Surface Catalytic Recombination

If the surface of the flight vehicle acts as a third body in the chemical recom­bination reactions discussed in the previous section, we speak about catalytic surface recombination, which is a “heterogeneous” reaction. Catalytic surface recombination is connected to the thermal state of the surface. We will see that, on the one hand, it is depending on the surface temperature (thermo­chemical thermal-surface effect), but also influencing this temperature. On the other hand, it has an effect on thermal loads. Because of these two ef­fects catalytic surface recombination is of interest for hypersonic flight vehicle design.

We keep in mind that of the flight vehicles considered, Chapter 1, RV’s bear the largest thermal loads. Due to material limitations currently surface temperatures of up to about 2,000 K can be permitted. Because we have radiation-cooled surfaces, these maximum temperatures occur only in the stagnation point region, and then drop fast to values as low as about 1,000

K, depending on flight speed and vehicle attitude.[49] The heat flux in the gas at the wall, qgw, shows a similar qualitative behavior.

A catalyst reduces the necessary activation energy of a reaction, and hence more collisions lead to reactions. Accordingly more reaction heat is released. Hence the surface material (coating) should be a poor catalyst in order to re­duce the release of reaction heat at the surface. Catalytic recombination helps to proceed towards equilibrium faster, but does not change the equilibrium composition of a gas.

As limiting cases regarding high catalycity two conditions are often con­sidered, see, e. g., [18]: equilibrium wall and fully catalytic wall. With respect to the gas composition the two cases are equivalent, given that the conditions (T and p) allow a full recombination.

Regarding the maximum heat flux towards the wall (qgw, max) it is ob­served, that the fully catalytic wall gives a heat flux similar to that of the equilibrium wall. Therefore often the equilibrium wall is taken as the reference case for the largest heat load.[50]

In [19] the two concepts are distinguished in the following way:

— Equilibrium wall: If the flow past a flight vehicle would be in chemical equi­librium, a cold surface—we have seen above, that the surface temperature in our cases is at most around 2,000 K—would shift the gas composition at the wall into the respective equilibrium wall composition. This compo­sition could be, depending on the temperature and density/pressure levels, locally still a mixture of molecules and atoms.

— Fully catalytic wall: The fully catalytic wall, in contrast to the equilibrium wall, would lead at the wall to a recombination of all atoms, even if wall temperature and density/pressure would atoms permit to exist.

We discuss now the basics of catalytic surface recombination in a phe­nomenological way. We introduce the recombination coefficient of atomic species [19]

Here jia is the mass flux of the atomic species ia towards the surface, and ja the mass flux of actually recombining atoms.

The recombination coefficient depends on the pairing gas/surface species, like the surface accommodation coefficients, Section 4.3, and on the wall temperature TW.

It has been observed in experiments, [19], that the energy transferred during the recombination process is less than the dissociation energy (par­tial energy accommodation), so that another recombination coefficient, the energy transfer recombination coefficient can be introduced. The effect, how­ever, seems to be of minor importance and often is neglected in computational methods.

The catalytic recombination rate kWia is a function of the wall temper­ature and of the gas-species properties. It is expressed in the form (Hertz – Knudsen relation):[51]

RqT 27Г Mja

(5.41)

Yia

With the catalytic recombination rate the mass flux of atoms actually recombining at the surface can be written as

ji^r Yia kWia Pia •

The mass flux of the atoms towards the surface is

Jiyr folVia Pi’ Ъа

(5.43)

i

We distinguish three limiting cases:

— Yi, a ^ 0: no recombination occurs, the surface is non-catalytic, the catalytic recombination rate goes to zero: kWia ^ 0.

— 0 < Yia < 1: only a part of the atoms recombines, the surface is partially catalytic, the catalytic recombination rate is finite: 0 < kWia < to.

— Yia ^ 1: all atoms recombine, the surface is fully catalytic. For this case one finds in literature that the recombination rate is considered to be as infinitely large: kWia ^ to.

We discuss now the possible boundary conditions for the mass-transport equations, Sub-Section 4.3.3:

— Equilibrium conditions for the species:

— ui(P, T )|w.

This case would not involve the solution of the species-continuity equations. Hence no boundary conditions need to be considered.

— Vanishing mass-diffusion flux of species i:

jiy w 0.

If this holds for all species, it is the boundary condition for the case of the non-catalytic surface, in which no net flux of atoms and molecules towards the surface happens. The non-catalytic surface does not influence the gas composition at the wall.

— Fully catalytic surface recombination:

^ia w °.

The complete vanishing of the atoms of species i is prescribed.

— Finite catalytic surface recombination:

jia w Pia kWia w.

The partial vanishing of atoms of species i is prescribed.

In closing this section we discuss some results from [12] and [20] in order to illustrate surface catalytic recombination effects. In Fig. 5.11, [12], distri­butions of the heat flux in the gas at the wall qgw at an hyperbola with nose radius R = 1.322 m and opening angle Ф = 41.7° are given. The generator of the hyperbola approximates the contour of the lower symmetry line at the first seven meters of the forward part of the Space Shuttle Orbiter. The flow parameters are given in Table 5.6. Although the surface temperature is still rising at that trajectory point, a constant temperature Tw = 800 K was cho­sen, like for the Direct Simulation Monte Carlo (DSMC) computations [21]. The error in Tw is about 5 per cent.

Table 5.6. Parameters of the (laminar) flow past the hyperbola under reentry conditions at 85.74 km altitude [12]. Moo Vcc [m/s] Too [K] pc. о [kg/m3] UJN2 Uo2 T„ [K] 27.35 7,511.4 187 6.824-1СГ6 0.738 0.262 800

At the chosen trajectory point we are at the border of the continuum regime. Slip effects were not modeled in [12], the comparison with DSMC results served the validation of the Navier-Stokes method CEVCATS.

Fig. 5.11 shows everywhere a good agreement between the results of the two methods. The assumption of a non-catalytic surface yields the smallest heat flux, that of a fully catalytic surface a heat flux approximately twice as large. The finite catalytic case yields results not much higher than that of the non-catalytic case. In all cases we have to a good approximation the cold-wall
laminar-flow behavior of qw ж (x/L)-0-5 as discussed in Sub-Section 3.2.1 (eq. (3.27)). Up to x « 2 m the flight data are met by the finite catalytic case, and after x « 4 m by the fully catalytic case. Here the surface is cold enough to support fully catalytic recombination. The transition from one case to the other is not predicted.

0.15

0.05 0.00

x (ml

Fig. 5.11. Distribution of the heat flux in the gas at the wall (q = qgw) of the Space Shuttle Orbiter equivalent hyperbola with different surface-catalytic recombination models in comparison to in-flight measurements [12] (STS-1: first Space Shuttle Or­biter flight, DSMC: Direct Simulation Monte Carlo [21], NS: Navier-Stokes method CEVCATS).

In Fig. 5.12 we show a comparison of computed, [12], and flight-measured distributions, [22], of the radiation-adiabatic temperature along the lower symmetry plane of the Space Shuttle Orbiter. The configuration used in the computations is the, on the leeward side simplified, Space Shuttle Orbiter configuration, known as HALIS configuration, which was introduced in [23].

The flow parameters are given in Table 5.7. The surface temperature is assumed to be the radiation-adiabatic temperature. The surface emissivity is assumed to be e = 0.85. Computations with CEVCATS were made for the non-catalytic, the finite catalytic, and the fully catalytic case. Results are shown up to approximately 75 per cent of the vehicle length.

Presented in Fig. 5.12 are computed data, and flight-measurement data from ordinary tiles, and from gauges with a catalytic coating. In general we see the drop of the wall temperature with increasing x as predicted quali­tatively in Sub-Section 3.2.1. The temperature difference between the fully catalytic and the non-catalytic case is strongest in the vehicle nose region

Moo	Vcc [m/s]	Too [K]	pec [kg/m3]	UJN2	Uo2	Lref [m]	a [°]	6
24	7,027.54	212.65	5.5-10~6	0.738	0.262	32.77	40	0.85

Table 5.7. Parameters of the (laminar) flow past the HALIS configuration under reentry conditions at 72 km altitude [12].

2UUU

=2 1400

200 1000 800

Fig. 5.12. Distributions of the radiation-adiabatic temperature (e = 0.85, T = Tra) along the lower symmetry line of the HALIS configuration for different surface- catalytic recombination assumptions. Comparison of in-flight measurement data with CEVCATS data [12].

with approximately 450 K. The results for the finite catalytic case lie be­tween the results of the two limiting cases. The measured data are initially close to the computed finite catalytic data, and then to the non-catalytic data. This in contrast to the data shown for the heat flux in Fig. 5.11. The data measured on the catalytic coatings partly lie above the computed fully catalytic data.

Finally results from [20] are presented. The objective of that study was to determine the influence of the assumptions “fully catalytic” and “finite catalytic” wall on the wall temperature along the windward side of the X-38 with deflected body flap. The computations were made with the Navier – Stokes code URANUS with an axisymmetric representation of the windward symmetry-line contour. In Table 5.8 the flow parameters are given.

Fig. 5.13 shows that the computation with finite catalytic wall results in smaller temperatures than that with fully catalytic wall. The differences

are about —200 K in the nose region and at parts of the body, but small and reverse at the flap. The atomic nitrogen recombination coefficient yn is large at the nose and again at the flap, indicating strongly catalytic behavior regarding N. The atomic oxygen recombination coefficient yo is moderate at the body and very large at the flap. There the finite-rate temperature Tw, fr is even larger (about 50 K) than the fully-catalytic temperature Twjc. This is due to the very strong catalytic behavior of the surface with regard to O and the resulting transport of atomic species in the boundary layer towards the wall. For the TPS design these data constitute the uncertainties range, which must be covered by appropriate design margins.

contour length [m]