Computation of Surface Catalysis for Graphite Exposed to High-Enthalpy Nitrogen Flow

14 Pages·2011·9.56 MB·English

AIAA 2012-0534
50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition
09 - 12 January 2012, Nashville, Tennessee
Computation of Surface Catalysis for Graphite
Exposed to High-Enthalpy Nitrogen Flow
Abhilasha Anna∗ and Iain D. Boyd†
Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI, 48109
Thehightemperaturesonahypersonicvehiclesurfacecausedbyheatloadsencountered
during (re-)entry through a planetary atmosphere require a reliable Thermal Protection
System (TPS) that makes a good understanding of the physical and chemical processes
34 essential for its design. Surface catalysis is a crucial chemical process that directly impacts
5
12- aerothermal heating of the vehicle TPS. To study the effects of this process, a binary
0
6.2 catalytic atom recombination model is implemented in a computational fluid dynamics
14/ (CFD) code. The study examines the effects of surface catalysis for graphite exposed to
5
0.2 high enthalpy nitrogen flow. As expected, surface catalysis strongly affects the boundary
1
OI: layer gradients of temperature and species concentration, and heat transfer to the surface.
D A fully catalytic surface causes the heat flux to increase by a factor of approximately
org | 3.5. The physical accuracy of the model is assessed using data from experimental tests
aa. conducted in the Inductively Coupled Plasma (ICP) Torch Facility at the University of
ai
c. Vermont. Comparisons are presented of computed results with measured experimental
ar
p:// data for translational temperature and relative nitrogen atom number density in the flow
htt in front of the test article.
3 |
1
0
2
pril 3, Nomenclature
A
N on D12 binary diffusion coefficient between species 1 and 2 [m2/s]
A J species diffusion flux [kg/m2/s]
G sp
HI M˙ mass flux [kg/m2/s]
C
MI N number of species in the mixture [dimensionless number]
F sp
O T translational-rotational temperature [K]
Y
T Y mass fraction [dimensionless number]
SI
VER hsp species enthalpy [J/kg]
NI kB Boltzmann constant
U
by kw wall catalytic speed [m/s]
ed m particle mass [kg]
d
oa q total heat flux [W/m2]
nl
Dow qconv convective heat flux [W/m2]
q diffusive heat flux [W/m2]
diff
γ wall catalytic efficiency [dimensionless number]
κ thermal conductivity [W/m/K]
ρ density [kg/m3]
subscripts
w wall value
tr translational-rotational energy mode
ve vibrational-electronic energy mode
∞ reference freestream conditions
sp species value
∗GraduateStudent,StudentMemberAIAA.
†JamesE.KnottProfessor,FellowAIAA.
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Copyright © 2012 by Abhilasha Anna and Iain D. Boyd. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
AmericanInstituteofAeronauticsandAstronautics
I. Introduction
Hypersonic vehicles experience heat loads during high-speed flight through the atmosphere that cause
very high temperatures on their surface. Therefore, such vehicles use a Thermal Protection System
(TPS) to protect them from aerodynamic heating and maintain acceptable temperatures on their surface.
The prolonged exposure to high temperature and chemical reactions can cause the TPS materials to fail.1
The need to design a reliable TPS necessitates good understanding of the physical and chemical processes
that determine the aerothermal heating environment.
Depending on the heat load encountered during hypersonic flight, an ablative or non-ablative TPS could
be used.2 Non-ablative or reusable materials are used where the re-entry conditions are mild while ablative
TPS materials are used where high heating rates are generated. There is no change in mass or properties of
the non-ablative material whereas ablative TPS materials accommodate high heating rates and heat loads
through phase change and mass loss. Ablative TPS has been used for most planetary entry probes and
high velocity Earth atmosphere re-entry vehicles. An ablative TPS surface can be heated3 by (1) convective
heating as a result of gas particle collisions and their interactions with the surface and (2) radiative heating
asaresultofradiationfromexcitedparticlesintheflow. CatalycityofanablativeTPSmaterialisoneofthe
4
3
5 factors that impacts the heating of the vehicle surface. Very high temperatures in the boundary layer can
2-
01 causethegasspeciestodissociate. IftheheatedTPSmaterialactsasacatalystanddissociatedatomsdiffuse
2
4/6. tothesurface,itcancauserecombinationofdissociatedboundarylayerspecieswhichincreasestheconvective
1
25 heating to the surface. Thus, a less catalytic surface is desirable to minimize this additional heating. Also,
0.
OI: 1 when the vehicle surface is heated, the surface material may chemically react with the boundary layer gases
D and can lead to surface recession as a result of surface material consumption. These chemical reactions can
g | be endothermic (vaporization, sublimation) or exothermic (oxidation) and will affect the net heating to the
or
aa. surface. Therefore, detailed studies of these interactions that occur between the surface and the atmosphere
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arc. gas are required.
p:// Accurate modeling of surface catalysis is a key factor in the prediction of aerothermal heating of the
3 | htt vehicle TPS and in characterizing TPS materials. The accurate prediction of the aerothermal environment
01 is necessary to determine the TPS sizing, uncertainties in which could lead to an over-sized TPS.4 The
2
3, objective of this research is to implement and assess a surface catalysis model for investigating the effect of
April catalycityonthespeciesconcentrationandtemperaturegradientsnearthematerialsurface,andontheheat
on transfer to the material surface.
N
A Tostudytheeffectsofsurfacecatalysis,theentryflightenvironmentconsideredisthepostshocksubsonic
G
HI highenthalpygasflow. TocharacterizeaTPSmaterial,itneedstobetestedinanexperimentalfacilitythat
C
MI can create conditions representative of real entry flight conditions. It is challenging and expensive to fully
OF reproduce real flight conditions in existing ground facilities.5 Therefore, a partial simulation of the flight
Y
T conditions that involves subsonic high enthalpy flow for the purpose of this study is considered. This paper
SI
ER describes the numerical approach used to simulate these conditions along with the experimental approach
V
NI taken to assess the computational results. Figure 1 shows a full hypersonic flowfield computed around a
U
y capsuletakenfromRef.6. Theinsertshowsthepost-shock,high-enthalpy,subsonicregionconsideredinthe
b
ed present study. The comparative analysis of the computed profiles of gas temperature and relative nitrogen
d
oa atom density with the experimental tests conducted at the University of Vermont is presented. The paper
nl
ow ends with some conclusions and suggestions for future work.
D
II. Technical Approach
A. Numerical Method
The numerical simulations in this study are conducted using the Michigan Aerothermodynamic Navier-
Stokes computational fluid dynamics (CFD) code LeMANS,7–9 developed at the University of Michigan. It
isageneralpurpose,parallel,three-dimensionalcodethatsolvesthelaminarNavierStokesequationsinclud-
ing chemical and thermal nonequilibrium effects on unstructured computational grids. The flow is modeled
assuming the continuum approximation is valid. The set of partial differential equations are solved using
a finite-volume method on unstructured grids. The inviscid fluxes across cell faces are discretized using a
modified form of the Steger-Warming Flux Vector Splitting (FVS) scheme10 which is less dissipative and
produces better results in boundary layers. The viscous terms are calculated using the values of properties
at the cell centers and at the nodes. Time integration is performed using a point implicit or a line implicit
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4 !
3
5
2-
1
0
6.2 Figure 1. Flow regime investigated
4/
1
5
2
0.
1
OI: method. LeMANSisparallelizedusingMETIS11 thatpartitionsthecomputationalgridbetweentheproces-
D
g | sors and Message Passage Interface protocol (MPI) to communicate information between processors. It is
or assumed that the translational and rotational energy modes of all species can be described by two different
a.
a
c.ai temperatures T and Tr respectively, while the vibrational energy mode and electron energy of all species
p://ar can be described by a single temperature Tv.12 LeMANS can simulate two-dimensional/axisymmetric flows
htt using any mixture of quadrilaterals and triangles, and three-dimensional flows using any mixture of hexahe-
3 | dra, tetrahedral, prisms and pyramids. All the simulations are performed in this study using computational
1
0
3, 2 grids that contained quadrilateral elements.
pril
A
n 1. Species boundary conditions
o
N
A
G Surfacecatalycityeffectscanbeaccountedforbyfourtypesofconditionsatthewallboundaryasshown
CHI in Table 1. In LeMANS, prior to the present work, wall catalycity effects were accounted for by choosing
MI a non-catalytic or a super-catalytic surface as the species boundary condition. A super-catalytic boundary
F
Y O conditionisinappropriateforthepresentflowsthatarecomprisedofdissociatedspeciesasthisconditionwill
SIT lead to the same composition at the wall as in the free stream which is undesirable for conditions where the
R
E effectofrecombinationontheheattransferistobestudied. Forthesimulationofthefullrangeofcatalycity
V
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y
b Table 1. Species boundary conditions.
d
e
d
a
nlo Boundary Condition Description
w
o
D Non-catalytic No recombination of atoms on the surface
Super-catalytic Atomsthatstrikethesurfacerecombinetothe
free stream gas composition
Fully-catalytic Allatomsthatstrikethesurfacerecombineto
form molecules
Partially-catalytic Some atoms reflect and some recombine
regimes, froma non-catalyticwallto afully-catalytic wall, asimplified catalyticatom recombinationmodel,
i.e. a binary interaction model with full energy accommodation,13,14 is implemented in LeMANS. It is
implementedbybalancingthemassfluxoftherelevantspeciestakingtheconsumption/productionatthewall
intoaccount. Themodelisappliedtoaspeciesboundaryconditionbyconsideringafirstorderrecombination
reaction for a binary gas at the wall. The boundary condition for the mass fraction Y of atomic nitrogen
N
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and Y of molecular nitrogen in a binary mixture (N -N) is given by the expression shown in Eq. 1.
N2 2
∂Y
D N =k Y
12 ∂n wN N
Y =1−Y (1)
N2 N
where D is the binary diffusion coefficient between atomic and molecular species, n is the wall normal
12
directionandk isthecatalyticrecombinationspeedgivenbytheHertz-KnudsenrelationshowninEq. 2.
wN
(cid:114)
k T
k =γ B (2)
wN N 2πm
N
In this model, the atoms that impinge on a surface either reflect from the surface and neither gain nor
lose energy at the surface, or become adsorbed where an atom may react with another atom to produce a
molecule. In the latter case, the energy released by the reaction, which is highly exothermic, is assumed
to be entirely transferred to the wall and this phenomenon is called full accommodation. In this model,
34 a dimensionless surface recombination coefficient13,15,16 γ (also referred to as the catalytic efficiency) is
5
2- introduced. It is defined as the ratio of the flux of atoms that recombine on the surface M˙ to the total
6.201 flux of atoms that impinge on the surface M˙ imp and the expression is shown in Eq.3. rec
4/
1
5
OI: 10.2 γ = MM˙˙rec (3)
D imp
g |
or This coefficient depends on the particular atom and surface involved. If the wall is fully-catalytic, then γ
a. N
a
ai and the corresponding boundary condition for the atom becomes,
c.
ar
http:// γN =1
3 | Y =0 (4)
01 N
2
3,
pril If the wall is non-catalytic, then γN is set to zero that implies the species concentration gradient is zero
A at the wall (Eqn. 5). If the wall is partially catalytic, γ is set to a value between 0 and 1 based on the
n N
o
N catalycity of the surface.
A
G
HI ∂Y ∂Y
MIC ∂nN =− ∂nN2 =0 (5)
F
O
Y
T 2. Thermochemical model
SI
R
E
V For this study, nitrogen gas mixture is considered composed of atomic and molecular nitrogen using the
NI
U following dissociation-recombination reaction:
y
b
aded N2+M (cid:10)2N +M
o
wnl M =N,N2 (6)
o
D
The mixture transport properties are modeled using Wilke’s semi-empirical mixing rule17 with species vis-
cosities calculated using Blottner’s model18 and the species thermal conductivities are determined using
Eucken’s relation.19 The species mass production rates are modeled using a finite-rate chemistry model.20
In this study, dissociation reactions are modeled using Park’s two-temperature model wherein it is assumed
that the rotational and translational energy modes of all species can be described by a single temperature
T and the vibrational energy mode of all species and the electron energy can be described by a single
tr
temperature T .21
ve
3. Heat flux at the wall
Heat transfer to the surface is composed of convective heat flux q and heat flux q due to diffusion of
conv diff
species to the surface. The convective heat flux is composed of convection q due to the translational
conv,tr
and rotational modes and q due to the vibrational mode when thermal nonequilibrium is accounted
conv,ve
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for. The convective heat flux is modeled according to Fourier’s law and species diffusion heat fluxes are
modeled using a modified form of Fick’s law.22 They are given by the following expressions:
q =q +q
conv diff
∂T
q =−κ tr,ve
conv,tr,ve tr,ve ∂n
Nsp
(cid:88)
q = h J (7)
diff i i
i=1
whereκ isthethermalconductivityforeachenergymode,h isthespeciesenthalpyandJ isthenormal
tr,ve i i
species diffusion flux. The wall is assumed isothermal and is set to the prescribed wall temperature T .
w
B. Experimental Technique
Assessment of the computations is performed using experimental tests that were conducted in the 30 kW
34 Inductively Coupled Plasma (ICP) Torch Facility23,24 at the University of Vermont. It is designed to test
5
12- scaled material samples in high enthalpy gas flows for simulation of planetary entry and Earth atmosphere
0
6.2 re-entry trajectory heating conditions. It is configured for operation with subsonic flow to simulate post
4/
1 shock conditions of high enthalpy flight for a stagnation point geometry. An advantage of the inductively
5
2
0. coupledapproachisthatthefreestreamisusuallyfreeofmetalcontaminants(e.g. copper)asthisapproach
1
OI: is electrode-less as opposed to using arc jets in which particles from the electrodes are often found in the
D
g | free stream.1
a.or The primary components of the facility are the power supply, plasma generation system and the test
a
ai chamber. The power is supplied by an induction heating generator that can deliver up to 30 kW of energy.
c.
p://ar Theplasmagenerationsystemiscomprisedoftheinductancecoil,quartzconfinementtubeandgasinjection
htt system. A radio frequency electrical power is supplied to the 6 turn helical coil that provides an oscillating
13 | magnetic field within the 36 mm internal diameter quartz confinement tube. A gas injection system delivers
0
3, 2 test gas that enters the confinement tube and thus hot plasma gas is generated. This hot plasma flows out
pril of the quartz tube into the test chamber towards the mounted test article. The design and the fabrication
A
n of the facility is described in detail in the work by Owens et al.24
o
N For this study, experimental results from POCO graphite grade DFP2 samples tested in the nitrogen
A
HIG plasma stream are used. Most ablative TPS materials are organic composites that makes it necessary to
MIC studyinteractionwithcarbonbasedmaterials. Theexperimentaltestswereaimedatmeasuringthenitrogen
F atomnumberdensityandtranslationaltemperatureinthereactingboundarylayerabovethegraphitesurface
O
Y using a two-photon laser induced fluorescence (LIF) technique. A two color infrared optical pyrometer was
T
SI used to measure surface temperature and sample ablation was also quantified by determining carbon mass
R
E
V loss from pre-and post-test mass measurements.
NI
U
y
b
d III. Numerical Setup
e
d
a
o
nl
w The test article is a 19.05 mm diameter graphite sample mounted at a distance of 116 mm from the
o
D
quartz tube exit. Hot nitrogen plasma flows out through the quartz tube at a flow rate of 38.1 standard
liters/minute. Figure 2 shows the graphite sample during exposure to the nitrogen plasma in the ICP Torch
Facility. The free stream conditions and wall temperature used for this study are based on the experimental
setupandareprovidedinTable2. ThefreestreamKnudsennumberfortheseconditionsiscalculatedtobe
5.6 x 10−4 indicating that the flow is in the continuum regime. The diameter of the test sample is chosen to
be the characteristic length. The free stream Reynolds number for this flow is 512 indicating that the flow
is laminar. The characteristic length chosen is the length of the test article plus the length of the holder.
Table 2. Freestream and wall boundary conditions.
Mach Number, Temperature, Density, ρ N Density, ρ N Density, ρ Wall Temperature,
∞ 2 N2∞ N∞
M T [K] [kg/m3] [kg/m3] [kg/m3] T [K]
∞ ∞ w
0.11 7000 3.36 x 10−3 0.35 x 10−3 3.01 x 10−3 1590
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!
4
3
5
2- Figure2. Experimentalsetupwithgraphitesampleinnitrogenplasma(sectioninboxistheportionsimulated)
01 (Source: Prof. D.G. Fletcher25).
2
6.
4/
1
5
2
0.
DOI: 1 lateTdhuesienqgutihliebrNiuAmSAcopmropgorsaitmionChoefmniitcraolgEeqnugilaisbrmiuixmtuwriethfoArpthpelicgaivtieonnste26m(pCeEraAtu).rTehanisdpproregsrsaumrec2a3nacreomcaplucute-
org | the chemical equilibrium compositions of mixtures for assigned thermodynamic states. The states may be
aa. specified by assigning two thermodynamic state variables, which are temperature (7000 K) and pressure (95
ai
arc. Torr) for this study. The results of this computation show a significant level of nitrogen dissociation. The
p:// prominent species present in the gas mixture are molecular and atomic nitrogen. Other species present are
3 | htt N+, N2+ and e− which are not included in the computation because of their negligible quantities. The high
1
0 temperature flow field is examined for thermal and thermochemical nonequilibrium effects. The plasma exit
2
April 3, v(Nel2o)cigtyasi.s cTahlceublaotuenddtaorybeco2n3d1itmio/nssfrsoetmfotrhethgeivseinmvuolalutimone flaorewsrhaotwenofin38Fsitgd. 3li.teTrshpeetremstinchuatemobferniwtraolgleins
on constructedofstainlesssteelandiswatercooled. Itissetasanon-catalyticwall27,28 withawalltemperature
N
A of 300 K. The enthalpy of the flow is calculated to be 37 MJ/kg based on CEA values for equilibrium condi-
G
HI tions. Thecatalycitymodelisappliedtothetestarticlesurface. Thegridisgeneratedusingthecommercial
C
MI meshgenerationsoftwarePointwise.29 Gridindependenceisachievedforaflowinthermalequilibriumusing
F
O a grid with 113,000 quadrilateral cells. This grid is used for all the test cases studied.
Y
T
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V
NI
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b
d
e
d
a
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w
o
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Figure 3. Boundary conditions
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IV. Results
In this section, the results of the study that use the CFD code LeMANS to determine surface catalycity
effectsonagraphitesampleexposedtoahighenthalpyandlowpressureflowareprovided. Theflowphysics
models and the species catalytic efficiency γ used for each test case are shown in Table 3. The test cases
N
arechosentostudytheinfluenceofdifferentflowphysicsassumptionsandsurfacecatalysisonthenumerical
solution. Thethreeflowphysicsmodelsaredefinedasfollows. Aflowinthermalequilibrium(TE)meansthat
allenergymodeshavethesametemperatureandtheflowisnotchemicallyreacting. Thermalnonequilibrium
(TNE) means that the flow considers vibrational nonequilibrium and the flow is not chemically reacting. In
this case, the finite rate of vibrational relaxation is accounted for. The translational and rotational modes
are assumed to be equilibrated. Thermochemical nonequilibrium (TCNE) means that the flow is both in
vibrational and chemical nonequilibrium. With these assumptions, the finite rate of chemical relaxation is
included, along with vibrational relaxation. The catalytic efficiency γ is set to zero for a non-catalytic
N
wall and is set to 1 for a fully-catalytic wall. The main calculated parameters analyzed are translational
temperature, relative nitrogen atom density, and surface heat flux.
4
3
5
2- Table 3. Different flow field conditions used.
1
0
2
6. Case Flow field condition Catalytic efficiency γ
4/ N
1
5
0.2 Case 1 Thermal equilibrium (TE) γN =0
1
OI: Case 2 Thermal nonequilibrium (TNE) γN =0
D
g | Case 3 Thermochemical nonequilibrium (TCNE) γN =0
or
a. Case 4 Thermal nonequilibrium (TNE) γ =1
aia N
arc. Case 5 Thermochemical nonequilibrium (TCNE) γN =1
p://
3 | htt The comparisons between the numerical results and experimental LIF measurements are presented for
01 translational temperature and relative nitrogen atom density in the test sample boundary layer along the
2
3, stagnation streamline and in the radial direction at a distance of 1.52 mm from the test article surface. The
pril relativenitrogenatomdensityiscalculatedbyscalingthenumericalprofileobtainedfromLeMANSforCase5
A
on (which is expected to provide the best agreement with the measurements) to agree with the measurement
N
A at the largest distance from the test sample and then the scaled factor is used to obtain the relative axial
G
HI stagnationlineandradialprofilesforallfivesimulationconditions. Thestagnationlineboundarylayerresults
C
MI are shown in Fig. 4, with translational temperature in Fig. 4(a) and the relative nitrogen atom density in
F
O Fig.4(b). Theradialprofileresultsfortranslationaltemperatureandrelativenitrogenatomnumberdensity
Y
T are shown in Figs. 5(a) and 6(a), respectively. Figure 7 presents the calculated wall heat fluxes for different
SI
R flow field conditions and values of γ. The total heat flux is shown in Fig. 7(a) and the components that
E
V
NI contribute to the total heat flux, viz. translational convective heat flux, vibrational convective heat flux
U
y and diffusive heat flux, are shown in Figs. 7(b), 7(c) and 7(d), respectively. The results are discussed in
b
d three sections. Section A presents the thermal and thermochemical nonequilibrium effects. The effects of
e
d
oa a fully-catalytic boundary condition and comparison with the experimental measurements are discussed in
nl
w Section B. The possible causes of nitrogen atom loss observed in the experiment are discussed in Section C.
o
D
A. Effect of thermal and thermochemical nonequilibrium
Results for the simulations run with different flow field physics models described in Table 3 for a non-
catalytic (γ =0) surface, i.e. Cases 1, 2 and 3, are discussed in this section. Thermal nonequilibrium
N
effects are evaluated for the vibrational mode. The simulation run time for thermal equilibrium, thermal
nonequilibriumandthermochemicalnonequilibriumcasesareapproximately90,180and185hourswitheach
simulationusing16,32,and32processors,respectively. ThesimulationforCases1and2shownosignificant
difference in the results and therefore, results for Case 1, i.e. thermal equilibrium, are not presented. The
reasonforthisagreementbetweenthetwocasesisthatatthishightemperatureof7000K,theflowismostly
dissociated. Thefractionoftotalenergycontainedinthevibrationalmodeofthemoleculesisthereforesmall,
and hence the vibrational nonequilibrium effects are negligible for a non-catalytic wall.
For the case of thermochemical nonequilibrium, a rise in temperature in the boundary layer is seen both
in the axial and radial profiles as shown in Figs. 4(a) and 5(a), respectively. The axial and radial relative
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10000 30
TTNCEN E!N ! =N =0 0 28 TTNCEN E!N ! = =0 0
9000 TTNCEN E!N ! = =1 1 26 TNE !N =N 1
ExperimNent TCNE !N = 1
24 Experiment
8000 y
sit22
K]7000 en20
re [ m d18
atu6000 to16
r a
pe N-14
m5000 e
e v12
T ti
4000 a10
el
R 8
34 3000 6
5
12- 4
20 2000
6. T = 1590 K 2
4/ wall
1
0.25 100-00.004 -0.0035 -0.003 -0.0025 -0.002 -0.0015 -0.001 -0.0005 0 -00.004 -0.0035 -0.003 -0.0025 -0.002 -0.0015 -0.001 -0.0005 0
1 Distance from the surface [m] Distance from the surface [m]
OI:
D (a) Translationaltemperature (b) RelativeN-atomdensity
g |
or
a.
aia Figure 4. Comparison of translational temperature and relative N-atom density along the stagnation line
arc. between the computational and experimental data.
p://
htt
3 |
1
0
2
3,
pril
A
n
o
AN 10000
MICHIG 9000 TTTNNCEEN E!!NN ! ==N =01 0
OF STCamNEpl !eN r =a d1ius = 0.0095m
Y 8000 Experiment
T
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ER K]
NIV e [7000
U ur
by at6000
ed er
d p
oa m
ownl Te5000
D
4000
3000
2000
0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
Distance from centerline [m]
(a) Translationaltemperature (b) Translationaltemperaturecontours
Figure 5. (a) Comparison of translational temperature between the computational and experimental data
in the radial direction at a distance of 1.52 mm from the stagnation point. (b) Translational temperature
contours for thermochemical nonequilibrium (γ=1) showing the region of radial measurement.
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12
TNE ! = 0
N
TCNE ! = 0
N
TNE ! = 1
N
TCNE ! = 1
10 SampleN radius = 0.0095m
y Experiment
sit
n
e
m d 8
o
t
a
-
N
e 6
v
ti
a
el
R
4
4
3
5 2
2- 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016
1
20 Distance from centerline [m]
6.
4/
1 (a) RelativeN-atomdensity (b) RelativeN-atomdensitycontours
5
2
0.
1
OI: Figure 6. Comparison of relative N-atom density between the computational and experimental data in the
org | D rthaderiamlodcihreecmtiiocnalantoanedqisutialinbcreiuomf 1(.γ5=21m)mshofrwoimngththeestraeggnioantioonf rpaodiinatl.m(bea)sRureelamtievnet.N-atom density contours for
a.
a
ai
c.
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p:// nitrogen atom density profiles for this case as shown in Figs. 4(b) and 6(a), respectively, show a loss in the
htt
3 | number of nitrogen atoms in comparison with the thermal nonequilibrium case. The reason for this loss is
1
0 explainedbyasmallbutfinitenetrateofrecombinationreactionsinthechemicallyreactingnonequilibrium
2
April 3, flinotwo.acScionucentt.hDeufleowtoitshcehheimghicacollnycreenatcrtaitniogn, tohfenditirsosgoecniataitoonm-rsecinomthbeinfraeteiostnreraemac,tiaolnonggivweinthbythEeqre.l6atiisvetalokneng
n
o characteristic flow time associated with the subsonic velocity, recombination dominates over dissociation.
N
A This explanation is confirmed by plotting the normalized mixture total and species number densities for
G
HI the thermal and thermochemical nonequilibrium cases as shown in Fig. 9(a). The number densities are
C
MI normalizedbytheirrespectivevaluesatadistanceof4mm(approximatethermalboundarylayerthickness)
F
O from the stagnation point. The relative nitrogen atom, nitrogen molecule and total mixture number density
Y
T overlayeachotherforthermalnonequilibrium. Forthecaseofthermochemicalnonequilibrium, thenitrogen
SI
ER atomnumberdensityincreasesslowlyandthenitrogenmoleculenumberdensityincreasesmorerapidlythan
V
NI thetotalnumberdensity,indicatinganeteffectofrecombinationresultinginanincreaseinnitrogenmolecule
U
y concentration. The influence of this chemical nonequilibrium can be seen in the increased wall heat flux in
b
ed Fig. 7. As a result of recombination, some energy is transferred into the vibrational mode because of the
d
a
o additionofnitrogenmolecules. ItseffectcanbeseeninFig.7(c)bytheincreasedvibrationalconvectiveheat
nl
w
o fluxforthermochemicalnonequilibriumascomparedtothermalnonequilibrium. Themaximumcontribution
D
to the total heat flux is from the translational-rotational energy modes for these cases. The diffusive heat
flux is negligible for all cases with a non-catalytic wall. Figure 8 shows a comparison of translational
temperature contours between the thermochemical nonequilibrium (top half) and thermal nonequilibrium
(bottomhalf)simulations. Ariseintemperaturecanbeseenalongthestagnationlineforthethermochemical
nonequilibrium flow condition. This rise in temperature can be explained by the plot of nitrogen atom and
molecule mole fractions along the stagnation line as shown in Fig. 9(b). An increase in nitrogen molecules
anddecreaseinnitrogenatomscanbeseenforthermochemicalnonequilibriumandisexplainedbytheeffect
ofchemicalnonequilibriumcausingthereleaseofenergyduetorecombinationofnitrogenatomstomolecules
and therefore causing a rise in temperature in the flow field.
B. Effects of surface catalysis
The effects of a fully-catalytic test article surface (γ=1) on the boundary layer parameters and surface
properties are discussed in this section. It can be seen in Fig. 4(b) that there is a decrease in relative
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Distance from stagnation point [m] Distance from stagnation point [m]
(c) Vibrationalconvectiveheatflux (d) Diffusiveheatflux
Figure 7. Comparison of wall heat flux between the computational and experimental results for different test
conditions listed in Table 3.
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