Proceedings of CHT-08 ICHMT International Symposium on Advances in Computational Heat Transfer May 11-16, 2008, Marrakech, Morocco CHT-08-330

EFFECTS OF SURFACE CATALYTICITY ON COMPUTED HEAT TRANSFER OVER A REENTRY VEHICLE A. Viviani§, G. Pezzella, C. Golia Seconda Università di Napoli, Dipartimento di Ingegneria Aerospaziale e Meccanica via Roma 29, 81031 Aversa, Italy § Correspondence author. Fax: +39 081 5010204, Email: [email protected]

ABSTRACT This paper reports on the research activities performed by the authors for the assessment of the aeroheating environment around a reentry vehicle devoted to manned or unmanned low earth orbit missions. Since hypersonic flow conditions are such that gas dissociation occurs, the surface convective heating rate may be significantly affected by recombination at the vehicle surfaces promoted by the wall catalyticity. In this context, good capabilities of simulating the flowfield environment around the descent vehicle are fundamental to detect the high-temperature phenomena of thermochemically reacting hypersonic flows occurring at the vehicle surface. Herein, both axisymmetric and 3D Navier-Stokes equations are numerically solved for non equilibrium airflow around a capsule-type reentry vehicle at the peak heating conditions. Computed stagnation point heating rates are compared with results from the Fay Riddell and Goulard formulae, and the effect of surface catalyticity on the heat shield thermal loading is highlighted and discussed.

NOMENCLATURE a D h kw Le Mi Pr q& RN s S t u v Y

= = = = = = = = = = = = = = =

sound speed capsule diameter enthalpy catalytic reaction rate constant Lewis number molecular mass Prandtl number heat transfer rate heat shield nose radius curve length boundary layer diffusion rate entry interface time velocity along x axis velocity chemical species mass fraction

Greek symbols α = angle of attack β = energy accommodation coefficient

γ γi ε η θ λ μ ρ σ τ &a ω

= = = = = = = = = = = =

Ωμ

= collisional integral

Δh of

Subscripts a = co = e = D = i = t2 = v = w = ∞ =

specific heats ratio TPM efficiency for recombination heat of formation TPS emissivity recombination rate of atoms diffusing to wall capsule sidewall angle / flight path angle gas thermal conductivity viscosity density Stefan Boltzmann constant / collision cross section cell height species source term

atomic species stagnation point boundary layer edge conditions dissociation ith chemical species stagnation point conditions downstream a normal shock wave vibrational wall conditions freestream conditions INTRODUCTION

In the framework of designing thermal shields of reusable vehicles, a reliable prediction of reentry heat flux by means of numerical computations is ever more important. In this context, the capabilities of simulating flowfield environment around the descent vehicle should be able to account for the interaction of the high-temperature phenomena of thermo-chemically reacting hypersonic flows with the vehicle walls surface. The present work confirms that dissociated gas may increase the heat load that the vehicle heat shield has to withstand, due to the heterogeneous catalysis phenomena that eventually take place at the vehicle surface. In fact, real gas thermodynamics, transport properties and finite rate chemistry have pronounced effects on heterogeneous chemical reactions at vehicle walls which in turn affect the vehicle thermal shield performances. The risk involved, due to an inadequate knowledge of real gas effects, is that integrity and performance of the vehicle may be severely compromised due to wrong design choices as, for example, additional weight for the thermal protection system (TPS) in the case of fully catalytic wall design hypothesis. For instance, the thermal protection material (TPM) may promote the chemical recombination, at walls, of atomic species produced by dissociation in the flow when the gas passes through the strong vehicle bow shock wave [e.g., Viviani et Al. 2007a,b]. These recombination reactions, by means of the heat of formation of the molecular species leaving the heat shield surface, increase the overall heat flux up to about two times, or more, higher than the one predicted with the assumption of non-catalytic wall [Marichalar 2006]. These phenomena depend both on reentry energy and vehicle configuration; thus, the first goal of the present research is to highlight the importance of catalytic effects by simulating the flowfield around the ELECTRE probe tested in Plasma Wind Tunnel (PWT), and around an Apollo-style vehicle that is foreseen to be used as Crew Return Vehicle (CRV) for the International Space

Station (ISS) and/or as LEO (Low Earth Orbit) mission support vehicle (for example, for Hubble space telescope servicing). As second goal, since the heat shield development program for ablative TPS in moderate aeroheating environment is not yet mature, this work aims to assess the performance of a capsule forebody thermal shield built of Shuttle-like TPS tiles. To this purpose, the aeroheating environment of CRV is herein reported, with respect to both ballistic and lifting reentry trajectories. To accomplish the paper goals, two levels of numerical simulations are adopted. The first one refers to engineering analyses performed by the ENTRY tool (see below), and the second one to detailed CFD (computational fluid dynamics) analyses. The ENTRY (ENtry TRajectorY) tool is a versatile conceptual/preliminary design tool, developed at DIAM (Dipartimento di Ingegneria Aerospaziale e Meccanica), aimed to support the preliminary design phase of a reentry mission and to provide a quick reliable insight into the feasibility of a vehicle concept at an early stage of the mission design [Viviani et Al. 2006]. Instead, for the CFD analyses, both axisymmetric and 3D Navier-Stokes computations are performed with different wall boundary conditions: non catalytic wall (NCW), partially catalytic wall (PCW), fully catalytic wall (FCW).

OVERVIEW OF MODELS FOR THERMAL SHIELD CATALYTICITY In order to make a safe land, the descent vehicle has to reduce its energy (kinetic plus potential) by heating the surrounding airflow. The efficiency of this energy conversion depends on many factors and processes. The main one is the vehicle configuration and, hence, its reentry trajectory. As well stated, the most favourable condition to transfer vehicle energy into the atmosphere is attained when high pressure drag configurations, i.e. blunt bodies flying at high AoA (Angle of Attack) are employed. In this case, a strong detached shock wave forms ahead of the reentry vehicle and, due to the large total enthalpy of the freestream, the airflow behind the bow shock results into a plasma which impinges on the vehicle wall. When the atoms, resulting from the dissociation into the flow, reach the vehicle wall, some of them recombine in molecules either in the boundary layer or at the vehicle surface, where they dump their energy of recombination. This process depends on vehicle surface temperature and on flow chemical conditions, within shock and boundary layer, and provides an additional contribution to the heat transfer, due to species diffusion, which is generally of the same order of magnitude of the Fourier contribution. For instance, neglecting heat conduction into the vehicle wall and radiation from the gas, the energy balance at vehicle surface can be described in terms of two main contributions:

⎛ ∂ Yi ⎞ ⎛ ∂T ⎞ 4 q& w = −λ ⎜ ⎟ − ρ ∑i D im h Di ⎜ ⎟ = σε Tw ⎝ ∂n ⎠ w ⎝ ∂n ⎠ w

(1)

The first term is the conductive heat-flux from fluid to the wall, due to the temperature gradient, the second one is the diffusion term due to the species gradient. The latter contribution depends strongly on the surface catalytic properties of TPS. In fact, as the chemical non equilibrium flow enters the boundary layer (reacting boundary layer) the vehicle surface may acts as third body promoting heterogeneous reactions that take place at the wall. So the TPM may be involved in the surface recombination which becomes the main factor of the aerodynamic heat transfer, especially when gas phase recombination in the boundary layer is frozen and the wall absorbs the entire energy released by surface reactions (i.e. FCW with frozen boundary layer) [Fay Riddell 1958]. Therefore, in order to protect the CRV from this intense heat, the catalytic properties of the heat shield TPM candidate must be carefully known. For instance,

close to the wall, the effect of TPM on the recombination rates of heterogeneous reactions is accounted for by the catalytic efficiency coefficients γi. The recombination coefficient γi is a combination of the probability (γ’i) that atoms of the species i recombine as they collide on the surface and of the dissociation energy fraction (β) effectively released to the surface (also known as accommodation coefficient):

γ i = γ i' β

(2)

where γ’i is the ratio of the number of atoms recombining in molecules to the overall number of atoms striking on the surface:

γ i' =

& i ,recomb m & i ,all m

(3)

When γ’i =1 all atoms reaching the wall recombine and leave it as molecules: the wall is referred to as fully catalytic (FCW); on the other side, when γ’i =0 recombination does not occur and the wall is said non-catalytic (NCW). These two extreme cases are not encountered practically. Real TPMs (e.g. like C/SiC) have a finite catalyticity and γ’i takes values between 0 and 1. Silicates and ceramics are fair approximations to non catalytic surfaces while metals and metal oxides are strongly catalytic. For example, values of γi are of the order less than 0.01 on ceramic surfaces; on metallic, metallic oxide or graphitic surfaces values might be expected greater than 0.1 and are normally assumed as fully catalytic [Clark 1995]. Values of γi for nitrogen on metals can be from 0.1 to 0.2 and the metal impurities are thought to be the primary cause of surface reactivity [e.g., Kolodziej 1987]. Regarding β, experimental observations suggest that numerical modeling need to take into account an incomplete energy release at the surface:

β=

q& ,recomb & i ,recomb ⋅ h Di m

(4)

stating that the energy release due to the combined atoms differs from the total available dissociation energy of the atoms. However, for real space vehicle TPMs, very little is known about this coefficient and, for simplicity sake, β=1 is generally accepted (conservative condition), so that:

γ i = γ i'

(5)

This is the case when the residence time of the recombined molecules is long enough to transfer all the chemical energy, created by surface recombination, to the heating of the vehicle wall. One argument to support this assumption is that the energy cannot be released in the boundary layer, because of the adverse temperature gradient, and hence enters the wall, although there are some evidences that glassy materials might have partial energy accommodation, i.e. β<1. When the wall behaves as partially catalytic, several wall catalysis models exist to describe the catalytic efficiency coefficients. One first way to obtain a model of γi is the one-step global mechanism: A(g) + A(g) → A2(g)

(6)

with the reaction rate given by the catalytic reaction rate constant, kwA. This results in a significant improvement of the model since elementary reaction rates depend only on the temperature. Therefore, generally, γi is independent on pressure and density, as most recombination reactions are first order, but depends on the surface temperature (Tw):

γi = γi (Tw)

(7)

and is a characteristic of the recombining gaseous species and of the wall material involved. Eq.(7) is mainly available at the elevated temperatures experienced in hypersonic flight and for a small number of reactions, e.g. nitrogen/oxygen recombination, either by fitting experimental data or by some physical model. The available data suggest an Arrhenius type expression which leads to an analogy with gas-phase reactions and an energy barrier or activation energy which must be overcome by atoms colliding with the surface: ⎛ E ⎞ γ i = Pi exp ⎜ − i ⎟ ⎝ kTw ⎠

(8)

where Pi is a spherical factor accounting for directional effects, and Ei is the activation energy. This has been done for different TPMs based on different ground experiments in arc-jets and Shuttle flight data [Miller 1985]. Kolodziej [1987], for example, provided the following values for single species O and N recombination on reaction cured glass (RCG) coating for the Shuttle hightemperature reusable surface insulation (HRSI) tiles: ⎛ 11440 ⎞ γ O = 40 exp ⎜ − ⎟ Tw ⎠ ⎝

for 1435 K < Tw< 1580 K

(9)

⎛ 21410 ⎞ γ O = 39 ×10−9 exp ⎜ ⎟ ⎝ Tw ⎠

for 1580 K < Tw < 1845 K

(10)

⎛ 2480 ⎞ γ N = 6.1×10−2 exp ⎜ − ⎟ ⎝ Tw ⎠

for 1410 K < Tw < 1640 K

(11)

⎛ 5090 ⎞ γ N = 6.1×10−4 exp ⎜ ⎟ ⎝ Tw ⎠

for 1640 K < Tw < 1905 K

(12)

One short-cut with such models is that usually activation energies cannot really be considered as unique over the considered wide range of temperatures. Moreover such a relation obtained by empirical fitting is limited to conditions very similar to that of the fit process and extrapolation is a risky procedure. As an example, no maximum can be inferred from above formula for γi whereas experimental data do exhibit such a maximum. For high temperatures, these models are limited to a constant maximum value. Further, TPM catalytic data are also provided by means of the reaction rate kw of the first-order reactions that occur in the homogeneous gaseous phase (see Eq.(6)). The results of the laboratory and flight experiments on the Space Shuttle tiles heat shield can be approximated by the dependences [Marichalar 2006]:

⎛ −1875 ⎞ k wi = 53exp ⎜ ⎟ ⎝ T ⎠ ⎛ −8017 ⎞ k wi = 660 exp ⎜ ⎟ ⎝ T ⎠

500 K < Tw < 900 K

(13)

900 K < Tw < 1670 K (14)

The catalytic reaction rate constant, kw, is related to the recombination coefficient γi by means of the Hertz-Knudsen relationship:

k wi

⎛R T = γ i ⎜⎜ 0 w ⎝ 2πM A

⎞ ⎟⎟ ⎠

0.5

(15)

where MA is the atomic mass of i and R0 the universal gas constant. Measurements on the Space Shuttle surface insulation lead to values of the reaction rate constants for atomic oxygen and nitrogen of about 1 m/s [Miller 1985]. It is worth noting that the experimental values of γi and β are characterized by heavy scatter since they strongly depend on the conditions under which were obtained. In general, the use of effective coefficients does not make possible to describe correctly the heat transfer over the entire wall surface and along the whole reentry trajectory. MATHEMATICAL MODELING The numerical analyses of the influence of surface catalyticity on reentry aerothermodynamics and heat shield design are accomplished by means of CFD computations, employing the mathematical modeling recognized hereafter. Flowfield governing equations. The numerical simulation of the chemically reacting flowfield in the continuum regime (Kn<10-2) needs to solve the compressible Navier-Stokes equations, together with the conservation of total mass and the balance equations for the chemical species. They reads: Continuity:

Species:

∂ ( ρYi ) ∂t

r ∂ρ r + ∇ ⋅ ρV = 0 ∂t

( )

(16)

r r r r &i + ∇ ⋅ ρVYi + ∇ ⋅ Ji = ω

(17)

(

)

where & i = Mi ∑ ω & ik ω

(18)

k

Momentum:

r ∂ ρV

rr r r rr ( ) + ∇r ⋅ ρVV + ∇p = 2∇ ⋅ ⎡μ ( ∇V ) ⎤ ( ) ⎣⎢ ⎦⎥ ∂t s

o

where

rr

rr T 1 r r 1⎡ rr ∇ V + ∇V ⎤ − ∇ ⋅ V U ⎥⎦ 3 = 2 ⎢⎣

(20)

r r r rr s r r & i − ∑ e& vj + ∇ ⋅ ⎡⎣( ρE + p ) V ⎤⎦ = ∇ ⋅ ⎡λ∇T + 2μ ∇V ⋅ V + ∑ h i Ji ⎤ − ∑ h i ω o i j ⎣⎢ ⎦⎥ i

(21)

( ∇V ) Energy:

∂ ( ρE ) ∂t

Vibrational energy:

(19)

s o

=

( ) ( )

(

)

( )

∂ ( ρe vj ) ∂t

r r + ∇ ⋅ ρVe vj = e& vj

(

)

(22)

For each species the perfect gas model applies and the Dalton’s law is applicable: p = ∑ pi i

(23)

where the summation is extended to all the species of the gas mixture. As a consequence, the following relation for density holds: p ρ= (24) R 0 T ∑ Yi / M i i

The internal energy of the mixture is defined as: e = ∑ ( Yi ei )

(25)

i

where ei, the internal energy of the i-th component gas, is the sum of the energies representing the different degrees of the freedom of the molecules. From these expressions, the specific enthalpy for each species can be calculated as: h i = ei + R i T

(26)

Transport properties. Computation of the diffusive fluxes requires knowledge of the transport coefficient. For pure species, the following expressions are derived from kinetic theory of gases: Viscosity:

2.6693 ×10−6 M i T σi2 Ωμi

(27)

15 ⎛ μi R 0 ⎞ ⎛ 4 c pi M i 1 ⎞ + ⎟ ⎜ ⎟⎜ 4 ⎝ M i ⎠ ⎝ 15 R 0 3⎠

(28)

μi = Thermal conductivity: λi =

Mass diffusivity:

Dij =

0.0188 × T

3 2

(M

i

+ M j ) / Mi M j

(29)

pσij2 Ω Dij

For the global transport properties of the gas mixture, semi-empirical rules are applied, such as Wilke’s mixing rule for viscosity μ and thermal conductivity λ : a=

∑ i χi a i 1 1 1 2⎫ ⎧ − ⎡ ⎤ 2 2 ⎪ 1 ⎛ Mi ⎞ ⎢ ⎛ a i ⎞ ⎛ Mi ⎞ 4 ⎥ ⎪ ∑ jχj ⎨ ⎜⎜ 1 + ⎟⎟ ⎢1 + ⎜⎜ ⎟⎟ ⎜⎜ ⎟⎟ ⎥ ⎬ M 8 j ⎪ ⎝ ⎠ ⎢ ⎝ aj ⎠ ⎝ Mj ⎠ ⎥ ⎪ ⎣ ⎦ ⎭ ⎩

a = μ, λ

(30)

where χi is the mole fraction of specie i and ai (equal to μi or λi ) is obtained by kinetic theory of gases. For the diffusion coefficient of the species i in the reacting mixture, the multicomponent diffusion coefficient is applied: Di =

(1 − χi ) χ ∑ i j D i, j

(31)

with Di,j evaluated by kinetic theory. Finally, vibrational relaxation is modelled using the Landau-Teller formulation, where relaxation times are obtained with Millikan and White formula, assuming simple harmonic oscillators.

Reactions mechanism. The gas behind the bow shock wave for reentry at orbital velocities is herein approximated as a finite-rate chemistry mixture of N2, O2, NO, N, O, with reaction mechanism consisting of three dissociation reactions and two exchange reactions:

O2 + M ↔ O + O + M N2 + M ↔ N + N + M NO + M ↔ N + O + M NO + O ↔ O 2 + N

(32)

N 2 + O ↔ NO + N In Eq.(32), M is a reacting partner (third body) and can be any of the above five species. The forward reaction rates, kf,r that appears in the source terms ( ω& i ) of the species transport equations, are expressed under the Arrhenius form as: ⎛ Ea ⎞ β k f ,r = k f ,r ( T ) = k f T a Tvb = A f ,r T f ,r exp ⎜⎜ − f ,r ⎟⎟ (33) ⎝ R oT ⎠

(

)

with the constant according to Park’s two-temperature approximation (T, Tv) kinetic model. Boundary Conditions. Eq.(1) states that the properties of a surface are represented by the emissivity (ε) and by the wall chemical activity (i.e. γi or kwi). Since atoms produced by dissociation strike the surface, the catalyticity property of a surface is implemented by means of a production & wi ≠0 ) for the wall conditions in the boundary layer problem to be solved. Indeed, by term (i.e. ω imposing steady-state mass atomic conservation at the wall, it follows that the production of i-th atomic species at wall ( ( ω& a ) w ) due to the catalytic recombination rate must be balanced by the rate

of diffusion to the surface:

( ω& a )w = − ( ρa va )w

(34)

where the source term is given by the Goulard’s [1958] relationship:

& a = k wa ( ρw Yiw ω

)

p

(35)

with p the reaction order. The diffusive flux ρava is expressed by means of Fick’s law: ρa va = −ρDa

∂Ya ∂n

(36)

When the TPM does not promote any particular reaction, the TPS surface refers as NCW (i.e. kwi=0 and γi=0): the wall is considered absolutely indifferent to the chemical kinetics and there is no species production at the wall. On the contrary, if the TPM can activate any reactions at its surface it is called FCW (i.e. kwi=∞ and γi=1): there is complete recombination and the flow tends towards chemical equilibrium at the wall. The molecular species concentrations at wall refers to their equilibrium concentrations according to the local temperature and pressure. For wall temperatures below 2000 K (cold wall) this corresponds to the freestream composition. Between these two limit cases (i.e. 0< γi <1) the vehicle surface is considered as PCW and the heat fluxes to the vehicle can greatly differ depending on the value of γi. Furthermore, when a low conductive TPS protects the vehicle (as modern ceramic fibre material with high emissivity), the radiative equilibrium boundary condition holds at vehicle surface (i.e. the heat flux transported through conductive and diffusive mechanisms towards the wall is fully reradiate into the atmosphere). Therefore, during numerical simulations the wall temperature is

calculated by Stephan-Boltzman law (see. Eq.(1)) and is updated explicitly at each streamwise station by means of a Newton-Raphson approach that usually achieves convergence within a number of few iterations. Numerical technique. The field equations have been numerically solved with a finite volume methods, which deals with a system of partial differential equations that in the general form reads:

(

)

r r r % 1 ∂U % + ∑ F − G ⋅ Ai = H i ∂t V i

(37)

Non-dissipative fluxes are computed according to the flux difference splitting technique proposed by Roe [1986], while dissipative fluxes are computed by the Gauss theorem. The method is second order accurate in space. Multigrid techniques are used to accelerate convergence. Time integration is performed by an explicit multi-stage Runge-Kutta scheme. NUMERICAL RESULTS

In order to assess the catalyticity effects in high enthalpy flow conditions, numerical flowfield simulations describing the high temperature effects in hypersonic gas flow were carried out by using data from wind tunnel and free flight experimental analyses. CFD computations of flowfield around the ELECTRE model and an Apollo-like reentry vehicle are provided. In both cases flowfield simulations were performed by means of several Navier-Stokes computations assuming perfect gas and chemically reacting gas models, with surface reactions at the walls and radiative equilibrium temperature; all the simulations have been performed assuming conditions of steady laminar flow.

Y (m)

ELECTRE Model Some experimental activities performed in plasma wind tunnel with ELECTRE standard probe have been duplicated numerically. Comparison of numerical and experimental results concerning the hypersonic flow around the test model are reported. ELECTRE test article (see Fig. 1) consists of a blunt conical surface with total length of 0.4 m, semiaperture cone angle of 4.6° deg, and hemispherical nose with radius of 0.035 m. It was tested in flight and in wind tunnel, becoming a standard reference model to study non-equilibrium hypersonic flow past blunt-body configurations [Muylaert 1999].

0.2

0.1

0

0

0.1

0.2

0.3

0.4

X (m)

Figure 1. ELECTRE test article geometry and axisymmetric mesh domain (60x120 cells).

The computational domain used for CFD analyses is shown in Fig.1. It consists of 60x120 cells with a minimum normal wall spacing of 10-5m, as a sensitivity of the computed solutions with respect to the grid has shown to be necessary to obtain a sufficient resolution of the important flow features. This mesh have been selected by means of several accuracy tests performed starting from a coarse mesh of 50x70 cells and also taking into account comparisons between CFD and engineering results. Table 1 Reference calibration point conditions of the HEG nozzle ρ∞ T∞ P∞ (K) (Pa) (kg/m3) 790 430 1640x10-6

YO YN YNO V∞ M∞ Re∞/m (-) (-) (-) (m/s) (-) (1/m) 3 -6 5919 9.7 270x10 0.179 1.0x10 3.3x10-2

YO2 (-) 3.6x10-2

Test conditions are summarized in Table1. They correspond to operating conditions of the HEG wind tunnel located at DLR Gottingen [Muylaert 1999]. In correspondence of these test conditions, CFD analyses were performed considering alternatively the wall as NCW and FCW for N and O species. The computations refer to laminar non-equilibrium flow conditions with wall temperature fixed at Tw=300 K. The flow field past the test bed is shown in Fig.2, where the mach number contour field is plotted, comparing the results obtained in the case of perfect gas and real gas model.

Perfect gas model

Real gas model

Mach Number: 0.3 0.8 1.3 1.7 2.2 2.7 3.2 3.7 4.1 4.6 5.1 5.6 6.0 6.5 7.0 7.5 8.0 8.4 8.9 9.4

Figure 2. Mach number contours field. Comparison between perfect gas (up) and real gas model (down). Details of the nose region of test bed (right). As one can see, the flowfield around ELECTRE in the case of real gas model markedly differs from the perfect gas one, since the shock envelopes more closely the body than in the perfect gas case. In Figure 3 and Figure 4 are reported some comparisons for temperature and pressure distribution along the stagnation line, in the case of perfect gas and real reacting gas, the last one for both case of NCW and FCW. The pressure coefficient and wall heat flux distributions for different wall catalytic conditions are reported in Fig. 5. In both plots, the CFD results were compared with

available experimental results of HEG test campaign (i.e. shot157, shot159, shot164) [Muylaert 1999]. Figure 5 shows that the pressure coefficients from numerical and experimental results compare well, especially in the first part of the test specimen, giving differences only at the end of the model. It is worth nothing that no differences exist between NCW and FCW boundary condition, as expected. On the other hand, the heat flux distribution (see right side of Fig. 5) shows a good agreement with the numerical FCW solution (the red curve) even if on the rear part of cone there is a mismatch between experimental data and CFD results, as already seen in the case of pressure coefficient. Both these mismatches could be probably caused by flowfield perturbations due to the support of the experimental model that is located at the end of the test bed. 60

60

FCW NCW

50

50

40

40

Pressure, (kPa)

Pressure, (kPa)

Perfect gas NCW

30

20

30

20

10

10

0

-0.008

-0.006

-0.004

-0.002

0

0

Distance along stagnation line, (m)

-0.008

-0.006

-0.004

-0.002

Distance along stagnation line, (m)

Figure 3. Pressure distribution along the stagnation line. Comparison between perfect gas and reacting (e.g. NCW and FCW) gas case.

20 18 Perfect gas NCW

Temperature, (kK)

16 14 12 10 8 6 4 2 0

-0.008

-0.006

-0.004

-0.002

0

Distance along stagnation line, (m)

Figure 4. Temperature distribution along the stagnation line. Comparison between perfect gas and reacting (e.g. NCW and FCW) gas case.

0

8

10

1

10

Fluent cat Fluent noncat

Fluent cat Fluent noncat shot 157 shot 159 shot 164 off axis

shot 157 shot 159 shot 164 off axis 7

0

10 Heat flux density, W/m2

Pressure coefficient, cp

10

-1

10

-2

10

6

10

5

0

0.1

0.2

0.3

0.4 0.5 0.6 0.7 Nondimensional length along axis, x/L

0.8

0.9

1

10

0

0.2

0.4 0.6 Nondimensional length along axis, x/L

0.8

1

Figure 5. Pressure coefficient and heat flux. Comparison between numerical and experimental data [Muylaert 1999]. Apollo-style vehicle The reentry from LEO of an Apollo-like capsule, close to the CEV (Crew Exploration Vehicle) Orion, was investigated as CRV for ISS support servicing. Note that in view of the Space Shuttle retirement, capsule technology is still the safest and cheapest way to get into orbit and to return back to Earth, especially in the case of high energy reentry as those for manned space exploration missions to Moon and Mars. Viviani et Al. [2006, 2007a] has shown that the fluid dynamics computations of flowfield for an Apollo-like shape reveal interesting high temperature effects on the flow structure around the vehicle. Vehicle configuration The reentry capsule (Fig. 6) measures about 5 [m] in diameter, with a nose radius of 6.05 [m], a sidewall angle of 33 [°deg], and an overall height of 3.8 [m]. X

Y

Z

θ= 33° (deg)

3.8 (m)

RN= 6.05 (m)

H 5.0 (m)

Figure 6. Vehicle configuration. Reentry flight scenario Reentry analysis from ISS orbit was performed by using the ENTRY code that is able to run entry trajectories with three degree of freedom (3-dof), using the US Standard Atmosphere (1976) with a non rotating oblate Earth model. Once the vehicle ballistic coefficient and its aerodynamic database are known, ENTRY provides a number of reentry profiles for various couples of reentry velocity and angle (vE, θE). As preliminary design phase, two descent trajectories were computed by considering a vehicle gross weight of about 9 [ton], the atmospheric entry interface at hE=120 [km], while inertial vE=8 [km/s], and θE= -2° [deg]. For these conditions

ENTRY provides the reentry flight scenario plotted in the altitude-velocity plane of Fig.7, where are also reported the iso-Mach and iso-Reynolds curves. 4

10

x 10

lifting trajectory, AoA=20° Ballistic trajectory 9

8 ReD=1e5 7 ReD=5e5

Altitude [m]

6 ReD=1e6 5 ReD=5e6 4

ReD=1e7

3

2

1 M=4 0

0

1000

M=8

2000

M=12 3000

M=16

4000 5000 Velocity [m/s]

M=20

6000

M=24

7000

8000

9000

Figure 7. Reentry flight scenario, starting from LEO orbit [Viviani et Al. 2007a,b].

The blue curve is a ballistic reentry trajectory and represents the worst-case from the heat flux point of view. Along the red curve the capsule is flying trimmed at an angle of attack of 20° (deg) constant over the critical heating regime, thus employing aerodynamic lift to sustain the descent flight path (i.e. lifting return). These entry trajectories result in an aerothermodynamic environment that must be accurately predicted, for a reliable TPS design, taking care of the heat shield catalytic effects. To this scope, the trajectories flight conditions have been used to perform aeroheating computations as reported in the following. Aerothermal environment The work done by the drag force, during the capsule aerodynamic braking, produces a severe heating of the vehicle that depends on the vehicle configuration and, hence, on the descent trajectory kind (i.e. ballistic or lift sustained). Two critical regions onto the vehicle heat shield were expected [Viviani et Al. 2006, 2007a]. They are the heat shield stagnation point and the capsule side corner, (i.e. the corner of the forebody facing the flow when the capsule is at AoA). The aerothermal loading corresponding to the flight scenario proposed for the CRV is summarized in Fig. 8, where stagnation point heating rates versus the altitude are shown in the case of lifting and ballistic descent, respectively. Note that due to relatively low entry velocities no radiation heat flux is expected and only convective heat flux applies.

All heat flux densities were provided versus NCW, PCW and FCW boundary conditions, following Fay-Riddell and Goulard relationships, with an emissivity equal to 0.85 to compute the radiation equilibrium wall temperature on which the heating rates are based. When the CRV performs the lifting reentry a peak heating of about 372 [kW/m2] occurs at hph=62.3 [km] and Mph=21.8 conditions, when the heat shield is supposed FCW. If the TPM is NC a value of 245 [kW/m2] is foreseen; when the PCW is considered, the values of 275 [kW/m2] is obtained at capsule stagnation point. On the other hand, for the reference ballistic trajectory ENTRY evaluates a peak heating (ph) of about 430 [kW/m2] attained at hph=57.1 [km] and Mph=20.2 conditions, in the case of FCW, a

value of 280 [kW/m2] for the case of NCW, and, finally, in the case of PCW the value of 325 [kW/m2]. 450

400

FCW PCW NCW

400

350 FCW PCW NCW

350

300 Heat flux density, kW/m2

Heat flux density, kW/m2

300

250

200

150

250

200

150

100

100 50

0

50

0

2

4

6 Altitude, m

8

10

12

0

0

2

4

4

x 10

6 Altitude, m

8

10

12 4

x 10

Figure 8. Vehicle aeroheating environment for lifting (left) and ballistic (right) reentry. Although engineering analyses provide some insight into the trends to be expected, computational aerothermodynamic analysis (e.g. CFD) is mandatory to provide deep knowledge of the flowfield surrounding the descent capsule, especially at the most critical flight conditions. To this scope a detailed CFD aerothermodynamic analysis was made at peak heating flight conditions, as herein discussed. The computational grid domain Generally, accurate computations of the gradients appearing in the field equations require structured grids, which have been used for all computations in the present work. A close-up view of a 3-D mesh can be seen in Fig. 9. It consists of 50 cells in the body-normal direction, 40 cells circumferentially, and 150 in streamwise direction for a volume mesh size of 300000 cells. All the computational grid domains are tailored for freestream conditions at the selected trajectory points of peak heating, which are summarized in Table 2.

Figure 9. Multiblock computational grid.

Table 2 Freestream conditions of trajectories peak heating points Altitude Velocity Trajectory [km] [m/s] Ballistic Lifting

57.1 62.3

6469 6788

Mach [-]

Pressure [Pa]

Temperature [k]

20.2 21.8

32.78 16.69

255.27 241.53

Angle of attack [deg] 20° 20°

The baseline grid topology for this work consists of 32 grid blocks and is constructed to permit local refinement of the shoulder and the wake core regions, while maintaining point matching at every block interface. The mesh was initially generated algebraically and then adapted as the solution evolved, aligning the grid with the bow shock and clustering points in the boundary layer. The distribution of surface grid points was dictated by the level of resolution desired in various areas of vehicle such as stagnation region and base fillet, according to the computational scopes. For example, the distribution of grid points in the wall-normal direction is driven by a pre-specified value of cell Reynolds number: ρ a τ Recell = w w w (38) μw at the wall, as a constraint; where ρw , aw and μw are the density, sonic velocity and viscosity evaluated at the surface of the vehicle. A cell Reynolds number of 10 was found to be able to determine a grid spacing (τw) for a reliable laminar heating predictions. The grid have sufficient points in the shoulder region to capture the rapid expansion and accurately predict the flow separation and the angle of the resulting shear layer. At the end, grid refinement in strong gradient regions of flowfield was made through an adaptive solution approach.

DISCUSSION OF RESULTS

Axisymmetric and three-dimensional CFD solutions were computed for ballistic and lifting descent case, at the freestream conditions listed in Table 2. The farfield is assumed to be composed of 79% of molecular nitrogen (N2) and 21% of molecular oxygen (O2). In order to accomplish the vehicle’s heat shield design for both entry scenarios, let us suppose that the ballistic entry is performed at the same angle of attack as the guided case (i.e. α=20°). The flowfield solutions about CRV were generated considering the wall alternatively as non catalytic (NC), partially catalytic (PC), and fully catalytic (FC), at radiative equilibrium temperature condition (at ε=0.85). No heat shield ablation and recession have been assumed. CFD numerical computations reveal that both for ballistic and lifting reentry the flowfield is dominated by real gas effects. Since capsule vehicle is flying at high velocity, the resulting strong bow shock wave thermally excites and dissociates the gas so that a thick boundary layer along the forebody surface with large thermal and chemical species gradients exist in the flowfield [Viviani 2006, 2007]. On the other hand, even if the vehicle configuration is geometrically quite simple, it is very difficult to compute because of the forebody thermal shield (see Fig.10) is wetted by a low Mach number in the subsonic shock layer. Several flowfield features were recognized both in axisymmetric and 3-D numerical computations as recognized hereinafter. Axisymmetric CFD results A close up view of the flowfield about the capsule is shown in Fig.10, where the Mach number contours were reported in the case of perfect gas model.

Looking at the right side of Fig.10, one can appreciate that the sonic line occurs near the junction between the forebody heat shield and the corner fillet of capsule, being the vehicle windward shape a truncated spherical cap. As a consequence, the entire flowfield in the subsonic portion of the shock layer is modified, and the streamwise velocity gradients are relatively large in order to produce sonic flow at the base fillet of the capsule. Figure 11 shows, instead, the contour fields of static pressure (Pa) and temperature (k) in the case of perfect gas model, respectively.

Figure 10. Mach number contours field in the capsule pitch plane. 2D-computation.

Figure 11. Contours fields of static pressure – Pa – (left) and temperature – k – (right) in the pitch plane: 2D axisymmetric computation.

As one can see, the static temperature reaches unrealistic values up to 20000 K. Fortunately, in reality, those values are never reached thanks to real gas effects (see Fig.15); on the contrary the pressure field is close to reality because it is only a dynamic driven flowfield feature. Note that with pressure contours are also plotted the streamtraces surrounding the vehicle, thus highlighting flowfield features such as the strong recirculation zones in the leeside. Finally, in order to appreciate the effects of surface catalyticity on heating, numerical computations with real gas model for different wall recombination probability γi were provided. For each γi the stagnation point heat transfer has been computed. These data were summarized in Fig. 12 where the stagnation-point heat flux ratio is reported as a function of the surface recombination probability γi. For the NCW (γi= 0, the heating rate is about 55% of the fully catalytic value (γi= l), which indicates the advantage of having, basically, a non-catalytic surface. 1.2

0.8 0.6 0.4

Heat Flux ratio

1

0.2 0 1

0.1

0.01

0.001

0.0001

Recombination probability

Figure 12. Effects of surface catalysis on stagnation point heating. As a result, a decreasing of the maximum surface heat flux by nearly a factor of two may be verified for NCW. In the other cases (e.g. 0 ≤ γ i ≤ 1 ), Fig. 12 recalls that the heat flux is S-shaped function of the catalytic recombination coefficient, as expected. In particular when γi ranges between 0.01 and 0.1 (PCW) the heat flux is nearly 70% of the fully catalytic value. 3-D CFD results. Increasing complexity, in Fig.13 the Mach number contours of a non-equilibrium flow for M=21.8 are shown compared to a perfect-gas solution for 3-D computation. As one can see, the flow behind the bow shock in the reacting gas case behaves very differently from that of the perfect gas. On the windside, the subsonic region is much larger in the case of perfect-gas due to a larger shock stand-off distance. In particular, the separation on the leeward, obtained for perfect gas, is much larger than for non-equilibrium air, with a considerably different shape of the wake flow. Strong differences between shear layers and recirculating flow structures can also be appreciated if one compares both solutions. Further, it can be seen that, as the flow turns around the shoulder of the capsule, suddenly expands and then on the vehicle leeside separates. On the windside, instead, it remains attached up to the rearside.

Moreover, Fig 14 shows the temperature contours in the xz plane of capsule (see Fig.9 for this plane) for perfect gas and reacting gas cases. Figure 14 confirms that in the reacting gas case the bow shock is much more close to the capsule. The motivation of these differences have to be found in the fact that because the flow molecules become vibrationally excited, and being sufficient energy to start dissociation, some energy is removed from the translational-rotational mode. This results in a lower peak of translational-rotational temperature and higher density rise across the shock wave compared to the perfect gas case. The rise in density, due to the real gas effects,

changes also the bow shock shape by lowering the shock angle. This alters the surface pressure distribution over the vehicle giving a trim angle of attack lower than the one of perfect gas case.

Figure 13. Mach number contours field in the capsule pitch plane for 3D-computation Comparison between perfect gas (left) and non-equilibrium flow (right).

Figure 14. Temperature comparison between perfect gas (down) and reacting gas (up) cases in the xz plane of the capsule.

Illustrated in Fig. 14 is also the presence of a rapid expansion as the highly compressed gas turns around the shoulder of the vehicle. This expansion, dominated by inviscid effects, has the effect of rapidly lowering the translational temperature, density and pressure of the gas, while the chemical state of the gas and the temperatures, characterizing the energy of the internal modes, tend to remain frozen with the gas still dissociated and excited. This aspect is more important for capsule heat shielding. In fact, as the gas flows downstream, because the recombination occurs slowly, the

vibrational temperature of gas rises still higher with the consequence that the gas can radiate significantly in the afterbody region. A further look insight the differences existing between perfect gas and reacting gas can be done by comparing the temperature of the flow along the stagnation line as shown in Fig. 15. 25000

Temperature (k)

20000

15000 T 10000

5000

Ttr-rot

Tvib tr-rot 0

-0.8

-0.6

-0.4

-0.2

0

Distance along stagnation line (m)

Figure 15. Perfect gas temperature and reacting gas translational-rotational and vibrational temperatures along stagnation line Figure 15 confirms that the perfect gas temperature is unrealistic if compared with the maximum translational-rotational temperature of the reacting gas case; the vibrational temperature profile shows that the thermal non equilibrium region extends only close to the shock region. In fact, even if Tvib increases much more slowly due to its density dependence, the two temperature are nearly equilibrated throughout the shock layer. Figure 16 shows the effect of chemical non equilibrium by means of the values of species mass fractions along the stagnation line. Behind the bow shock, the oxygen is fully dissociated and only about 40% of the flow is diatomic nitrogen. The effect of a FCW on the boundary layer chemistry is also clearly evident: at wall the species mass fraction reaches the freestream value. Therefore, the shock layer is essentially composed of N2, N and O while the NO mass fraction is very low and exists only close to the shock region. Non catalytic wall

Fully Catalytic wall

0,90

0,90

0,80

0,80

0,70 Species mass fraction

Species mass fraction

0,70 N2

0,60 0,50 0,40 N

0,30

0,50 0,40 N 0,30 0,20

0,20 O2

O2

O

-1,0

-0,8

O

0,10

0,10 0,00 -1,2

N2 0,60

-0,6

-0,4

-0,2

Nondimensional distance along stagnation line

0,0

0,00 -1,2

-1,0

-0,8

-0,6

-0,4

-0,2

0,0

Nondimensional distance along stagnation line

Figure 16. Species mass fraction along stagnation streamline, in the case of FCW (left) and of NCW (right), for the ballistic reentry.

O

N

O2

N2

Species mass fraction

Figure 17. Mass fraction comparison between atomic (up) and molecular (down) species in the plane xz of the flow velocity, for FCW case and ballistic reentry. A close-up view of species field in the plane xz of the flow velocity can be seen in Fig. 17, where the mass fraction comparison between atomic (up) and molecular (down) species was reported for the FCW case and a ballistic entry return. To illustrate the magnitude of the effects of catalytic activity on TPS, Fig.18 shows the comparison of the heat flux along the forebody centreline at wall radiative equilibrium conditions, between the cases of FCW, PCW and NCW for both ballistic and lifting reentry.

800

700

700 600

FCW PCW NCW

600

FCW PCW NCW

Heat flux density, KW/m2

Heat flux density, KW/m2

500

500

400

300

400

300

200

200

100

100

0 -1.5

-1

-0.5 0 0.5 Nondimensional forebody length, s/Rb

1

1.5

0 -1.5

-1

-0.5 0 0.5 Nondimensional forebody length, s/Rb

Figure 18. Heat flux on the forebody OML. Nondimensional surface distance measured from centerline. Ballistic (left ) and Lifting (right) trajectory.

1

1.5

As one can see, the overheating caused by the catalytic action is potentially very large compared with the case of NCW, thus confirming that significant reduction in convective heat flux occurs if the thermal shield is built with a non-catalytic TPM. In particular, the largest difference occurs at the sphere-cone junction (corner fillet) where large changes in the flow gradients along the surface occur. This makes the corner radius the dominant geometric feature for the convective heating (instead of heat shield radius of curvature). For example, the heat flux attained in correspondence of the hotter capsule corner ranges from about 500 to 800 KW/m2 in the case of ballistic reentry, while when the capsule vehicle performs a lifting return, the heating range refers to about 400 ÷700 KW/m2. In reality, TPS tiles are generally coated with far less catalytic layer as RCG (Reaction Cured Glass), the heating rates should be refer to PCW boundary conditions. In this case, the radiative equilibrium temperature comparison between ballistic and lifting return can be seen in Fig.19. This figure confirms that the ballistic reentry represents a more challenging trajectory from the aeroheating point of view. Figure 19 also shows that the temperature of the thermal shield stagnation point (s/Rb≅0.5) decreases of about 50 K from ballistic to lifting return.

2000 PCW-Lifting return PCW-Ballistic return

Radiative equilibrium temperature, K

1800

1600

1400

1200

1000

800 -1.5

-1

-0.5 0 0.5 Nondimensional forebody length, s/Rb

1

1.5

Figure 19. Radiative equilibrium temperature at capsule forebody OML. Ballistic (red) and lifting (green) return for PCW thermal shield.

CONCLUSIONS

A possible reentry scenario and associated aeroheating environment were generated to support the CRV development for LEO servicing. The proposed reentry trajectories and aerothermal environments were intended to represent a possible range of reentry scenarios and TPS requirements for CRV vehicle concepts. Both engineering and CFD computations were performed. At engineering level, ENTRY tool applications were provided, to obtain a rapid and accurate generation of aeroheating environments and data required for TPS design and analysis, and to rapidly assess heat shield environments as vehicle, mission, and reentry trajectories evolve. Increasing the complexity, CFD analyses were performed to simulate the flowfield and forebody heating environment about the capsule vehicle.

Using CFD simulations, the effects of flow physics on the aerothermodynamics of the aerobraking vehicle have been shown, with particular attention to their influence on the capsule heat shield design. To this scope, in fact, axisymmetric and 3-D flow fields surrounding the capsule vehicle at angle of attack (no side slip) are computed and the effects of chemical and thermal non equilibrium on the vehicle thermal shield design were highlighted. The convective heat flux and the corresponding radiative equilibrium temperature distributions over the centreline of the vehicle forebody are also provided. This work confirms that an exact prediction of the heat transfer and chemical environment is crucial for the design of the vehicle TPS, and the possibility to reduce the heat load on vehicles, entering the Earth atmosphere from LEO missions, by using a TPM of low heterogeneous catalyticity has been highlighted.

REFERENCES

Anderson, L.A.[1973], Effects of Surface Catalytic Activity on Stagnation Heat Transfer Rates, AIAA Journal , Vol. 11, No. 5, pp 649-656. Clark, R. K., Cunnington, G. R., Wiedemann, K. E. [1995], Determination of the Recombination Efficiency of Thermal Control Coatings for Hypersonic Vehicle, Journal of Spacecraft and Rockets , Vol. 32, No. 1, pp 89-96. Fay, J. A., Riddell, F. R. [1958], Theory of Stagnation Point Heat Transfer in Dissociated Air, Journal of the Aeronautical Sciences, Vol. 2, No. 25, pp 73-85. Goulard, R. [1958], On Catalytic Recombination Rates in Hypersonic Stagnation Heat Transfer, Jet Propulsion, Vol. 28, No.11, pp 737–745. Kolodziej, P., Stewart, D.A. [1987], Nitrogen Recombination on High-Temperature Reusable Surface Insulation and the Analysis of its Effects on Surface Catalysis, 22nd Thermophysics Conference, 8-10 June 1987 Honolulu (HI), paper AIAA-1987-1637. Marichalar, J. J., et al. [2006], Boundary Layer/Streamline Surface Catalytic Heating Predictions on Space Shuttle Orbiter, Journal of Spacecraft and Rockets , Vol. 43, No. 6, pp 1202-1215. Miller, J.H., Tannehill, J. C., et al. [1985], Computation of Hypersonic Flows with Finite Catalytic Walls, Journal of Thermophysics and Heat Transfer, Vol. 9, No. 3, pp 486-493. Muylaert, J., Walpot, L., Wennemann. D. [1999], A Review of European Code-Validation studies in High-Enthalpy Flow, Phil. Trans. R. Soc. Lond. A 357, pp 2249-2278. Roe, PL. [1986], Characteristic based schemes for the Euler equations, Annual Review of Fluid Mechanic, Vol. 18, pp 337-365. Viviani, A., Pezzella, G., Cinquegrana D. [2006], Aerothermodynamic Analysis of an Apollo-like Reentry Vehicle, 14th AIAA/AHI Space Planes and Hypersonic Systems and Technologies Conferences; 6-9 November 2006, Canberra (AU), paper AIAA-2006-8082. Viviani, A., Pezzella, G. [2007a], Catalytic Effects on Non-Equilibrium Aerothermodynamics of a Reentry Vehicle, 45th AIAA Aerospace Sciences Meeting and Exhibit; 8-11 January 2007, Reno, NE (USA); paper AIAA-2007-1211. Viviani, A., Pezzella, G. [2007b], Influence of Surface Catalyticity on Reentry Aerothermodynamics and Heat Shield, 39th AIAA Thermophysics Conference; 25-28 Jun 2007, Miami, FL (USA), paper AIAA-2007-4047.