Steady-State Multiplicity in Catalytic Microcombustors
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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) simula- tions, 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 mi- croreactor. 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. 2. The Model A two-dimensional CFD model was developed to simulate the coupling of the fluid flow and the chemical processes at the 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 d w ) 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 Momentum Species (i ) 1, ..., N s - 1, where N s is the number of species) * 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. V x ∂ F ∂ x +V y ∂ F ∂ y +F ( ∂ V x ∂ x + ∂ V y ∂ y ) ) 0 (1) ∂ FV x V x ∂ x + ∂ FV x V y ∂ y )- ∂ p ∂ x + ∂ τ xx ∂ x + ∂ τ yx ∂ y (2) ∂ FV x V y ∂ x + ∂ FV y V y ∂ y )- ∂ p ∂ y + ∂ τ xy ∂ x + ∂ τ yy ∂ y (3) ∂ FV x Y i ∂ x + ∂ FV y Y i ∂ y ) ∂ ∂ x ( FD i,m ∂ Y i ∂ x ) + ∂ ∂ y ( FD i,m ∂ Y i ∂ y ) + R hom,i (4) Ind. Eng. Chem. Res. 2010, 49, 2130–2134 2130 10.1021/ie901615d 2010 American Chemical Society Published on Web 02/02/2010
Transcript of Steady-State Multiplicity in Catalytic Microcombustors
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 thepossibility of a link between the initial conditions and the occurrence of blowout for a parallel-plate catalyticmicrocombustor. 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 isconcluded that investigations into the thermal behavior of catalytic microcombustors have to deal withappropriate and aware choices of the initial conditions.
1. Introduction
Catalytic microcombustors exhibit wider operating maps thanhomogeneous microcombustors.1,2 The catalysts in such reactorsallow chemical reactions to be sustained at lower temperaturesand in the presence of higher heat losses, thus reducing theimpact of thermal quenching.
The challenge for catalytic microcombustors for applicationsin microelectromechanical systems (MEMS) is to attain stablesteady-state conditions at high inlet gas velocities and, thus,high input power densities.
Literature results have shown that the range of operabilityfor catalytic microcombustors is limited by extinction at lowinlet velocities (∼0.1 m/s) and blowout at relatively high inletvelocities (∼10 m/s).1-5 At extinction, the flame quenchesbecause the heat released by combustion is not sufficient tocounterbalance heat losses. At blowout, the reaction front isswept out of the reactor owing to the low residence time.
By means of computational fluid dynamics (CFD) simula-tions, we have shown that it is possible to operate a catalyticmicrocombustor at high inlet gas velocities (i.e., up to thevelocity value limiting the laminar regime for the incoming flow)without encountering blowout.6,7
These apparently contradictory results can be explained bystudying the opportunity for the occurrence of steady-statemultiplicity for catalytic microcombustors. In the literature,steady-state multiplicity has been found for both meso andmacrocatalytic combustors.8,9
In the present work, we aimed to investigate the possibilityof a link between the operating and initial conditions and theoccurrence of blowout and steady-state multiplicity for catalyticmicrocombustors.
To this end, we performed a continuation analysis by meansof direct (CFD) simulations of a parallel-plate catalytic mi-croreactor. We ran simulations starting from different initialconditions (different gas velocities). We then continued thesolution branch changing the inlet gas velocity, eventuallybuilding the entire operating map for the catalytic microcombustor.
2. The Model
A two-dimensional CFD model was developed to simulatethe coupling of the fluid flow and the chemical processes at the
gas-solid interface and in the gas phase for combustion of alean propane/air mixture.
In Figure 1, the scheme of the catalytic microcombustor isshown, which consists of two parallel (infinitely wide) plateswith 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 theenergy equation in the solid wall. Steady-state simulations werecarried out.
The conservation equations in the fluid are as follows(conventional notation is adopted):
Continuity
Momentum
Species (i ) 1, ..., Ns - 1, where Ns is the number of species)
* To whom correspondence should be addressed. Tel.: +390817622673. Fax: +39 0817622915. E-mail: [email protected].
Figure 1. Scheme of the catalytic microcombustor (parallel-plate reactor).The dashed line is the axis of symmetry.
Vx∂F∂x
+ Vy∂F∂y
+ F(∂Vx
∂x+
∂Vy
∂y ) ) 0 (1)
∂F VxVx
∂x+
∂F VxVy
∂y) -∂p
∂x+
∂τxx
∂x+
∂τyx
∂y(2)
∂F VxVy
∂x+
∂F VyVy
∂y) -∂p
∂y+
∂τxy
∂x+
∂τyy
∂y(3)
∂F VxYi
∂x+
∂F VyYi
∂y) ∂
∂x(FDi,m
∂Yi
∂x ) + ∂
∂y(FDi,m
∂Yi
∂y ) + Rhom,i
(4)
Ind. Eng. Chem. Res. 2010, 49, 2130–21342130
10.1021/ie901615d 2010 American Chemical SocietyPublished on Web 02/02/2010
Energy
Equations 1-5 are coupled to the ideal-gas equation
and the energy equation in the solid wall reads as
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, Danckwertsboundary conditions were used. At the exit, a static pressureequal to the atmospheric pressure was imposed, and far-fieldconditions were specified for the remaining variables.
At the fluid-wall interface, no-slip boundary conditions wereassigned (so that the fluid had zero velocity relative to theboundary) and coupled to the species balances (so that the massflux of each species, FJi, was equal to the corresponding rate ofproduction/consumption, ωy,i)
Further, the energy balance was expressed as
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 convectionwas used at the outer surface of the wall
where h is the exterior convective heat-transfer coefficient, Tw,ext
is the temperature at the exterior wall surface, and Ta,ext is theexternal temperature () 300 K).
The reaction rate for homogeneous propane combustion wascalculated according to the single-step reaction rate expressionof Westbrook and Dryer10
with the activation energy in J/kmol and the concentrations inkmol/m3.
The catalytic reaction was assumed to be irreversible, first-order in fuel concentration, and zeroth-order in oxygen con-centration.4 The reaction rate, referred to platinum as the catalyst,was calculated according to
again with the activation energy in J/kmol and the concentrationin kmol/m2.
The molecular viscosity was approximated through Suther-land’s law for air viscosity. The fluid specific heat and thermalconductivity were calculated by a mass-fraction-weighted aver-age of species properties. The species specific heat was evaluatedas a piecewise fifth-power polynomial function of temperature.
The model equations were discretized using a finite-volumeformulation on a structured mesh built by means of the Gambitpreprocessor of the Fluent package.11 Grid-independent solutionswere found using cells with dimensions equal to 2.5 × 10-2
mm.The spatial discretization of the model equations used first-
order schemes for all terms, except for the diffusion terms, whichwere treated with a second-order central-difference scheme.
Computations were performed by means of the segregatedsolver of the Fluent code11 that employs the SIMPLE methodfor treating pressure-velocity coupling. All residuals werealways smaller than 1.0 × 10-7.
The operating and initial conditions for simulations aresummarized in Tables 1 and 2, respectively. Initial conditionsA (IC_A) and B (IC_B) differ for the values of the gas velocityand, thus, Peclet number (i.e., the ratio of the diffusion time tothe residence time). To implement these conditions in anexperiment or in an actual microcombustor, one needs to feedthe propane/air mixture at ambient temperature with a velocityequal to 0.5 m/s (IC_A) or 4 m/s (IC_B) and then to supplypower 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 andVy) are shown, as computed at Vin ) 0.5 m/s starting from initialconditions IC_A (Table 2).
Homogeneous reaction is absent in the first part of themicrochannel where the catalytic reaction occurs. At the light-off position, where ignition of the catalytic reaction process takesplace, a perturbation of the fluid flow is observed owing to thegas expansion induced by the heat release. This is a typicalbehavior also for catalytic macrocombustors.12,13
Downstream of the first part of the microcombustor, homo-geneous reaction is also activated, leading to a hot spot insidethe bulk phase with subsequent gas expansion and acceleration(Vx).
Starting from initial conditions IC_A, we performed directsimulations using the inlet gas velocity as the bifurcation parameterto build the operating map of the catalytic microcombustor.
In Figure 3, the solutions in terms of maximum walltemperature and propane conversion are shown (IC_A_forward),
∂F Vxh
∂x+
∂F Vyh
∂y) ∂
∂x(λ ∂T∂x ) + ∂
∂y(λ ∂T∂y ) +
∑i)1
Ns (∂(hiFDi,m
∂Yi
∂x )∂x
+∂(hiFDi,m
∂Yi
∂y )∂y
) - ∑i)1
Ns
hiRhom,i (5)
F )pWmix
RT(6)
0 ) λw(∂2Tw
∂x2+
∂2Tw
∂y2 ) (7)
FJi ) ωy,i (8)
λ ∂T∂y
) λw
∂Tw
∂y+ ωh (9)
q ) h(Tw,ext - Ta,ext) (10)
Rhom ) 4.836E + 9 exp(-1.256E + 8RT )(CC3H8
)0.1(CO2)1.65
[ kmol
(m3 s)] (11)
Rcat ) 2.4E + 5 exp(-9.06E + 7RT )CC3H8 [ kmol
(m2 s)](12)
Table 1. Operating Conditions for Simulations
parameter value
inlet gas temperature, Tin (K) 300inlet gas velocity, Vin (m/s) variesinlet propane mole fraction, YC3H8,in 0.024exterior convective heat-transfer coefficient, h [W/(m2 K)] 20pressure, p (bar) 1solid thermal conductivity, λw [W/(m K)] 2
Table 2. Initial Conditions for Simulations
parameter IC_A IC_B
gas temperature, T (K) 750 750gas velocity, V (m/s) 0.5 4propane mole fraction, YC3H8
0.024 0.024wall temperature, Tw (K) 750 750pressure, p (bar) 1 1Peclet number ∼10 ∼90
Ind. Eng. Chem. Res., Vol. 49, No. 5, 2010 2131
along with the solutions obtained by decreasing the inlet gasvelocity from Vin ) 30 m/s (IC_A_backward). Two solutionbranches are observed, suggesting the presence of steady-statemultiplicity.
Along the IC_A_forward solution branch, the wall temper-ature reaches an asymptotic value (∼1150 K), the propaneconversion decreases to about 10%, and blowout does not occurup 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 temperaturereaches a maximum and then starts decreasing up to blowoutconditions.
Moving along the IC_A_backward solution branch, a hys-teresis is encountered starting from Vin ) 1.5 m/s.
To further investigate the bifurcation behavior of the micro-combustor, we also carried out direct simulations at differentvalues of the inlet velocity starting from initial conditions IC_B(Table 2).
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 columnIC_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 Table2).
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In Figure 4, the operating map is shown: As the inlet gasvelocity is increased, the wall temperature reaches a maximumand then falls at the blowout point. This is the typical behaviorobserved by previous authors.1-5
Comparison of the upper (IC_A_forward) and lower (IC_B_forward) branches shows that the upper branch is characterizedby a higher maximum wall temperature (∆Tw,max ≈ 40 K) anda higher propane conversion at each value of the inlet gasvelocity.
In Figure 5, the temperature maps in the microchannel atdifferent inlet gas velocities (0.5, 2, 10, and 15 m/s) for thelower- and upper-branch solutions are presented.
The solutions for the upper branch exhibit a light-off positionvery close to the inlet section of the microcombustor, with avery high wall temperature along the whole length of themicrochannel. Conversely, in the solutions for the lower branch,the light-off position is located further downstream, and the walltemperature is significantly lower.
It is worth noting that, in the lower-branch solutions, whenthe inlet gas velocity is increased, the light-off position shiftsdownstream to leave the microcombustor (i.e., up to blowout).Conversely, in the upper-branch solutions, the light-off positionis substantially unaffected by the inlet gas velocity. Blowoutdoes 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 behaviorscan be distinguished.
In the steady states of the upper branch of Figure 4, blowoutdoes not occur. The wall temperature remains high even at highinlet gas velocities. The high wall temperature allows a mass-transport-limited regime to be established with a non-nullpropane conversion. In the maps of Figure 5 (right-hand side),it can be observed that the catalytic wall remains unaffected bythe thermal conditions of the bulk gas phase, as was also foundin our previous studies.6,7
Conversely, under the conditions of the lower branch ofFigure 4, blowout occurs: As the inlet gas velocity is increased,the decrease of the residence time leads to a shift of the reactionwave downstream toward the exit section of the microcombus-tor. Under these conditions, the wall temperature is lower thanin the upper-branch solutions, and it is also much more sensitiveto the conditions in the bulk gas (Figure 5). Indeed, it appearsthat the bulk gas phase dominates the thermal behavior of thewhole microreactor, by cooling the wall and dragging thereaction front out along the microchannel toward the exit.
The results obtained here should be useful in driving thestartup strategies of microdevices. As pointed out by Kaisareet al.,14 the ignition mode can affect the maximum walltemperature reached at steady state, as well as emissions andtime during ignition. The main applicable conclusion of thepresent work is that the appropriate choice of the initialconditions, in terms of power supplied during resistive preheat-ing, can allow the range of inlet gas velocities at which stableoperation is attained to be enlarged, thus avoiding blowout.
4. Conclusions
In this work, two-dimensional CFD simulations have beenrun to investigate the possibility of a link between the initialconditions and the occurrence of blowout for a parallel-platecatalytic microcombustor.
The results demonstrate that steady-state multiplicity occurs:The choice of the initial conditions significantly affects the finalsteady-state operating point. Depending on the startup mode,the range of inlet gas velocities at which stable operation isattained can be enlarged to avoid blowout. Consequently, wheninvestigating 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 technicalassistance in the computing activity.
Literature Cited
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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.
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(8) Gupta, N.; Balakotaiah, V.; West, D. H. Bifurcation Analysis of a Two-Dimensional Catalytic Monolith Reactor Model. Chem. Eng. Sci. 2001, 56, 1435.
(9) Di Benedetto, A.; Cimino, S.; Pirone, R.; Russo, G. TemperatureExcursions during the Transient Behaviour of High Temperature CatalyticCombustion Monoliths. Catal. Today 2003, 83, 171.
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ReceiVed for reView October 16, 2009ReVised manuscript receiVed January 8, 2010
Accepted January 14, 2010
IE901615D
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