Post on 10-Apr-2020
PECOSPredictive Engineering and Computational Sciences
Detailed and simplified kinetic mechanisms for highenthalpy flows
Application to the analysis of the Fire II flight experiment
Marco Panesi?, Anne Bourdon†, Arnaud Bultel‡, Thierry Magin§
? Institute for Computational Engineering and Sciences, The University of Texas at Austin, U.S.A.† CNRS Research Fellow, EM2C Laboratory
‡ CORIA, CNRS UMR 6614, Universite de Rouen§von Karman Institute for Fluid Dynamics
Symposium in Honor of Prof Mario Capitelli
January 31st, 2011Marco Panesi Non-equilibrium ionization January 31st , 2011 1 / 22
Outline
1 Introduction
2 Atomic and Molecular Energy Levels
3 Coupled Fluid & Collisional Radiative modelsKinetic ProcessesRadiative ProcessesFluid Model and Radiation Transfer
4 ResultsFIRE II: non-equilibrium ionizationEAST: Comparison with shock tube data.Grouping of the levels
5 Conclusions
Marco Panesi Non-equilibrium ionization January 31st , 2011 2 / 22
Introduction
Motivations and Objectives of the Project
Pecos
0 100 200
Radiative Heating [W/cm2]
0
0.005
0.01
0.015
0.02
Mar
gina
l PD
F σ = 45.54 [W/cm2]
Mode = 44.08 [W/cm2]
µ = 76.69 [W/cm2]
Specair (Laux)
Goals• Development of an accurate kinetic mechanism for earth entry applications.
• Determination of a reduced mechanism for CFD applications.
Bultel, A. et al., “Collisional-radiative model in air for earth re-entry problems”Physics of Plasmas, 2006, 13, 11
Marco Panesi Non-equilibrium ionization January 31st , 2011 3 / 22
Atomic and Molecular Energy Levels
Atomic StructureAtomic chemical components: N,O, N+, O+
NITROGEN
0 5 10 15 20Energy [eV]
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
Nor
mal
ized
Pop
ulat
ion
[m-3
]NISTAbba
N II (3P
0)
• Nitrogen 46 lumped levels: Combination of real and lumped levels (NIST 381).
• Oxygen 40 lumped levels: Combination of real and lumped levels (NIST 614).
Marco Panesi Non-equilibrium ionization January 31st , 2011 4 / 22
Atomic and Molecular Energy Levels
Molecular structureN2 system NO+ system
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6R, a. u.
0
0.1
0.2
0.3
0.4
0.5
0.6
Vr,
s a. u
.
X
A
B
C
1.5 2 2.5 3 3.5 4 4.5 5 5.5 6R, a. u.
0
0.1
0.2
0.3
0.4
0.5
0.6
Vr,
s a. u
.
X
A
Schwenke D. AIAA-2007-811
• Molecular chemical components: N2, NO, O2, N+2 , NO+, O+
2
• Electronic specific treatment of the electronic molecular systems (27 states).• Boltzmann assumption for the ro-vibrational structure, except for NO+.
Tv,Me = Tv,N2X Tr,Me = Tr,N2X
Marco Panesi Non-equilibrium ionization January 31st , 2011 5 / 22
Coupled Fluid & Collisional Radiative models Kinetic Processes
Kinetic Processes⇒ Collisional excitation (/ionization) and de-excitation (heavy/light).
I Atomic processes:
A(Ei) + C ↔ A(+)(Ej) + C(+e) C ∈ [e,H]
I Molecular processes, (Averaged over the ro-vibrational structure)
M(Ei) + C ↔M(+)(Ej) + C(+e) C ∈ [e,H]
⇒ Collisional dissociation (heavy/light)
⇒ Exchange reactions (Zeld’ovich reactions)
⇒ Charge exchange
⇒ Dissociative recombination / Associative ionizationI NO+(X1Σ+, v) + e↔ N + O, Motapon et al.I O+
2 , N+2 , Boltzmann averaged values.
I (Not included in the present model)
⇒ Over 100 K elementary processes included
Bultel, A. et al., “Collisional-radiative model in air for earth re-entry problems”Physics of Plasmas, 2006, 13, 11
Marco Panesi Non-equilibrium ionization January 31st , 2011 6 / 22
Coupled Fluid & Collisional Radiative models Radiative Processes
Line radiationThe atomic bound-bound radiation
Ni(v, E0i ) + hν (n, dΩν) Nj(v, E
0j ) (1)
Nj(v, E0j ) + hν (n, dΩν)→ Ni(v, E
0i ) + 2hν (n, dΩν) (2)
Detailed balance
Bj,i,(ν) =c2
8πhν3Aj,i,(ν) gjBj,i,(ν) = giBi,j,(ν)
The B coefficients defined originally by Einstein, and still sometimes usedin literature, differ from the Einstein-Milne coefficients by a factor (c/4π).
Marco Panesi Non-equilibrium ionization January 31st , 2011 7 / 22
Coupled Fluid & Collisional Radiative models Radiative Processes
Radiative Recombination and photo-ionization
The atomic photoionisation corresponds to:
Ni(v, E0i ) + hν (n, dΩν) N+
j (v, E+j ) + e−
(ve, d
3ve)
(3)
Q(0,+)i,j,(ν) = 2
(g+j
g0i
)me
(hν)2c2EeQ(+,0)
j,i,(Ee)
We define the cross section for induced free-bound processes as follows
Q(0,+)j,i,(ve)
Q(0,+)j,i,(ve)
=
(c2
2hν3
)
Marco Panesi Non-equilibrium ionization January 31st , 2011 8 / 22
Coupled Fluid & Collisional Radiative models Radiative Processes
Transition RatesBound-Bound rates[
dn(i,s)
dt
]=
∑j>i
[Aj,ins,j − (Bi,jns,i − Bj,ins,j)
∫ ∞0
GνΦi,jν dν
]
−∑i>j
[Ai,jns,i − (Bj,ins,j − Bi,jns,i)
∫ ∞0
GνΦi,jν dν
](4)
Bound-Free rates[dn(i,s)
dt
]+(i,s)
= n+(j,s) neve
∫ ∞0
Q(0,+)j,i,(εe)
εe exp (−εe)dεe
+ n+(j,s) neve
∫ ∞0
Gν Q(0,+)j,i,(εe)
εe exp (−εe)dεe
[dn(i,s)
dt
]−(i,s)
= n(i,s)
∫ ∞0
GνhνQ(0,+)i,j,(ν)dν
Marco Panesi Non-equilibrium ionization January 31st , 2011 9 / 22
Coupled Fluid & Collisional Radiative models Radiative Processes
Radiative Transfer Equation
µdIλ(τ, µ)
dτλ+ Iλ(τλ, µ) =
ηλκλ
(τλ) = Sλ(τλ) (5)
Incident Intensity:
Gλ(τ) = 2π
[I+λ (τλ,b)E2(τλ) + I−λ (τλ,s)E2(τλ,s − τλ) +
∫ τ
τb
SλE1 (τλ − τ ′λ) dτ ′λ
+
∫ τs
τ
SλE1 (τ ′λ − τλ) dτ ′λ
]Radiative heating and its divergence
qλ(τ) = 2π
[I+λ (τλ,b)E3(τλ) +
∫ τ
τb
SλE2(τλ − τ ′λ)dτ ′λ
− I−λ (τλ,s)E3(τλ,s − τλ)−∫ τs
τ
SλE2(τ ′λ − τλ)dτ ′λ
]Marco Panesi Non-equilibrium ionization January 31st , 2011 10 / 22
Coupled Fluid & Collisional Radiative models Fluid Model and Radiation Transfer
Modeling of non-equilibrium flows
• Euler eqs.: conservation of mass for species i, momentum and totalenergy
d
dt
ρiρuρE
+d
dx
ρiuρu2 + pρuH
=
Miωi0
−∇ · qrad
⇒ MultiT models: additional energy conservation eqs., e.g. vibrational
energy eq.
d
dt(ρem) +
d
dx(ρuem) = Ωm −∇ · qmrad + · · ·
⇒ Radiation transport models
µdIλ(τ, µ)
dτλ+ Iλ(τλ, µ) = Sλ(τλ)
Marco Panesi Non-equilibrium ionization January 31st , 2011 11 / 22
Coupled Fluid & Collisional Radiative models Fluid Model and Radiation Transfer
Radiation Coupling
Loosely coupled (explicit coupling) strategy
• Flow quantities SHOCKING
U = [Ni, Ti, p]T
• Spectral quantities HPC-RAD
Iλ = Iλ (ελ, κλ)
• Divergence and Intensity
I = [ωrad, ~∇ · q]
SHOCKING
HPC-RAD
Spectral Properties
RADIATIONTRANSPORT
PTiNi
Marco Panesi Non-equilibrium ionization January 31st , 2011 12 / 22
Results
Results• Fire II - Fully coupled
• EAST - Comparison with experiments
• Fire II - Reduction of the model
References:
Panesi, M. et al. “Analysis of the Fire II Flight Experiment by means of a Collisional RadiativeModel”
Journal of Thermophysics an Transfer, 2009, 23, 236-248
Panesi, M. et al. “Electronic Excitation of atoms and molecules for the Fire II Flight Experiment”Journal of Thermophysics an Transfer, 2011, accepted
Panesi, M. et al. “Non-equilibrium ionization phenomena behind shock waves”27th International Symposium on Rarefied Gas Dynamics, 2010
Marco Panesi Non-equilibrium ionization January 31st , 2011 13 / 22
Results FIRE II: non-equilibrium ionization
FIRE IIObjective
• Study the behavior of the electronically excited states ofatomic and molecular species in the post shock area.
• Investigate the validity of the Q.S.S. assumption.
• Characterization of the ionization process.
Time [s] 1634p1 [Pa] 2.0T1 [K] 195u1 [m/s] 11 360p2 [Pa] 3827T2 [K] 62 377u2 [m/s] 1899
Flow characteristic quantities
Marco Panesi Non-equilibrium ionization January 31st , 2011 14 / 22
Results FIRE II: non-equilibrium ionization
Flowfield quantities
0 0.02 0.04 0.06 0.08 0.1Distance from the shock [m]
0
10000
20000
30000
40000
50000
60000
70000
Tem
pera
ture
[K
] TT
V
0 0.02 0.04 0.06 0.08 0.1Distance from the shock [m]
0.0
5.0×1020
1.0×1021
1.5×1021
2.0×1021
2.5×1021
3.0×1021
Num
ber
Den
sity
[m
3 ]
Thick limitThin limitCoupled calculation
Figure: Post-shock temperature (left) and electron number density (right) profilesfor a fluid particle as a function of the distance from the shock
Marco Panesi Non-equilibrium ionization January 31st , 2011 15 / 22
Results FIRE II: non-equilibrium ionization
Internal distribution functions
0 5 10 15 20Energy [eV]
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
Nor
mal
ized
Pop
ulat
ion
[m-3
] Thin LimitBoltzmannThick LimitCoupled calculation
0 5 10 15 20Energy [eV]
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
Nor
mal
ized
Pop
ulat
ion
[m-3
] Thin LimitBoltzmannThick LimitCoupled calculation
Figure: Electronic energy distribution function for atomic nitrogen (left) andoxygen (right) at 1 cm from the shock front
Marco Panesi Non-equilibrium ionization January 31st , 2011 16 / 22
Results FIRE II: non-equilibrium ionization
Atomic spectra
0 500 1000 1500 2000Wavelength [nm]
101
102
103
104
105
Inte
nsity
[W
/cm
2 -µm
-sr]
0 500 1000 1500 2000Wavelength [nm]
101
102
103
104
105
Inte
nsity
[W
/cm
2 -µm
-sr]
Figure: Atomic spectra: non-equilibrium (left) and equilibrium (right) atomic lineradiation at 1 cm from the shock front
Marco Panesi Non-equilibrium ionization January 31st , 2011 17 / 22
Results EAST: Comparison with shock tube data.
EAST experiment: Simplified radiation
P = 13 [Pa] and Vs = 9.165 Km.s−1
0 1 2 3 4Distance from the shock front [cm]
0
50000
1e+05
1.5e+05
2e+05
I / D
EAST exp.AbbaModified AbbaPark TT
v
∆ λ (nm) = [700,830] ∪ [850,880]
0 1 2 3 4Distance from the shock front [cm]
0
2
4
6
8
10
I / I
EQ
EAST exp.AbbaModified AbbaPark TT
v
∆ λ (nm) = [700,830] ∪ [850,880]
ABSOLUTE MEASUREMENT RELATIVE MEASUREMENT
Boltzmann results over-predict the radiative peak.by a factor 4
Marco Panesi Non-equilibrium ionization January 31st , 2011 18 / 22
Results Grouping of the levels
Grouping of the high-lying excited states
0 2 4 6 8 10 12 14Energy Levels [eV]
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
Popu
latio
n/de
gene
racy CR ABBA
BoltzmannReduced ABBA
GROUPING STRATEGY COMPARISON REDUCED/FULL MODEL
Marco Panesi Non-equilibrium ionization January 31st , 2011 19 / 22
Results Grouping of the levels
Acknowledgments
The author want to acknowledge:
NASA Ames Research Center, USA• Richard Jaffe
• Winifred Huo
• Yen Liu
• David Schwenke
• Alan Wray
• Duane Carbon
for the very insightful discussions.
Marco Panesi Non-equilibrium ionization January 31st , 2011 20 / 22
Conclusions
CONCLUSIONS:
We have studied the departures of the electronic energy populations fromBoltzmann distribution for one-dimensional air flows obtained in ashock-tube.
⇒ Validation and improvement of the model is obtained comparing ourresults with shock tube experiments.
⇒ The atomic (and molecular) excited species distribution are found todepart from Boltzmann.
⇒ Importance of self-consistent coupling of collisional and radiativeprocesses.
FUTURE WORK:
⇒ Improvement of dissociation model: Bin model (N2).
⇒ Modeling of diatomic and triatomic molecular radiation.
⇒ Non-Boltzmann treatment of the free electrons (Colonna).
Marco Panesi Non-equilibrium ionization January 31st , 2011 21 / 22
Conclusions
Happy Birthday !!!
The Abba Group
Marco Panesi Non-equilibrium ionization January 31st , 2011 22 / 22