the activation energy in J/kmol and the concentrations in kmol/m3. The catalytic reaction was assumed to be irreversible, firstorder in fuel concentration, and zeroth-order in oxygen concentration.4 The reaction rate, referred to platinum as the catalyst, was calculated according to Rcat ) 2.4E + 5 exp
+7 ( -9.06E )C RT
C3H8
[ ]
value
inlet gas temperature, Tin (K) inlet gas velocity, Vin (m/s) inlet propane mole fraction, YC3H8,in exterior convective heat-transfer coefficient, h [W/(m2 K)] pressure, p (bar) solid thermal conductivity, λw [W/(m K)]
300 varies 0.024 20 1 2
Table 2. Initial Conditions for Simulations
and the energy equation in the solid wall reads as 0 ) λw
parameter
kmol (m2 s)
(12)
again with the activation energy in J/kmol and the concentration in kmol/m2.
parameter
IC_A
IC_B
gas temperature, T (K) gas velocity, V (m/s) propane mole fraction, YC3H8 wall temperature, Tw (K) pressure, p (bar) Pe´clet number
750 0.5 0.024 750 1 ∼10
750 4 0.024 750 1 ∼90
The molecular viscosity was approximated through Sutherland’s law for air viscosity. The fluid specific heat and thermal conductivity were calculated by a mass-fraction-weighted average of species properties. The species specific heat was evaluated as a piecewise fifth-power polynomial function of temperature. The model equations were discretized using a finite-volume formulation on a structured mesh built by means of the Gambit preprocessor of the Fluent package.11 Grid-independent solutions were found using cells with dimensions equal to 2.5 × 10-2 mm. The spatial discretization of the model equations used firstorder schemes for all terms, except for the diffusion terms, which were treated with a second-order central-difference scheme. Computations were performed by means of the segregated solver of the Fluent code11 that employs the SIMPLE method for treating pressure-velocity coupling. All residuals were always smaller than 1.0 × 10-7. The operating and initial conditions for simulations are summarized in Tables 1 and 2, respectively. Initial conditions A (IC_A) and B (IC_B) differ for the values of the gas velocity and, thus, Pe´clet number (i.e., the ratio of the diffusion time to the residence time). To implement these conditions in an experiment or in an actual microcombustor, one needs to feed the propane/air mixture at ambient temperature with a velocity equal to 0.5 m/s (IC_A) or 4 m/s (IC_B) and then to supply power in order to preheat the reactor to 750 K. 3. Results and Discussion In Figure 2, maps of the propane mole fraction, temperature, homogeneous reaction rate, and velocity components (Vx and Vy) are shown, as computed at Vin ) 0.5 m/s starting from initial conditions IC_A (Table 2). Homogeneous reaction is absent in the first part of the microchannel where the catalytic reaction occurs. At the lightoff position, where ignition of the catalytic reaction process takes place, a perturbation of the fluid flow is observed owing to the gas expansion induced by the heat release. This is a typical behavior also for catalytic macrocombustors.12,13 Downstream of the first part of the microcombustor, homogeneous reaction is also activated, leading to a hot spot inside the bulk phase with subsequent gas expansion and acceleration (Vx). Starting from initial conditions IC_A, we performed direct simulations using the inlet gas velocity as the bifurcation parameter to build the operating map of the catalytic microcombustor. In Figure 3, the solutions in terms of maximum wall temperature and propane conversion are shown (IC_A_forward),
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Figure 2. Maps of the propane mole fraction (YC3H8), temperature (T, K), homogeneous reaction rate [Rhom, (kg mol)/(m3 s)], and velocity components (Vx, Vy, m/s) for Vin ) 0.5 m/s (initial conditions listed in column IC_A of Table 2).
Figure 3. Maximum wall temperature (top) and propane conversion (bottom) as functions of the inlet gas velocity (initial conditions listed in column IC_A of Table 2).
Figure 4. Maximum wall temperature (top) and propane conversion (bottom) as functions of the inlet gas velocity (initial conditions reported in Table 2).
along with the solutions obtained by decreasing the inlet gas velocity from Vin ) 30 m/s (IC_A_backward). Two solution branches are observed, suggesting the presence of steady-state multiplicity. Along the IC_A_forward solution branch, the wall temperature reaches an asymptotic value (∼1150 K), the propane conversion decreases to about 10%, and blowout does not occur up to Vin ) 30 m/s (velocity value limiting the laminar regime). This is in contradiction to the literature results,1-5 which show
that, as the inlet gas velocity is increased, the wall temperature reaches a maximum and then starts decreasing up to blowout conditions. Moving along the IC_A_backward solution branch, a hysteresis is encountered starting from Vin ) 1.5 m/s. To further investigate the bifurcation behavior of the microcombustor, we also carried out direct simulations at different values of the inlet velocity starting from initial conditions IC_B (Table 2).
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Figure 5. Temperature (K) maps in the microchannel at Vin ) 0.5, 2, 10, and 15 m/s for the lower and upper branches.
In Figure 4, the operating map is shown: As the inlet gas velocity is increased, the wall temperature reaches a maximum and then falls at the blowout point. This is the typical behavior observed by previous authors.1-5 Comparison of the upper (IC_A_forward) and lower (IC_B_ forward) branches shows that the upper branch is characterized by a higher maximum wall temperature (∆Tw,max ≈ 40 K) and a higher propane conversion at each value of the inlet gas velocity. In Figure 5, the temperature maps in the microchannel at different inlet gas velocities (0.5, 2, 10, and 15 m/s) for the lower- and upper-branch solutions are presented. The solutions for the upper branch exhibit a light-off position very close to the inlet section of the microcombustor, with a very high wall temperature along the whole length of the microchannel. Conversely, in the solutions for the lower branch, the light-off position is located further downstream, and the wall temperature is significantly lower. It is worth noting that, in the lower-branch solutions, when the inlet gas velocity is increased, the light-off position shifts downstream to leave the microcombustor (i.e., up to blowout). Conversely, in the upper-branch solutions, the light-off position is substantially unaffected by the inlet gas velocity. Blowout does not occur: The wall remains hot even at high inlet velocity (15 m/s), whereas the gas phase becomes cooler. Based on the results obtained, it is possible to state that, depending on the initial conditions, two main thermal behaviors can be distinguished. In the steady states of the upper branch of Figure 4, blowout does not occur. The wall temperature remains high even at high inlet gas velocities. The high wall temperature allows a masstransport-limited regime to be established with a non-null propane conversion. In the maps of Figure 5 (right-hand side), it can be observed that the catalytic wall remains unaffected by the thermal conditions of the bulk gas phase, as was also found in our previous studies.6,7 Conversely, under the conditions of the lower branch of Figure 4, blowout occurs: As the inlet gas velocity is increased, the decrease of the residence time leads to a shift of the reaction wave downstream toward the exit section of the microcombustor. Under these conditions, the wall temperature is lower than in the upper-branch solutions, and it is also much more sensitive to the conditions in the bulk gas (Figure 5). Indeed, it appears that the bulk gas phase dominates the thermal behavior of the whole microreactor, by cooling the wall and dragging the reaction front out along the microchannel toward the exit.
The results obtained here should be useful in driving the startup strategies of microdevices. As pointed out by Kaisare et al.,14 the ignition mode can affect the maximum wall temperature reached at steady state, as well as emissions and time during ignition. The main applicable conclusion of the present work is that the appropriate choice of the initial conditions, in terms of power supplied during resistive preheating, can allow the range of inlet gas velocities at which stable operation is attained to be enlarged, thus avoiding blowout. 4. Conclusions In this work, two-dimensional CFD simulations have been run to investigate the possibility of a link between the initial conditions and the occurrence of blowout for a parallel-plate catalytic microcombustor. The results demonstrate that steady-state multiplicity occurs: The choice of the initial conditions significantly affects the final steady-state operating point. Depending on the startup mode, the range of inlet gas velocities at which stable operation is attained can be enlarged to avoid blowout. Consequently, when investigating the thermal behavior of catalytic microcombustors, it is essential to highlight the role of the initial conditions. Acknowledgment The authors wish to thank Dott. V. Smiglio for his technical assistance in the computing activity. Literature Cited (1) Maruta, K.; Takeda, K.; Ahn, J.; Borer, K.; Sitzki, L.; Ronney, P. D.; Deutschmann, O. Extinction Limits of Catalytic Combustion in MicroChannels. Proc. Combust. Inst. 2002, 29, 957. (2) Kaisare, N. S.; Deshmukh, S. R.; Vlachos, D. G. Stability and Performance of Catalytic Microreactors: Simulations of Propane Catalytic Combustion on Pt. Chem. Eng. Sci. 2008, 63, 1098. (3) Norton, D. G.; Wetzel, E. D.; Vlachos, D. G. Thermal Management in Catalytic Microreactors. Ind. Eng. Chem. Res. 2006, 45, 76. (4) Spadaccini, C. M.; Peck, J.; Waitz, I. A. Catalytic Combustion Systems for Microscale Gas Turbine Engines. J. Eng. Gas Turbines Power 2007, 129, 49. (5) Karagiannidis, S.; Mantzaras, J.; Jackson, G.; Boulouchos, K. Hetero-/Homogeneous Combustion and Stability Maps in Methane-Fueled Catalytic Microreactors. Proc. Combust. Inst. 2007, 31, 3309. (6) Di Benedetto, A.; Di Sarli, V.; Russo, G. Effect of Geometry on the Thermal Behavior of Catalytic Micro-Combustors. Catal. Today, published online Mar 14, 2009, http://dx.doi.org/10.1016/j.cattod.2009.01.048. (7) Di Benedetto, A.; Di Sarli, V.; Russo, G. A Novel CatalyticHomogeneous Micro-Combustor. Catal. Today 2009, 147S, S156.
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(8) Gupta, N.; Balakotaiah, V.; West, D. H. Bifurcation Analysis of a TwoDimensional Catalytic Monolith Reactor Model. Chem. Eng. Sci. 2001, 56, 1435. (9) Di Benedetto, A.; Cimino, S.; Pirone, R.; Russo, G. Temperature Excursions during the Transient Behaviour of High Temperature Catalytic Combustion Monoliths. Catal. Today 2003, 83, 171. (10) Westbrook, C. K.; Dryer, F. L. Simplified Reaction Mechanisms for the Oxidation of Hydrocarbon Fuels in Flames. Combust. Sci. Technol. 1981, 27, 31. (11) Fluent, version 6.3.26; Fluent Inc.: Lebanon, NH, 2007; http:// www.fluent.com (accessed Sep 30, 2009). (12) Di Benedetto, A.; Marra, F. S.; Russo, G. Heat and Mass Fluxes in Presence of Superficial Reaction in a Not Completely Developed Laminar Flow. Chem. Eng. Sci. 2003, 58, 1079.
(13) Di Benedetto, A.; Marra, F. S.; Donsı`, F.; Russo, G. Transport Phenomena in a Catalytic Monolith: Effect of the Superficial Reaction. AIChE J. 2006, 52, 911. (14) Kaisare, N. S.; Stefanidis, G. D.; Vlachos, D. G. Comparison of Ignition Strategies for Catalytic Microburners. Proc. Combust. Inst. 2009, 32, 3027.
ReceiVed for reView October 16, 2009 ReVised manuscript receiVed January 8, 2010 Accepted January 14, 2010 IE901615D
