HETEROGENEOUS CATALYSIS: THEORY, MODELS

0 downloads 0 Views 315KB Size Report
THEORY, MODELS AND APPLICATIONS. M. BARBATO .... Heterogeneous Catalysis : there is a phase boundary separating the cat- alyst from the .... Large savings in TPS appear, in principle, possible if could be deter- mined reliably and ...

HETEROGENEOUS CATALYSIS: THEORY, MODELS AND APPLICATIONS M. BARBATO CRS4 Research Center Cagliari, Italy AND C. BRUNO Dip. Meccanica e Aeronautica { Universita di Roma I Roma, Italy

1. Introduction When air ows past a body moving at high Mach numbers, a bow shock forms in front of the body. If the ight Mach number is high enough, air will dissociate and form species as O, N , NO; if the Mach number corresponds to energies of order about 1 eV (about 11,000 K), ionization also takes place, and O+ , NO+ , N + and e will appear. Past the bow shock the air ow entering the shock layer will eventually reach the body surface, which (for structural reasons) must be kept at surface (or: wall) temperatures Tw of order 300 K - 2000 K at most. At these temperatures the greatest part of the species above will tend to recombine. Recombination will occur throughout the shock layer, since the gas temperature drops going from the shock toward the wall, and a (usually) substantial percentage of atoms that have escaped gas-phase recombination will recombine on the surface of the body. Solid surfaces may be thought as a medium where bonds present inside the bulk of the material have been severed by the fabrication process. Besides, the complex solid structure has many more degrees of freedom than molecules in the gas. It is intuitive that gas species will naturally tend to form bonds with the surface that may facilitate recombination. When this occurs, the surface is said to be catalytic. If surface recombination occurs, the formation energy of the recombining species will initially stay within the new species formed. For instance, when two O atoms recombine, initially the total formation energy of the two O

2

M. BARBATO AND C. BRUNO

atoms will tend to stay within the O2 formed. But then the O2 just formed would be translationally and roto-vibrationally excited so much that it would again dissociate, unless part of its energy is deposited on the surface. Since formation energies of O, N or ionized species are large, even if the percentage deposited is small, the surface may be considerably heated by catalytic recombination. This heat ux is additional to molecular conduction and that due to sensible enthalpy transported by di using individual species (convective uxes at the surface are zero, if the surface velocity is assumed zero, as is the case for non-permeable or non porous walls). Convincing estimates of the heat ux contribution due to catalysis yield as much as 40% of the total heat ux inside the stagnation region [1]. Since the inception of the manned space program, there has been therefore much interest in preventing recombination over the Thermal Protection System (TPS). In essence, one would like to coat TPS with materials as little catalytic as possible. Old work on recombination (dating back to the '50s and '60s, and performed at room temperature) indicated that glass is among the best material, a fact well known to combustion researchers investigating explosion limits [2]. Follow-on research and testing have shown that even glasses tends to increase their "catalyticity" with temperature, and by a large factor. Much work has been performed to predict this increase, since the actual composition of dissociated air during a re-entry trajectory is dicult to measure, and some sort of modeling is needed to preliminarily predict heat uxes. To bypass this problem, back in the early '70s, an extreme assumption became popular, i.e., the surface was assumed to be "fully catalytic", meaning that all species would recombine and form O2 and N2 only. In this case the heat ux contribution due to catalysis is maximum, which at rst sight sounds like a conservative way of designing TPS. However, this assumption results also in overestimating Boundary Layer temperatures, therefore underestimating densities, and eventually wrong Cp predictions. Ever since, there has been an acute awareness of the need to understand nite-rate recombination. What follows wants to be a primer of what is known to-date in this area; it is hoped that the material covered will be used as a starting point toward better understanding and modeling of surface catalysis in hypersonics.

2. Heterogeneous Catalysis The word catalysis was rst used by Berzelius in 1835: "Catalysts are substances that by their mere presence evoke chemical reactions that would not otherwise take place" [3]. Wilhelm Ostwald de ned a catalyst as: "a substance that changes the velocity of a chemical reaction without itself

HETEROGENEOUS CATALYSIS

3

appearing in the end products" [3]. In accord with that, the Chinese word used for a catalyst is "tsoo mei" which also mean "marriage broker". This brief historical introduction brings to the real meaning of catalyst. A catalyst participating to a reaction does not appear in the stoichiometric equation of the reaction. His e ect, for an assigned reaction, is to increase the reaction velocities for an assigned temperature or to decrease the temperature at which the reaction achieves a given rate. For simple reactions, without thermodynamically unstable intermediate product, this means that the catalyst action is to increase both the reaction velocities (forward kf and backward kb) in such a manner that the ratio kf =kb does not change. For this reason equilibrium obtained with a catalyst is the same as that ultimately arrived at when no catalyst is present. It is important to notice that the catalyst cannot initiate a reaction which is thermodynamically impossible [4]. Its action is always subject to the laws of thermodynamics. The "speed-up" obtained using a catalyst is due to a reduction of the activation energy E necessary for a speci c reaction (see Fig. 1). For example, we consider a solid catalyst: according to "transition state theory" a higher reaction velocity means a higher velocity constant [4]: 4Gz =RT e kv = kT h

(1)

where k is the Boltzmann constant, h is the Plank constant, T is the temperature, R is the gas constant and 4Gz is the free energy for the activated state. For a xed temperature, an higher kv means a lower free energy 4Gz for the catalysed reaction. But

4Gz = 4H z T 4 S z (2) and for the catalysed reaction 4S z is lower than the same quantity for the

non catalysed reaction because the particle bonded on the surface of the catalyst loses some degree of freedom. This means that, to have a lower 4Gz with respect to the non-catalysed reaction, the 4H z must be lower. From transition state theory we know that 4H z = Ea provided there is no change in the number of molecules in the reaction, which explains the activation energy reduction (see Fig. 1). It is possible to specify di erent kinds of catalysis depending on the chemical phase of catalyst and reactants: Homogeneous Catalysis : the catalyst is in the same phase as the reactants and no phase boundary exists; Heterogeneous Catalysis : there is a phase boundary separating the catalyst from the reactants; Enzymatic Catalysis : neither a homogeneous nor heterogeneous system.

4

E heter

E homog

Energy

M. BARBATO AND C. BRUNO

Reactants Adsorbed Reactants

Homogeneous Reaction Heterogeneous Products

Reaction Adsorbed Products

Reaction Coordinate

Figure 1. Energy reaction path for heterogeneous and homogeneous reaction.

A gas ow past a solid wall belongs to the second case: the reactants are the gas chemical species and the wall is the catalyst. 2 Modelling Heterogeneous Catalysis

A scheme representing the elementary steps involved in heterogeneous catalysis can be drawn as follow [3]: 1 di usion of reactants to the surface; 2 adsorption of reactants at surface; 3 chemical reactions on the surface; 4 desorption of products from the surface; 5 di usion of products away from the surface. Each one of these steps has a di erent velocity and the slower one is the process-determining rate. Steps 1 and 5 are usually fast; exceptions exist when the catalyst is very ecient. The limit for the catalytic reaction rate is the quantity of reactants that goes to the wall, and the surface reaction rates become independent of the kinetics properties of the surface [5]. This is the case of "di usion controlled" catalysis. Coatings for space vehicles TPS are studied to have very low catalytic eciency, to lower, as much as possible, the surface heat ux due to recombination e ects. Therefore, for these applications, the rate determining step for the heterogeneous catalysis process has to be found among steps

HETEROGENEOUS CATALYSIS

5

2, 3 and 4. In the following we will focus our attention on these elementary steps. 2.1. ADSORPTION

Adsorption is the formation of a bond between the atom, or the molecule, and the solid surface [4]. We speak of physisorption (physical adsorption) when the bond between surface and gas particles is due to van der Waals forces (forces between inert atoms and molecules). The forces involved are electrostatic forces for molecules with permanent dipole moments, induced polar attractions for readily polarizable molecules, dispersion forces for non polar atoms and molecules (forces due to the uctuation of electron density). The strength of these bonds depends upon the physical properties of the adsorbed gas, and is connected to the boiling point (or condensation) of the gas. Physisorption does not depend much on the chemical nature of the solid [4]. The particle-surface bond energy is low (10-50 kJ/mole) and the bond is important only at low temperatures ( 100-300 K): as the temperature rises the gas is removed more or less completely [6]. In heterogeneous catalysis, the importance of this kind of adsorption lies in the fact that it can be a precursor step for chemisorption. Chemisorption is associated to the solid surface properties. The surface of a solid can have properties markedly di erent from those of the bulk solid because on the surface there are unsaturated bonds. In fact, an atom on the surface is not in the same condition of a "bulk" atom, because it does not have its full complement of neighbors [4]. This is true either for a covalent solid (e.g. SiO2, SiC ) as for an ionic solid (e.g. NaCl). A simple way to understand this situation is to think about an ideal fracture of a crystal: the fracture sides are new surfaces where atoms which were before inside the bulk are now surface atoms with "dangling" bonds. When a free gas atom is near to a solid surface there is an attractive interaction between it and the surface atoms: the atom is attracted to the surface and it can nd in one of the "dangling" bonds a site, i.e. a physical location corresponding to a potential well (low energy state) where it remains trapped. The bond formed is a true chemical bond, usually covalent: there is an interpenetration of particle shells with electron sharing and the bond energy is high (40-800 kJ/mole [4]). Chemisorption occurs until the unsaturated surface valences are lled. This explains why, if multilayer physisorption is possible, no more than one layer can be adsorbed via chemisorption [7] although new species can form at surface (e.g. due to oxidation in metals). Physisorption and chemisorption are spontaneous (4H < 0) but the latter can have a substantial activation energy EA (see

6

M. BARBATO AND C. BRUNO

Fig. 2). This means that it starts at temperatures higher than those relative to physisorption. Energy

(a) (b)

EA

Distance z

z’ Q

Figure 2. Potential energy curves for adsorption: (a) physisorption of a molecule; (b) chemisorption of two atoms.

Two kinds of chemisorption are possible: the rst one is called associative or non-dissociative and it occurs to atoms (O, N , H , ...) and to molecules (CO, OH ) without molecular bond breaking. A very simple schematic representation of associative chemisorption is:

A +  ! A where the "" represent the site and the A the adsorbed atom (adatom). Assuming a uniform surface with uniformly distributed sites and assuming sites activity do not be function of the fraction of surface already covered, , the adsorption rate can be expressed as:

vads = s0 vc (1 ) where s0 is the initial sticking coecient, representing the probability of a molecule to stick on a bare surface, and vc is the collision rate:  8kT  n vc = 4 m where n is the gas particle density and m the particle mass.

HETEROGENEOUS CATALYSIS

7

The second kind of chemisorption is called dissociative and it may occur to diatomic molecules like O2, N2, H2 and CO. In this case chemisorption occurs with breaking of molecular bonds. Each atom is adsorbed from one site:

A2 + 2 ! 2A For this reaction the rate of adsorption reads:

vads = s0vc (1 )2 2z

where z represents the number of neighbors sites. In fact, in this case we assume that the atoms coming from the broken molecule can adsorb only on adjacent sites. Dissociative adsorption may occur also following another path:

A2 +  ! A + A In this case the striking molecule dissociates, an atom is adsorbed and the other goes back to the gas. Usually this process is far less probable than the previous one. In fact the energy content of the system adatom plus atom is greater than the energy associated to the system of two adatoms. Before describing the reaction step, we need to spend a few words about the initial sticking coecient expression. This important quantity, assuming an uniform sites activity over the surface, depends on T . For atoms impinging on a surface a general expression is [8]:

s0 = Pe

E=(kT )

where P is expected to be < 1. s0 decreases with temperature and this behavior can be understood with simple considerations: with increasing temperature gas atoms impinging on the surface have higher kinetic energy and thus higher probability to "rebound" after the collision with a site without sticking. Notice that for impinging molecules this trend can be the reverse (s0 increases with T ): in fact, if there is an activation energy associated to dissociative adsorption, at higher temperature it becomes easier to overcome this energy barrier. 2.2. REACTION The kind of reactions interesting to hypersonics applications are recombinations of atoms forming O2 and N2 and reactions producing NO, CO, and CO2 .

8

M. BARBATO AND C. BRUNO

In heterogeneous catalysis at least one of the reacting particles must be rst chemisorbed in order to react catalytically on a solid surface [4]. Therefore, if physisorption does not play a direct role, chemisorption is a fundamental step to "prepare" atoms and molecules to react. This mechanism furnishes a reaction path with an activation energy lower than the one of the correspondent homogeneous reaction (see Fig. 1). The rst reaction mechanisms we consider is the recombination between an atom from the gas and an adsorbed one: the free gas atom strikes the adatom and reacts with it. The result is a recombined molecule. This is called the Eley-Rideal mechanism (E-R) and a simple scheme of it is [9]:

A + B ! AB where the symbols A, B mean an atom. After the recombination the molecule AB  is still adsorbed. The rate of this reaction depends by the partial pressure of the gas phase atoms and by the surface coverage. On this basis for the step rate we can write [10]:

vER = k [A] [B ] The second mechanism is the recombination between two adatoms: this is called the Langmuir-Hinshelwood mechanism (L-H) and a schematic representation is [9]:

A + B ! AB +  Obviously this kind of reaction is possible if adatoms di use over the surface. For adatoms a way to move it is to "hop" from one potential well to another [8] overcoming a potential barrier Em that is lower than the desorption energy Ed ; in fact particles during this movement do not leave the surface completely. In literature it can be found that Em  0.1 0.2 Ed . This value depends on the surface coverage extent (it decreases when  increases), on the surface defects and on the crystallographic orientation of the surface. The presence of the energy barrier Em implies that the L-H mechanism is an activated process which becomes ecient at higher temperature with respect to the E-R mechanism. This is evident in catalysis involving metal surfaces were the recombination coecient drops sharply when the L-H mechanism starts (see Fig. 3). 2.3. DESORPTION After a E-R or a L-H recombination, there is not chemical bond between surface and molecule, which is free to leave the wall. This phenomenon

9

HETEROGENEOUS CATALYSIS

N Recombination Probability

0.9 0.8

Nasuti et al. Model Halpern-Rosner Data

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

3

10 /T(K)

Figure 3. Nitrogen recombination over tungsten: vs inverse temperature. From [15]. N

is called desorption. It may happen that desorption is not "immediate" and the molecule may fall in a physisorption well before the leaving (see Fig. 1). In any case, desorption is a very fast process and many authors consider reaction and desorption like a single step. The importance of this phenomenon lies in the fact that recombination energy can be left, in part or totally, on the wall when the molecule leaves the wall. The characteristic time of desorption is strictly linked to the amount of energy left on the wall by the molecular internal energy relaxation process [11]. This means that the molecule can leave the surface in an excited state and "quench" later in the gas near the wall, or they can leave the surface in thermal equilibrium with it. To take in to account this phenomenon a chemical energy accomodation (CEA) coecient is de ned as the fraction of the equilibrium dissociation energy delivered to the catalyst surface per recombination event [11]: q_ (3) = DAB _n=2 where q_ is the e ective energy ux to the wall, _n is the ux of recombined atoms and DAB is the AB molecule dissociation energy. Experimental values of [11] show a dependence on the interaction between surface and recombined molecules. If the bond between recombined molecule and surface is "strong" there is enough time to have a total ac-

10

M. BARBATO AND C. BRUNO

comodation ( = 1). On the contrary, if the bond is "weak" the molecules desorb rapidly and the energy left on the wall is smaller ( < 1). Large savings in TPS appear, in principle, possible if could be determined reliably and accurately, and if it could be "designed" a priori based on material properties and recombining atoms type. This is a frontier of surface catalysis still in need of exploration. 2.4. THERMAL DESORPTION Besides the mechanisms cited, we have to consider also thermal desorption. In fact, adsorbed atoms vibrate with the frequency kT=h; at suciently high temperatures this vibrations can extract the atom from the potential well leading to desorption [12]: A ! A +  : Following transition state theory, the rate of desorption reads [8]: 4S=k 4H=(kT ) vdes = Na kT he e

(4) where 4S and 4H are respectively entropy and enthalpy di erences between two states (adsorbate-gas). Usually 4H is supposed to be of the same order of magnitude of the adsorption energy. Due to the high values of the latter, thermal desorption becomes important at high temperatures (e.g. T > 2000 for N over W [11]). 2.5. RATE DETERMINING STEP In the following we will make some considerations about the rates of heterogeneous phenomena on a generic surface. For this reason we will speak about low and high temperatures without any precise speci cations. In any case, what we mean for "low" are temperatures not far for ambient, and for "high" temperatures over 1000 K. In a more detailed discussion, it would be better to distinguish between metallic and non-metallic surfaces, but the following discussion is general enough to t both cases. At low temperatures the surface coverage  is near to unity; this because the atoms mobility is very low and thermal desorption is not ecient. In these conditions the E-R recombination mechanism is expected to be more e ective with respect to L-H [13]. In fact, there is a very high probability, for an incoming atom, to strike an adsorbed one. In this conditions the rate of adsorption is expected to be larger than the rate of surface atoms depletion:

vads  vreac ; vdes

HETEROGENEOUS CATALYSIS

11

When the temperature rises, the coverage reduces both due to thermal and L-H recombination desorption. High temperature enhances adatom mobility and consequently their probability of recombination. Besides, the L-H mechanism is very ecient because it removes two adatoms at once. The E-R mechanism become less e ective due to the low probability of a collision between a gas atom and an adatom, since surface coverage is low and adatoms are very mobile and dicult "targets" for striking gas atoms. Under these conditions the rate limiting step can be adsorption:

vdes ; vreac  vads Besides de ning a rate limiting steps, the previous discussion leads to some further comment. We can observe that the molecules formed via a E-R mechanism with high probability are, more likely to leave the surface in an excited state [13]. They would then take with them part of the recombination energy. This is not the case of L-H recombined molecules, because they would have enough time to leave all the energy excess energy to the surface, and would desorb in thermal equilibrium. Therefore the factor would be expected to be small at low temperatures and to increase toward unity with increasing temperature.

3. Surface kinetics for reentry ows For reentry applications, one of the problems to solve is to predict the catalytic activity of TPS surfaces. The US Shuttle TPS coatings are made of borosilicate Reacting Cured Glass (RCG: 92% SiO2, 5% B2 O3, 3% SiB4), a surface that can be thought as a pure SiO2 surface. In fact, there is experimental evidence that a RCG surface may be more similar to SiO2 than to the borosilicate bulk [14]. This is the reason why the existing models simulating RCG catalytic activity, built by starting from the gas/surface physics seen above, are based on SiO2 structure. These models can be used to set realistic catalytic boundary conditions in CFD codes, and in the following we will present three of the most recent. Before going through these models we recall here some de nitions starting from the Molecular Recombination Coecient [1]: of atoms recombining at surface

= ux

ux of atoms impinging the surface

represents also the recombination probability for an atom impinging the surface. The Thermal Recombination Coecient is de ned as [1]:

0 =

12

M. BARBATO AND C. BRUNO

This coecient is a measure of the energy e ectively left on the surface by heterogeneous chemistry. In fact values of can be lower than 0.1 [14], meaning that only a small portion of recombination energy is left on the wall. If recombination rates (or probabilities) are measured via calorimetry, telling and 0 apart is a dicult task. Finally we recall the expression for the surface catalytic recombination rate, usually named catalitycity [1]: s w (5) Kw = 2kT m where the subscript w stands for "wall" and m is the atom mass. 3.1. HETEROGENEOUS CATALYSIS MODELS A model for recombination of Oxygen atoms on SiO2 has been presented by Jumper and Seward [16]. These authors assume the surface adsorption sites are the Si atoms of the SiO2 crystal lattice. They assume that an O atom of the SiO2 surface can desorb, either thermally or after a recombination with a gas atom (E-R mechanism), leaving available a Si atom that becomes a site where an oxygen atom can adsorb forming a double bond. Therefore the number of adsorption sites available on the surface is equal to the number of Si atoms on the surface (see Table 1). To obtain the recombination coecient , Jumper and Seward write the equation for the time rate variation of the surface concentration of oxygen atoms (ns ) [16]:

dns = n_ (6) ads n_ tdes n_ rec dt where n_ ads represents the rate at which O adsorbs at surface, n_ tdes the rate at which the adatoms desorb without recombination, and where n_ rec is the

rate at which atoms leave the surface after recombination with a gas atom following the E-R mechanism. Jumper and Seward, assuming steady state ( dndt = 0), calculate the surface coverage and the recombination coecient that are functions of wall temperature and O partial pressure. The initial sticking coecients are function of wall temperature too (see Table 1). This model was extended to RCG in [17] and these same authors, together with Newman and Kitchen, proposed a similar model for N recombination over SiO2-based TPS also [18]. These models are the rst that can simulate heterogeneous catalysis in Hypersonics taking into account the local ow and wall characteristics. A model for air recombination over SiO2-based materials has been presented by Nasuti et al. [15]. In this model the recombination coecients s

HETEROGENEOUS CATALYSIS

13

are also obtained by writing a surface balance for incoming and leaving particles based on [11]. For steady state conditions the ux of atoms adsorbing on the surface has to be balanced by the ux of atoms desorbing due to thermal desorption, E-R recombination and L-H recombination (in the latter case two atoms desorb at one time). Therefore simultaneous E-R and L-H recombination mechanisms are accounted for. The surface considered is SiO2 and adsorption sites are speci ed as potential energy wells. This model calculates the recombination coecients for N2, O2 and also NO surface formation. Therefore it produces 3 independent recombination coecients functions of wall temperature and of O and N surface partial pressures [15]. Constant values are assumed for the initial sticking coecients. This model depends on knowledge of basic surface physics, and in principle may be extended to any kind of gas species and any surface. The last model recently proposed is by Deutschmann et al. [19]. In this case, again for a SiO2 surface, a more conventional kinetic approach is used. Rate constants for adsorption, thermal desorption surface reactions, including E-R and L-H mechanisms, and desorption after recombination are calculated. The rate constants for reaction and desorption are in Arrheniuslike form. Recombination coecients (for N2 and O2 only) depend on the wall temperature and on adsorbed species concentration. As in Nasuti et al. [15], constant values for the initial sticking coecients are assumed. Whereas in the other two models the desorption step is always assumed to be collapsed in the reaction step, Deutschmann et al. assume this to be true for the E-R mechanism only. In fact, after L-H recombination, the molecule is assumed still adsorbed and a rate for the desorption step is calculated (a very low activation energy is actually used: 20 kJ/mol). In accordance with that, these authors assume complete accomodation ( = 1) for L-H recombined molecules, while they assume a constant = 0:2 for E-R recombined molecules. The crucial point of these models is the incorporation of physiochemical quantities, such as, for example, atoms adsorption energies, sticking coecients, number of sites for unit area and others. There is still a large range of uncertainty in the determination of these quantities and in each model more or less complicated expressions for steric factor are used to cover these "holes". In any case the e ort to produce such a models, in our opinion, has to be appreciated. In fact, these tools are valid under several ow conditions, and wall temperatures [21]. They can cover a wide range of ight and wind tunnel ow conditions with a larger exibility with respect to experimental ts obtained for a small range of temperature. For example, a spacecraft with a complex geometry re-entering our atmosphere, undergoes di erent ow conditions near to the surface at di erent locations and in this case using a single t could be too restrictive.

14

M. BARBATO AND C. BRUNO

TABLE 1. Main parameters for recombination coecient models: initial sticking coecient s0 ; surface site density N (sites=m2 ); steric factor S ; desorption energy E (kJ=mole). s

d

authors Jumper-Seward (SiO2 ) Jumper-Seward (RCG) Nasuti et al. Deutschmann et al.

s0 0:05 e0 002 1:00 e0 002 0:05 0:10 



N 5:00 2:00 4:50 1:39 s

:

T

:

T

S 2:24 10 2:00 10 0:1

1018 18  10 18  10 19  10 -







E

d

5 4

 

e0 00908 e0 003 :

:

T

T

339 339 250 200

Oxygen recombination coecient calculated using the three models presented above are shown in Fig. 4. These results, obtained for an O partial pressure = 400 Pa, are compared with the experimental data of Greaves and Linnett (SiO2) [22] and of Kolodziej and Stewart (RCG) [23]. All the three models represent qualitatively well the high temperature behavior by reproducing the O rollover for T  1600 K shown by the experimental results of [23]. In all three this second order e ect has been found to be due mainly to thermal desorption, the most important process at those temperatures. Moving toward the low temperature range, the Deutschmann et al. model underpredicts of order of magnitude showing its intentional high-temperature-addressed design. The other two models represent qualitatively and quantitatively well the recombination coecient trend. An evident di erence between these two models is their di erent curvatures. It is due to the di erence in the sticking and steric factors laws chosen by the authors: Nasuti et al. assume constant values whereas Jumper and Seward adopt temperature dependent expressions (see Table 1). These factors are one critical to such a models, because by necessity, they try to include physics not otherwise modeled by elementary steps. A way to clarify this point may be to have more experimental data for and 0 over a wide range of temperature going from ambient to the material melting limit.

4. Heterogeneous catalysis applications to hypersonic ows It is already some time that the CFD community is moving towards the inclusions of this kind of models in complex thermochemical nonequilibrium

ow solvers [20], [21], but often "rude" boundary conditions, such as "fully catalytic wall" or "non catalytic wall", are still used. The only justi cation for them is that they are simple to understand and to implement in a code. Clearly this is not acceptable when real conditions are very far from these extremes. In the following some results showing the large di erences due to

15

HETEROGENEOUS CATALYSIS

O Recombination Coefficient

10

Greaves & Linnett Kol.-Stew. 235.0 Pa

-1

Kol.-Stew. 360.0 Pa Kol.-Stew. 411.0 Pa

10-2

Kol.-Stew. 824.0 Pa Nasuti et al. 400.0 Pa

10

-3

10-4

10

Jumper-Seward

-5

Deutschmann et al.

0.5

1.0

1.5

2.0

2.5

3.0

1000/T

Figure 4. for TPS coating materials: comparison among several models. O

the use of one or another condition are reported. A brief summary of the di erent wall boundary conditions used in CFD for heterogeneous catalysis and for a 5 species air is [21]: 1 Non catalytic wall:

i = 0 i = O; N The wall is completely indi erent to the ow chemistry. 2 Fully catalytic wall:

i = 1 i = O; N in this case the wall is a "perfect catalyst" and catalysis is "di usion controlled." Since each atom hitting the wall recombines, the catalytic eciency depends by the velocity of di usion of atomic species trough the boundary layer. 3 Fully Equilibrium wall: Yi = Y i i = O2; N2; NO; O; N where Y i are the equilibrium species mass fractions for the local values of temperature and pressure. This is a very strong condition. It forces the ux of atoms to the wall (usually is YO = YN = 0) imposing very strong mass fractions gradients at the wall. Without any doubt these boundary conditions are stressing over the limit the near wall chemistry.

16

M. BARBATO AND C. BRUNO

4 Finite rate catalysis: 0 < i < 1 i = O; N In this case a measure of real interface physics is introduced in the CFD ow solver. This means attributing the same importance to homogeneous and heterogeneous chemistry. 4.1. SOME APPLICATIONS Solving hypersonic ows, the additional computational e ort required by Finite Rate Catalysis (FRC) models is balanced by the increase in quality of the results. This concept can be clari ed by a simple example: we consider a

ow past a 40 cm long blunt cone (scaled down ELECTRE reentry capsule geometry). The in ow conditions are those of the HEG [24] shock tunnel test chamber for p0 = 500 Pa, T0 = 9500 K stagnation conditions [25]. The body surface is assumed to be at 1500 K. The ow is solved with the TINA code [26] and two di erent Boundary Conditions (BCs): (a) nite rate catalysis; (b) fully catalytic wall. The results of these calculations are shown in Figs 5 and 6. From the stagnation line results, shown in Fig. 5, we see that, besides the expected results for the wall mass fractions, i.e. YN(b2) > YN(a2), YO(b2) > YO(a2), the wall NO mass fraction in the fully catalytic case is higher than in the nite rate catalysis case, notwithstanding the fact that the FRC model used [15] predicts also catalytic NO formation. The reason for this result is that in case (b) the strong production of N2 and O2 (b) (b) (KwO ' KwN ) and the di usion of these species away from the surface 2 2 due to the strong species gradients, drive the gas phase mechanism: O2 + N ! NO + O + 32.4 kcal/mole (7) N2 + O + 76.4 kcal/mole ! NO + N (8) This mechanism pumps NO in the ow and stores energy in the gas phase; it is very e ective slightly away from the surface and it quenches near to the wall, where YO ; YN ! 0. For case (a) instead this mechanism is not e ective: in the gas phase a smaller quantity of NO is produced by the reaction (8), whereas in the zone close to the wall, due to the surface formation of O2 and to the presence of N atoms, reaction (7) produces NO and releases energy. This latter phenomenon is similar to what was reported by Tirsky in [27], where an exchange mechanism "(7) + reverse of (8)" is presented as very e ective in the gas close to the wall when KwO2 > KwN2 . Notice that in the case (a) shown here, in the zone closer to the wall, there is not any sensible contribution from either reaction (8) direct or reverse.

17

HETEROGENEOUS CATALYSIS Fin. Rate Fully Cat

0.3 Yi

N2

Y N2 0.7

0.2 O 0.6

N 0.1 NO

O2

0.5

0.0 -0.0004

-0.0003

-0.0002 -0.0001 x [m]

0.0000 wall

0.4 0.0001

Figure 5. Comparison between two solutions with di erent catalytic boundary conditions at T = 1500 K : stagnation line mass fractions. w

The e ects of this on the surface heat ux can be seen in Fig. 6 where the ratio qi =qtot for i = "tr (translational), vib (vibrational), df (di usive)" are plotted along the body. For case (b) the strong recombination leads to qdf=qtot > 0.4 all along the body, whereas for case (a) this ratio is < 0.3. Still for case (a), the energy released by reaction (7) near to the surface yields a quite larger qtr =qtot with respect to case (b). This result is also partly due to the desorption of a larger amount of molecules than in case (b). In fact, assuming that the recombined molecules leave the wall in thermal equilibrium (T = TV = Tw ), the BL gas is cooled by this "cold" ow of particles. Therefore, due to the larger recombination, in case (b) the wall 5T and 5TV are smaller than in case (a). An other important issue arises when we compare ow conditions for

ight and wind tunnels simulations. In Fig.s 7-10 we show the results of two calculations performed for the same shape (i.e. sphere plus cone) and obeying to the binary scaling rule (1 L =0.0006) For the two cases the amount of dissociated species reaching the wall is quite di erent, as shown by Fig.s 7 and 8. This leads to di erent amounts of recombined species. In fact the atoms depletion term can be expressed as: w_ a = Kwaw Ywa (9) where Ywa is the atoms mass fraction at the wall.

18

M. BARBATO AND C. BRUNO

1.0

Finite Rate Fully Cat.

q/qtot 0.8

qtr

0.6 0.4

qdf

0.2

qvib

0.0 0.0

0.1

0.2

0.3

0.4

x (m)

Figure 6. Comparison between solutions with di erent catalytic boundary conditions at T = 1500 K : di erent contributions as a percent of the total wall heat ux. w

Y i 0.25

Y N2 0.75

0.20

0.15

N2 N O2

0.10

O NO

0.70 0.65 0.60 0.55

0.05

0.50 0.00 -0.020

-0.010

x (m)

0.000

0.45

wall

Figure 7. Stagnation line mass fractions for "in ight" numerical simulation: Ma = 15.3, 1 = .00033 kg=m3 , L = 2.0 m, T = 1000 K . w

19

HETEROGENEOUS CATALYSIS

Y i 0.25

Y N2 0.75

0.20 0.70 0.15

0.10

0.05

N2 N O2 O NO

0.65 0.60 0.55 0.50

0.00 -0.003

-0.002

x (m)

-0.001

0.45 0.000

wall

Figure 8. Stagnation line mass fractions for shock tunnel numerical simulation: Ma = 9.7, 1 = .002017 kg=m3 , L = .33 m, T = 1000 K . w

Therefore the catalytic activity has di erent e ects as it is shown by di usive contribution to the total surface heat ux in Fig. 10. In fact, along the body the ratio qdf =qtot is higher than 0.15 for the wind tunnel numerical simulation whereas, apart from the zone near to the stagnation point, it is lower than 0.1 for the "in ight" case. Near the stagnation zone this di erence reduces, and on the stagnation point the two contributions are very close to each other. For the "in ight" numerical simulation we see a rapid decrease of the catalytic activity from the stagnation point to x=L ' 0.16. In cases similar to the latter presented here, the necessary "binary scaling" principle is insucient to guarantee reactive ow similarity then, to do that, the Damkoheler numbers related to heterogeneous chemistry (i.e., inside the BCs) must be the same of ight conditions. This further condition yields that, to reproduce "real ight conditions" in a wind tunnel, a coating material di erent from that applied to the ying object must be used. A consequence of what presented above is that numerical simulations with realistic catalytic boundary conditions may help in the design of ground testing models. In fact the choice of the model skin has to be done on the basis of "scaling factors" for the heterogeneous chemistry. Therefore the main question is how important is the in uence of catalysis on the quantities measured in a test; if this importance is high, the similarity

20

M. BARBATO AND C. BRUNO q [W/m2]

qd

In flight

qtot In flight

7

10

qd Wind Tunnel qtot Wind Tunnel

6

10

105 104 103 102

0.0

0.2

0.4

0.6

0.8

1.0

x/L

Figure 9. Wall heat uxes for shock tunnel and "in ight" numerical simulations. q [W/m2]

Wind Tunnel In flight

0.8

0.6

qtr

0.4

qdf 0.2

0.0 0.0

qvib 0.2

0.4

0.6

0.8

1.0

x/L

Figure 10. Comparison between shock tunnel and "in ight" numerical simulations: di erent contributions as a percent of the total wall heat ux.

parameters (Damkoheler numbers), associated with catalytic activity must be set identical to those in ight. This conclusion should be supported by

HETEROGENEOUS CATALYSIS

21

two suggested actions: (a) an experimental study of the catalytic behavior of several materials, from oxides to metals, resulting in a database containing data for a wide range of temperatures; (b) starting from these data, the de nition of more accurate and more e ective models for the catalytic activity of a set of materials of interest for hypersonic ight. Finally, the right coupling among numerical simulations, ground testing and in ight measurements may lead to more reliable predictions.

5. Conclusions The brief discussion presented here has the aim of stimulate the interest in FRC models and on their use in CFD hypersonic ow solvers. This choice becomes necessary if one wants to move towards a more quantitative evaluation of thermal loads, a real estimate of gas composition near the wall and also in the entire boundary layer. Several models are now available that couple homogeneous and heterogeneous chemistry for hypersonic reactive

ows. The catalytic activity of a surface is strongly dependent on surface structure, on temperature and on local ow conditions. The use of existing ts is a way to account for heterogeneous chemistry but it is also a poor substitute of that o ered by FRC models. Clearly these models are still far from being perfect but, based on the availability of more experimental data, work can be done to make them more and more reliable.

6. Acknowledgement The authors would like to acknowledge Dr. Jean Muylaert for his interest and his support. This work has been carried out with the nancial support of the Sardinia Regional Government.

References

1. Scott, C.D. (1987) The E ects of Thermochemistry, Non-Equilibrium and Surface Catalysis in the Design of Hypersonic Vehicles, 1th Joint Europe-US Short Course on Hypersonics, Paris, France. 2. Lewis, B. and von Elbe, G. (1987) Combustion, Flames and Explosions of Gases, Academic Press, Orlando. 3. Moore, W.J. (1978) Physical Chemistry, Longman Group Limited, London. 4. Bond, G.C. (1974) Heterogeneous Catalysis: Principles and Applications, Clarendon Press, Oxford. 5. Rosner, D.E. (1966) Convective Di usion Limitations on the Rates of Chemical Reactions at Solid Surfaces - Kinetic Implications, 11th Symposium (International) on Combustion, The Combustion Institute, Pittsburgh. 6. Kensington, A. N. (1968) The Physics and Chemistry of Surfaces, Dover Publications Inc., New York. 7. Tamaru, X. (1978) Dynamic Heterogeneous Catalysis, Academic Press, New York.

22

M. BARBATO AND C. BRUNO

8. Boudart, M. and Djega-Mariadassou, G. (1984) Kinetics of Heterogeneous Catalytic Reactions, Princeton University Press,Princeton N.J.. 9. Zangwill, A. (1988) Physics at Surfaces, Cambridge University Press, Cambridge. 10. Atkins, P.W. (1994) Physical Chemistry, Oxford University Press, Fifth Edition, Oxford. 11. Halpern, B. and Rosner, D.E. (1978) Chemical Energy Accomodation at Catalyst Surfaces, Chemical Society, Faraday Transactions I, 74, 1833-1912. 12. Park, C. (1990) Non-Equilibrium Aerothermodynamics, John Wiley & Sons, New York. 13. Bruno, C. (1989) Nonequilibrium Thermochemistry and Catalysis, 2nd Joint Europe-US Short Course on Hypersonic, US Air Force Academy, Colorado Springs, CO. 14. Carleton, K.L. and Marinelli, W. J. (1992) Spacecraft Thermal Energy Accomodation from Atomic Recombination, J. of Thermophysics and Heat Transfer, 6, 4, 650-655. 15. Nasuti, F., Barbato, M. and Bruno, C. (1995) Material-Dependent Catalytic Recombination Modeling for Hypersonic Flows, also AIAA Paper 93-2840, revised and accepted for publication in J. of Thermophysics and Heat Transfer. 16. Seward, W.A. and Jumper, E.J. (1991) Model for Oxygen Recombination on SiliconDioxide Surface, J. of Thermophysics and Heat Transfer, 5, 3, 284-291. 17. Jumper, E.J. and Seward, W.A. (1994) Model for Oxygen Recombination on Reaction-Cured Glass, J. of Thermophysics and Heat Transfer, 8, 2, 460-465. 18. Jumper, E.J., Newman, M., Seward, W.A., and Kitchen, D.R. (1993) Recombination of Nitrogen on Silica-Based, Thermal-Protection-Tile-Like Surfaces, AIAA Paper 93-0477, 31st Aerospace Sciences Meeting & Exhibit, Reno, NV. 19. Deutschmann, O., Riedel, U., and Warnatz, J. (1994) Modeling of Nitrogen and Oxygen Recombination on Partial Catalytic Surface, ASME J. of Heat Transfer, June, Preprint 23. 20. Grumet, A.A., and Anderson, J.D. Jr. (1994) The e ects of Surface Catalysis on the Hypersonic Shock Wave/Boundary Layer Interaction, AIAA Paper 94-2073, 6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. 21. Barbato, M., Giordano, D. and Bruno, C. (1994) Comparison Between Finite Rate and Other Catalytic Boundary Conditions For Hypersonic Flows, AIAA Paper 942074, 6th AIAA/ASME Joint Thermophysics and Heat Transfer Conference. 22. Greaves, J.C. and Linnett, J.W. (1955) Recombination of Oxygen Atoms on Silica from 20 C to 600 C , Transactions of the Faraday Society, 55, 1355-1361. 23. Kolodziej, P. and Stewart, D.A. (1987) Nitrogen Recombination on HighTemperature Reusable Surface Insulation and the Analysis of its E ects on Surface Catalysis, AIAA Paper 87-1637, 22nd Thermophysics Conference, Honolulu, Hawaii. 24. Eitelberg, G. (1993) Calibration of the HEG and Its Use for Veri cation of Real Gas E ects in High Enthalpy Flows, AIAA Paper 93-5170, AIAA/DGLR Fifth International Aerospace Planes and Hypersonic Technologies Conference. 25. Walpot, L.M.G. (1991) Quasi One Dimensional Inviscid Nozzle Flow in Vibrational and Chemical Non-Equilibrium, Technical Report EWP-1664, ESA-Estec, Noordwijk, The Netherlands. 26. Netter eld, M.P., (1992) Validation of a Navier-Stokes Code for Thermochemical Non-Equilibrium Flows, AIAA Paper 92-2878, 27th Thermophysics Conference, Nashville, TN. 27. Tirsky, G.A. (1993) Up-to-Date Gasdynamic Models of Hypersonic Aerodynamics and Heat Transfer with Real Gas Properties, Annual Review of Fluid Mechanics, 25, 151-181.

Suggest Documents