Effects of the Surface Catalysis on High-Enthalpy Shock- Wave/Turbulent Boundary-Layer Interactions

American Institute of Aeronautics and Astronautics

1

Effects of the Surface Catalysis on High-Enthalpy Shock-

Wave/Turbulent Boundary-Layer Interactions

Giuliano Ranuzzi *

CIRA, Italian Aerospace Research Center, 81043 Capua, Italy

Francesco Grasso �

University of Rome “La Sapienza”, 00184 Rome, Italy

Stefano Bisceglia �

University of Rome “La Sapienza”, 00184 Rome, Italy

In the present paper the effects of the surface catalysis on turbulent hypersonic flows

dominated by shock-wave boundary-layer interactions over wing-flap configurations are

analyzed. The approach relies on a linear eddy viscosity two-equation turbulence modeling

that accounts for the coupling of turbulence with chemistry and vibration, and it employs a

total variation diminishing finite volume numerical methodology. Two different catalysis

models due to Kurotaki and Nasuti et al. have been implemented to account for the atomic

oxygen and nitrogen recombination over silica-based surfaces. Several simulations have been

carried out for sphere-cone and double-wedge configurations, and results have been

compared with experiments. The effects of the surface catalytic efficiency, Mach number

and wall temperature on the separation and aerothermal loads have been studied.

Nomenclature

E = total energy

e = internal energy

ev = vibrational energy

n = outward unit normal

R = universal gas constant

Sv = thermal nonequilibrium source term

ω = chemical nonequilibrium source term

X = molar fraction

Y = mass fraction

∆h0 = enthalpy of formation

η = thermal conductivity

D = diffusion coefficient

µ = mixture viscosity

a′ = fluctuations in Reynolds decomposition

a ′′ = fluctuations in Favre decomposition

γ = recombination probability

Ui = upstream influence

FC = fully catalytic wall

FRC = finite-rate catalytic wall

NC = non catalytic wall

* Research Engineer, Aerothermodynamics and Space Propulsion Laboratory �Professor, Department of Mechanics and Aeronautics, via Eudossiana 18, Associate Fellow AIAA � Aeronautical Engineer, Department of Mechanics and Aeronautics, via Eudossiana 18

AIAA/CIRA 13th International Space Planes and Hypersonics Systems and Technologies AIAA 2005-3219

Copyright © 2005 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


2

I. Introduction

hock wave / turbulent boundary layer interactions are important since they play a significant role in many

technical applications. The occurrence of such interactions over the control surfaces of hypersonic vehicles such

as Reusable Launch Vehicles (RLV) can cause flow separation and high heating rates, both of which are critical for

the design of their aerodynamic shape and thermal protection.

The position of the primary separation and the extension of the recirculation region determine the location of the

shock configuration that affects the aerodynamic quantities (drag, efficiency, hinge moment) and may deteriorate the

aerodynamic effectiveness of the surfaces. Aerodynamic heating has always been a problem during reentry of space

vehicles at hypersonic speeds, and one of the critical areas in the design of hypersonic vehicles is the aerodynamic

heating of control surfaces.

The high enthalpy shock-wave/turbulent boundary layer interaction is complicated by the simultaneous presence

of flow separation, turbulence, thermal and chemical nonequilibrium and surface catalysis effects.

Davis and Sturtevant1 have investigated experimentally and theoretically nonequilibrium effects on separation

length using a double-wedge geometry and nitrogen test gas. Those authors have concluded that, for weak shock

strength, dissociation reactions outside the boundary layer may yield a reduction of separation length depending on

the freestream dissociation; likewise, recombination reactions within the boundary layer and upstream of separation

are responsible for a slight decrease of separation length, with respect to a nonreacting boundary layer. In addition,

in Ref. 1 it is shown that at high enthalpy the separation extent increases due to recombination in the free-shear layer

downstream of separation, mainly because of the combined effects of freestream dissociation and a cold wall.

Grasso et al.2 have studied the influence of vibrational excitation and chemical reactions and their coupling with

turbulence for hypersonic flows dominated by shock-wave/turbulent boundary-layer interaction over a body-flap of

reusable launch vehicle configurations. In Ref. 2 it was assessed the effects of the control surface deflection angle,

wall temperature and laminar to turbulent flow transition on the separation, aerothermal loads and flap efficiency.

The analysis has shown that for flap deflection angles greater than a critical value, turbulence avoids the crisis of the

flap efficiency that is observed under laminar conditions, extending the operating capabilities of the control surfaces.

To accurately determine the local heat loads that could occur in the separation region of a flow dominated by

high enthalpy shock-wave/ boundary-layer interactions, the effects of surface catalysis must be necessarily

accounted for. As observed by Grumet and Anderson3 with regard to the coupling between catalytic heating and the

separation region of the shock-wave/ boundary-layer interactions, a comparison of results obtained from both mildly

and highly separated flows indicate that surface catalysis significantly increases the heat transfer downstream of the

separation region.

Basic models assume wall to be non- or fully-catalytic. While, until recently, the design calculations have been

done assuming the most unfavorable conditions (i.e. fully catalytic wall), designing aerodynamic surfaces with fully

catalytic condition may be too conservative because it may lead to an overestimation of weight of TPS. The design

of next-generation reusable space vehicles needs a better estimation of the finite rate catalysis of the TPS materials,

in order to reduce weight and operative costs. Nevertheless, little quantitative data has been obtained in the past

about the effects of the surface catalysis on high enthalpy shock-wave / boundary layer interactions.

Catalytic recombination effects in CFD are usually accounted for by the catalytic efficiency coefficients, defined

as the ratio of the number of atoms impinging on the surface which recombine in molecules to the overall number of

atoms impinging on the surface. These coefficients essentially depend on the surface structure and coverage, wall

and local gas temperature and composition, and are obtained by fitting experimental data or by physical models.

Halpern and Rosner4 have proposed a model of the recombination process of the dissociated species on metal

surfaces. In Ref. 4 it was described the general approach that relies on a recombination modeling based on the

description of each phenomenon contributing to atoms and molecules adsorption, reaction and desorption on the

surface.

Nasuti Barbato and Bruno5 have presented a model of catalytic recombination of O and N atoms over SiO2

derived directly from surface properties. The model, based on the approach of Halpern and Rosner, produces

recombination probabilities in good agreement with experimental measurements at high surface temperatures.

Kurotaki6 has constructed a model describing heterogeneus catalysis on the surface of SiO2- based materials for

O2-O and N2-N mixture gas and airflow. In Ref. 6 the model has been applied to flight trajectories of OREX and

Space Shuttle and calculated results have been compared with the stagnation heat flux data. It was shown that the

agreement between the model and experimental data are good.

S


3

This paper presents a numerical investigation of the surface catalysis effects on shock-wave/ turbulent boundary

layer interactions in the presence of thermal and chemical nonequilibrium. The complexity and the design

implications of these phenomena require an understanding of the controlling mechanisms and their quantitative

estimation. The objective of this study is to provide more insight into the flow physics governing this process.

In particular, a model is developed by assuming 1) a single translational temperature to characterize the

translational and rotational modes, 2) a single vibrational temperature for vibrational excitation of the diatomic

species that are assumed to behave as harmonic oscillators, 3) finite-rate chemistry for nonionizing air, 4) finite-rate

chemistry for surface catalysis and 5) a gradient-law assumption to account for the turbulent transport of

momentum, energy (translational, rotational and vibrational) and species partial masses. The methodology relies on

a linear eddy viscosity two-equation (K-ε) model that accounts for the coupling of turbulence with chemistry and

vibration through properly defined turbulent Prandtl numbers, and it employs a numerical scheme based on a finite

volume total variation diminishing approach with a point-implicit treatment of the source terms.

A parametrical study summarizing the effects of the surface catalytic efficiency (k

γ ), Mach number (M) and

wall temperature (Tw) on the separation and aerothermal loads has been carried out varying the values ofk

γ , M and

Tw as reported in the test matrix (see Table 2). The analysis was performed on both laminar and turbulent shock

wave/boundary layer interactions, in order to isolate the turbulence effects.

In the following sections the physical model and the numerical approach are developed, the test cases are

described, the results of the parametric studies are discussed, and conclusions are given.

II. Governing Equations

The governing equations are the Reynolds-averaged conservation equations for a mixture of gases in thermal and

chemical nonequilibrium, when we have adopted the Favre average for the species mass fraction K

Y and molar

fraction K

X , the energy (total E and vibrational v

e ), and the velocity field i

u and the time average for pressure

p and the total density ρ . In differential form the equations are

( ) ( ) ( )kkjjk

j

jk

j

kYuJ

xuY

xY

tωρρρ +′′′′+

∂

∂−=

∂

∂+

∂

∂,

5,1=k

( ) ( ) ( )jiijij

j

ji

j

iuup

xuu

xu

t′′′′+−

∂

∂−=

∂

∂+

∂

∂ρσδρρ

( ) ( )Vjtjjijjiji

j

j

j

eueuuuuqux

pEu

xE

t′′′′−′′′′−′′′′−−

∂

∂=

+

∂

∂+

∂

∂ρρρσ

ρρρ

( ) ( ) ( )VVjjV

j

jV

j

VSeuq

xue

xe

t+′′′′−

∂

∂−=

∂

∂+

∂

∂ρρρ

, (1)

where

ijllijijSS δµµσ

3

22 −= �

j

k

kjkx

XDJ

∂

∂−= ρ

,

( ) ∑∂

∂−

∂

∂−

∂

∂+−=

k j

k

kk

j

V

V

j

rottrjx

XDh

x

T

x

Tq ρηηη

∑∂

∂−

∂

∂−=

m j

m

mmV

j

V

VjVx

XDh

x

Tq ρη

,

KeYeYuuhYeeEm

mVm

k

kTk

k

iikkVT ∑∑∑ +′′′′+′′′′++∆++=2

10 (2)


4

and ( )ijjiij

xuxuS ∂∂+∂∂= 21 is the symmetric part of the mean strain tensor, and k

ω and 0

kh∆ are, respectively,

the average reaction rate production and the enthalpy of formation of species k; in addition, subscript m refers to

molecular species.

The mean pressure p is determined from the equation of state, i.e.,

( )∑ ′′′′+=k

kkkTYTYRp ρ (3)

The Favre-averaged internal energy contributions that depend on the translational (t

e ) and vibrational (V

e )

temperatures are defined according to Ref. 7, as well as the molecular mixture viscosity µ , the thermal conductivity

coefficients, tr

η , rot

η and V

η , and the diffusion coefficients of species k in the mixture k

D , the internal energy

ke and the enthalpy

kh of species k and the vibrational energy contribution

mVe .

The reaction rate productions have been determined assuming the 17-reaction mechanism of Ref. 7 whereby the

coupling between vibration and dissociation has been taken into account by introducing a reaction-rate-controlling

temperature of the dissociation7,8

. The vibrational source term V

S are defined according to Ref. 7.

A. Turbulence model

The closure of the governing equations (1) and (2) is obtained by a gradient-law assumption and the use of a

linear two-equation K-ε eddy viscosity model that accounts for compressibility effects as well as non-equilibrium

effects due to vibration and finite rate chemistry, following the approach proposed in Ref. 2.

B. Finite Rate Catalysis model

When the gas in the boundary layer is dissociated, atomic species can recombine in the proximity of the surface.

These chemical processes could release reaction energy increasing the thermal load on the surface. It is very

important to calculate this additional thermal flux in order to design efficient Thermal Protection Systems for space

vehicles.

The effect of the body surface on the recombination rates near the wall is described by the catalytic efficiency

coefficients (k

γ ), which are defined as the ratio of the number of atoms impinging on the surface which recombine

in molecules to the overall number of atoms impinging on the surface.

The catalytic efficiency coefficients range from the fully catalytic condition ( 1=k

γ ) to the non catalytic one

( 0=k

γ ). A fully catalytic wall will cause the recombination to occur instantaneously and the composition on the

wall will be limited by the speed with atoms diffuse to the wall. If the wall is non catalytic, no recombination occurs

at the wall and the resulting heat transfer can be much less. A finite-rate catalytic wall is one which produces a

situation between these two extremes.

1. The model of Nasuti, Barbato and Bruno5

The model is based on the phenomenological description of the recombination process of the dissociated species

on metal surfaces proposed by Halpern and Rosner9. A scheme representing the elementary steps involved in the

process can be drawn as follows: 1) adsorption of atoms, 2) adsorption of molecules, 3) recombination between gas

atoms and adsorbed atoms (adatoms) in gas molecules (Eley-Rideal recombination), 4) recombination between

adatoms in gas molecules (Langmuir-Hinshelwood recombination), and 5) thermal desorption.

The recombination probability is computed by analyzing the behavior of the atoms and molecules striking the

surface. This analysis is based on the kinetic theory of gases, on the atomic structure of the surface, and on the

energies involved in the chemical bonds between atoms and molecules of the gas and the surface atoms.

In the single species model the gas phase is a mixture of molecules 2

A and atoms A . The number of atoms

impinging on the surface is given from the kinetic theory of gases

kTm

pZ

a

a

a

π2= (4)


5

where a

p , a

m , k and T are, respectively, atoms partial pressure and mass, Boltzmann constant and temperature.

The recombination probability is expressed as the ratio of the flux of recombining atoms ar

Z to the impinging

atoms flux

a

ar

AAZ

Z=

− 2γ (5)

erdtaaarZZZZ +−= (6)

where dtaa

ZZ − are the atoms which are adsorbed but which do not desorb as atoms and er

Z are the atoms which

strike an adatom recombining with the E-R process. Following the approach proposed in Ref. 2, aa

Z , dt

Z , er

Z and

then a

γ , can be obtained as functions of flow-conditions and local gas composition if the values of some parameters

characterizing the surface material are given.

2. The model of Kurotaki6

The model is derived from the phenomenological theory proposed by Kovalev et. al.10 and it describes

heterogeneous catalysis on the surface of SiO2-based materials. Each unknown variables are evaluated from the

kinetic theory and the transition state theory. Surface properties are determined by comparing with experimental

data in such a way that catalytic efficiency can be predicted in a wide range of surface temperature and partial

pressure of dissociating gas.

For the NN −2

binary mixtures of interest for the applications of the present work, the expression of catalytic

efficiency is given by,

( )( ) ( )

θθθ

θθπγ

N

NN

NN

NNX

pKKkkXKkk

KkkKkkkkRTm

2262264

26426242

2/22

8

+++

++=

− (7)

( )( ) ( )

2262264

262

/22

2

pKKkkXKkk

XKkk

NN

NNN

θθ

θ

θ

θ

+++

+= (8)

1=+N

θθ (9)

where n

k and n

K are, respectively, the rate constant of forward reaction and the equilibrium constant of chemical

reaction n that occur on the surface, N

θ the surface fraction of the adsorbed species N, and θ the surface fraction of

the free adsorption surface sites.

Following the approach proposed by Kurotaki in Ref. 6, the catalytic efficiency can be calculated from the above

relations when the surface properties are determined.

C. Catalytic Boundary conditions

Boundary conditions of densities of each species for the Navier-Stokes equations in the finite rate catalysis

model are given by considering the balance between the mass formation rates at the wall and the diffusion mass flux

away from the wall,

w

k

kwkn

YD

∂

∂−= ρω (10)

where n is the coordinate locally normal to the wall. The source term is evaluated using the Goulard’s relation11

,

kwkYk

kρω = (11)


6

The catalytic reaction rate constant kw

k is related to the recombination probability k

γ by means the Scott’s relation3

k

kwm

RTk

k πγ

2= (12)

In the present work the values of k

γ are calculated by means of the catalysis models described in the previous

paragraph. Although Scott12

shows some evidence that glassy material might have incomplete energy

accommodation, in the present work fully energy accomodation assumption is applied in the heat flux calculation at

the wall.

III. Numerical Solution

The approach followed in the present paper is based on a finite volume formulation of the governing equations

that relies on a second-order, upwind biased total variation diminishing discretization of the inviscid fluxes and

central differencing of the viscous one. The time integration is performed by a three-stage Runge-Kutta algorithm

with a point implicit treatment of the source terms. The approach also relies on a linear eddy viscosity two-equation

turbulence modeling that accounts for the coupling of turbulence with chemistry and vibration. Two different

catalysis models (Kurotaki6; Nasuti et al.

5) have been implemented to account for the atomic oxygen and nitrogen

recombination over silica-based surfaces. Both non-catalytic and fully catalytic wall boundary conditions have been

implemented as limiting cases.

IV. Results

To assess the capability of the model, we have first computed the flow around the ELECTRE model (test 1) that

has been tested in the HEG high-enthalpy wind tunnel. The model has then been applied to simulate shock-

wave/turbulent boundary layer interactions in the presence of the surface catalysis around the double-wedge model

(test 2) used by Davis and Sturtevant1 at T5 Hypervelocity Shock Tunnel conditions, well representative of a typical

control surface configuration. The objective of the study has been to assess the effects of surface catalytic efficiency,

Mach number and wall temperature on the separation around the body flap and the related aerothermal loads.

A. Test 1: Electre in HEG

The Electre model (see Fig. 1) is an axisymmetric sphere-cone which was tested in flight by ONERA during the

early seventies and subsequently tested as a standard model in several European wind tunnels. Its shape is

characterized by a smooth sphere-cone junction in terms of wall longitudinal curvature variation, due to a clothoidal

profile matching sphere and cone. The model length, up to the end of the cone, is 40 cm and the nose radius is 3.5

cm.

2

2

3

3

4

4

4

5

5

5

5

667

8

10

15

15 112.682814 80.3755

13 57.330912 40.8935

11 29.168910 20.8059

9 14.84068 10.5856

7 7.55066 5.3858

5 3.84164 2.7402

3 1.95452 1.3942

1 0.9944

Norm pressure

Figure 1. Test EL_NC; computational grid and pressure contours.


7

The test conditions are relative to the Reference Calibration Point of the DLR High Enthalpy Shock Tunnel

Goettingen (HEG) nozzle ( 7.9=∞

M , 41070.2m ⋅=∞

Re , K 790=∞

T and sV m 5919=∞

) and are close to the

thermal equilibrium. The initial air composition in terms of mass fraction is 2

2106.3

−⋅=O

Y , 179.0=O

Y ,

6100.1 −⋅=N

Y , 2103.3 −⋅=NO

Y ; the wall temperature is fixed to K 300=w

T .

For this test case three different wall catalytic conditions have been considered 1) non-catalytic wall (EL_NC),

2) fully-catalytic wall (EL_FC), 3) finite-rate catalytic wall for N and O species and non catalytic wall for NO

species (EL_FRC1, EL_FRC2). The recombination probabilities of O (2OO−

γ ) and N (2NN −

γ ) atoms on the surface

for the EL_FRC1 test are fixed at the (same) experimental12

value of4

109.2−⋅ . To assess the sensitivity of the model

to different values ofk

γ , for the test EL_FRC2 2OO−

γ and 2NN −

γ are fixed at value of 2

10−

(see Table 1).

40x120300 KLam2.9E-4 (exp.)2.9E-4 (exp.)9.7EL_FRC1

1.E-2

1

0

γO-O2

40x120300 KLam09.7EL_NC

300 K

300 K

Tw

40x120Lam1.E-29.7EL_FRC2

40x120Lam19.7EL_FC

GridFlow cond.γN-N2

MTest

40x120300 KLam2.9E-4 (exp.)2.9E-4 (exp.)9.7EL_FRC1

1.E-2

1

0

γO-O2

40x120300 KLam09.7EL_NC

300 K

300 K

Tw

40x120Lam1.E-29.7EL_FRC2

40x120Lam19.7EL_FC


MTest

Table 1. ELECTRE (EL); Test Matrix.

Three grid levels have been employed to achieve grid-independence of the numerical solution (40x60, 40x120,

80x120). The grid sensitivity analysis has been focused on the non catalytic wall test EL_NC. All computations have

been performed on the 40x120 grid, whose minimum nondimensional spacings in streamwise and normal-to-the-

wall directions are, respectively, 31006.1 −⋅ and 61008.4 −⋅ . Figure 2 shows the grid independence of results in terms

of surface distributions of heat fluxes along the wall. The picture shows that a good grid independence is reached for

the 40x120 grid, since for the next grid level no appreciable differences are shown.

100000

1e+006

1e+007

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

qw

all (

W/m

^2

)

x(m)

ELECTRE in HEG; wall heat flux distribution

EL_NC_C (40x60)

EL_NC (40x120)

EL_NC_F (80x120)

Figure 2. Test EL_NC; grid independence of results in terms of surface distributions of heat fluxes.

The wall heat flux distributions, for the different wall catalytic conditions, are reported in Fig. 3 compared with

the available experimental results. The heat flux distribution show an agreement between experimental and

numerical results for the FRC test in the nose region whereas on the conical part of the model there is a better

agreement with the fully catalytic solution. The pictures show a strong dependence of the wall heat fluxes on the

surface catalytic efficiency, in particular on the conical portion of the model.


8

100000

1e+006

1e+007

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45

qw

all (

W/m

^2

)

x(m)

ELECTRE in HEG; wall heat flux distribution

EL_FRC1

EL_FRC2

EL_NC

EL_FC

Exp data-shot 157

Exp data-shot 159

Exp data-shot 162

Exp data-shot 164

1e+006

1e+007

0 0.005 0.01 0.015 0.02

qw

all (

W/m

^2

)

x(m)

EL_FRC1

EL_FRC2

EL_NC

EL_FC

Exp data-shot 157

Exp data-shot 159

Exp data-shot 162

Exp data-shot 164

�� Figure 3. Test EL: a) surface distributions of heat fluxes along the wall at various wall catalytic conditions;

b) Detail of the nose region.

B. Test 2: Double Wedge

The main objective of this study is to analyze the effects of the surface catalysis on shock-wave/turbulent

boundary-layer Interactions. In the present work we have considered the the double wedge test model (see Fig. 4)

used by Davis and Sturtevant1 in the experiments performed in the T5 Hypervelocity Shock Tunnel to investigate

nonequilibrium effects on separation length in high enthalpy shock-wave/ boundary-layer Interactions. The model

consists of a forward plate (20.32 cm span x 10.16 cm chord) followed by a full-span trailing flap (5.08 cm chord).

All simulations have been carried out on a configuration with forward plate and flap incidence angles equal,

respectively, to 40 and 55 degrees. The x-coordinate of the hinge location in such configuration ( ( ) cm 78.7=LHX

from the forward plate leading edge) has been assumed as normalization length.

0 0.1 0.2X(m)

0

0.05

0.1

0.15

0.2

Y(m

)

Computational grid

Figure 4. Test DW4, geometry and grid.

This geometry is representative of a deflected aerodynamic control surface configuration (e.g. wing-flap or body-

flap) of a hypersonic vehicle. To assess the importance of the surface catalysis on the aerothermal loads over the

flap, we have carried out a parametric study in terms of Mach number, flow conditions (laminar or turbulent) and

wall temperature in the presence of different wall catalysis assumptions. All the computations have been realized

with the same pressure and temperature freestream flow conditions ( K 2700=∞

T , Pa 12000=∞

P ) and Nitrogen as

working gas.

The definitions of the computed test cases are reported in Table 2. The effects of the laminar to turbulent flow

transition have been assessed by varying the transition location. Two transition points have been fixed: 1)

( ) 78.0=LHXXtr (upstream of the laminar flow separation point); 2) ( ) 03.1=LHXXtr (downstream of the

laminar flow reattachment point).


9

As a compromise between accuracy and computational cost, all numerical simulations have been performed on a

180x60 grid (see Fig. 4) whose minimum nondimensional spacings in streamwise and normal-to-the-wall directions

are, respectively, 31079.0

−⋅ and 71055.0

−⋅ The grid has been selected through a grid sensitivity analysis both for

laminar and turbulent conditions. All the computations have been performed in fully catalytic wall conditions and

M=5.34. The results of the grid sensitivity are reported in Fig. 5 in terms of separation location ( )LHXXsep

,

separation extent ( )LHXLsep

and normalized peak pressure ( )100inf

⋅PPpeak

as a function of grid resolution

(defined as the inverse of the square root of the total number of cells, (N). Figure 5 shows that both the laminar and

turbulent peak pressures are grid independent; however, the distributions of the turbulent separation location and

extent as a function of grid resolution indicate that for the turbulent computations a further grid refinement should be

necessary.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0.007 0.008 0.009 0.01 0.011 0.012 0.013 0.014 0.015

Xsep/X

(LH

), L

sep/X

(LH

), P

_peak/P

inf/

100

sqrt(1/N)

Xsep/X(LH) LamLsep/X(LH) Lam

P_peak/Pinf/100 LamXsep/X(LH) TurLsep/X(LH) Tur

P_peak/Pinf/100 Tur

Figure 5. Test DW; grid sensitivity analysis.


10

180x60300 KTurb, Xtr/X(LH)=0.7805.34DW1_NC_T2

180x60300 KTurb, Xtr/X(LH)=0.782.9E-45.34DW1_FRC_T2

180x60300 KTurb, Xtr/X(LH)=1.0305.34DW1_NC_T

180x60300 KTurb, Xtr/X(LH)=1.032.9E-45.34DW1_FRC_T

180x60300 KTurb, Xtr/X(LH)=1.0315.34DW1_FC_T

180x60300 KTurb, Xtr/X(LH)=0.7815.34DW1_FC_T2

300 K

300 K

300 K

300 K

300 K

300 K

Tw

180x60Lam06.67DW2_NC_L

180x60Lam2.9E-46.67DW2_FRC_L

180x60Lam16.67DW2_FC_L

180x60Lam2.94E-4 (exp.)5.34DW1_FRC_L




MTest

180x60300 KTurb, Xtr/X(LH)=0.7805.34DW1_NC_T2

180x60300 KTurb, Xtr/X(LH)=0.782.9E-45.34DW1_FRC_T2

180x60300 KTurb, Xtr/X(LH)=1.0305.34DW1_NC_T

180x60300 KTurb, Xtr/X(LH)=1.032.9E-45.34DW1_FRC_T

180x60300 KTurb, Xtr/X(LH)=1.0315.34DW1_FC_T

180x60300 KTurb, Xtr/X(LH)=0.7815.34DW1_FC_T2

300 K

300 K

300 K

300 K

300 K

300 K

Tw


180x60Lam2.9E-46.67DW2_FRC_L


180x60Lam2.94E-4 (exp.)5.34DW1_FRC_L




MTest

1000 K

1000 K

1000 K 180x60Lam15.34DW4_FC_L


180x60LamM15.34DW4_FRC_L 1000 K

1000 K

1000 K 180x60Lam15.34DW4_FC_L


180x60LamM15.34DW4_FRC_L

180x601000 KLamM25.34DW4_FRC2_L

180x601500 KLamM15.34DW5_FRC_L

1500 K

1500 K

1500 K 180x60Lam15.34DW5_FC_L


180x60LamM25.34DW5_FRC2_L

180x601000 KLamM25.34DW4_FRC2_L

180x601500 KLamM15.34DW5_FRC_L

1500 K

1500 K

1500 K 180x60Lam15.34DW5_FC_L


180x60LamM25.34DW5_FRC2_L

300 K

300 K

300 K 180x60Lam18.01DW3_FC_L


180x60Lam2.9E-48.01DW3_FRC_L 300 K

300 K

300 K 180x60Lam18.01DW3_FC_L


180x60Lam2.9E-48.01DW3_FRC_L

Table 2. Double-Wedge (DW); Test Matrix.

In Fig. 6 we show the pressure contours lines and the streamlines (with a zoom of the flap region) for the

conditions corresponding to a freestream Mach number of 5.34, laminar flow and fully catalytic wall assumption

(test DW1_FC_L). The flowfield exhibits a separation region around the hingeline with a multiple-vortex structure.

The interaction between the leading edge oblique shock and the separation and reattachment shocks generates a

further bow shock around the second wedge.

In Fig. 7 we report the distributions of the Stanton number for laminar (DW1_FC_L) and turbulent

(DW1_FC_T) flow conditions along the body surface under fully catalytic wall conditions. The numerical results

are compared with the experimental measurements obtained by Davis and Sturtevant in Ref. 1. The figure shows

that the shock/wave boundary layer interaction is indeed transitional, with transition occurring past the separation,

around the hingeline (at ( ) 03.1=LHXXtr , as assumed in the computation).


11

0 0.1 0.2X(m)

0

0.05

0.1

0.15

0.2

Y(m

)

0.074 0.076 0.078 0.08

X(m)

0.062

0.063

0.064

0.065

0.066

0.067

0.068

0.069

Y(m

)

� Figure 6. Test DW1_FC_L; a) pressure contours; b) zoom of the streamlines around the hingeline.

0.1

1

10

100

1000

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Sta

nto

n x

1000

X/X(LH)

DW1_FC_T

DW1_FC_L

Exp. (Davis and Sturtevant)

Figure 7. Test DW1; surface distributions of Stanton number along the wall.

Relevant parameters for shock wave/boundary layer interactions have been identified in the literature14,15,16

as the

Mach and Reynolds number of the freestream flow, the strength of the interaction, the flow conditions (laminar or

turbulent) of the boundary layer, the wall-to-total temperature ratio. Moreover some authors3,13

have shown that

surface catalysis affects the extent of the separation zone to a significant degree. The present study concentrates on

the effects of surface catalysis, Mach number, wall temperature and flow conditions on the high enthalpy shock

wave boundary layer interactions.

1. Effects of Surface Catalysis

The coupling between turbulence and surface catalysis affects significantly both the extent of the separation

region and the heat loads.

In the presence of surface catalysis the fraction of the atoms that recombines in the proximity of the wall is

increased, thus causing a growth of the gas mixture density. As a consequence the subsonic layer becomes thinner

and the upstream influence reduces.


12

Figures 8 and 9 show, respectively, the surface distributions of pressure and friction coefficient along the wall

for different values of 2NN −

γ . Figures indicate that surface catalysis inhibits the upstream propagation of disturbance

thus delays the separation.

Surface catalysis significantly increases the wall heat fluxes as compared to the non catalytic case, and coupling

between turbulence and catalysis further amplifies the effects of gas-surface interaction on the heat loads (see Fig.

10). In fact, in turbulent cases the transport of dissociated atoms toward the wall increases with the subsequent

recombination and heat release.

The effects of catalysis and turbulence on the upstream influence are illustrated in Fig. 11, where Ui length is

reported as a function of the catalytic efficiency for laminar and transitional cases. Figure indicates that when

transition occurs in the separation region (at ( ) 03.1=LHXXtr ) the upstream influence is controlled by both gas-

surface interaction and turbulence effects, while it is essentially controlled by turbulence effects when transition

occurs upstream of the separation shock (at ( ) 78.0=LHXXtr ).

20

25

30

35

40

45

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

P/P

inf

X/X(LH)

DW1_FRC_L

DW1_NC_L

DW1_FC_L

DW1_FRC_T2 (Xtr/X(LH)=0.78)

DW1_NC_T2 (Xtr/X(LH)=0.78)

DW1_FC_T2 (Xtr/X(LH)=0.78)

Figure 8. Test DW1; effects of catalytic efficiency and laminar to turbulent transition on the wall pressure

distributions.

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.8 0.85 0.9 0.95 1 1.05

Cf

x/x(LH)

Double-wedge; Friction coefficient distribution

DW1_FRC_L

DW1_NC_L

DW1_FC_L

2NN−γ

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.8 0.85 0.9 0.95 1 1.05

Cf

x/x(LH)

Double-wedge; Friction coefficient distribution

DW1_FRC_L

DW1_NC_L

DW1_FC_L

2NN−γ

Figure 9. Test DW1; effects of the catalytic efficiency on the friction coefficient distributions.


13

6

8

10

12

14

16

18

20

22

1.1 1.12 1.14 1.16 1.18 1.2 1.22 1.24 1.26 1.28 1.3

Sta

nto

n x

10

00

X/X(LH)

DW1_NC_L

DW1_FC_L

DW1_FRC_L

DW1_NC_T (Xtr/X(LH)=1.03)

DW1_FC_T (Xtr/X(LH)=1.03)

DW1_FRC_T (Xtr/X(LH)=1.03)

Figure 10. Test DW1; effects of catalytic efficiency and laminar to turbulent transition on the wall Stanton

number distributions. Zoom of the region downstream of the hingeline.

Non Catalytic Fully Catalytic

0.05

0.06

0.07

0.08

0.09

0.1

0.11

1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

Ui/X

(LH

)

Gamma N-N2

Ui; Tw=300K; Laminar

Ui; Tw=300K; Tr. (Xtr/X(LH)=0.78)

Ui; Tw=300K; Tr. (Xtr/X(LH)=1.03)

Non Catalytic Fully Catalytic

0.05

0.06

0.07

0.08

0.09

0.1

0.11

1e-008 1e-007 1e-006 1e-005 0.0001 0.001 0.01 0.1 1

Ui/X

(LH

)

Gamma N-N2

Ui; Tw=300K; Laminar

Ui; Tw=300K; Tr. (Xtr/X(LH)=0.78)

Ui; Tw=300K; Tr. (Xtr/X(LH)=1.03)

Figure 11. Effects of the catalytic efficiency and laminar to turbulent transition on the upstream influence

(M=5.34).

2. Effects of Mach Number

Figures 12 and 13 illustrate the effects of Mach number and surface catalysis on pressure distribution and

upstream influence. The freestream Mach number has been changed from the starting value 34.5=∞

M to 6.67 (that

is 1.25 times the starting value) and 8.01 (that is 1.50 times the starting value), in order to maintain the invariance of

the shock configuration. Separation occurs for the three test cases. Figure 12 indicates that the pressure levels

strongly increase with the Mach number, and similarly the extent of the separation region reduces, mainly due to the

shift of the separation location toward the hingeline (and also due to a slightly anticipated flow reattachment on the

flap).


14

M=5,34

M=6,67

M=8,01

20

30

40

50

60

70

80

90

100

110

120

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

P/P

inf

X/X(LH)

DW1_FRC_L

DW1_NC_L

DW1_FC_L

DW2_FRC_L

DW2_NC_L

DW2_FC_L

DW3_FRC_L

DW3_NC_L

DW3_FC_L

M=5,34

M=6,67

M=8,01

20

30

40

50

60

70

80

90

100

110

120

0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2

P/P

inf

X/X(LH)

DW1_FRC_L

DW1_NC_L

DW1_FC_L

DW2_FRC_L

DW2_NC_L

DW2_FC_L

DW3_FRC_L

DW3_NC_L

DW3_FC_L

Figure 12. Test DW1, DW2, DW3; effects of Mach number and catalytic efficiency on the wall pressure

distributions.

Figure 13 shows that the upstream influence decreases with Mach number because of the thinning of the

subsonic portion of the boundary layer. Surface catalysis amplifies this trend by further reducing the subsonic layer

thickness.

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

5 5.5 6 6.5 7 7.5 8 8.5

Ui/X

(LH

)

Mach

Ui; Tw=300; gamma=0.0

Ui; Tw=300; gamma=2.9E-4


2NN −γ

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.1

0.11

5 5.5 6 6.5 7 7.5 8 8.5

Ui/X

(LH

)

Mach


Ui; Tw=300; gamma=2.9E-4


2NN −γ

Figure 13. Effects of Mach number and catalytic efficiency on the upstream influence.

3. Effects of Wall Temperature

In Figs. 14-16 are reported the results of the test cases DW1_FC_L, DW4_FC_L and DW5_FC_L obtained by

the fully catalytic wall assumption for 34.5=∞

M . The surface temperature has been changed from 300=Tw K to

1000 K and 1500 K.

By increasing surface temperature, plateau pressure and flap pressure recovery reduce slightly (Fig. 14), the

boundary layer thickens, the upstream influence increases (with separation location moving upstream) and the skin-

friction (Fig. 15) and Stanton number levels (Fig. 16) are reduced.


15

20

25

30

35

40

45

0.8 0.85 0.9 0.95 1 1.05

P/P

inf

X/X(LH)

DW1_FC_L (Tw=300K)

DW4_FC_L (Tw=1000K)

DW5_FC_L (Tw=1500K)

Tw

20

25

30

35

40

45

0.8 0.85 0.9 0.95 1 1.05

P/P

inf

X/X(LH)

DW1_FC_L (Tw=300K)

DW4_FC_L (Tw=1000K)

DW5_FC_L (Tw=1500K)

Tw

Figure 14. Effects of surface temperature on the wall pressure distributions.

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.8 0.85 0.9 0.95 1 1.05

Cf

X/X(LH)

DW1_FC_L (Tw=300K)

DW4_FC_L (Tw=1000K)

DW5_FC_L (Tw=1500K)

Tw

-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.8 0.85 0.9 0.95 1 1.05

Cf

X/X(LH)

DW1_FC_L (Tw=300K)

DW4_FC_L (Tw=1000K)

DW5_FC_L (Tw=1500K)

Tw

Figure 15. Effects of surface temperature on the wall skin friction distribution.


16

0.1

1

10

100

0.8 0.85 0.9 0.95 1 1.05

Sta

nto

n x

10

00

X/X(LH)

T=300K FC

T=1000K FC

T=1500K FC

Tw

0.1

1

10

100

0.8 0.85 0.9 0.95 1 1.05

Sta

nto

n x

10

00

X/X(LH)

T=300K FC

T=1000K FC

T=1500K FC

Tw

Figure 16. Effects of surface temperature on the wall Stanton number distribution.

In Fig. 17, upstream influence is reported as a function of the wall temperature for different values of the

catalytic efficiency in the laminar case. The results show a nearly linear increase of Ui with Tw for the non-catalytic

and the fully catalytic cases. Since there is a strong dependence of the catalytic rates on the surface temperature, the

partially catalytic results, obtained by means of the models of Nasuti et. al. (M1) and Kurotaki (M2) show different

behavior on Tw variations, where the maximum difference can be observed for Tw=1000 K. In particular, in the

range of temperature considered, model M1 shows a (nearly) linear increase of Ui with Tw, whereas model M2

shows a non linear behavior.

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.135

200 400 600 800 1000 1200 1400 1600

Ui/X

(LH

)

Tw (K)

Ui; M=5.34; gamma=0.0

Ui; M=5.34; gamma=f(Tw, pN) (M1)


Ui; M=5.34; gamma=1.0

NC

FC

FRC (M1)

FRC (M2)

0.09

0.095

0.1

0.105

0.11

0.115

0.12

0.125

0.13

0.135

200 400 600 800 1000 1200 1400 1600

Ui/X

(LH

)

Tw (K)

Ui; M=5.34; gamma=0.0



Ui; M=5.34; gamma=1.0

NC

FC

FRC (M1)

FRC (M2)

Figure 17. Effects of surface temperature and catalysis modeling on the upstream influence (M=5.34).


17

V. Conclusion

In the present paper we have studied the influence of the surface catalysis on high enthalpy shock-wave/turbulent

boundary layer interactions. The numerical methodology employed is based on a finite volume, total variation

diminishing approach with a point-implicit treatment of source terms and a linear eddy viscosity two-equation

turbulence modeling that accounts for the coupling of turbulence with thermal and chemical nonequilibrium

phenomena. To account for the atomic oxygen and nitrogen recombination over silica-based surfaces two different

catalysis models (Kurotaki6; Nasuti et al.

5) have been used.

The capabilities of the model have first been assessed by computing the flow around a sphere-cone configuration

with a comparison with experimental measurements. The simulations indicate that the thermal loads are strongly

influenced by the surface catalytic efficiency.

The model has then been applied to analyze the flow around a typical wing-flap configuration. In particular, we

have focused our attention on the effects of surface catalysis, Mach number and wall temperature on separation and

on the aerothermal loads acting on the flap. Results have been obtained for non catalytic, partially catalytic and fully

catalytic surfaces both for laminar and turbulent flows. The results show that surface catalysis significantly increases

the heat transfer in shock wave/boundary layer interactions and amplifies both the effects of laminar to turbulent

transition and the effects of the Mach number. Consequently the surface catalysis acts on the extent of the separation

region. In addition it has been shown that turbulence acts as an amplification factor of the catalysis effects on the

surface heat fluxes and consequently in turbulent shock wave/boundary layer interactions the heat transfer due to the

catalysis effects is significantly larger than the one obtained in the laminar case.

References

4Davis, J.P., Sturtevant, B., “Separation Length in High-Enthalpy Shock/Boundary-Layer Interaction”, Physics of Fluids,

Vol. 12, No. 10, 2000, pp. 2661-2687.

2Grasso, F., Marini, M., Ranuzzi, G., Cuttica, S., Chanetz, B., “Shock-Wave/Turbulent Boundary-Layer Interactions in

Nonequilibrium Flows”, AIAA Journal, Vol. 39, No. 11, 2001, pp. 2131-2140.

3Grumet, A. A., Anderson Jr, J. D., “The Effects of Surface Catalysis on the Hypersonic Shock Wave/Boundary Layer

Interaction”, AIAA/ASME 6th Joint Thermophysics and Heat Transfer Conference, June 20-23, 1994, Colorado Springs, CO.

4Halpern, B., and Rosner, D.,E., “Chemical Energy Accomodation at Catalyst Surfaces”, J. Chem Soc., Faraday Trans. I, Vol.

74 part 8, 1978, pp. 1883-1912.

5Nasuti, F., Barbato, M. and Bruno, C., “Material-Dependent Catalytic Recombination Modeling for Hypersonic Flows”,

Journal of Thermophysics and Heat Transfer, Vol.10, No. 1, pp. 131-136, 1996.

6Kurotaki, T., “Construction of Catalytic Model on SiO2 – Based Surface and Application to Real Trajectory”, 34th AIAA

Thermophysics Conference 19-22 June 2000/ Denver CO.

7Grasso, F., Capano, G., “Modeling of Ionizing Hypersonic Flows in Nonequilibrium”, Journal of Spacecraft and Rockets,

Vol. 32, No. 2, 1995, pp. 217-224.

8Park, C., “Nonequilibrium Hypersonic Aerothermodynamics”, Wiley, New York, 1990, pp. 43-143.

9Gupta, R. N., Yos, J. M., Thompson, R. A., and Lee, K. P., “A Review of Reaction Rates and Thermodynamic and

Transport Properties for an 11-Species Air Model for Chemical and Thermal Nonequilibrium Calculations to 30,000 K”, NASA

RP 1232, Aug. 1990.

10Kovalev, V. L., Suslov, O. N. and Triskiy, G. A., “Phenomenological Theory for Heterogeneous Recombination of Partially

Dissociated Air on High-Temperature Surfaces”, Molecular Physics and Hypersonic Flow, ed. Capitelli, M., Kluwer Academic

Publishers, pp. 193-202, 1996.

11Goulard, R., “On catalytic recombination rates in hypersonic stagnation heat transfer”, Jet Propulsion, Vol. 28, No. 11,

Nov. 1958, pp. 733-745.

12Scott, C. D., “Catalytic Recombination of Nitrogen and Oxygen on High Temperature Reusable Surface Insulation”, AIAA

Paper 80-1477, 1980.


18

13Grumet, A. A., “A Numerical Study of Shock Wave/Boundary Layer Interaction in Nonequilibrium Chemically Reacting

Air: The Effects of Catalytic Walls”, Master’s thesis, University of Maryland at College Park, 1990.

14Grasso, F., Marini, M., “Analysis of Hypersonic Shock-Wave/Laminar Boundary-Layer Interaction Phenomena”,

Computers and Fluids, Vol. 25, No. 6, 1996, pp. 561-581.

15Simeonides, G., “Hypersonic Shock-Wave Boundary-Layer Interactions over Simplified Deflected Control Surface

Configurations”, AGARD Report R-792, Paper 7, 1993.

16Holden, M. S., “Boundary-Layer displacement and leading-edge bluntness effects on attached and separated laminar

boundary layers in a compression corner. Part II: Experimental study”, AIAA Journal, Vol. 9, No. 1, 1971, pp. 84-93.

17Hankey W. L., Holden, M. S., “Two dimensional shock-wave boundary-layer interactions in high-speed flows”,

AGARDograph, No. 203, Part II, 1975.

18Needham, D. A., Stollery, J. L., “Boundary-Layer separation in Hypersonic flow”, AIAA Paper 66-455, 1966.

19Grasso, F., Leone, G., Delery, J. M., “A validation procedure for the analysis of shock-wave boundary-layer interactions

problems”, AIAA Journal, Vol. 32, No. 9, 1994, pp. 1820-1827.

Effects of the Surface Catalysis on High-Enthalpy Shock- Wave/Turbulent Boundary-Layer Interactions

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