Rovibrational internal energy excitation and ... - (cnr) - (bari)

Rovibrational internal energy excitation and dissociation
of molecular nitrogen in hypersonic flows
Thierry MAGIN, 1 Marco PANESI, 2 Anne BOURDON, 3
Richard JAFFE, 4 and David SCHWENKE 4
Thanks to: Winifred Huo, 4 Galina Chaban, 4 Yen Liu, 4 and Christophe Laux 3
1 Aeronautics and Aerospace Department, von Karman Institute for Fluid Dynamics, Belgium
2 Institute for Computational Engineering and Sciences, The University of Texas at Austin
3 EM2C Laboratory, CNRS UPR 288 – Ecole Centrale Paris, France
4 NASA Ames Research Center
Symposium in honour of Prof. Mario Capitelli on the occasion of his 70 th birthday
Chemical Physics of Low Temperature Plasmas
31 Jan – 1 Feb 2011, University of Bari, Italy
Prof. 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 N 2 + N system
Rovibrational collisional model
1D shock-tube simulations
Full Master equation
Coarse 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 at
v>10km/s (Moon and Mars returns)
For a correct interpretation of experimental measurements
In flight
In ground wind-tunnels
Calculated and measured intensity N 2 (1+) system
⇒ Standard nonequilibrium models for
hypersonic flows were mainly
developed in the 1980’s (correlation
based)
e.g. dissociation model of Park
Multitemperature model:
T = T r , T v = T e = T ele
Average temperature √ T T v for
fictitious 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 for
reentry flows based on microscopic theory and applying
them to macroscopic scale
⇒ work at the interface between computational chemistry, experimental
measurements, and CFD
Computational methods
Physico−chemical models
Experimental data
N 3 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 N 2 + N system
Internal energy excitation and dissociation derived from
ab initio calculations
Characterization of nonequilibrium air chemistry from first principles
by 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 N 2 are split into
Bound levels below the dissociation energy
Quasi-bound or predissociated levels above the dissociation energy
but below the centrifugal barrier of the potential
Potential curve of N 2 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 N 2 + 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 potentials
2 Classical trajectory method for the reaction cross-sections
e.g. N 2 + N system:
9390 (v,J) rovibrational energy
levels for N 2
23 × 10 6 reaction mechanism
N 2(v, J) + N ↔ N + N + N
N 2(v, J) ↔ N + N
N 2(v, J) + N ↔ N 2(v ′ , J ′ ) + N
Experimental data are used only for
validation
⇒ This model has a wide application
range (physics based)
N 3 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 rovibrational
energy levels i = (v, J) for N 2 , and for N atoms coupled with eqs. of
conservation of momentum and total energy
⎛ ⎞ ⎛ ⎞ ⎛ ⎞
ρ i
ρ i u M N2 ω i
d
⎜ρ N
⎟
dt ⎝ρu⎠ + d
⎜ ρ N u
⎟
dx ⎝ρu 2 + p⎠ = ⎜M N ω N
⎟
⎝ 0 ⎠
ρE
ρuH
0
... 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
dt ρ v + d
dx (ρ v u) = M N2 ω v
The energy levels are lumped for each v assuming a rotational energy
population 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 and
include in a bin all levels with similar energies
25x10 -19
20x10 -19
Energy [ J ]
15x10 -19
10x10 -19
5x10 -19
0.0
0 2000 4000 6000 8000 10000
Index [ - ]
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 average
energy
∑
i∈I
Ē k = k
g i E i
,
ḡ k
with the bin degeneracy ḡ k = ∑ i∈I k
g i
The energy level populations are assumed to be uniform within a bin
n i
¯n k
= 1 ḡ k
g i ,
i ∈ I k
The initial population of the bins is assumed to follow a Maxwell-Boltzmann
distribution
( )
¯n k
= ḡk −
n N2
¯Q(T int ) exp Ē k
k B T int
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-Hugoniot
jump relations
The 1D Euler eqs. for collisional model comprises
Mass conservation eqs. for N
Mass conservation eqs. for the 9390 rovibrational levels of N 2
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 by
LSODE
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 11 / 18

Results
Simulation of internal energy excitation and dissociation
processes behind a strong shockwave in N 2 flow
Simulations based on different models:
Full master eq. model
Coarse graining model
Vibrational collisional model
Multitemperature model for the 2-species mixture with simplified
mechanism
Free stream (1), post-shock (2), and LTE (3) conditions
1 2 3
T [K] 300 62,546 11,351
p [Pa] 13 10,792 13,363
u [km/s] 10 2.51 0.72
x N 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 , T v (v = 1), T int (v = 0, J = 10)
Temperature [K]
70000
60000
50000
40000
30000
20000
T full CR: no pred.
T int
T full CR
T int
T vibrational CR
T v
T 2-species Park
Mole fractions [-]
1
0.8
0.6
0.4
N 2 full CR : no predis.
N
N 2 full CR
N
N 2 vibrational CR
N
T v
2.0×10 -6 4.0×10 -6 6.0×10 -6 8.0×10 -6 10×10 -6
10000
0.2
0
2.0×10 -6 4.0×10 -6 6.0×10 -6 8.0×10 -6 10×10 -6
Time [s]
0
Time [s]
Free stream: T 1 = 300 K, p 1 = 13 Pa, u 1 = 10 km/s, x N1 ∼ 2.8%, 10 −5 s ↔ 2.5 cm
⇒ Thermalization and dissociation occur after a larger distance for the
full collisional model
Prof. Capitelli’s symposium (U Bari) Rovibrational collisional model 31 Jan – 1 Feb 2011 13 / 18

Results
Rovibrational energy population of N 2
n(v, J) in function of E(v, J) at t = 2.6 × 10 −6 s (7mm)
A rotational temperature T r (v) is introduced for each vibrational energy level v:
PJ max(v)
n(v, J)∆E(v, J)
J=0
=
PJ max(v)
n(v, J)
J=0
PJ max(v)
J=0
“ ”
−∆E(v,J)
g J ∆E(v, J) exp
kTr (v)
“ ”
−∆E(v,J)
kTr (v)
PJ max(v)
g
J=0 J exp
⇒ 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 applications
Coarse-graining model: lumping the energy levels into bins as a
function of their global energy
70000
Temperature [K]
60000
50000
40000
30000
20000
2
5
10
20
40
100
150
Full CR
10000
0
0
2×10 -6 4×10 -6 6×10 -6 8×10 -6 10×10 -6
Time [s]
Without predissociation reactions
Free stream: T 1 = 300 K, p 1 = 13 Pa, u 1 = 10 km/s, x N1 ∼ 2.8%, 10 −5 s ↔ 2.5 cm
⇒ The uniform distribution allows to describe accurately the internal
energy 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 the
internal energy relaxation and dissociation processes behind a strong
shockwave in a nitrogen flow
The 9390 rovibrational energy levels of the nitrogen molecule of the ab
initio NASA Ames database are taken into account in the master eq.
Thermalization and dissociation occur after a larger distance for the full
collisional model than for the multitemperature model and vibrational
collisional model (distinct rotational temperatures per vibrational level)
The uniform distribution bin model allows to describe accurately the
internal energy relaxation and dissociation processes based on a
reduced number of eqs.
Further development
Lessons learned will allow to investigate the N 2 (v, J) + N 2 (v ′ , J ′ )
system (AIAA 2010-4517)
A coarse graining model based on a M-B distribution of the levels
within a bin is being developed for CFD applications (AIAA 2010-4332)
A sound Chapman-Enskog method is being derived for
multitemperature models [ESA WG, D. Giordano]
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