Rovibrational internal energy excitation and dissociation of - CNR

Rovibrational internal energy excitation and dissociationof molecular nitrogen in hypersonic flows

Thierry MAGIN,1 Marco PANESI,2 Anne BOURDON,3

Richard JAFFE,4 and David SCHWENKE4

Thanks to: Winifred Huo,4 Galina Chaban,4 Yen Liu,4 and Christophe Laux3

1 Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Belgium2 Institute for Computational Engineering and Sciences, The University of Texas at Austin

3EM2C Laboratory, CNRS UPR 288 – Ecole Centrale Paris, France4NASA Ames Research Center

Symposium in honour of Prof. Mario Capitelli on the occasion of his 70th birthday

Chemical Physics of Low Temperature Plasmas

31 Jan – 1 Feb 2011, University of Bari, ItalyProf. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 1 / 18

Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 2 / 18

Outline

Outline

Introduction

NASA ARC database for N2 + N system

Rovibrational collisional model

1D shock-tube simulations

Full Master equationCoarse graining model

Conclusion


Introduction Motivation

Motivation: developing high-fidelity nonequilibrium models

⇒ Understanding thermo-chemical nonequilibrium effects is important

For an accurate prediction of the radiative heat flux for reentries atv>10km/s (Moon and Mars returns)For a correct interpretation of experimental measurements

In flightIn ground wind-tunnels

Calculated and measured intensity N2(1+) system

⇒ Standard nonequilibrium models forhypersonic flows were mainlydeveloped in the 1980’s (correlationbased)

e.g . dissociation model of ParkMultitemperature model:T = Tr ,Tv = Te = Tele

Average temperature√

T Tv forfictitious Arrhenius rate coefficient


Introduction Objective

Objective: developing reduced nonequilibrium models forreentry flows based on microscopic theory and applyingthem to macroscopic scale

⇒ work at the interface between computational chemistry, experimentalmeasurements, and CFD

Experimental data

Computational methods

Physico−chemical models

N3 Potential Energy Surface

NASA Ames Research Center

Blast capsule simulation

VKI COOLFluiD / Mutation

Diagnostics in plasma jet

VKI Plasmatron



Internal energy excitation and dissociation derived fromab initio calculations

Characterization of nonequilibrium air chemistry from first principlesby the chemistry group of NASA Ames Research Center

⇒ Papers AIAA 2008-1208, 2008-1209, 2009-1569, 2010-4517, RTO-VKI LS 2008

The 9390 (v,J) rovibrational energy levels for N2 are split intoBound levels below the dissociation energyQuasi-bound or predissociated levels above the dissociation energybut below the centrifugal barrier of the potential

Potential curve of N2 for J=0,20,40,. . .

⇒ Complementary work at Bari (PHYS4ENTRY) and U Minnesota (MURI)Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 6 / 18


A novel approach for nonequilibrium models...

Computation from first principles at NASA ARC in 2 steps:1 Quantum chemistry calculations to generate realistic nuclear

interaction potentials2 Classical trajectory method for the reaction cross-sections

e.g. N2 + N system:9390 (v,J) rovibrational energylevels for N2

23× 106 reaction mechanism

N2(v, J) + N↔ N + N + NN2(v, J)↔ N + NN2(v, J) + N↔ N2(v′, J′) + N

Experimental data are used only forvalidation

⇒ This model has a wide applicationrange (physics based)

N3 Potential Energy Surface

NASA Ames Research Center


Rovibrational collisional model Master equation

Detailed chemical mechanism coupled with a flow solver

Full master eq. of conservation of mass for the 9390 rovibrationalenergy levels i = (v , J) for N2, and for N atoms coupled with eqs. ofconservation of momentum and total energy

d

dt

ρi

ρN

ρuρE

+d

dx

ρiuρNu

ρu2 + pρuH

=

MN2ωi

MNωN

00

... but computationally too expensive for 3D CFD applications

⇒ reduction of the chemical mechanism by lumping the energy levels i :e.g . vibrational state-to-state models (AIAA 2009-3837, 2010-4335)

d

dtρv +

d

dx(ρvu) = MN2ωv

The energy levels are lumped for each v assuming a rotational energypopulation following a Maxwell-Boltzmann distribution at T


Rovibrational collisional model Bin model

Coarse graining model

Another lumping scheme is to sort the (v,J) levels by energy andinclude in a bin all levels with similar energies

0 2000 4000 6000 8000 10000Index [ - ]

0.0

5x10-19

10x10-19

15x10-19

20x10-19

25x10-19

Ene

rgy

[ J

]


Rovibrational collisional model Bin model

Coarse graining model

The energy for level i = (v , J) is constant in bin k and equal to the averageenergy

Ek =

∑i∈Ik

giEi

gk,

with the bin degeneracy gk =∑

i∈Ikgi

The energy level populations are assumed to be uniform within a bin

ni

nk=

1

gkgi , i ∈ Ik

The initial population of the bins is assumed to follow a Maxwell-Boltzmanndistribution

nk

nN2

=gk

Q(Tint)exp

(−Ek

kBTint

)


Rovibrational collisional model Numerical method

Numerical method

The post-shock conditions are obtained from the Rankine-Hugoniotjump relations

The 1D Euler eqs. for collisional model comprises

Mass conservation eqs. for NMass conservation eqs. for the 9390 rovibrational levels of N2

Momentum conservation eq.Total energy conservation eq.

The backward reaction rate coefficients are based on microreversibility

The conservative form is transformed into an ODE system solved byLSODE


Results

Simulation of internal energy excitation and dissociationprocesses behind a strong shockwave in N2 flow

Simulations based on different models:

Full master eq. modelCoarse graining modelVibrational collisional modelMultitemperature model for the 2-species mixture with simplifiedmechanism

Free stream (1), post-shock (2), and LTE (3) conditions1 2 3

T [K] 300 62,546 11,351

p [Pa] 13 10,792 13,363

u [km/s] 10 2.51 0.72

xN 0.028 0.028 1


Results

Temperature and composition profiles

Temperatures T , Tv (v = 1), Tint (v = 0, J = 10)

2.0×10-6

4.0×10-6

6.0×10-6

8.0×10-6

10×10-6

Time [s]

0

10000

20000

30000

40000

50000

60000

70000

Tem

per

ature

[K

]

T full CR: no pred.T

int

T full CR T

int

T vibrational CRT

v

T 2-species ParkT

v

2.0×10-6

4.0×10-6

6.0×10-6

8.0×10-6

10×10-6

Time [s]

0

0.2

0.4

0.6

0.8

1

Mole

fra

ctio

ns

[-]

N2 full CR : no predis.

NN

2 full CR

NN

2 vibrational CR

N

Free stream: T1 = 300 K, p1 = 13 Pa, u1 = 10 km/s, xN1 ∼ 2.8%, 10−5 s↔ 2.5 cm

⇒ Thermalization and dissociation occur after a larger distance for thefull collisional model


Results

Rovibrational energy population of N2

n(v , J) in function of E(v , J) at t = 2.6× 10−6s (7mm)

A rotational temperature Tr (v) is introduced for each vibrational energy level v :

PJmax(v)J=0

n(v, J)∆E(v, J)PJmax(v)J=0

n(v, J)

=

PJmax(v)J=0

gJ ∆E(v, J) exp“−∆E(v,J)

kTr (v)

”PJmax(v)

J=0gJ exp

“−∆E(v,J)

kTr (v)

”⇒ The assumption of equilibrium between the rotational and

translational modes is questionable...Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 14 / 18

Results

Coarse graining model for 3D CFD applicationsCoarse-graining model: lumping the energy levels into bins as afunction of their global energy

0 2×10-6

4×10-6

6×10-6

8×10-6

10×10-6

Time [s]

0

10000

20000

30000

40000

50000

60000

70000

Tem

per

atu

re [

K]

25102040100150Full CR

Without predissociation reactions

Free stream: T1 = 300 K, p1 = 13 Pa, u1 = 10 km/s, xN1 ∼ 2.8%, 10−5 s↔ 2.5 cm

⇒ The uniform distribution allows to describe accurately the internalenergy relaxation and dissociation processes for ∼20 bins

A M-B distribution is being investigated for CFD applications


Conclusion and further development

Conclusion

A 1D rovibrational collisional model was developed to describe theinternal energy relaxation and dissociation processes behind a strongshockwave in a nitrogen flowThe 9390 rovibrational energy levels of the nitrogen molecule of the abinitio NASA Ames database are taken into account in the master eq.Thermalization and dissociation occur after a larger distance for the fullcollisional model than for the multitemperature model and vibrationalcollisional model (distinct rotational temperatures per vibrational level)The uniform distribution bin model allows to describe accurately theinternal energy relaxation and dissociation processes based on areduced number of eqs.

Further development

Lessons learned will allow to investigate the N2(v, J) + N2(v′, J′)system (AIAA 2010-4517)A coarse graining model based on a M-B distribution of the levelswithin a bin is being developed for CFD applications (AIAA 2010-4332)A sound Chapman-Enskog method is being derived formultitemperature models [ESA WG, D. Giordano]


Rovibrational internal energy excitation and dissociation of - CNR

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