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numerical predictions are compared with recent experiment andnumerical data.

2 Mathematical Model and Solution Procedure

The numerical model for laminar flow, heat transfer, gas-phase combustion, and catalytic surface reactions is presented.The flow configuration investigated in the present paper is thatof a rectangular channel burner. Finite-volume equations areobtained by formal integration over control volumes surround-ing each grid node. Hybrid differencing is used to ensure thatthe finite-difference coefficients are always positive or equal tozero to reflect the real effect of neighboring nodes on a typical

central node. The finite-volume equations of the reacting gasflow properties are solved by a combined iterative-marchingalgorithm. On the platinum surfaces, surface species balanceequations, under steady-state conditions, are solved numeri-cally. A nonuniform computational grid is used, concentratingmost of the nodes in the boundary sublayer adjoining the cata-lytic surfaces. The flow configuration is shown in Fig. 1. Thenumerical model can be classified into four main groups ofequations as follows.

2.1 Continuity and Momentum Equations. The mass conti-nuity of the reacting flow may be written as

@q

@t

@qui

@x

i

0 (1)

The momentum equation for the laminar reacting flow may bewritten in Cartesian tensor notations as [9]

@ quj @t

@

@xiqujui

@

@xil@uj@xi

@ P

@xj

@

@xi

l@ui@xj

2

3

@uk@xk

dij

!(2)

where q is the gas density; uj is the gas velocity along coordinatexj; l is the dynamic viscosity.

2.2 Energy Equations. The energy equation for the reactingflow is

@qhg@t

@

@xiquihg

@

@xiCh

@hg@xi

Xj

DHj

Wj (3)

where hg is the gas sensible enthalpy;Ch is the thermal diffusivity;DHj and Wj are the enthalpy of reaction and reaction rate of chem-ical reaction j of the reaction mechanism involving hydrogen-airmixtures; in the above equations, the subscript g denotes the gasphase. The gas temperature at any point is directly related to thelocal gas sensible enthalpy (hg), gas species mass fractions (Yj),and constant-pressure specific heats, namely

hg

Xj

CpjYj

dT (4)

The lower limit of the above integration is 298 K, while the upperlimit equals the local gas temperature, Tg.

2.3 Species Mass Fraction Equations. The species massfractions for the reacting channel flow may be written as

@qYl@t

@ quiYl

@xi @

@xiCYl

@Yl@xi

Ml

Xm

lmWm (5)

where Yl is the mass fraction of species l while CYl is its moleculardiffusivity; Ml is the molecular mass of species l; lm is the stoi-chiometric coefficient of species l in reaction m while Wm is thereaction rate of the elementary chemical reaction m of the presentreaction mechanism. It consists of 24 elementary reactions. Thepresent hydrogen-air chemical kinetic mechanism involves eightspecies, namely, O2, O, OH, H, H2, H2O, H2O2, and HO2. The ele-mentary reaction mechanism for hydrogen-air mixtures adopted inthe present work is the same as given by Tong et al. [10].

It should be mentioned here that lm is taken as a positive valuefor products and negative for reactants as required for proper sum-mation of the effect of each reaction on the net production of aparticular species.

2.4 Surface Reactions. For a steady-state problem, the solu-tion has no change with respect to time. Thus, surface coverage ofany surface species with respect to time is zero. The variation ofthe surface coverage with respect to time can be computed fromthe net production of each surface species. The conservation ofthe surface coverage of surface species kmay be written as [5]

dzk

dt

_sk

Z(6)

where zk is the surface coverage of surface species k, Zis the totalsurface site density, and the surface density used in the present pa-per is 1.63

1015 cm2 [6]; _s

kis the net surface production rate,

in mol cm2 s1, of the surface species k.Since the present reacting flow includes gas-surface interac-

tions, the mass transfer between the gas phase and the catalyticsurface needs to be included while solving the species mass frac-tions of the gas species in the flow. The mass fluxes transferredthrough the convection and the diffusion processes at the gas-surface interface of any gas-phase species are balanced by the netproduction or depletion rates of that species by surface reactions.The surface boundary condition of each gas-phase species k basedon the mass balance is given by Coltrin et al. [8] as

n qYk Vk u _skMk (7)

where n is the unit normal vector pointing outward with respect to

the surface, u is the bulk fluid velocity, Vk is the diffusion veloc-ity, Mk is the molecular weight of species k, _sk is the net produc-tion or depletion rates of gas-phase species k involved in surfacereactions.

The production rate of each species _sk, either gas-phase speciesor surface species, may be written as [11]

_sk XKsj1

kjkfjYNgNsk1

Xk 0kj (8)

where Ks is the total number of elementary surface reactions; 0kj

is left hand side stoichiometric coefficients of the reaction

Fig. 1 Layout of the configuration of reacting hydrogen-airmixture flow inside platinum-coated rectangular channel

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equation; vkj is the right hand side minus left hand side stoichio-metric coefficients of the reaction equation; kfj is the forward ki-netic rate constants; [Xk] is the species concentrations; the units ofgas-phase species and surface species concentrations are molcm3 and mol cm2, respectively; Ng is the number of gas-phasespecies while Ns is the number of surface species.

A detailed surface reaction mechanism is used to model thegas-surface interaction between the fuel and the platinum-coatedsurface. The surface reaction mechanism adopted in the presentwork, for hydrogen-air mixtures reacting over platinum-coated

surfaces, is established by Deutschmann et al. [6]. The surfacereaction mechanism consists of 16 elementary reactions andinvolves four gas-phase species, namely, O2, OH, H2, H2O, andfive surface species, namely, O(s), OH(s), H(s), H2O(s), and Pt(s).The reaction rate constants are described in terms of either theArrhenius expression or a sticking coefficient, c. The Arrheniusexpression form is

kfj Aj expEjRT

(9)

The sticking coefficient can be converted to the usual kinetic rateconstants via the relation given by Coltrin et al. [8]

kfj c

1 c=2

1

ZmffiffiffiffiffiffiffiffiffiffiRT

2pMr (10)

where Z is total surface site concentration, m is sum of the surfacereactants stoichiometric coefficient, R is the universal gas con-stant, Tis the gas temperature at the catalytic surface, and Mis themolecular weight of the gas-phase species. The thermochemicaldata needed to determine the rate coefficients for the reverse reac-tions and enthalpies of the surface species are provided by War-natz et al. [5].

In the present work, steady-state conditions of the flowing gasand the surface species are assumed. Equations (6) and (8), in thiscase, can be used to compute the surface species mole fractions,given the gas species mole fractions at the interface between thecatalytic surface and the flowing gas phase. Equations (7) and (8),on the other hand, are used to compute gas species fluxes at the

gas-surface interface. Although these fluxes do not appear explic-itly in Eq. (5), they are used to impose the proper boundary condi-tions on the flowing gas species finite-volume equations.

It should be mentioned here that the gas physical properties arecomputed from temperature dependent relations. At any point inthe flowing gas phase, the density is computed from the ideal gasequation of state, while the viscosity is computed from a tempera-ture polynomial of the third order. The species specific heats arecomputed from temperature polynomials of the sixth order, whichare valid for 300 K to 2500 K temperature range [12]. The remain-ing physical properties are deduced from the above properties andPrandtl and Lewis numbers specified as 0.7 and 1.0, respectively,for most gas species. However, the Lewis numbers of H2 and Hare taken as 0.3 and 0.2, respectively, to reflect the faster diffusionof these species with respect to the other heavier species such as

H2O and O2.

2.5 Numerical Solution Procedure. The two-dimensionalflow inside the catalytic rectangular channel, shown in Fig. 1, isoverlaid with a finite grid of nodes. Equations (2), (3), and (5) andthe pressure correction counterpart of Eq. (1) are formally inte-grated over the control volume surrounding each grid node. Thetime dependent terms of the governing equations were droppedout since the reacting flow considered is under steady-state condi-tions. The faces of the control volume bisect the distancesbetween the particular node and the four nearest neighbor nodes.The formal integration is performed with due care to preserve thephysical meaning and overall balance of each dependent variable.

The final form of the finite-volume equations are written as fol-lows [9]:

Xan SP

Wp

XanWn Su (11)

where W stands for any of the dependent variables; namely, axialand radial velocity components, gas sensible enthalpy, speciesmass fractions, or the pressure correction which is used to satisfyboth mass continuity and momentum equations simultaneously.The summation (R) is over the n four neighbors of a typical nodep. The above finite-difference coefficients an are computed usingthe hybrid method, such that these coefficients are always non-negative to give the proper combined effects of convection anddiffusion. The above hybrid method is a combination of upwindand central differencing schemes. Each scheme prevails for a par-ticular range of the cell Peclet numbers, as given in detail byAbou-Ellail et al. [9]. Sp and Su are the coefficients of the inte-grated source terms at node p. The flow in a rectangular channelwith dominant streamwise direction is parabolic in nature andthus the hybrid scheme is accurate enough to eliminate any falsediffusion. In this case, the computational grid directions arealigned along the main flow direction and normal to it.

The solution procedure is based on the, line-by-line, tridiagonalmatrix algorithm (TDMA). The finite-volume equations (Eq. (11))for each dependant variable are modified at the boundaries of the

solution domain, shown in Fig. 1, to impose the conditions there.On the catalytic surface where y 0.0 mm, the velocity compo-nents vanish while all other dependent variables normal gradientsreflect the mass and heat fluxes due to surface reactions. Alongthe axis of symmetry where y 3.5 mm and the exit section of theflow, the normal gradient is equal to zero. Moreover, for the cata-lytic channel flow, the transverse velocity is equal to zero at theupper boundary where y 3.5 mm. At the inlet section, all varia-bles are uniform. Within each computational loop of the gasphase, Eq. (6) is solved, for all surface species concentrations,iteratively at each transverse plane for steady-state conditions,i.e., d(zk)/dt 0. The validation of the present numerical algo-rithm is presented by Tong et al. [12] for heat and mass transfer inimpinging flows on a hot catalytic surface. Tong et al. [12] com-pared their results for temperature and species mole fractions in

the reacting impinging jet with numerical data of Deutschmannet al. [6]. The agreement they obtained confirms the accuracy ofthe present numerical procedure [12]. Moreover, standard laminarthermal boundary layer thickness and heat transfer data [13] werealso used for validation purposes by Tong et al. [14]. Further vali-dation is given in the present work by comparing the present nu-merical results with the experimental and numerical data of Appelet al. [15].

3 Presentation and Discussion of Results

The catalytic surface reactions in channel flows are investigatednumerically in this section. The numerical results are comparedwith the recent experimental measurements conducted by Appelet al. [15]. The rectangular channel, used by Appel et al. [15], has

its upper and lower plates coated with platinum. The height,width, and length of the channel are equal, respectively, to 7 mm,110mm, and 300 mm. The ratio of width of the channel to theheight of the channel is large enough so that the flow could beconsidered two-dimensional in the vertical plane passing by thecenterline. The hydrogen-air mixture flows through the channeland reacts on the catalytic surface. The schematic plot of the chan-nel flow is shown in Fig. 1. The channel geometry shown in Fig.1is used in the present numerical model. The grid used for thechannel flow, namely the number of grid nodes along the x-axisand y-axis is 10,000 and 330, respectively. Due to symmetry, onlythe lower half of the computational plane, indicated in Fig. 1,needs to be overlaid with the above grid of nodes. Moreover, theaxial increment Dx is taken as 3.0 102 mm. The transverse grid

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nodes are arranged such that 200 nodes lay inside the boundarysublayer, i.e., in the range 0.0 < y< 1.0 mm. The rest of the trans-verse nodes lay outside the boundary sublayer, i.e., in the range1.0< y< 3.5 mm. The above number of grid nodes is sufficient tohandle the fast changing gas density and viscosity, both axiallyand transversely inside the rectangular channel, as well as insuringa grid-independent solution. With a total number of 3.3 million

grid nodes, it was necessary to utilize the parabolic nature of theflow. This is done through the use of a line-by-line TDMA schemeto obtain numerical solutions in such a way to sweep the solutiondomain from the inlet section to the exit section. The field valuesof the dependent variables are stored and then updated during thesubsequent iterations. The iterations are stopped when the finite-volume equations of the dependent variables are satisfied witherrors less than 0.1%. This criterion is achieved with only threeiterations. The present numerical simulator is actually a combina-tion of parabolic and elliptic procedures. It can thus be referred toas a parabolic-elliptic procedure.

For the case being studied in the present work, the inlet velocityof the gaseous mixture is 1.6m/s, the inlet gas temperature is313 K, and the equivalence ratio is 0.32. This case is referred to ascase 2 in the experimental work of Appel et al. [15]. The surface

temperature profile of the channel wall, along the x-axis was alsomeasured by Appel et al. [15]. Figure 2 shows the catalytic walltemperature profile along the streamwise direction. As shown inFig. 2, the surface wall temperature is not uniform. The wall tem-perature at channel entrance is about 1060 K. It graduallyincreases to a temperature around 1255K then decreases to1200 K near the channel exit section. This temperature profile wasmaintained by Appel et al. [15] with the help of guard heaters andceramic insulation. They also allowed the first 60 mm of the chan-nel to radiate to the cold surroundings to prevent the wall tempera-

ture from reaching super-adiabatic levels as a result of the fasterdiffusion of the low- Lewis-number fuel, namely H2.

The curve fitting equations that accurately describe the surfacetemperature profile (Ts) are given below as

Ts 1062 0:0089x2:57; 0 < x < 20 (12a)

Ts 1079 1:80x 201:05; 20 < x < 80 (12b)

Ts 1208 3:20x 800:66; 80 < x < 130 (12c)

Ts 1248:5 0:23x 130

0:76

; 130 < x < 210 (12d)Ts 1254:3 0:029x 210

2:02; 210 < x < 265 (12e)

Equations (12a)(12e) are used in the present work as the bound-ary condition for the catalytic surface temperature axial profile ofthe channel flow of Appel et al. [15]. Therefore, the heat gener-ated by catalytic chemical reactions on the surface is not explicitlyconsidered in the present numerical computations. Figure 3 showsthe present numerical temperature transverse profiles togetherwith the experimental data of Appel et al. [15], at x 25, 85, 105,165, and 235 mm. However, no experimental data for the 265-mmsection can be found. The present temperature profiles for themeasured five sections are in good agreement with the experimen-tal data of Appel et al. [15]. Numerical computations were alsoconducted by Appel et al. [15] using a fully elliptic computer

code that required 20,000 to 30,000 iterations depending on theinitial guess. They used 340 nodes along x-axis and 90 nodesalong the y-axis. They overpredicted the temperature of most ofthe sections reported with a maximum error of 110K betweentheir numerical and experimental data. However, as it can be seenfrom Fig. 3, the experimental data of the gas temperature are wellpredicted in the present work. This can probably be attributed tothe much finer grid adopted in the present work. However, whilethe present computer code uses a parabolic-elliptic solution proce-dure that requires few iteration loops, Appel et al. [15] fully ellip-tic procedure converged in 20,000 to 30,000 iterations dependingon the initial guess.

Figure 4 shows the mole fractions of H2 and H2O at differentstreamwise locations of 25, 85, 105, 165, and 235 mm. The molefraction of H2 is multiplied by a factor of 2 for the purpose of

clarity. The predicted mole fraction streamwise profiles are com-parable with the measured data of Appel at al. [15]. The stream-wise mole fraction profiles of H2 are in good agreement with theexperimental data up to a distance of 165 mm along the x-axis.However, for x > 165mm, the H2 mole fraction is slightly under-predicted by the present solution procedure. Moreover, the nu-merical results of Appel et al. [15] slightly underpredicted theirexperimental data for all reported transverse planes, althoughthey used a costly fully elliptic numerical procedure. The pre-dicted mole fraction transverse profiles of H2O are compared to

Fig. 2 Catalytic surface temperature profile for the channelflow of Appel et al. [15]

Fig. 3 Transverse temperature profiles at streamwise distances of 25 mm, 85mm, 105 mm, 165mm, 235 mm, and 265mm



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the experimental data of Appel et al. [15], as depicted in Fig. 4.The predicted mole fraction profiles of H2O are in good agree-ment with the experimental data for the first three transverse

planes. However, the numerical mole fraction profiles of H2Ooverpredict the experimental data for the last two planes, asshown in Fig. 4. This is an indication of an overprediction of theH2O production rate that the adopted surface reaction mechanismcomputes at the downstream locations where most of the plati-num is inactive. Moreover, the numerical data of Appel et al.[15] slightly overpredicted the experimental data for the last twopanes with x 165 and 235mm. The difference in the level ofagreement between the present results and Appel et al. [15] pre-dictions could hardly be attributed to the difference in the solu-tion procedures. However, this better agreement is attributed tothe modification in Eq. (10) that Appel et al. [15] adopted tocompute kfj in their numerical model. This modification reducesthe specific reaction rate constants of the H2 and O2 adsorptionreactions at lower values of Pt(s) prevailing in the downstream

area of the inlet section.In order to assess the merits of the present numerical work, theratio of the execution times of the present and Appel et al. [15] so-lution procedures is thus estimated. The TDMA is used in thepresent work and will be hypnotized as the solution scheme forAppel et al. [15]. In the present work, TDMA is performed onlyalong the transverse direction and is repeated for all transversesections. However, for a fully elliptic solution procedure theTDMA is normally applied along the streamwise (Nx) and thetransverse (Ny) directions. It should be mentioned here that Nxand Ny are the number of nodes along the x- and y-coordinates.The ratio between the execution time of Appel et al. [15] and thepresent work is estimated as the ratio between the two numbers ofiterations times the ratio between the two execution times per iter-

ation. The execution time of the TDMA(Nx) together with theexecution time for computing the finite-difference equation coeffi-cients is commonly assumed to vary with Nx to an exponent hav-

ing a value between 1.0 and 2.0. If this exponent is taken as 1.5,the estimated execution time of Appel et al. [15] is roughly 2orders of magnitude higher than the present parabolic-elliptic so-lution procedure execution time. As the TDMA algorithm is con-sidered one of the most economical finite-difference equationsolvers, the above result should be taken as a nominal value ratherthan an exact one.

The predicted oxygen mole fraction transverse profiles at differ-ent streamwise locations are depicted in Fig. 5 for streamwise dis-tances of 25mm, 85 mm, 105 mm, 165 mm, 235 mm, and 265 mm.The maximum value at each section occurs at the channel center-line, as the oxygen is mostly consumed at the walls. Atx 265 mm, the profiles are completely flat indicating the end ofmost surface and gas reactions. Since the equivalence ration ofthis flow is 0.32, then residual oxygen is expected at the exit sec-

tion as can be seen from Fig. 5.Figure 6 shows the transverse profiles of the streamwise veloc-ity at distances along the x-axis of 25mm, 85mm, 105 mm,165mm, 235mm, and 265 mm. The streamwise velocity showsnearly a uniform profile near the inlet section changing to a para-bolic profile near the exit section as it would be for flow betweenparallel plates. However, because of the excessive heating of thegas mixture as it flows along the channel axis, the centerline ve-locity increases from 1.6 m/s at the inlet section to approximately9 m/s at the exit section.

Figure 7 depicts the numerical transverse profiles of the trans-verse velocity at streamwise sections of 25 mm, 85 mm, 105 mm,165 mm, 235 mm, and 265 mm. The transverse velocity is highestnear the inlet section peaking to a value of about 2.2 cm s1.

Fig. 4 Mole fractions of H2 and H2O at streamwise distances of 25 mm, 85mm, 105 mm, 165mm, 235 mm, and 265 mm

Fig. 5 Mole fraction of O2 at streamwise distances of 25mm, 85 mm, 105mm, 165 mm, 235mm, and 265 mm



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Because of the symmetry of the channel flow, the transverse ve-locity is asymmetric with respect to the x-axis.

The OH mole fraction transverse profiles are shown in Fig. 8,for streamwise distances of 25 mm, 85mm, 105mm, 165 mm,235mm, and 265 mm. For x < 105 mm, the highest OH mole frac-tions occur at the walls. However, at x 105 mm a peak for OH isimmerging which indicates the onset of a gas-phase ignition. Thepeak OH value continues to increase at the subsequent sectionsuntil it starts to decrease after x 235 mm.

Figure 9 shows the H mole fraction transverse profiles at differ-ent streamwise sections. Near the inlet section the H mole fractionis highest at the walls. However, a peak starts to appear awayfrom the wall for streamwise distances greater than 85 mm. This

peak increases with streamwise distances up to 165 mm where itdecreases with further increase in the streamwise distance. Thisbehavior is concurrent with that of OH. The O mole fraction trans-verse profiles are depicted in Fig. 10 for streamwise distances of25 mm, 85 mm, 105 mm, 165 mm, 235 mm, and 265mm. Here thetrend of the O mole fraction profiles is similar to both mole frac-tion profiles of OH and H. It is possible to conclude that a form ofhigh gas-phase reaction rates occur in the range of streamwise dis-tances of 85 mm105mm. This could be attributed to local gas-phase ignition.

The mole fraction transverse profiles of H2O2 are depicted inFig. 11 for streamwise distances of 25mm, 85mm, 105 mm,165mm, 235mm, and 265 mm. Near the inlet section, the H2O2

Fig. 6 Streamwise velocity, u, at streamwise distances of 25 mm, 85mm, 105 mm, 165 mm, 235mm, and 265mm

Fig. 7 Transverse velocity, v, at streamwise distances of 25 mm, 85mm, 105 mm, 165mm, 235 mm, and 265 mm

Fig. 8 Mole fraction of OH at streamwise distances of 25mm, 85 mm, 105 mm, 165 mm, 235 mm, and 265mm



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mole fraction essentially vanishes. It starts to form two clear peaksfor x ranging from 85 mm to 165mm. The H2O2 mole fraction

profiles start to form one peak at the channel centerline for valuesof x > 165 mm where the temperature reaches its minimum value,at each section. This behavior is dictated by two of the main ele-mentary reactions that produce H2O2. These two reactions (R11and R12f) increase with decreasing temperatures either because ofnegative activation energy or negative temperature exponent [10].Figure 12 shows the mole fraction transverse profiles of HO2 forstreamwise distances of 25mm, 85mm, 105 mm, 165 mm,235mm, and 265 mm. Near the channel walls, two HO2 peaksstart to form for streamwise distances of 85 mm, 105 mm, and165 mm. They collapse into a central peak for streamwise distan-ces in the range of 235 mm265mm. The production/consumptionrates of HO2 are controlled by reactions R (5f) and R (5 b). Thefirst reaction increases with decreasing gas temperatures while R

(5 b) is controlled by two temperature-conflicting-effect terms[10].

Figure 13 depicts the streamwise profiles of the production rateof H2O and consumption rates of H2 and O2. It is interesting tonotice that the production rate of H2O is nearly equal to the con-sumption rate of H2. Moreover, the consumption rate of H2 isnearly equal to twice the consumption rate of O2. This suggeststhat the surface reactions can be summed up to a one step gas-phase reaction as H2 2 O2 ! H2O. In this case, the importantparameter would be the reaction rate in the above reaction. A cor-relation for this reaction rate can be arrived at either experimen-tally or from numerical data similar to the present data [12,14].The H2O production rate decreases sharply in a short streamwisedistance of about 10 mm, as can be seen from Fig. 13. Figures 14and 15 depict the surface coverage streamwise profiles of surfacespecies Pt(s), O(s), OH(s), H2O(s), and H(s). The surface platinum

Fig. 9 Mole fraction of H at streamwise distances of 25mm, 85 mm, 105 mm, 165 mm, 235 mm, and 265mm

Fig. 10 Mole fraction of O at streamwise distances of 25 mm, 85mm, 105mm, 165 mm, 235 mm, and 265mm

Fig. 11 Mole fraction of H2O2 at streamwise distances of 25mm, 85 mm, 105mm, 165 mm, 235mm, and 265mm



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decreases sharply from 1.0 to about 0.03 in a short distance ofabout 5 mm; concurrently the O(s) surface coverage increasessharply from 0.0 at the entrance to 0.97 at a streamwise distanceof about 5 mm, as can be seen from Fig. 14. Pt(s) then remainsnearly constant for most of the channel length, as can be seenfrom Fig. 15. However, for x> 150 mm the platinum surface cov-erage gradually decreases to a value of 0.008. The reduction in theplatinum surface coverage implies that the adsorption reaction

rates must decrease. However, if the modifications in the surfacereaction rate constant equation were included in the present workthen these reaction rates would further decrease. The channel sur-face remains mostly covered with O(s) for the remaining length ofthe channel, as can be seen from Fig.15. Figure 15 depicts also thesurface overages of OH(s), H2O(s), and H(s). Along the channelwalls, the surface species OH(s), H2O(s), and H(s) increasesharply from 0.0 to 4.0 104, 5.0 108, and 1.5 108,

Fig. 12 Mole fraction of HO2 at streamwise distances of 25mm, 85 mm, 105mm, 165 mm, 235mm, and 265mm

Fig. 13 Surface production rate of H2O and Surface consumption rates of H2 and O2

Fig. 14 Surface coverage of surface species for 0< x

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respectively. These surface species continue to decrease along thechannel wall. At the channel exit section, the reductions in OH(s),H2O(s), and H(s) are of orders of magnitudes ranging betweenone and two. The streamwise pressure difference (p p in) profileis shown in Fig. 16. It is clear that the pressure decreases linearlyalong the streamwise direction. The pressure difference stream-wise gradient is approximately equal to 133N m3. This pres-sure gradient could be useful in designing rectangular channelcatalytic burners.

4 Conclusions

The present parabolic-elliptic solution procedure is testedagainst recent experimental and numerical data for reacting flowsin catalytic rectangular channels. Through this study several con-clusions emerged:

1. The agreement between the present results and the experi-mental data is generally good and in some cases surpassesthe published numerical data for the same flow. Moreover,the present solution procedure is roughly two orders of mag-nitude faster than the published fully elliptic numerical pro-cedure for the same flow conditions. The H2O isoverpredicted for sections near the exit section and is attrib-

uted to higher values of the adsorption reaction constants inthe downstream area, where the surface platinum is mainlycovered with O(s). The first 0.7 L of the channel is vital inbuilding up the surface species and the depletion of theactive platinum sites. The numerical results show high pro-duction rates of H2O in the vicinity of streamwise distanceof about 15 L.

2. The channel flow computational results are compared withrecent detailed experimental data for similar geometry andshowed that the present numerical results for the gas temper-ature, water vapor mole fraction, and hydrogen mole fractionagree well with the experimental measurements, especiallyin the first 105 mm. However, some differences are observedin the vicinity of the exit section of the rectangular channel.

The numerical results show that the production of watervapor is very fast near the entrance section flowed by amuch slower reaction rate. Gas-phase ignition is noticednear the catalytic surface at a streamwise distance of about120 mm. This gas-phase ignition manifests itself as a suddenincrease in the mole fractions of OH, H, and O.

Nomenclature

an finite-difference coefficients due to combined convectionand diffusion, kg s1

Cp constant-pressure specific heat, J kg1 K1

DHj enthalpy of reaction for reaction j, J mol1

h heat transfer coefficient, W m2 K1

hg gas sensible enthalpy, J kg1

kc mass transfer coefficient, kg m

2 s

1

L height of the computational domain, mM molecular weight, kg kmol1

N number of grid nodesNu Nusselt number

P gas pressure, N m2

Pr Prandtl numberR universal gas constant, J mol1 K1

Re Reynolds numberRs surface reaction rate, mol cm

2 s1

_sk surface production or depletion rate of the surface speciesk, mol cm2 s1

Sh Sherwood number

Fig. 15 Surface coverage of surface species for the total channel length (0300mm)

Fig. 16 Streamwise pressure difference profile (p-pin)



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SPR surface production rate, mol cm2 s1

T temperature, Kui velocity in direction i, m s

1

U1

uniform free stream axial velocity, m s1

Wj reaction rate of reaction j, mol cm3 s1

x streamwise distance, mxi distance along direction i, m (here, x x1 and y x2)X mole fraction

[X] generalized concentration (gas phase: mol cm3, surfacephase: mol cm2)

y transverse distance, mY species mass fractionZ surface site concentration, mol cm2

zk surface site fraction ofkspecies (surface coveragefraction)

Greek Symbols

d thermal boundary layer thickness, mCh thermal diffusivity, kg m

1 s1

CYl molecular diffusivity of species l, kg m1 s1

l dynamic viscosity, kg m1 s1

q density, kg m3

c sticking coefficient

Subscripts

g gass surface

x at a distance x from the inlet sectiony distance from the wall

References[1] Cattolica, R. J., and Schefer, R. W., 1982, Effect of Surface Chemistry on the

Development of the (OH) in a Combustion Boundary Layer, 19th Symposium(International) on Combustion, The Combustion Institute, Pittsburgh, PA,pp. 311318.

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[3] Williams, W. R., Stenzel, M. T., Song, X., and Schmidt, L. D., 1991,Bifurcation Behavior in Homogeneous-Heterogeneous Combustion: I. Experi-mental Results Over Platinum, Combust. Flame, 84, pp. 277291.

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http://dx.doi.org/10.1080/00102208308923620http://dx.doi.org/10.1080/00102208308923620http://dx.doi.org/10.1016/0010-2180(91)90006-Whttp://dx.doi.org/10.1016/0010-2180(91)90007-Xhttp://dx.doi.org/10.1016/0010-2180(94)90107-4http://dx.doi.org/10.1016/0920-5861(94)80168-1http://dx.doi.org/10.1016/S0920-5861(00)00271-6http://dx.doi.org/10.1002/kin.v23:12http://dx.doi.org/10.1016/S0920-5861(00)00279-0http://dx.doi.org/10.1016/S0920-5861(00)00279-0http://dx.doi.org/10.2514/1.27014http://dx.doi.org/10.2514/1.27014http://dx.doi.org/10.1115/1.2737479http://dx.doi.org/10.1016/S0010-2180(01)00363-7http://dx.doi.org/10.1016/S0010-2180(01)00363-7http://dx.doi.org/10.1115/1.2737479http://dx.doi.org/10.2514/1.27014http://dx.doi.org/10.2514/1.27014http://dx.doi.org/10.1016/S0920-5861(00)00279-0http://dx.doi.org/10.1002/kin.v23:12http://dx.doi.org/10.1016/S0920-5861(00)00271-6http://dx.doi.org/10.1016/0920-5861(94)80168-1http://dx.doi.org/10.1016/0010-2180(94)90107-4http://dx.doi.org/10.1016/0010-2180(91)90007-Xhttp://dx.doi.org/10.1016/0010-2180(91)90006-Whttp://dx.doi.org/10.1080/00102208308923620http://dx.doi.org/10.1080/00102208308923620

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