Effect of Physical Adsorption on Heat Fluxes to Catalytic
Surfaces in Carbon Dioxide
Valery Kovalev, Nataly Afonina, Valery Gromov
Moscow State University named after M.V. Lomonosov, Russia
Abstract. A model of the heterogeneous catalysis of a dissociated carbon dioxide mixture on high–temperature heat shield
coating has been developed. The model takes into account both chemical and physical adsorption and desorption of oxygen atoms
at vacant active sites on the surface; recombination of chemisorbed oxygen atoms with gas phase of O atoms and of CO
molecules (Eley – Rideal recombination) and with physisorbed atoms (Langmuir – Hinshelwood recombination). Note that the
physisorbed atoms either are desorbed from the surface or diffused to the nearest chemisorbed site. Therefore some of these
diffusing atoms will be able either to occupy vacant active sites or to react with chemisorbed atoms. The developed here kinetic
model for surface reactions provides closed expression for effective probabilities of heterogeneous reactions
CO + O → CO 2
and
C + 2O → CO 2
O + O → O2 ,
on the quartz surface in terms of the rate constants and the activation energies of
the elementary studies of these reactions. Based on comparison of the calculated heat fluxes in dissociated carbon dioxide with
those measured on the VGU-4 plasma generator of the Institute for Problems in Mechanics of the RAS, the parameters of the
present catalysis model were chosen for
SiO 2 - based coating materials. The different mechanisms effect of above-mentioned
heterogeneous reactions on recombination probabilities and heat fluxes to coatings was investigated.
INTRODUCTION
One of the main factors determining the heat transfer intensity during a space vehicle at the Martian atmosphere
entry is represented the recombination of the components of dissociated carbon dioxide, which consists of about
96% of the atmosphere. Even at flight velocities of the order of 6 km/s, carbon dioxide has been dissociated
practically totally in crossing the bow shock. At the same time, owing to the high rarefaction of the atmosphere, the
gas-phase recombination in the vicinity of the vehicle surface is near-frozen. Theoretically, at using noncatalytic
coatings, a fourfold reduction in the heat flux to the frontal surface of the vehicle may be achieved on most part of
the entry path, including the peak thermal loaded region.
High-temperature catalysis in dissociated air has been studied extensively experimentally and theoretically, in
connection with the development of thermal protection systems for Space Shuttle and Buran aero assisted orbital
transfer vehicles [1-4]. Originally, heterogeneous catalysis in theoretical models was described by first-order
reactions with experimentally obtained rate constants. Recently, more accurate models [5-13] based on ideally
CP663, Rarefied Gas Dynamics: 23rd International Symposium, edited by A. D. Ketsdever and E. P. Muntz
© 2003 American Institute of Physics 0-7354-0124-1/03/$20.00
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adsorbed Langmuir layer theory [14] were developed. These models describe adequately the aerodynamic heating on
the windward side of reusable vehicles along the entry path [15].
At the same time, few studies have been devoted to high-temperature heterogeneous catalysis in dissociated carbon
dioxide. In studying the Martian atmosphere entry, mainly the limit cases of an ideal catalytic surface (with a maximum
rate of heterogeneous recombination of the dissociated carbon dioxide components) and a noncatalytic surface were
considered in the literature [16-18]. Phenomenological models of the catalytic properties of heat-shield coatings of
spacecraft entering the Martian atmosphere based on a detailed analysis of the heterogeneous catalytic reaction
mechanism were suggested in [19, 20].
The first results of measurements of the dissociated carbon dioxide flow parameters, as well as the heat fluxes to a
catalytic surface and the temperature of the latter, were published in [21, 22] for three coating materials types and
quartz. The approach developed in [5, 19, 20] was used to model the catalytic properties of heat-shield coatings in a
dissociated CO2 - N2 mixture in [23, 24]. On the basis of the experimental data interpretation, explicit relationships
between the catalytic activities and the near-surface conditions (temperature, pressure, and concentrations) were derived
for the coatings studied in [21,25]. For each of these coatings, the heat fluxes at the Mars Miniprobe stagnation point
were calculated along the vehicle's entry trajectory into the Martian atmosphere and the coatings usability in the thermal
protection system of the vehicle was established.
In this paper the effect of the physisorbed atoms recombination in Eley – Rideal and Langmuir – Hinshelwood
mechanisms and evaluated recombination of C atoms on the surface is investigated.
CATALYTIC MODEL
We consider the flow of a dissociated carbon dioxide mixture past a catalytic surface body. The mixture includes
such species as O, C, O2, CO, and CO2 and simulates the gas in the shock layer at the vehicle entry into the Martian
atmosphere with velocities as high as 8 km/s. The heterogeneous catalytic reaction mechanism consists of the following
reactions listed below:
1. O + S v ↔ O s , 2. O s + O ↔ S v + O 2 , 3. O s + CO ↔ S v + CO 2 , 4. O + Fv ↔ O f ,
5. Of + Sv ↔ Os + Fv , 6. Os + O f ↔ O 2 + Fv + Sv , 7. Os + Os ↔ O 2 + 2Sv , 8. Os + C ↔ CO + Sv ,
s
f
where O and O are chemisorbed and physisorbed atoms respectively;
S v and Fv denote vacant chemisorption
and physisorption sites.
In our model we neglected a number of other possible reactions such as, for example, interaction either between
two physically adsorbed atoms, as well as processes involving adsorbed molecules and dissociative chemisorption of
molecules. Ignoring the dissociative chemisorption is justified for the relatively low surface density of active sites
and low wall temperatures, due to high-energy thresholds associated with such reactions. For the same reason we
can discount reaction between two chemically adsorbed atoms (reaction 7). The other processes, due to the lack of
pertinent data on rate constants, are overlooked here for simplicity. The effect of this reaction is investigated on the
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basis of data on rate constant [11, 12]. Reaction 8 is considered in two limit cases: when it is frozen or when it is
fast.
Rate constants of adsorption and Eley – Rediel reaction are determined by the formula
8kT
πM m
k i+ = γ i vm / 4 N v , vm =
where
Nv
γ i is
is
reaction probabilities; vm
N vf or N vs ; N vf
,
denotes the mean velocity of the gas phase particle m near the surface;
s
is active sites number for physical adsorption and N v is active sites number for
chemical adsorption per unit area;
Mm
is molecular weight.
Rate constants of Langmuir – Hinshelwood reactions are determined by the formula
ki+ = γ i Dm , Dm =
ν Dm
4Nv
exp(− E Dm / T ) ,
here ν Dm is frequency factor and EDm activation energy of surface diffusion. For reactions 5 and 6 ν Dm
[26, 27], for reaction 7
ν Dm = CD vm
, where
= 1013 c −1
CD = 2.2 ⋅ 1010 m −1 [11]. It is assumed that N vf = 10 20 m −2 , and
N vs = 5 ⋅ 1018 m −2 (See [11,26,27]).
Reaction probabilities are determined by the formula γ i =
is assumed equal zero. Note that activation energies
term as sums. Thus it may be assumed that
sums of reagents [23, 24], then for
Ai exp(− Ei / RT ) . Adsorption activation energy Ei
EDm and Ei of Langmuir – Hinshelwood appear in exponent
EDm = 0. Equilibrium constants K j are expressed in terms of statistic
k −j we have k +j / k −j = K j . It is supposed that statistic sums adsorbed particles
and free sites are equal. Catalytic model parameters are given in Table.1.
TABLE 1. Catalytic model parameters.
Reaction
1
2
3
4
5
6
7
For reaction 1-3 parameters
A
0.025
0.015
0.015
0.5
0.53
0.53
0.02
1.0
E, Kj/mol
0
25
15
0
0
0
125
500
Q, Kj/mol
300
20
-
Ref.
[23, 24]
[23, 24]
[23, 24]
[26, 27]
[26, 27]
[26, 27]
[12]
[11]
Ai and Ei were determined in [24] ground a comparison of the calculated heat fluxes
in dissociated carbon dioxide with those measured on VGU–4 plasma generator of the Institute for Problems
mechanics of RAS [21, 28]. Catalytic model parameters for reactions 4–6 were determined from analysis data [27]
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and from comparison calculated and measured heat fluxes in the third regime of subsonic flow past the model at low
temperature (Table 2).
COMPARISON WITH EXPERIMENTAL DATA
In this study, the heat fluxes were calculated the same way as [21], that is described in details in [29,30], within the
framework of the finite-thickness boundary layer problem using the gaseous medium model. In this approach, the gas
composition at the outer edge of the boundary layer is assumed to be equilibrium. The gas temperature at the outer edge
of the boundary layer is found from the condition that the calculated and measured heat fluxes qwf to a cold, ideal
catalytic surface (Tw=300°K, γi*=1) coincide. The measured values are chosen around an analysis of the experimental
data for copper and silver surfaces [21, 28] and are given in Table 2. In this table the velocity Vs of the subsonic jet at
the center of the exit section of the plasma generator discharge channel, the measured pressure Pe at the outer edge of
the boundary layer, the power N supplied to the induction coil, and the ram pressure ∆p are given for six flow regimes
also.
TABLE 2. Regimes of subsonic flow past the model.
Regimes/Parameters
1
3320
T ,K
e
2
4360
3
5800
4
6256
5
6600
6
6875
Vs , m/c
47,3
76,1
105,6
118,0
145,0
164,0
q wfc ,Wt/cm 2
46,4
74,4
103,7
130
175,0
208,0
N, kWt
29
10,5
37
17,5
44
24,5
52
26,2
64
33,75
72
38,8
∆p , Pa
In Fig. 1 it is shown the surface temperature dependence of calculated heat fluxes to coatings based on SiO 2 for
different test regimes. The curves number correspond regimes number in Table 2. The calculation results, ignoring
processes with physisorbed atoms, are marked by dotted lines. Points 1 ( × ) relate to the experimental results in
accordance with which the rate constants of reactions 1-3 are chosen in [23]. Note that at low temperature the predicted
heat fluxes are in good agreement with the experimental values for quartz (points 2– •) for all regimes. Neglecting
processes with physisorbed atoms at low temperature decrease the heat fluxes significantly.
ef
, determined by the formula
In Fig. 2, 3 the effective coefficients of heterogeneous recombination γOef and γCO
RO = - ρ γ O
ef
RT
2π mO
cO , R CO = - ρ γ CO
ef
RT
2π mCO
cCO are plotted according to the inverse temperature for different
test regimes. Note that the calculations are carried out taking into account the reactions of chemisorbed atoms both with
physisorbed atoms (Hinshelwood-Hinshelwood mechanism) and gas phase atoms (Eley-Rideal mechanism).
Taking into consideration both mechanisms allow to explain the non-Arrhenius temperature dependencies γ O and γCOef
ef
in a wide temperature range, from 300 up to 2000 K. This can be seen especially on Fig. 2. Thus, a clearly defined
maximum is formed at Tw ≈ 1350°K. The reason for this behavior is that at sufficiently high temperatures (specific to
each type of coating) thermal desorption processes predominate, the degree of occupancy of the surface diminishes, and
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qw, W/сm2
160
1E+000
γ efO
1E-001
120
5
80
1E-002
1
2
5
4
1E-003
3
2
40
1E-004
1
0
300
600
900
1
2
5
1E-005
300
1200 1500 1800 2100
600
900
Tw,K
Fig.1
1200 1500 1800 2100
Tw,K
Fig.2
1E-002
γ efCO
5
2
1
1E-003
1E-004
5
2
1
1E-005
300
600
900
1200 1500 1800 2100
Tw,K
Fig.3
qw, W/сm2
80
qw, W/сm2
200
160
6
3
60
120
2
40
4
80
3
1
20
40
0
300
600
900
1200 1500 1800 2100
Tw, K
0
300
600
900
1200 1500 1800 2100
Tw,K
Fig.5
Fig.4
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the resulting rate constant for the heterogeneous recombination of oxygen atoms also decreases. This was discovered
earlier for dissociated air [5,6] and confirmed experimentally in [32]. Here you see minimum of
γ Oef
at Tw ≈ 600°K
also. It may be explain by intensification processes with physisorbed atoms.
In Fig. 4 the surface temperature dependence of calculated heat fluxes to coatings based on SiO 2 is plotted for
different test regimes when fast reaction 8 is also considered. One can see that this reaction effect on heat fluxes is too
large if the power N supplied to the induction coil.
In Fig. 5 the heat flux is presented (at the stagnation point on the surface versus the surface temperature when we have
used rate constants for reaction 7 from [12] (dotted lines). Note a certain stratification of the curves at high
temperatures. Taken from [11] the rate constants for this reaction provide the same results as in the case the reaction is
absent. The investigations show that additional experimental data are needed over a wider temperature range for
adequately modeling the Langmuir-Hinshelwood processes with chemisorbed atoms on catalytic surface.
SUMMARY
On the basis of ideal adsorbed Langmuir layer theory, an interaction model of dissociated carbon dioxide mixture
with a catalytic surface has been developed. The model takes into account both chemical and physical adsorption
and desorption of O atoms at vacant active sites on the surface; recombination of chemisorbed of O atoms with gas
phase of O atoms and of CO molecules (Eley – Rideal recombination) and with physisorbed atoms (Langmuir –
Hinshelwood recombination). The structural formulas for the catalytic activity coefficients as function of the surface
conditions (temperature, pressure, and species concentrations) are derived. By interpreting the experimental data,
obtained on an inductive plasma generator, model parameters are determined for SiO 2 - based coating materials.
Comparison the calculated and measured heat fluxes shows, that the model may predict heat-transfer in a wide
temperature range, from 300 up to 2000 K.
ACKNOWLEDGMENTS
The study was carried out with the support of the Russian Foundation for Basic Research (project No.02-01-00759)
and A.M. Liapunov Franco-Russian Institute (Project 02-06).
REFERENCES
1. Baronets, P. N. , Gordeev, A. N. , Kolesnikov, A. F. , et al., Gagarin Scientific Studies on Aviation and Cosmonautics, 1990,
1991
[in Russian], Nauka, Moscow, 1991, p. 41.
2. Lozino-Lozinskii ,G. E., Gagarin Scientific Studies on Aviation and Cosmonautics, 1989 [in Russian], Nauka, Moscow,1990, p. 6.
3. Scott, C. D., J. Spacecraft Rockets, 22, 489 (1985).
1006
4. Polyanskii,. O. Yu. , Kuznetsov, M. M., Men'shikova V. L. , et al., Effect of the Real Gas Properties on the Aerodynamic and
Thermal Characteristics of Hypersonic Vehicles [in Russian], Central Aerohydrodynamics Institute, Department of Scientific and
Technological Information, Review No. 676 (1987).
5. Kovalev. V. L., and Suslov, O. N.
, Investigation of Hypersonic Aerodynamics and Heat Transfer with Allowance for
Nonequilibrium Chemical Reactions [in Russian], Moscow University Press, Moscow, 1987, p. 58.
6. Kovalev, V. L., and Suslov, O. N. , Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 5, 179, (1996).
7. Zalogin, G. N., and Lunev, V. V., Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza 5, 161 (1997).
8. Jumper, E. J., and Seward, W. A. , J. Thermophysics Heat Transfer, 5, 284 (1991).
9. Willey, R. J., J. Thermophysics Heat Transfer, 7, 55 (1993).
10. Deutschmann, O., Riedel, U., and Warnatz, J., Universitet Stuttgart, Institut for Technische Verbrennung, Preprint No. 23
(1994).
11. Nasuti, F., Barbato, M., and Bruno, C., J. Thermophysics Heat Transfer, 10, 131 (1996).
12. Daiss, A., Fruhauf, H.- H. , and Messerschmidt, E. W. , J. Thermophysics Heat Transfer, 11, 346 (1997).
13. Korotaki, T, AIAA Paper 2000 -- 2366. (2000).
14. Langmuir, J. Chem. Soc., 4, 511 (1940).
15. Kovalev, V.L, Kolesnikov, A. F., Krupnov, A. A., and Yakushin, M. I. , Izv. Ross. Akad. Nauk, Mekh. Zhidk. Gaza, 6, 133
(1996).
16. Chen, Y.-K., Henline,W.D., Stewart, D.A., and Candler, G.V. , J. Spacecraft Rockets, 30, 32 (1993).
17. Mitcheltree. R.A., and Gnoffo, P.A., J. Spacecraft Rockets, 32, 771 (1995).
18. Gupta R.N., Lee K.P., and. Scott, C.D., J. Spacecraft Rockets, 33, 61 (1996).
19. Kovalev, V.L., Proceedings of the 14th International Workshop on Models in the Continuum Mechanics [in Russian], Moscow
Physical and Technical Institute (1998), p. 83.
20. Kovalev, V.L., Vestn. MGU, Ser. 1, Mat. Mekh., 1, 37 (1999).
21. Bykova, N. G. , Vasil'evskii, S. A., Gordeev, A. N. , Kolesnikov, A. F. , Pershin, I. S. , and M. I. Yakushin, Izv. Ross. Akad.
Nauk, Mekh. Zhidk. Gaza, 6, 144 (1997).
22. Serpka S., Chen Y-K., and Marshall J., J. Termophysics and Heat Transfer., 14, 1, 45 – 52, (2000).
23. Afonina, N.E. , Gromov, V.G. , and Kovalev, V.L.,.35, 1,87-94, (2000).
24. Afonina, N.E. , Gromov, V.G. , and Kovalev, V.L., AIAA Paper 01-2832, (2001).
25. Kravetskii, G. A. , Kuznetsov, A. V. , Kostikov, B. I. , and V. V. Rodionov, Proceedings of the 1st International Aerospace
Symposium "Man-Earth-Space", 1992, Vol. 5, Materials and Production Technology of Aerospace Engineering [in Russian],
Engineering Academy Press, Moscow (1995), p. 249.
26. Kim Y.C., and Boudart M., J. Langmuir, 7, 2999 – 3005, (1991).
27. Gordiets B.F., and Ferreira C.M. , AIAA J., 36, 9, 1643-1651, (1998).
27. Kolesnikov, A.F. , Pershin, I.S. , Vasilevskii, S.A., and .Jakushin, M.I, AIAA Paper 98- 2847, (1998).
29. Final Project Technical Report of ISTCN 036-96 , Moscow, 16-25, (1999) .
30. Afonina, N. E. , and Gromov, V. G. , Moscow State University, Institute of Mechanics, Preprint No. 31-97 (1997).
31. Afonina, N.E. , and Gromov, V.G. Proceedings of 3d European Symposium on Aerothermo-dynamics for Space Vehicles.
ESTEC. Noordwijk, the Netherlands. 24 - 26 November 1998, 179-186, (1998), .
32. Kolodziej P. , and Stewart, D. A. , AIAA Paper 87-1637 (1987).
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