Rovibrational internal energy excitation and dissociation of - CNR
Transcript of 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
Outline
Outline
Introduction
NASA ARC database for N2 + N system
Rovibrational collisional model
1D shock-tube simulations
Full Master equationCoarse graining model
Conclusion
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 3 / 18
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 4 / 18
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 5 / 18
NASA ARC database for N2 + N system
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
NASA ARC database for N2 + N system
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 7 / 18
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 8 / 18
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
]
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 9 / 18
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
)
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 10 / 18
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 11 / 18
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 12 / 18
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 13 / 18
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
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 15 / 18
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]
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 16 / 18