detailed and simplified kinetic mechanisms for high...

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


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).


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


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


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).



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

)



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



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)


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


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


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



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



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



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


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


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


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.


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).


Conclusions

Happy Birthday !!!

The Abba Group


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