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Transient performance of catalytic combustors for gas turbine applications
ChonirdEngineering .Scicmcc, Vol. 4k. No. Printed in Great Britain.
I. pp. 5564,
TRANSIENT COMBUSTORS
1986. Q
@309-2509/X6 53.00 + 0.00 1986. Pergamon Press Ltd.
PERFORMANCE OF CATALYTIC FOR GAS TURBINE APPLICATIONS
T. AHN, W. V. PlNCZEWSKIt and D. L. TRIMM School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Kensington, NSW 2033, Australia (Received
29 January 1985)
transient response of a monolith catalytic combustor to changes in operatingconditionsand monolith designparameters has been examined on the basis of a mathematical model. The model considers both catalyticand gas phase reactionsand allows for axial conduction of heat in the solid substrate.The transientresponsetime is shown to be determined primarily by the thermal inertia of the monolith with
Abstract-The
metallic monoliths, having lower thermal inertia, offering superior performance to ceramics. Improved performance is also favoured by a square cell geometry rather than triangular or sinusoidal geometry because of the better heat and mass transfercharacteristics of the squarecell geometry. Higher inlet temperatures, operatingpressuresand lower gas velocities are shown to result in faster response times. A step decrease in inlet gas temperature may result in catalyst overheating when either the catalytic (solid phase) or the homogeneous (gas phase) reactions are dominant.
INTRODUCTION Catalytic combustion has been the subject of a number of studies in recent years [l, 21, largely because it is more efficient than gas phase combustion, produces fewer pollutants and can operate with a wide range of fuels and fuel-air ratios. Catalytic combustors used as car exhaust catalysts are perhaps the best known example [3,4] but catalytic units suitable for heaters, boilers and gas turbines have also been developed Cl. 21. Studies of high throughput systems such as gas turbine catalytic combustors show that both catalytic and gas-phase oxidation reactions occur [l, 2, 5, 63. Since both types of reaction produce the same products, a combination of experimental testing and mathematical modelling is required to design and optimize the operation of these devices. Using this approach, it has been possible to develop predictive models which explain the steady-state behaviour of these combustors [7]. In actual applications, however, the cembustors are subjected to frequent changes in operating conditions and therefore it is also necessary to model their transient operation. The purpose of the present study is to develop such a model and to use it to predict the transient behaviour of a typical catalytic gas turbine. Related studies have been carried out by Young and Finlayson [S] and Oh and Cavendish [9] for the car exhaust catalysts, in which homogeneous reactions were assumed negligible_ A transient model for combustors involving both catalytic and gas phase reactions was reported by Tien [lo], but this model was primarily concerned with the homogeneous reactions taking place in the downstream section of the catalyst bed. Moreover, the influence of thermal conduction in
the solid phase on overall combustor performance was ignored. The present paper describes the development o@_ one-dimensional mathematical model which accounts for both catalytic and homogeneous reactions and which includes the effect of solid substrate conductivity on overall monolith combustor performance. The effect of various monolith design parameters and the effect of changes in operating conditions on the transient behaviour of the combustor are examined. DEVELOPMENT OF THE MATHEMATICAL MODEL The monolith converter consists of a large symmetrical array of uniform channels arranged in the form of a honeycomb. The channel walls are coated with catalyst material and the chemical reactions which accompany the gas flow can take place both on the catalyst surface (heterogeneous reaction) and in the gas phase (homogeneous reaction). For the gas turbine converter conditions investigated in the present study, gas velocities in the channels were in the range 15-35 m/s, corresponding to gas phase Reynolds numbers in the range 440-1030. The flow in the channels is therefore laminar. The interaction between the gas flow, the highly exothermic chemical reactions and the simultaneous processes of heat and mass transfer between the gas and the solid substrate are modelled using the following assumptions:
(1) The converter is adiabatic and the flow is uniform
(2)
+To whom correspondence should be addressed. 55
over the cross-section of the converter. All flow channels are thus identical and it is only necessary to model a single flow channel. Radial temperature gradients in the solid phase are negligible. This assumption is justified for r&/r& > 20 [ll]. The value of this ratio is greater than 60 for the present conditions.
56
T.
&IN
et al.
(3) Thermal radiation may be neglected. The relative importance of radiation may be estimated from the ratio of the radiative heat flux to the convective flux written as [12]: o,xDLT: x =
VpC,T,
(1)
*
For the present conditions, this ratio is approximately 0.04, which indicates that little error is introduced into the gas-phase heat balance by neglecting heat transfer by radiation. The effect of radiation on the solid phase temperature is similar to that of a modcst’increase in the solid phase axial conductivity [13] (i.e. a modest reduction in Pe,). (4) Axial diffusion in the gas phase is negligible. This assumption is valid for gas-phase Peclet numbers (Pe,, Pe,) greater than 50 [ll]. For the present conditions Pe, > 310 and Pe, > 670. (6) Accumulation of mass and energy in the gas phase is negligible (quasi-static gas-phase approximation). The accumulation term in the gas-phase material balance may be neglected if the characteristic time for heat transfer between the gas and the solid phases is greater than the gas-phase residence time. Ferguson and Finlayson [14] define this ratio as ~4 -=
=3
(PC,),R,
3h
evaluation of transfer coeflkients as a function of distance from the monolith inlet. (7) Physical properties and velocity of the gas phase are evaluated as a function of temperature along the monolith at a constant or mean pressure, i.e. the pressure drop through the monolith is assumed small. The pressure drop through monoliths is usually small [8] and this has been confirmed for the present conditions by simple Fanning friction factor calculations. Moreover, Stevens and Ziegler [16] have demonstrated that for combustion in monoliths the assumption of constant pressure results in essentially the same temperature and conversion profiles as those obtained with the inclusion of pressure gradient terms, but with considerable savings in computational effort. (8) The surface reaction is taken to be first order in fuel concentration and zero order in oxygen concentration [7]. The gas phase reaction was assumed to be first order in fuel and first order in oxygen [7].
v
Based on these assumptions, the material and energy balances for the gas phase may be written as: s
a( Vcfg) + SZ, exp ___ ax
(
- +
>
8
(Co2
1”
+ ak CCf, - C,) = 0
(2)
Z’
wfd-
-svpC,~+ah(T.-Tg)+S(-AH)Z.
For the present conditions, a typical value of this ratio is 1120 and the gas-phase mass accumulation term may therefore be neglected. The gas-phase energy accumulation term may be neglected if the volumetric ratio of gas-phase and solid-phase heat capacities is less than 0.002 [14]. This ratio is given by
xexp The corresponding phase are
(
--
Et, RTB >
m (COJ
= 0.
For the conditions of the present investigation, C, is found to be less than 0.0006. (6) Radial variations of gas-phase temperature and concentration are integrated across the channel cross-section to yield average or lumped values which are functions only of distance from the converter inlet. The resistances to heat and mass transfer between the gas and solid phases are calculated using the transfer coefficients obtained from appropriate Nusselt and Sherwood number correlations [ 121: 0.45
(4)
> 0.45
Sh = 3.66
(
1 +O.O95RePrg
>
(5)
where the Nusselt and Sherwood numbers are evaluated at the mean of the inlet and outlet conditions. Calculations confirmed that this introduccd only minor errors as compared to point
(7)
balance equations for the solid
k(Cfs - Cfs) = Z, exp
1 +O.O95RePrg
(6)
(8) Cf*
=
P.C&~.
(9)
Also, from the stoichiometry and continuity:
CO* -=
(
P
VCfg
l- 9 1- ( VC,),
(Co210
v=
>
P(O, t) VW, 0.
(10) (11)
The appropriate boundary and initial conditions are Cf,
2
(09 t)
=
(0, t) =
Wf&JO
2
T,
(O,t)
=
V”),
(IL, t) = 0
Ts (x, 0) = specified ( = (T, )o).
The governing equations (6 j(9) are made dimensionless by introducing the following dimensionless variables:
Transientperformanceof catalytic combustors
57
bution of mass and energy over the channel crosssection, have been proposed [4,8,11-j, the simpler onedimensional models have been demonstrated to predict monolith behaviour which is quantitatively similar to that predicted by the two-dimensional models, but with a great reduction in computational effort [4, 81. Since gas velocity variations depend only on gas temperature, we may write -, m “=Y=Ig=, (14) *’ V, To Then,
_4exp(Yh(~-l))au"(l~~1--))
acfJ -=
ac-Jo(f+)y
(15)
+we,-0,) (17)
NUMERICAL
SOLUTION
g
=L
(0, es, 0,)
(21)
8
ae =x (a, es, 0,) ac
(22)
de,_, ac -
(23)
dR = Pe, I;(w.O~,O,)+~~ X (
aze, = Pe~!J~(~~--8,)-~TD,exp(Yc(~~~1))~f,
PROCEDURE
The set of eqs (14k(18) with boundary conditions (20) constitute the transient combustor model. The dependence of the governing equations on tir. is eliminated by substitution of eq. (17) into eqs (15) and (18). The second-order differential eq. (18) is split into two equivalent first-order differential equations. These operations result in the following set of equations:
)
(24)
where
x2
(18) where
--
--
012 J,
Yh
=
6,
RT,
Yc =
vt, (19)
= (,,(&, r = (Gs), (-AH)
EC
RT,
PoC,G
f4 = Jo+DCexp(Yc’e~~-l)).
Finally, the boundary and initial conditions become ~(0,~)
=
eg(o17) = i
(20)
8, (C,0) = specified ( = (O,to). The above assumptions and equations constitute a lumped parameter one-dimensional model similar to a number of previously proposed models for combustion in monoliths, e.g. [4, 7-l 1, 16, 173. These models all use heat, mass and momentum transfer coefficients for fully developed flow in the monolith channels to account for the resistance to transfer between the fluid and the channel wall. Although more complex twodimensional models, which account for the distri-
The above system of equations is solved numerically using a straightforward finite difference scheme; central difference operators are used to approximate the spatial derivatives and a backward difference approximation is used for the time derivative. These approximations reduce the system of partial differential equations to a system of non-linear algebraic equations, which are solved simultaneously using the Newton-Raphson method [ 1 S]. The Jacobians of fi to fj form a banded block bi-diagonal matrix and the block elimination procedure suggested by Lentini and Pereyra [ 193 was employed to solve the resultant set of linearized equations. The wall temperatures are estimated from either the initial condition or the previous time step calculations and the computations are continued in an iterative fashion until computed temperatures and concentrations show less than 0.5 y0 variation between consecutive iterations.
T.
58 RESULTS
AND
AHN et al.
DISCUSSION
The transient behaviour of a typical catalytic combustor was studied using propylene as a fuel for a variety of inlet conditions. The standard set of operating conditions adopted for this study correspond to those used in the experimental study reported by Engelhard El]: q,, = 662 K
P = 1 atm
5, = 18.3 m/s
Cp= 0.37. (26)
The kinetic parameters used in the computations are given in Table 1. The catalyst involved platinum suspended in an alumina washcoat and supported on a 31 cell/cm2 ceramic monolith with triangular channels. Typical dimensions and physical properties are listed in Table 2. Some calculations were also carried out with a metallic monolith of 62 cell/cm’ cell density; the properties of this material are also given in Table 2.
I
,1200\
,<’
4s a t %lOOO/
800-
Catalytic combustors need to bc preheated to a temperature where oxidation can begin. For the propylene/air fuel mixtures used in the present study, a temperature of 400 K is sufficient and all calculations were performed with the monolith preheated to this temperature. The computed warm-up response of a combustor burning fuel at the standard inlet conditions (26) is shown in Fig. 1, in which gas and solid phase temperatures along the monolith axis are plotted as a function Table
1. Kinetic parameters of propylene Pt/Al, 0, C71
oxidation
over
Forms of rate expression Homogeneous
- rs = 2, exp
Catalytic
-rc
= 2, exp
Value
Parameter 2.87 x 10” 40.~ 9.14 Y 104 12,000
=h
Eh =, Ee
cm3 mol-r cal mol-r ems-’ cal mol-’
s-r
Table 2. Properties of the monoliths [ZO]
Properties Length (cm) Diameter (cm) Cell area (cm2) Solid area (cm2) Wetted perimeter (cm) Thermal conductivity @l/cm s K) Fraction open area Density (g cm - 3, Heat capacity (cal g-r K-‘)
Metallic Ceramic (31 cell/cm*) (62 cell/cm’) 10
0.15 2.3 x lo-’ 9.3 X 1o-3 0.62 5.55 X 1o-4 0.713 2.5 0.219
10
0.12 1.5 X 10-Z 1.1 x 10-s 0.54 5.55 x lo- = 0.890 7.76 0.11
18s
/’
,sC/’
600 -
----
-.
-.
-__
Ts Tg
35 -;_,----
---_
t=o+
coo
0
warm-up
/-/’
//
I
Combustor
_---
J 4
I
z z
18s
/j
02
1
04 Monolith
06 length
0.8
1.0
Ix/L)
Fig. 1. Transient solid and gas-phase temperature profiles following a step increase in inlet gas temperature ITsi, = 662 K, P = 1 atm, Vi, = 18.3 m/s, 4 = 0.37, T,(x, 0) =4OOK). of combustion time. At early times (t = O-3 s) the inlet gas stream is hotter than the solid and the entire solid section is heated by convective heat transfer from the gas. Shortly after t = 3 s, the solid temperature at the inlet becomes sufficiently high to light-off the solidphase catalytic -reaction. The heat released by the surface reaction rapidly raises the temperature of the solid above that of the gas (t = 18 s) and heat is convected downstream by the gas. As the gas temperature increases with axial distance from the inlet, the temperature at the outlet becomes sufficient to lightoff the gas-phase homogeneous reaction (t > 18 s). The gas temperature in the upstream section of the monolith continues to rise as a result of the heat released by the catalytic surface reaction in the inlet section and, as a result, the temperature required to sustain a significant level of reaction in the gas phase moves upstream from the exit of the monolith (t = 38 s). The gas phase reaction is very fast and is accompanied by rapid heat release which raises the gas temperature above that of the solid. The downstream section of the monolith is then heated by convective heat transfer from the gas and the solid phase temperature in the downstream section of the monolith rises above that at the inlet. Steady-state conditions are reached after 68 s. The steady-state solid temperature profile displays a local minimum slightly upstream of the point at which the homogeneous gas-phase reaction becomes important, with the highest temperature being achieved near the monolith outlet. Gas phase temperature increases with axial distance from the monolith inlet, with the rate of temperature increase rising rapidly at the lightoff point for the homogeneous reaction. The minimum in the solid-phase temperature profile arises as a result
Transientperformanceof catalytic combtutors of the interaction between the heat released by the catalytic solid-phase reaction, the homogeneous gasphase reaction and the convective transport of this heat by the gas. At the monolith inlet (where the catalytic solid-phase reaction is dominant), the cooler gas stream cools the solid and solid temperature decreases with distance from the inlet. In the downstream section of the monolith (where the homogeneous gas-phase reaction is dominant), the gas is hotter than the solid and the hot gas heats the cooler solid phase. The solid increases with distance temperature therefore downstream resulting in a minimum in the temperature profile. In the early stages of warm-up, the transient response of the combustor is expected to be strongly influenced by the thermal inertia of the solid substrate. In the present model a measure of the substrate thermal capacity is given by the dimensionless parameter ai, where
a = 1
(PCp).S, @CpkS .
(27)
Figure 2 shows the results of a series of computations to determine the effect of substrate thermal capacity on the time required to achieve equilibrium conditions for the standard condition case, (26): the time taken to attain the steady-state condition is plotted against the thermal capacity ratio, al. The sharp decrease in the response time as a1 increases clearly indicates that a monolith with a smaller solid cross-sectional area (i.e. thin walls), a lower density and a lower heat capacity will result in a faster transient response. Similar conclusions have been reported by Tien [lo]. Variations in operating conditions Having established the behaviour of the monolith for standard conditions, the effect of changing operating conditions on monolith performance was studied by varying each of the conditions in turn whilst
59
maintaining the remaining conditions as for the standard case of (26). The first operating variable to be examined was the inlet gas temperature, and a plot of exit conversion vs. time for various values of the gas inlet temperature is shown in Fig. 3. At T in = 500 K, the catalytic reaction rate is slow and insu & crent heat is generated to initiate the gas phase reaction. At Tgin > 600 K, the increased heat release by the catalytic reaction is sufEcient to raise the gas phase temperature to levels sufficient to initiate the gas phase reaction, which is accompanied by a sharp increase in exit conversion. The higher the inlet gas temperature, the shorter the time to achieve a given level of conversion. Figure 4 shows the effect of increasing the equivalence ratio (4) on the exit conversion as a function of combustion time. The behaviour is similar to that of increasing inlet gas temperature discussed above. At low equivalence ratio (4 = 0.25) (i.e. low inlet fuel concentration), there is insufficient heat release by the catalytic reaction to initiate the homogeneous gasphase reaction. As the equivalence ratio is increased more heat is released by the catalytic reaction and td resulting gas temperature is sufficient to light-off the
Tnme
Is1
Fig 3. Effectof gas inlet temperatureon exit conversionas a function of time (P = 1 atm, V, = 18.3 m/s, d = 0.37, T,(x, 0) = 400 K). 120 r 9100.-E 4 f ; t z 2
80-
60-
LO-
20 t
I
L
OO
1000 CL.
Solid
to
gas
ZOW heat
capacity
3000
I
60
ratio
Fig. 2. Effect of solid to gas heat capacityratio on response time for converter.1, Time to reach steady-statesolid-phase temperature;2, time to reach steady-stateexit conversion (rain = 662 K, P = 1 atm, V, = 18.3 m/s, $ = 0.37).
Time
(sl
Fig. 4. E&et of fuel-air ratio I&) on exit conversion as a friction of time (Tsi, = 662 K,.p = 1 atm, Vb = 18.3 m/s, T,(x, 0) = 400 K).
T. AHN et al.
60
homogeneous reaction (r&= 0.33). At a higher equivalence ratio (4 = 0.4), the rate of heat release increases and the time required to light-off the homogeneous reaction decreases. The effect of inlet gas velocity on the time required to achieve a particular exit conversion is shown in Fig. 5. The effect of decreasing gas velocity is similar to that of increasing inlet gas temperature or increasing equivalence ratio. Increasing gas velocities result in reduced gas-phase residence times and increased heat and mass transfer coefficients. Figure 5 shows that the dominant effect is the reduction in gas-phase residence time and the consequent reduction in heat release by the catalytic reaction. At a high inlet gas velocity ( V, = 35 m/s), the heat release by the catalytic reaction is insufficient to heat the gas to the temperature required to light-off the homogeneous reaction. An inlet velocity of 25 m/s is sufficient to initiate the homogeneous reaction with lower velocities, resulting in earlier light-off and higher exit conversions. These findings are in accord with the experimental results reported by Prasad et ~2. [21]. The effect of pressure on monolith performance is considerably more complicated. This is because pressure affects a number of important parameters including mass flow rate through the combustor, reaction rates (fuel concentration) and both heat and mass transfer rates. These, in turn, have different effects on overall monolith performance. Figure 6 shows computed conversions as a function of time for pressures of 1, 2 and 3 atm, respectively. At earlier times (t = 3 s), conversion is primarily due to the progress of the solid-phase catalytic reaction. This is governed by the rate at which the hot gas heats the initially cooler solid by convective transport. The heat transfer coefficient at a pressure of 2 atm (Ju = 1.37) is higher than the corresponding value at 3 atm (Jr., = 1.01) and, as a result, the solid temperature is higher in the former case. The higher surface temperature results in a faster catalytic reaction and hence higher conversion for the 2 atm pressure case. Although the heat transfer coefficient is highest for the 1 atm
Time
Fig. 6. Effect of system pressure on exit conversion as a function of time (T&in = 662 K. Vi” = 18.3 m/s, 4 = 0.37, T, (x, 0) = 400 K). pressure case, here, the mass flow rate is comparatively low and hence the heating capacity of the gas stream is greatly reduced. Both solid surface temperature and conversion are therefore lowest for this case. At t = 13 s, the rate of catalytic reaction is high and conversion becomes mass-transfer limited. Since the mass transfer rate decreases with increasing pressure (.I,, = 1.12 at 1 atm, Jo = 0.68 at 2 atm and J, = 0.52 at 3 atm), the surface concentration of fuel and hence the catalytic reaction rate decrease with increasing pressure. Conversion at this time therefore decreases with increasing pressure. At t = 18 s, the gas temperature is sufficient to light-off the homogeneous reaction. Unlike the catalytic reaction, the homogeneous reaction is not mass-transfer limited and, as a consequence, the reaction rate and hence conversion, increases with the increasing fuel concentration associated with increasing pressure. Variations
I
60 Tim
c
(5)
Fig. 5. Effect of gas inlet velocity on exit conversion as a function of time (T’i,, = 662 K, P = 1 atm, 4 = 0.37,T’.(x, 0) =4OOK).
Is)
in mono&h
design parameters
Metallic or ceramic monoliths may be used in a catalytic combustor, and the length and shape of the monolith channels can be varied. The length of the monolith affects the residence time. The effect of residence time on transient behaviour has been discussed above and has been previously investigated using a steady-state model [9]. We therefore consider the effect of monolith type and channel geometry on overall combustor performance. The characteristics of the two types of monolith (metallic and ceramic) studied are given in Table 2. It is noted that a change from a cell density of 31 to 62 cell/cm’ is realized by changing the substrate material from ceramic to metallic. This, of course, results in a change in other monolith parameters, the most important of which is the lower thermal inertia of the metallic monolith. A comparison of the performance
Transient performance of catalytic combustors
of the two monoliths is shown in Fig. 7, in which exit conversion is plotted against combustion time. The metallic monolith clearly displays superior light-off and conversion characteristics. This is due to the higher surface to volume ratio of the metallic monolith which results in a larger catalytically active surface area and improved mass transfer performance. The metallic monolith is therefore much faster in responding to changes in operating conditions than the ceramic monolith. The effect of different channel geometries is shown in Fig. 8. Higher conversions are achieved with squareshaped channels than with triangular or sinusoidal channels. The asymptotic Nusselt (Nu) and Sherwood (Sh) numbers for laminar flow in ducts depend on duct shape and decrease in the order square > triangular > sinusoidal [22]. As a result, square channel ducts offer a lower resistance to heat and mass transfer between the flowing gas and the catalyst surface which results in an earlier light-off of the catalytic reaction and hence the homogeneous reaction.
.-z r=a.4 z ”
2
0.2
61
Over-temperature phenomenonfollowing a step decrease in the feed gas temperature No gas phase reaction. When the power requirement decreases, an initially hot monolith experiences a step decrease in the temperature of the inlet gas stream as a relatively cooler fuel-air mixture enters the monolith. Young and Finlayson [S] and Oh and Cavendish [93 have previously shown that, for car exhaust gas catalytic converters (no homogeneous gasphase reaction), this may result in a transient rise in the temperature of the solid phase above the initial temperature. This transient over-temperature phenomenon is important because it may lead to converter failure if the resulting monolith temperature approaches the solid softening or melting temperature. Figure 9 shows the computed response of a converter cooled from an initial solid phase of 700 K by a gas with an inlet temperature of 400K. Under these conditions, the homogeneous reaction is negligible (T. -z 750 K) and the response is similar to that reported previously [S, 91. The catalytic reaction in the front section of the monolith is quenched by the cooler gas stream and, as a consequence, unreacted fuel is transported downstream where the solid temperature is still high. The combination of high solid temperature and high fuel concentration results in rapid heat release by the catalytic surface reaction in the downstream section of the monolith. This causes the downstream solid temperature to rise. As the inlet section becomes cooler, more unreacted fuel is convected downstream and the temperature rise in the downstream solid increases (t = 18 s). As the temperature transient moves through the monolith, the reaction front moves towards the exit (t = 30 s) and eventually blows out. Steady-state conditions are reached after 86 s. Calculations have shown that, for the conditions of
l!!!_-
OO
10
20
Time
Is.1
30
Fig. 7. Effect of monolith type (metallic,ceramic) on exit conversionas a function of time (T&in = 662 K, P = 1 atm, & = 18.3 m/s, I$ = 0.37. T,(x,O) = 400 K).
800 t
-
Ts
lo-
___--I
0 Time
(sl
Fig. 8. Effect of monolith channel sha~sinusoidal, A exit don=12.12; triangular, A = 2.35; square, A =-2.9-n version as a function of time (T&in = 662 K, P = 1 atm, Vi, = 18.3 m/s, # = 0.37, T,(x, 0) = 400 K).
06s
I
02
OL tionolith
0.6 length
0.0
I
1.0
(x/L1
Fig. 9. Transient solid and gas-phase temperature profiles following a step decrease in the inlet gas temperature(TGin =4OK, P=latm, Vi:,,=18.3m/s, Q=O.2 T,(x,O) = 700 K).
T. AHN et
62
Fig. 9, the over-temperature phenomenon is absent if the monolith is cooled from 1000 K, and small if cooled from 800 K. At these temperatures the driving force for convective heat transfer from the wall to the cooler gas stream increases, whilst the heat release rate remains relatively constant because the surface reaction is mass-transfer limited. The increased rate of heat loss from the solid surface for these cases prevents serious solid over-temperature. A low equivalence ratio also prevents over-temperature of the solid because of the reduced rate of heat generation (low fuel concentration). Sur$ace and gas phase reactions. In gas turbine applications, both catalytic solid-phase and homogeneous gas-phase reactions contribute significantly to the overall combustion process with solid phase temperatures in the range 1360-1980 K at high load conditions [2]. Figure 10 shows computed temperature profiles for typical gas turbine conditions after a hot monolith at 14OOK has been subjected to a gas stream at 700 K. On the inlet section of the monolith, the solid phase temperature falls with time as the solid is cooled by the incoming gas stream. As the solid temperature falls, the rate of surface reaction decreases and unreacted fuel is convected downstream where temperatures are higher. As for the previously discussed case of car exhaust converters, the downstream solid temperature increases as a result of increased heat release by the solid phase reaction (x/L < 0.4). However, the temperature rise is small due to a predominantly mass-transfer limited condition. At x/L > 0.4 (t = 3 s), the gas temperature is sufficient to initiate the homogeneous reaction and the gas temperature increases rapidly to exceed the solid temperature (x/L = 0.8). The homogeneous reaction quickly reduces the fuel concentration in the gas phase and,
lSO0 r
_---_
----
I 0
1
I
I
0.6
0.8
10
I
02
0.4 Honollth
Ts Tg
length
Ix/L)
Fig. 10. Transient solid and gas-phase temperature profiles following a gas decrease in inlet gas temperature (Tain &, = 18.3 m/s, I$ = 0.25, T,(x.O) =7OOK, P= latm, = 1400 K).
al.
since the catalytic solid-phase reaction is mass-transfer controlled, the rate of heat generation on the solid is also reduced. As the monolith continues to cool (t = 18 s), the homogeneous reaction front moves further downstream and eventually blows out with a consequent decrease in the temperature of the gas phase. The bulk of reaction now takes place on the catalyst surface and hence the gas temperature falls below the solid temperature. After t = 48 s, the solid and gas phases reach their respective new steady-state temperatures. Similar computations for C$= 0.2 show the existence of smaller magnitude over-temperature effects in both gas and solid reflecting the lower heat generation capacity of the reactant mixture. This trend continues with decreasing equivalence ratio until the heat generated by catalytic and homogeneous reactions is insufficient to cause overheating. The major difference between the over-temperature phenomenon in car exhaust converters and gas turbine combustors is due to the importance of the gas phase reaction for the latter case. For car exhaust converters the heat is generating on the solid surface and heat is removed at a rate which is heat-transfer limited. For gas turbines, the bulk of the heat is generating in the gas phase (no mass transfer limitation) with the hotter gas convectively heating the solid. For the conditions shown in Figs 9 and 10 the solid over-temperature is of the order of 50 K. CONCLUSIONS
A transient catalytic combustor model which accounts for both catalytic and homogeneous reactions within the monolith channels has been developed and used to investigate the performance of gas turbine combustors. Computations based on the model show that fast combustor response to changes in operating conditions is favoured by monoliths with thin walls, low density and low heat capacity. High cell density metallic monoliths are therefore superior in their transient response performance to ceramic monoliths. Channel geometry affects monolith performance as a result of the differences in heat and mass transfer characteristics_ Square-shaped channels display a better overall performance than triangular or sinusoidal geometries. High inlet temperatures, equivalence ratios and low inlet velocities result in higher combustion efficiencies and shorter response times. Higher inlet pressures allow higher throughput even though the higher pressures are associated with increased heat and mass transfer resistance. This is largely due to the enhancement of the homogeneous gas-phase reaction with increasing pressure. When a cool reactant mixture is introduced into an initially hot catalytic monolith, it is possible to observe a solid wall over-temperature phenomenon in which the wall temperature temporarily exceeds the initial temperature. For conditions which result in gas temperatures sufficiently high to initiate the homogeneous gas-phase reaction, the gas temperature may temporarily exceed the solid phase temperature. This gas-
Transient performance
phase over-temperature converters
where
gas
does not occur in car exhaust phase
reactions
are
negligible
[S, 93. For the gas turbine conditions investigated, the magnitude of the over-temperature phenomenon was small and therefore unlikely to limit seriously combus-
of catalytic eombustors
homogeneous pre-exponential (g mol/cm3)’ -“- m/s
Zh Greek
thermal capacity ratio dimensionless adiabatic flame temperature dimensionless catalytic activation energy dimensionless homogeneous activation energy dimensionless axial distance ( = x/L) dimensionless gas temperature dimensionless solid temperature gas conductivity, cal/cm s K solid substrate conductivity, Cal/cm s K gas viscosity, g/ems dimensionless velocity density of gas, g/cm” density of solid, g/cm3 wetted perimeter, cm Stefan-Boltzman constant dimensionless time ratio of time constant for heat transfer to catalyst to gas residence time equivalent ratio
Acknow/edgemenr-The authors acknowledge with gratitude financial support from the Aero Division of Rolls-Royce Company.
NOTATION
Cfg Cfs
CO* CP C,
D,d
DC Dh
Di
EC Eh h (-AH)
JD JH k L m n
NU P Pe, Pe, Peh Pr R R, -rC -rH rhf Ihs
Re s Ss Sh t to Tg Tm Tin T, T S.0 V vim X =c
vO
factor,
letters
tor performance.
gas phase fuel concentration, g mol/cm’ solid phase fuel concentration, g mol/cm’ oxygen concentration, g mol/cm3 specific heat capacity, Cal/g K heat capacity ratio monolith channel diameter, cm catalytic Damkohler number homogeneous Damkohler number diffusivity coefficient, cm*/s catalytic activation energy, Cal/g mol homogeneous activation energy, Cal/g mol heat transfer coefficient, Cal/s cm2 K heat of reaction, Cal/g mol mass transport number heat transfer number mass transfer coefficient, cm/s monolith length, cm homogeneous reaction order with respect to fuel concentration homogeneous reaction order with respect to oxygen concentration Nusselt number ( = hd/Q pressure (atm) solid-phase Peclet number for heat transfer Peclet number for mass transfer Peclet number for heat transfer Prandtl number ( = C&As) universal gas constant ( = 82.05 cm3 atm/g mol K) channel radius surface reaction rate, g mol/cm2 s homogeneous reaction rate, g mol/cm3 s hydraulic radius of a channel hydraulic radius of solid Reynolds number ( = p Vd/p) channel cross-sectional area, cm* solid cross-sectional area, cm* Sherwood number ( = kd/DJ time, s arbitrary time scale factor, s gas temperature inlet gas temperature, K solid temperature, K solid temperature at the initial state linear velocity, cm/s inlet gas velocity, cm/s axial distance, cm catalytic pre-exponential factor, cm/s
63
= (
actual air/fuel ratio stoichiometric air/fuel ratio >
dimensionless dimensionless dimensionless dimensionless
gas-phase fuel concentration solid-phase fuel concentration solid temperature gradient mass fraction
REFERENCES
Pfefferle W. C., Heck R. M.,, Carrubba R. V. and Roberts G. W., A.S.M.E. Paper 1975 No. 75WA. Fu1. Siminski V. I. and Shaw H., 22nd Annual Lnt. Gas Turbine Conf., A.S.M.E., Philadelphia, PA, March 1977. Wei J., Adv. Catal. 1975 24 57. Heck R. H., Wei J. and Katzer J. R., A.1.Ch.E. J. 1976 22 47-i.
.
.
Pfefferle W. C., A.S.M.E. Paper 1979 No. 79-HT-52. Anderson D. N., 3rd Workshop on Catalytic Combustion, Asheville, NC, Oct. 1978. Cerkanowicz A. E., Cole R. B. and Stevens J. G., .I. Engng Power 1977 593. Young L. C. and Finlayson B. A., A.I.Ch.E. J. 1976 22 343.
Oh S. H. and Cavendish J. C., Ind. Engng Chem. Prod. Res. Dev. 1982 21 29. T’ien J. S., Combusr. Sci. Technol. 1981 26 65. Young L. C. and Finlayson B. A., A.I.Ch.E. J. 1976 22 331. Sinkule J. and Hlavacek V., Chem. Engng Sci. 1978 33 839. Eigenberger G., Chem. Engng Sci. 1972 27 1917. Ferguson N. B. and Finlayson B. A., A.1.Ch.E. J. 1974 20 539. Hawthorn R. D., A.I.Ch.E. Symp. Ser. 1974 70 428. Stevens J. G. and Ziegler E. N., Chem. Engng Sci. 1977 32 385. Votruba J.. Sinkule J.. Hlavacek V. and Skrivanek J. Chem. En& Sci. 197g 30 117. Carnahan B., Luther B. A. and Wilkes J. O., Applied
64
T. AHN et al.
Numerical Methods. p. 508. Wiley, New York 1967. 19] Lentini M. and Peceyra V., Math. Comput. 1974 23 98 1. E203 Cooper B. J. E/Pc/7370, R esearch Project No. 197. University of Trondheim, Norway 1978.
[21] [22]
Prasad R., Tsai H. L.. Kennedy L. A. and Ruckenstein E., Combust. Sci. Technol. 1980 25 71. Shar R. K. and London A. L.. Stanford University, Technical Report No. 75, 1971.
I. pp. 5564,
TRANSIENT COMBUSTORS
1986. Q
@309-2509/X6 53.00 + 0.00 1986. Pergamon Press Ltd.
PERFORMANCE OF CATALYTIC FOR GAS TURBINE APPLICATIONS
T. AHN, W. V. PlNCZEWSKIt and D. L. TRIMM School of Chemical Engineering and Industrial Chemistry, University of New South Wales, Kensington, NSW 2033, Australia (Received
29 January 1985)
transient response of a monolith catalytic combustor to changes in operatingconditionsand monolith designparameters has been examined on the basis of a mathematical model. The model considers both catalyticand gas phase reactionsand allows for axial conduction of heat in the solid substrate.The transientresponsetime is shown to be determined primarily by the thermal inertia of the monolith with
Abstract-The
metallic monoliths, having lower thermal inertia, offering superior performance to ceramics. Improved performance is also favoured by a square cell geometry rather than triangular or sinusoidal geometry because of the better heat and mass transfercharacteristics of the squarecell geometry. Higher inlet temperatures, operatingpressuresand lower gas velocities are shown to result in faster response times. A step decrease in inlet gas temperature may result in catalyst overheating when either the catalytic (solid phase) or the homogeneous (gas phase) reactions are dominant.
INTRODUCTION Catalytic combustion has been the subject of a number of studies in recent years [l, 21, largely because it is more efficient than gas phase combustion, produces fewer pollutants and can operate with a wide range of fuels and fuel-air ratios. Catalytic combustors used as car exhaust catalysts are perhaps the best known example [3,4] but catalytic units suitable for heaters, boilers and gas turbines have also been developed Cl. 21. Studies of high throughput systems such as gas turbine catalytic combustors show that both catalytic and gas-phase oxidation reactions occur [l, 2, 5, 63. Since both types of reaction produce the same products, a combination of experimental testing and mathematical modelling is required to design and optimize the operation of these devices. Using this approach, it has been possible to develop predictive models which explain the steady-state behaviour of these combustors [7]. In actual applications, however, the cembustors are subjected to frequent changes in operating conditions and therefore it is also necessary to model their transient operation. The purpose of the present study is to develop such a model and to use it to predict the transient behaviour of a typical catalytic gas turbine. Related studies have been carried out by Young and Finlayson [S] and Oh and Cavendish [9] for the car exhaust catalysts, in which homogeneous reactions were assumed negligible_ A transient model for combustors involving both catalytic and gas phase reactions was reported by Tien [lo], but this model was primarily concerned with the homogeneous reactions taking place in the downstream section of the catalyst bed. Moreover, the influence of thermal conduction in
the solid phase on overall combustor performance was ignored. The present paper describes the development o@_ one-dimensional mathematical model which accounts for both catalytic and homogeneous reactions and which includes the effect of solid substrate conductivity on overall monolith combustor performance. The effect of various monolith design parameters and the effect of changes in operating conditions on the transient behaviour of the combustor are examined. DEVELOPMENT OF THE MATHEMATICAL MODEL The monolith converter consists of a large symmetrical array of uniform channels arranged in the form of a honeycomb. The channel walls are coated with catalyst material and the chemical reactions which accompany the gas flow can take place both on the catalyst surface (heterogeneous reaction) and in the gas phase (homogeneous reaction). For the gas turbine converter conditions investigated in the present study, gas velocities in the channels were in the range 15-35 m/s, corresponding to gas phase Reynolds numbers in the range 440-1030. The flow in the channels is therefore laminar. The interaction between the gas flow, the highly exothermic chemical reactions and the simultaneous processes of heat and mass transfer between the gas and the solid substrate are modelled using the following assumptions:
(1) The converter is adiabatic and the flow is uniform
(2)
+To whom correspondence should be addressed. 55
over the cross-section of the converter. All flow channels are thus identical and it is only necessary to model a single flow channel. Radial temperature gradients in the solid phase are negligible. This assumption is justified for r&/r& > 20 [ll]. The value of this ratio is greater than 60 for the present conditions.
56
T.
&IN
et al.
(3) Thermal radiation may be neglected. The relative importance of radiation may be estimated from the ratio of the radiative heat flux to the convective flux written as [12]: o,xDLT: x =
VpC,T,
(1)
*
For the present conditions, this ratio is approximately 0.04, which indicates that little error is introduced into the gas-phase heat balance by neglecting heat transfer by radiation. The effect of radiation on the solid phase temperature is similar to that of a modcst’increase in the solid phase axial conductivity [13] (i.e. a modest reduction in Pe,). (4) Axial diffusion in the gas phase is negligible. This assumption is valid for gas-phase Peclet numbers (Pe,, Pe,) greater than 50 [ll]. For the present conditions Pe, > 310 and Pe, > 670. (6) Accumulation of mass and energy in the gas phase is negligible (quasi-static gas-phase approximation). The accumulation term in the gas-phase material balance may be neglected if the characteristic time for heat transfer between the gas and the solid phases is greater than the gas-phase residence time. Ferguson and Finlayson [14] define this ratio as ~4 -=
=3
(PC,),R,
3h
evaluation of transfer coeflkients as a function of distance from the monolith inlet. (7) Physical properties and velocity of the gas phase are evaluated as a function of temperature along the monolith at a constant or mean pressure, i.e. the pressure drop through the monolith is assumed small. The pressure drop through monoliths is usually small [8] and this has been confirmed for the present conditions by simple Fanning friction factor calculations. Moreover, Stevens and Ziegler [16] have demonstrated that for combustion in monoliths the assumption of constant pressure results in essentially the same temperature and conversion profiles as those obtained with the inclusion of pressure gradient terms, but with considerable savings in computational effort. (8) The surface reaction is taken to be first order in fuel concentration and zero order in oxygen concentration [7]. The gas phase reaction was assumed to be first order in fuel and first order in oxygen [7].
v
Based on these assumptions, the material and energy balances for the gas phase may be written as: s
a( Vcfg) + SZ, exp ___ ax
(
- +
>
8
(Co2
1”
+ ak CCf, - C,) = 0
(2)
Z’
wfd-
-svpC,~+ah(T.-Tg)+S(-AH)Z.
For the present conditions, a typical value of this ratio is 1120 and the gas-phase mass accumulation term may therefore be neglected. The gas-phase energy accumulation term may be neglected if the volumetric ratio of gas-phase and solid-phase heat capacities is less than 0.002 [14]. This ratio is given by
xexp The corresponding phase are
(
--
Et, RTB >
m (COJ
= 0.
For the conditions of the present investigation, C, is found to be less than 0.0006. (6) Radial variations of gas-phase temperature and concentration are integrated across the channel cross-section to yield average or lumped values which are functions only of distance from the converter inlet. The resistances to heat and mass transfer between the gas and solid phases are calculated using the transfer coefficients obtained from appropriate Nusselt and Sherwood number correlations [ 121: 0.45
(4)
> 0.45
Sh = 3.66
(
1 +O.O95RePrg
>
(5)
where the Nusselt and Sherwood numbers are evaluated at the mean of the inlet and outlet conditions. Calculations confirmed that this introduccd only minor errors as compared to point
(7)
balance equations for the solid
k(Cfs - Cfs) = Z, exp
1 +O.O95RePrg
(6)
(8) Cf*
=
P.C&~.
(9)
Also, from the stoichiometry and continuity:
CO* -=
(
P
VCfg
l- 9 1- ( VC,),
(Co210
v=
>
P(O, t) VW, 0.
(10) (11)
The appropriate boundary and initial conditions are Cf,
2
(09 t)
=
(0, t) =
Wf&JO
2
T,
(O,t)
=
V”),
(IL, t) = 0
Ts (x, 0) = specified ( = (T, )o).
The governing equations (6 j(9) are made dimensionless by introducing the following dimensionless variables:
Transientperformanceof catalytic combustors
57
bution of mass and energy over the channel crosssection, have been proposed [4,8,11-j, the simpler onedimensional models have been demonstrated to predict monolith behaviour which is quantitatively similar to that predicted by the two-dimensional models, but with a great reduction in computational effort [4, 81. Since gas velocity variations depend only on gas temperature, we may write -, m “=Y=Ig=, (14) *’ V, To Then,
_4exp(Yh(~-l))au"(l~~1--))
acfJ -=
ac-Jo(f+)y
(15)
+we,-0,) (17)
NUMERICAL
SOLUTION
g
=L
(0, es, 0,)
(21)
8
ae =x (a, es, 0,) ac
(22)
de,_, ac -
(23)
dR = Pe, I;(w.O~,O,)+~~ X (
aze, = Pe~!J~(~~--8,)-~TD,exp(Yc(~~~1))~f,
PROCEDURE
The set of eqs (14k(18) with boundary conditions (20) constitute the transient combustor model. The dependence of the governing equations on tir. is eliminated by substitution of eq. (17) into eqs (15) and (18). The second-order differential eq. (18) is split into two equivalent first-order differential equations. These operations result in the following set of equations:
)
(24)
where
x2
(18) where
--
--
012 J,
Yh
=
6,
RT,
Yc =
vt, (19)
= (,,(&, r = (Gs), (-AH)
EC
RT,
PoC,G
f4 = Jo+DCexp(Yc’e~~-l)).
Finally, the boundary and initial conditions become ~(0,~)
=
eg(o17) = i
(20)
8, (C,0) = specified ( = (O,to). The above assumptions and equations constitute a lumped parameter one-dimensional model similar to a number of previously proposed models for combustion in monoliths, e.g. [4, 7-l 1, 16, 173. These models all use heat, mass and momentum transfer coefficients for fully developed flow in the monolith channels to account for the resistance to transfer between the fluid and the channel wall. Although more complex twodimensional models, which account for the distri-
The above system of equations is solved numerically using a straightforward finite difference scheme; central difference operators are used to approximate the spatial derivatives and a backward difference approximation is used for the time derivative. These approximations reduce the system of partial differential equations to a system of non-linear algebraic equations, which are solved simultaneously using the Newton-Raphson method [ 1 S]. The Jacobians of fi to fj form a banded block bi-diagonal matrix and the block elimination procedure suggested by Lentini and Pereyra [ 193 was employed to solve the resultant set of linearized equations. The wall temperatures are estimated from either the initial condition or the previous time step calculations and the computations are continued in an iterative fashion until computed temperatures and concentrations show less than 0.5 y0 variation between consecutive iterations.
T.
58 RESULTS
AND
AHN et al.
DISCUSSION
The transient behaviour of a typical catalytic combustor was studied using propylene as a fuel for a variety of inlet conditions. The standard set of operating conditions adopted for this study correspond to those used in the experimental study reported by Engelhard El]: q,, = 662 K
P = 1 atm
5, = 18.3 m/s
Cp= 0.37. (26)
The kinetic parameters used in the computations are given in Table 1. The catalyst involved platinum suspended in an alumina washcoat and supported on a 31 cell/cm2 ceramic monolith with triangular channels. Typical dimensions and physical properties are listed in Table 2. Some calculations were also carried out with a metallic monolith of 62 cell/cm’ cell density; the properties of this material are also given in Table 2.
I
,1200\
,<’
4s a t %lOOO/
800-
Catalytic combustors need to bc preheated to a temperature where oxidation can begin. For the propylene/air fuel mixtures used in the present study, a temperature of 400 K is sufficient and all calculations were performed with the monolith preheated to this temperature. The computed warm-up response of a combustor burning fuel at the standard inlet conditions (26) is shown in Fig. 1, in which gas and solid phase temperatures along the monolith axis are plotted as a function Table
1. Kinetic parameters of propylene Pt/Al, 0, C71
oxidation
over
Forms of rate expression Homogeneous
- rs = 2, exp
Catalytic
-rc
= 2, exp
Value
Parameter 2.87 x 10” 40.~ 9.14 Y 104 12,000
=h
Eh =, Ee
cm3 mol-r cal mol-r ems-’ cal mol-’
s-r
Table 2. Properties of the monoliths [ZO]
Properties Length (cm) Diameter (cm) Cell area (cm2) Solid area (cm2) Wetted perimeter (cm) Thermal conductivity @l/cm s K) Fraction open area Density (g cm - 3, Heat capacity (cal g-r K-‘)
Metallic Ceramic (31 cell/cm*) (62 cell/cm’) 10
0.15 2.3 x lo-’ 9.3 X 1o-3 0.62 5.55 X 1o-4 0.713 2.5 0.219
10
0.12 1.5 X 10-Z 1.1 x 10-s 0.54 5.55 x lo- = 0.890 7.76 0.11
18s
/’
,sC/’
600 -
----
-.
-.
-__
Ts Tg
35 -;_,----
---_
t=o+
coo
0
warm-up
/-/’
//
I
Combustor
_---
J 4
I
z z
18s
/j
02
1
04 Monolith
06 length
0.8
1.0
Ix/L)
Fig. 1. Transient solid and gas-phase temperature profiles following a step increase in inlet gas temperature ITsi, = 662 K, P = 1 atm, Vi, = 18.3 m/s, 4 = 0.37, T,(x, 0) =4OOK). of combustion time. At early times (t = O-3 s) the inlet gas stream is hotter than the solid and the entire solid section is heated by convective heat transfer from the gas. Shortly after t = 3 s, the solid temperature at the inlet becomes sufficiently high to light-off the solidphase catalytic -reaction. The heat released by the surface reaction rapidly raises the temperature of the solid above that of the gas (t = 18 s) and heat is convected downstream by the gas. As the gas temperature increases with axial distance from the inlet, the temperature at the outlet becomes sufficient to lightoff the gas-phase homogeneous reaction (t > 18 s). The gas temperature in the upstream section of the monolith continues to rise as a result of the heat released by the catalytic surface reaction in the inlet section and, as a result, the temperature required to sustain a significant level of reaction in the gas phase moves upstream from the exit of the monolith (t = 38 s). The gas phase reaction is very fast and is accompanied by rapid heat release which raises the gas temperature above that of the solid. The downstream section of the monolith is then heated by convective heat transfer from the gas and the solid phase temperature in the downstream section of the monolith rises above that at the inlet. Steady-state conditions are reached after 68 s. The steady-state solid temperature profile displays a local minimum slightly upstream of the point at which the homogeneous gas-phase reaction becomes important, with the highest temperature being achieved near the monolith outlet. Gas phase temperature increases with axial distance from the monolith inlet, with the rate of temperature increase rising rapidly at the lightoff point for the homogeneous reaction. The minimum in the solid-phase temperature profile arises as a result
Transientperformanceof catalytic combtutors of the interaction between the heat released by the catalytic solid-phase reaction, the homogeneous gasphase reaction and the convective transport of this heat by the gas. At the monolith inlet (where the catalytic solid-phase reaction is dominant), the cooler gas stream cools the solid and solid temperature decreases with distance from the inlet. In the downstream section of the monolith (where the homogeneous gas-phase reaction is dominant), the gas is hotter than the solid and the hot gas heats the cooler solid phase. The solid increases with distance temperature therefore downstream resulting in a minimum in the temperature profile. In the early stages of warm-up, the transient response of the combustor is expected to be strongly influenced by the thermal inertia of the solid substrate. In the present model a measure of the substrate thermal capacity is given by the dimensionless parameter ai, where
a = 1
(PCp).S, @CpkS .
(27)
Figure 2 shows the results of a series of computations to determine the effect of substrate thermal capacity on the time required to achieve equilibrium conditions for the standard condition case, (26): the time taken to attain the steady-state condition is plotted against the thermal capacity ratio, al. The sharp decrease in the response time as a1 increases clearly indicates that a monolith with a smaller solid cross-sectional area (i.e. thin walls), a lower density and a lower heat capacity will result in a faster transient response. Similar conclusions have been reported by Tien [lo]. Variations in operating conditions Having established the behaviour of the monolith for standard conditions, the effect of changing operating conditions on monolith performance was studied by varying each of the conditions in turn whilst
59
maintaining the remaining conditions as for the standard case of (26). The first operating variable to be examined was the inlet gas temperature, and a plot of exit conversion vs. time for various values of the gas inlet temperature is shown in Fig. 3. At T in = 500 K, the catalytic reaction rate is slow and insu & crent heat is generated to initiate the gas phase reaction. At Tgin > 600 K, the increased heat release by the catalytic reaction is sufEcient to raise the gas phase temperature to levels sufficient to initiate the gas phase reaction, which is accompanied by a sharp increase in exit conversion. The higher the inlet gas temperature, the shorter the time to achieve a given level of conversion. Figure 4 shows the effect of increasing the equivalence ratio (4) on the exit conversion as a function of combustion time. The behaviour is similar to that of increasing inlet gas temperature discussed above. At low equivalence ratio (4 = 0.25) (i.e. low inlet fuel concentration), there is insufficient heat release by the catalytic reaction to initiate the homogeneous gasphase reaction. As the equivalence ratio is increased more heat is released by the catalytic reaction and td resulting gas temperature is sufficient to light-off the
Tnme
Is1
Fig 3. Effectof gas inlet temperatureon exit conversionas a function of time (P = 1 atm, V, = 18.3 m/s, d = 0.37, T,(x, 0) = 400 K). 120 r 9100.-E 4 f ; t z 2
80-
60-
LO-
20 t
I
L
OO
1000 CL.
Solid
to
gas
ZOW heat
capacity
3000
I
60
ratio
Fig. 2. Effect of solid to gas heat capacityratio on response time for converter.1, Time to reach steady-statesolid-phase temperature;2, time to reach steady-stateexit conversion (rain = 662 K, P = 1 atm, V, = 18.3 m/s, $ = 0.37).
Time
(sl
Fig. 4. E&et of fuel-air ratio I&) on exit conversion as a friction of time (Tsi, = 662 K,.p = 1 atm, Vb = 18.3 m/s, T,(x, 0) = 400 K).
T. AHN et al.
60
homogeneous reaction (r&= 0.33). At a higher equivalence ratio (4 = 0.4), the rate of heat release increases and the time required to light-off the homogeneous reaction decreases. The effect of inlet gas velocity on the time required to achieve a particular exit conversion is shown in Fig. 5. The effect of decreasing gas velocity is similar to that of increasing inlet gas temperature or increasing equivalence ratio. Increasing gas velocities result in reduced gas-phase residence times and increased heat and mass transfer coefficients. Figure 5 shows that the dominant effect is the reduction in gas-phase residence time and the consequent reduction in heat release by the catalytic reaction. At a high inlet gas velocity ( V, = 35 m/s), the heat release by the catalytic reaction is insufficient to heat the gas to the temperature required to light-off the homogeneous reaction. An inlet velocity of 25 m/s is sufficient to initiate the homogeneous reaction with lower velocities, resulting in earlier light-off and higher exit conversions. These findings are in accord with the experimental results reported by Prasad et ~2. [21]. The effect of pressure on monolith performance is considerably more complicated. This is because pressure affects a number of important parameters including mass flow rate through the combustor, reaction rates (fuel concentration) and both heat and mass transfer rates. These, in turn, have different effects on overall monolith performance. Figure 6 shows computed conversions as a function of time for pressures of 1, 2 and 3 atm, respectively. At earlier times (t = 3 s), conversion is primarily due to the progress of the solid-phase catalytic reaction. This is governed by the rate at which the hot gas heats the initially cooler solid by convective transport. The heat transfer coefficient at a pressure of 2 atm (Ju = 1.37) is higher than the corresponding value at 3 atm (Jr., = 1.01) and, as a result, the solid temperature is higher in the former case. The higher surface temperature results in a faster catalytic reaction and hence higher conversion for the 2 atm pressure case. Although the heat transfer coefficient is highest for the 1 atm
Time
Fig. 6. Effect of system pressure on exit conversion as a function of time (T&in = 662 K. Vi” = 18.3 m/s, 4 = 0.37, T, (x, 0) = 400 K). pressure case, here, the mass flow rate is comparatively low and hence the heating capacity of the gas stream is greatly reduced. Both solid surface temperature and conversion are therefore lowest for this case. At t = 13 s, the rate of catalytic reaction is high and conversion becomes mass-transfer limited. Since the mass transfer rate decreases with increasing pressure (.I,, = 1.12 at 1 atm, Jo = 0.68 at 2 atm and J, = 0.52 at 3 atm), the surface concentration of fuel and hence the catalytic reaction rate decrease with increasing pressure. Conversion at this time therefore decreases with increasing pressure. At t = 18 s, the gas temperature is sufficient to light-off the homogeneous reaction. Unlike the catalytic reaction, the homogeneous reaction is not mass-transfer limited and, as a consequence, the reaction rate and hence conversion, increases with the increasing fuel concentration associated with increasing pressure. Variations
I
60 Tim
c
(5)
Fig. 5. Effect of gas inlet velocity on exit conversion as a function of time (T’i,, = 662 K, P = 1 atm, 4 = 0.37,T’.(x, 0) =4OOK).
Is)
in mono&h
design parameters
Metallic or ceramic monoliths may be used in a catalytic combustor, and the length and shape of the monolith channels can be varied. The length of the monolith affects the residence time. The effect of residence time on transient behaviour has been discussed above and has been previously investigated using a steady-state model [9]. We therefore consider the effect of monolith type and channel geometry on overall combustor performance. The characteristics of the two types of monolith (metallic and ceramic) studied are given in Table 2. It is noted that a change from a cell density of 31 to 62 cell/cm’ is realized by changing the substrate material from ceramic to metallic. This, of course, results in a change in other monolith parameters, the most important of which is the lower thermal inertia of the metallic monolith. A comparison of the performance
Transient performance of catalytic combustors
of the two monoliths is shown in Fig. 7, in which exit conversion is plotted against combustion time. The metallic monolith clearly displays superior light-off and conversion characteristics. This is due to the higher surface to volume ratio of the metallic monolith which results in a larger catalytically active surface area and improved mass transfer performance. The metallic monolith is therefore much faster in responding to changes in operating conditions than the ceramic monolith. The effect of different channel geometries is shown in Fig. 8. Higher conversions are achieved with squareshaped channels than with triangular or sinusoidal channels. The asymptotic Nusselt (Nu) and Sherwood (Sh) numbers for laminar flow in ducts depend on duct shape and decrease in the order square > triangular > sinusoidal [22]. As a result, square channel ducts offer a lower resistance to heat and mass transfer between the flowing gas and the catalyst surface which results in an earlier light-off of the catalytic reaction and hence the homogeneous reaction.
.-z r=a.4 z ”
2
0.2
61
Over-temperature phenomenonfollowing a step decrease in the feed gas temperature No gas phase reaction. When the power requirement decreases, an initially hot monolith experiences a step decrease in the temperature of the inlet gas stream as a relatively cooler fuel-air mixture enters the monolith. Young and Finlayson [S] and Oh and Cavendish [93 have previously shown that, for car exhaust gas catalytic converters (no homogeneous gasphase reaction), this may result in a transient rise in the temperature of the solid phase above the initial temperature. This transient over-temperature phenomenon is important because it may lead to converter failure if the resulting monolith temperature approaches the solid softening or melting temperature. Figure 9 shows the computed response of a converter cooled from an initial solid phase of 700 K by a gas with an inlet temperature of 400K. Under these conditions, the homogeneous reaction is negligible (T. -z 750 K) and the response is similar to that reported previously [S, 91. The catalytic reaction in the front section of the monolith is quenched by the cooler gas stream and, as a consequence, unreacted fuel is transported downstream where the solid temperature is still high. The combination of high solid temperature and high fuel concentration results in rapid heat release by the catalytic surface reaction in the downstream section of the monolith. This causes the downstream solid temperature to rise. As the inlet section becomes cooler, more unreacted fuel is convected downstream and the temperature rise in the downstream solid increases (t = 18 s). As the temperature transient moves through the monolith, the reaction front moves towards the exit (t = 30 s) and eventually blows out. Steady-state conditions are reached after 86 s. Calculations have shown that, for the conditions of
l!!!_-
OO
10
20
Time
Is.1
30
Fig. 7. Effect of monolith type (metallic,ceramic) on exit conversionas a function of time (T&in = 662 K, P = 1 atm, & = 18.3 m/s, I$ = 0.37. T,(x,O) = 400 K).
800 t
-
Ts
lo-
___--I
0 Time
(sl
Fig. 8. Effect of monolith channel sha~sinusoidal, A exit don=12.12; triangular, A = 2.35; square, A =-2.9-n version as a function of time (T&in = 662 K, P = 1 atm, Vi, = 18.3 m/s, # = 0.37, T,(x, 0) = 400 K).
06s
I
02
OL tionolith
0.6 length
0.0
I
1.0
(x/L1
Fig. 9. Transient solid and gas-phase temperature profiles following a step decrease in the inlet gas temperature(TGin =4OK, P=latm, Vi:,,=18.3m/s, Q=O.2 T,(x,O) = 700 K).
T. AHN et
62
Fig. 9, the over-temperature phenomenon is absent if the monolith is cooled from 1000 K, and small if cooled from 800 K. At these temperatures the driving force for convective heat transfer from the wall to the cooler gas stream increases, whilst the heat release rate remains relatively constant because the surface reaction is mass-transfer limited. The increased rate of heat loss from the solid surface for these cases prevents serious solid over-temperature. A low equivalence ratio also prevents over-temperature of the solid because of the reduced rate of heat generation (low fuel concentration). Sur$ace and gas phase reactions. In gas turbine applications, both catalytic solid-phase and homogeneous gas-phase reactions contribute significantly to the overall combustion process with solid phase temperatures in the range 1360-1980 K at high load conditions [2]. Figure 10 shows computed temperature profiles for typical gas turbine conditions after a hot monolith at 14OOK has been subjected to a gas stream at 700 K. On the inlet section of the monolith, the solid phase temperature falls with time as the solid is cooled by the incoming gas stream. As the solid temperature falls, the rate of surface reaction decreases and unreacted fuel is convected downstream where temperatures are higher. As for the previously discussed case of car exhaust converters, the downstream solid temperature increases as a result of increased heat release by the solid phase reaction (x/L < 0.4). However, the temperature rise is small due to a predominantly mass-transfer limited condition. At x/L > 0.4 (t = 3 s), the gas temperature is sufficient to initiate the homogeneous reaction and the gas temperature increases rapidly to exceed the solid temperature (x/L = 0.8). The homogeneous reaction quickly reduces the fuel concentration in the gas phase and,
lSO0 r
_---_
----
I 0
1
I
I
0.6
0.8
10
I
02
0.4 Honollth
Ts Tg
length
Ix/L)
Fig. 10. Transient solid and gas-phase temperature profiles following a gas decrease in inlet gas temperature (Tain &, = 18.3 m/s, I$ = 0.25, T,(x.O) =7OOK, P= latm, = 1400 K).
al.
since the catalytic solid-phase reaction is mass-transfer controlled, the rate of heat generation on the solid is also reduced. As the monolith continues to cool (t = 18 s), the homogeneous reaction front moves further downstream and eventually blows out with a consequent decrease in the temperature of the gas phase. The bulk of reaction now takes place on the catalyst surface and hence the gas temperature falls below the solid temperature. After t = 48 s, the solid and gas phases reach their respective new steady-state temperatures. Similar computations for C$= 0.2 show the existence of smaller magnitude over-temperature effects in both gas and solid reflecting the lower heat generation capacity of the reactant mixture. This trend continues with decreasing equivalence ratio until the heat generated by catalytic and homogeneous reactions is insufficient to cause overheating. The major difference between the over-temperature phenomenon in car exhaust converters and gas turbine combustors is due to the importance of the gas phase reaction for the latter case. For car exhaust converters the heat is generating on the solid surface and heat is removed at a rate which is heat-transfer limited. For gas turbines, the bulk of the heat is generating in the gas phase (no mass transfer limitation) with the hotter gas convectively heating the solid. For the conditions shown in Figs 9 and 10 the solid over-temperature is of the order of 50 K. CONCLUSIONS
A transient catalytic combustor model which accounts for both catalytic and homogeneous reactions within the monolith channels has been developed and used to investigate the performance of gas turbine combustors. Computations based on the model show that fast combustor response to changes in operating conditions is favoured by monoliths with thin walls, low density and low heat capacity. High cell density metallic monoliths are therefore superior in their transient response performance to ceramic monoliths. Channel geometry affects monolith performance as a result of the differences in heat and mass transfer characteristics_ Square-shaped channels display a better overall performance than triangular or sinusoidal geometries. High inlet temperatures, equivalence ratios and low inlet velocities result in higher combustion efficiencies and shorter response times. Higher inlet pressures allow higher throughput even though the higher pressures are associated with increased heat and mass transfer resistance. This is largely due to the enhancement of the homogeneous gas-phase reaction with increasing pressure. When a cool reactant mixture is introduced into an initially hot catalytic monolith, it is possible to observe a solid wall over-temperature phenomenon in which the wall temperature temporarily exceeds the initial temperature. For conditions which result in gas temperatures sufficiently high to initiate the homogeneous gas-phase reaction, the gas temperature may temporarily exceed the solid phase temperature. This gas-
Transient performance
phase over-temperature converters
where
gas
does not occur in car exhaust phase
reactions
are
negligible
[S, 93. For the gas turbine conditions investigated, the magnitude of the over-temperature phenomenon was small and therefore unlikely to limit seriously combus-
of catalytic eombustors
homogeneous pre-exponential (g mol/cm3)’ -“- m/s
Zh Greek
thermal capacity ratio dimensionless adiabatic flame temperature dimensionless catalytic activation energy dimensionless homogeneous activation energy dimensionless axial distance ( = x/L) dimensionless gas temperature dimensionless solid temperature gas conductivity, cal/cm s K solid substrate conductivity, Cal/cm s K gas viscosity, g/ems dimensionless velocity density of gas, g/cm” density of solid, g/cm3 wetted perimeter, cm Stefan-Boltzman constant dimensionless time ratio of time constant for heat transfer to catalyst to gas residence time equivalent ratio
Acknow/edgemenr-The authors acknowledge with gratitude financial support from the Aero Division of Rolls-Royce Company.
NOTATION
Cfg Cfs
CO* CP C,
D,d
DC Dh
Di
EC Eh h (-AH)
JD JH k L m n
NU P Pe, Pe, Peh Pr R R, -rC -rH rhf Ihs
Re s Ss Sh t to Tg Tm Tin T, T S.0 V vim X =c
vO
factor,
letters
tor performance.
gas phase fuel concentration, g mol/cm’ solid phase fuel concentration, g mol/cm’ oxygen concentration, g mol/cm3 specific heat capacity, Cal/g K heat capacity ratio monolith channel diameter, cm catalytic Damkohler number homogeneous Damkohler number diffusivity coefficient, cm*/s catalytic activation energy, Cal/g mol homogeneous activation energy, Cal/g mol heat transfer coefficient, Cal/s cm2 K heat of reaction, Cal/g mol mass transport number heat transfer number mass transfer coefficient, cm/s monolith length, cm homogeneous reaction order with respect to fuel concentration homogeneous reaction order with respect to oxygen concentration Nusselt number ( = hd/Q pressure (atm) solid-phase Peclet number for heat transfer Peclet number for mass transfer Peclet number for heat transfer Prandtl number ( = C&As) universal gas constant ( = 82.05 cm3 atm/g mol K) channel radius surface reaction rate, g mol/cm2 s homogeneous reaction rate, g mol/cm3 s hydraulic radius of a channel hydraulic radius of solid Reynolds number ( = p Vd/p) channel cross-sectional area, cm* solid cross-sectional area, cm* Sherwood number ( = kd/DJ time, s arbitrary time scale factor, s gas temperature inlet gas temperature, K solid temperature, K solid temperature at the initial state linear velocity, cm/s inlet gas velocity, cm/s axial distance, cm catalytic pre-exponential factor, cm/s
63
= (
actual air/fuel ratio stoichiometric air/fuel ratio >
dimensionless dimensionless dimensionless dimensionless
gas-phase fuel concentration solid-phase fuel concentration solid temperature gradient mass fraction
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Pfefferle W. C., A.S.M.E. Paper 1979 No. 79-HT-52. Anderson D. N., 3rd Workshop on Catalytic Combustion, Asheville, NC, Oct. 1978. Cerkanowicz A. E., Cole R. B. and Stevens J. G., .I. Engng Power 1977 593. Young L. C. and Finlayson B. A., A.I.Ch.E. J. 1976 22 343.
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Numerical Methods. p. 508. Wiley, New York 1967. 19] Lentini M. and Peceyra V., Math. Comput. 1974 23 98 1. E203 Cooper B. J. E/Pc/7370, R esearch Project No. 197. University of Trondheim, Norway 1978.
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