Experimental study of Non-Equilibrium Dissociation of Molecular Oxygen
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Transcript of Experimental study of Non-Equilibrium Dissociation of Molecular Oxygen
1
Experimental study of Non-Equilibrium Dissociation
of Molecular Oxygen
N.G. Bykova, L.B. Ibraguimova, O.P. Shatalov, Yu.V. Tunik, I.E. Zabelinskii
Institute of Mechanics, Lomonosov Moscow State University, Moscow, Russia
4-th EUROPEAN CONFERENCE FOR AEROSPACE SCIENCES (EUCASS)
St. Petersburgh, July 17-22, 2011
2
Content• Measurement of time histories of vibrational temperature Тv and
concentration of oxygen molecules behind a front of shock wave.
• Determination of O2 dissociation rate constants both in the thermal non-equilibrium and thermal equilibrium zones behind the shock front.
• Determination of oxygen vibrational relaxation time at high temperatures.
• Testing some models of molecule dissociation.
3
Experiment:
Spectral region and technique:Measurement of light absorption in region =210-260 nm (electronic transitions X3-g →B3-u (Schumann-Runge system)).
Experimental setup: Shock tube; gas in high pressure section is O2 / H2/ Не; gas in low pressure section is undiluted O2.
Quantities measured: Initial gas pressure in low pressure section P1 (1 - 2 Torr); velocity of shock wave front V (3 - 4.5 km/s), absorbance in gas behind the front of shock wave– I/I0.
Gas parameters behind the shock front: Temperature range: 4000-10800 К, Gas pressure: 0.2 - 1 atm
4
Damper tank
Pumping system
Fillingsystem
О2
H2 O2
VM-1
U
Power ofPMP
PT
Pulsed lamp
Spectrograph
Ajilent 54624A;Ajilent DSO-5014A
PMP
ArHe
HPC M LPC
Experimental setup
460 465 470 475 480 485 490 495 500 505 510 515 5200,0
0,1
0,2
0,3
0,4
3
2
1
T=Tv
I,V
t, s
5
The light absorption and absorption cross sections
The Beer law describes the ratio I/I0 as:
where I0 and I are the intensities of source radiation past through the test section before and after the shock wave arrival, respectively;
σ(Tv,T) is the spectral absorption cross-section per molecule (cm2),
l is the length of optical path (cm), n is the concentration of absorbing molecules (cm-3); Tv is the vibrational temperature of molecules, T is gas temperature.
In the present work that corresponds to
optically thin layer of gas studied.
)),(exp(0
lnTTII
v
4.03.00 nlII
6
Initial conditions in gas: 100% O2 , P1 = 1 Torr, V=4.4 km/s,
T0 =10670K; А - λ=260 nm; В - λ=250 nm; С - λ=230 nm; D - λ=220 nm.
Absorption oscillogramms
420 421 422 423 424 4250,000
0,002
0,004
0,006
0,008
0,010
0,012A
I, V
t, s
260nm, V=4.4 km/s
415 416 417 418 419 4200,00
0,01
0,02
0,03
0,04
0,05
B
250 mm, V=4.39 km/s
I, V
t, s
346 347 348 349 3500,00
0,02
0,04
0,06
0,08
C
I, V
t, s
230 nm, V=4.4 km/s
417 418 419 420 421 4220,00
0,01
0,02
0,03D
I, V
t, s
220 nm, V=4.4 km/s
7
Measured and calculated absorption cross-sections of oxygen
1000 2000 3000 4000 5000 6000
0
2x10-19
4x10-19
6x10-19
8x10-19
Т, К
см2 210 нм 230 нм 240 нм 250 нм 260 нм 270 нм
8
Profiles of absorptions I/I0 and vibrational temperature behind the
shock wave front. 100% O2, P1 = 2 Torr, V =3.07 km/s, T0 = 5300 K.
-1 0 1 2 3 4 5 6 7-0,05
0,00
0,05
0,10
0,15
0,20
0,25
0,30
0,35
0,40
240 nm (1) 260 nm (2) 250 nm
-ln
(I/I
0)
t, s 0 1 2 3 4 50
1000
2000
3000
4000
5000 A
- 240 nm- 250 nm- 260 nm- 240 nm- on ratio
T1=4300 K
tm=0.72 s
Tfr=5300 K
Tv, K
t, s
9
0 1 2 3 4 5 6 7 8 9 100
1000
2000
3000
4000
5000
6000
7000
8000
Tv, К
t, mcs
100% О2, Т
0=9410К
0 5 10 15 20 250
1000
2000
3000
4000
5000
6000
7000
Травн
220,260,230нмТ
0=8620К, 100% О
2
Tv, K
t, мкс
Time histories of vibrational temperature including equilibrium
region (Т0=8620 и 9410 К)
10
Tv-time histories of vibrational temperatures
at different initial conditions.
0 1 2 3 4 50
2000
4000
6000
8000Т
0=5300КT
v, K
t, s0 1 2 3 4
0
2000
4000
6000
8000T
0=6470КT
v,K
t, s0 1 2 3 4
0
2000
4000
6000
8000Т
0=8620К
Tv,K
t, s0 1 2 3
0
2000
4000
6000
8000T=10820K
Tv, K
t, s A B C D
A – 100% O2, p1=2 Torr, V=3.07 km/s, T0=5300 K; B - 100% O2, p1=1 Torr, V=3.4 km/s, T0=6470 K;
C - 100% O2, p1=1 Torr, V=3.95 km/s, T0=8620 K; D - 100% O2, p1=0.8 Torr, V=4.44 km/s, T0=10820 K.
11
Fig. a. Black points are measured maximal vibrational temperature. Line 1 is an equilibrium vibrational temperature calculated on the assumption Tv=T before
dissociation onset, 100% О2.
Dependence of maximum vibrational temperatureon initial gas temperature
4000 6000 8000 10000
4000
6000
80001
Tv, K
T0, K
a
8800 9000 9200 9400 9600 9800
6000
7000
8000
9000
2
б
12
Scheme of experimental data handling for determination of kinetic
coefficients
)(,,,,)(22 222 labiOOOlabvlab tfpTnlawBeertTt
)();,( 22 OOTTk VTvdiss
13
Determination of T2, p2, ρ2, γO2, γO-parameters behind the shock front
))exp((,22 0 lnIInT OOv
A
OO N
n
2
2
})2(
2)2(
1)1(
1
2)1()1(22
)2()2(
2222
211221
20625.02
2/2/
1,
,,
VHvH
RTp
vpVpvV
i
i
ii
i
i
i
i
i
i Conservation equations system on the shock discontinuity
Known quantities
Molar-mass concentration of О2 molecules (mole/g)
14
Vibrational relaxation of oxygen at T>6000 K
BATp 3/1)lg(
kT
RTpZTPZ
/8,)]/exp(1[ 01
10
1100 ))}/exp(1(/8{ TPRTkTp
13/114 )]/exp(1[)7.172exp(108.8 TTTp
Millikan&White systematics:
Landau&Teller theory, harmonic oscillator, one-quantum transitions:
13/13/110 ))/exp(1()exp( ~,lg TBTTpTP
For oxygen:
Park model: state-to-state transition rate coefficients are based on the forced harmonic oscillator model.
15
Profiles of temperatures, density and O2 concentration (Т0=10820К)
-0,2 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4
0
2000
4000
6000
8000
10000 T2
Tv
100% O2, T
0=10820 K
T, K
t, s0,0 0,2 0,4 0,6 0,8 1,0
0,020
0,022
0,024
0,026
0,028
0,030
0,032
t, s
0,0 0,2 0,4 0,6 0,8
8,0x10-6
1,2x10-5
1,6x10-5
100% O2, T
0=10820K
, g.cm -3
t, s
22
2
2
OdO kdt
d
The kinetic equation for the O2- concentration can be presented in the form:
Here kd= kd(O2-O2) is a rate constant of dissociation near the shock front.
16
Dissociation rate constant
Curves:
1 is the data [1], 2 is the value k0 recommended in [2]
for conditions Tv=T,
[1] Baulch D.L., Drysdale D.D., Duxbury J., Grant S.J. 1976. Evaluated Kinetic Data for High Temperature Reactions. Vol.3.
[2] Ibraguimova L.B., Smekhov G.D., Shatalov O.P. 1999. Fluid Dynamics. 34:153-157
)( 22 OOkd
Black and white points are the rate constants measured in conditions of thermal non-equilibrium (Tv≠T) and thermal equilibrium (Tv=T), respectively.
1,0 1,5 2,0 2,5
10
11
12
13
3
1
2 O2+O
2=2O+O
2
lg k
, cm
3 .mo
le-1
.s-1
T-1
, 10- 4
K-1
17
Numerical modeling
AB
BAi
irii
idi N
NNNkGNkE
dt
d
()(0
BAirii
ABidii
AB NNNkNNkdt
dN
),,()(),( 0 vvd TTZTkTTk
)(0 Tk Baulch et al., 1976; Millikan R.C., White D.R., 1963.
Ibraguimova L.B., Smekhov G.D., Shatalov O.P., 2004
)( 220 OO
)( 20 OO
In our calculations the following values were used as initial version:
),( vTTZ is coupling factor.
- Treanor&Marrone model, 1962
18
Coupling factors
Kuznetsov model takes into account the preferred dissociation from high vibrational levels.
Kuznetsov N.M. 1971. Theor. Exp. Chem. 7:22-33 .
Dissociation from both high and low vibrational levels is considered in Macheret-Fridman model.
The quantity L has different expressions for rate constants under collisions “molecule-molecule” and
“molecule-atom”.
Sergievskaya A.L., Losev S.A., Macheret S., Fridman A. 1997. AIAA-Paper, 1997-2580.
TTE
T
TTTZ
vv
vv
11exp
)exp(1
)exp(1),( *
TTk
DL
a
11exp 0
TTk
DL
T
TTTZ
v
vv
11exp)1(
)/exp(1
)/exp(1),( 0
19
Testing Kuznetsov model at Т≤6000К
100% O2.
Fig. A: P1 =2 Torr, V = 3.07 km/s; Fig. B: P1=1.5 Torr, V = 3.22 km/s; Fig. С: P1= 1.5 Torr, V=3.4 km/s.
0 1 2 3 4 50
1000
2000
3000
4000
5000
B
1
T0=5800 K
Tv, K
t, mcs
0 1 2 3 4
1000
2000
3000
4000
5000
A
1
Т0=5300К
T, K
t, mcs0 1 2 3 4
0
1000
2000
3000
4000
5000
C
1
T0=6470К
Tv,K
t, 10- 6
s
The curve 1 is calculation using Kuznetsov model.
20
Testing Kuznetsov and Macheret-Fridman models at Т>6500K
100% O2; P1=1 Torr, V = 4.13 km/s, Т0=9410 К. Points are measured values Tv and T.
Calculations using Kuznetsov model, curves: 1 - , k0 ; 2, 2a – , 0.2∙k0 (0.2∙Z ) Calculation using Macheret-Fridman model, curve 3: , k0 .
0,0 0,5 1,0 1,5 2,0
0
2000
4000
6000
8000
10000
2a
T0=9410 K
3
2
1
T, K
t, s
0,0 0,5 1,0 1,5 2,00
2000
4000
6000
8000
10000
2a
T0=9410 K
3
2
1
T, K
t, s
5.10 5.10
5.10
21
Vibrational relaxation of oxygen
BATp 3/1)lg(
kT
RTpZTPZ
/8,)]/exp(1[ 01
10
1100 ))}/exp(1(/8{ TPRTkTp
13/114 )]/exp(1[)7.172exp(108.8 TTTp
Millikan&White systematics:
Landau&Teller theory, harmonic oscillator, one-quantum transitions:
13/13/110 ))/exp(1()exp( ~,lg TBTTpTP
For oxygen:
Park model: state-to-state transition rate coefficients are based on the forced harmonic oscillator model.
22
Temperature dependence of vibrational relaxation time .)( 22 OO
0,04 0,05 0,06 0,07 0,08-7,5
-7,0
-6,5
-6,0
-5,5
-5,0
based on Landau-Teller theory (1936)
Park, 2006
Milliken&White,1963
- Bykova et al.,2004 - Losev,Generalov,1962 - present work
C
O2- O
2
B
A
lg(p),
atm
.s
T-1/3, K
White triangles and points are
the experimental data [1, 2],
respectively.
Black triangles are the data of
present work.
Curves А and В are the data of
[3] and [4], respectively. Curve C
was taken from Park study [5].
[1] Losev S.A. and Generalov N.A. 1962.
[2] Bykova N.G., Zabelinskii I.E., Ibraguimova L.B. et al. 2004.
[3] Millikan R.C. and White D.R. 1963.
[4] Ibraguimova L.B., Smekhov G.D., Shatalov O.P. 2004.
[5] Park Ch., 2006.
23
Conclusions 1. Measurements of vibrational and translational temperatures behind the front
of a shock wave made it possible to ascertain that the vibrational relaxation and dissociation zones are separated at T< 6500 K, and the vibrational-translational equilibrium is attained before the dissociation onset.
2. At T > 6500 K the vibrational relaxation of molecules proceeds close to the shock front jointly with the dissociation, and the vibrational-translational equilibrium has no time to be attained before the dissociation onset.
3. The rate constants of oxygen molecule dissociation are determined for the collisions under both thermal equilibrium and thermal nonequilibrium conditions on the temperature range from 6500 to 10800 K.
4. It is shown that at T > 5000K the vibrational relaxation time of oxygen molecules decelerates by comparison with Millikan&White and Landau&Teller dependences.
5. It is shown that theoretical models completely describe the measured temperature profiles at temperatures in shock front less 6500 K. However, at the temperatures higher than 7000 K neither of the tested models describes the measured temperature profiles.
24
Thank you for your attention!
25
References• [1] Kovach E.A., Losev S.A., Sergievskaya A.L. 1995. Models of two-
temperature chemical kinetics for description of molecule dissociation in strong shock waves. Chem. Phys. Reports. 14:1353-1387.
• [2] Zabelinskii I.E., Ibraguimova L.B., Shatalov O.P., Tunik Yu.V. Experimental study and numerical modeling of profiles of oxygen vibrational temperature in a strong shock wave. Flight Physics. Ser. Progress in Propulsion Physics. - Moscow: Torus Press, 2011 3:71-82.
• [3] Thermodynamic properties of individual substances. Reference book. V.1. Bd.2. Ed. by V.P.Glushko. 1978. Moscow. Nauka. 327p. (In Russian).
• [4] Baulch D.L., Drysdale D.D., Duxbury J., Grant S.J. 1976. Evaluated Kinetic Data for High Temperature Reactions. Vol.3. London. Butterworths. 593 p.
• [5] Ibraguimova L.B., Smekhov G.D., Shatalov O.P. 1999. Dissociation rate constants of diatomic molecules under thermal equilibrium conditions. Fluid Dynamics. 34:153-157.
• [6] Treanor C.E., Marrone P.V. (1962) Effect of dissociation on the rate of vibrational relaxation. Phys. of Fluids. 5: 1022-1026.
• [7] Kuznetsov N.M. 1971. Kinetics of molecule dissociation in molecular gases. Theor. Exp. Chem. 7:22-33 (in Russian).
• [8] Sergievskaya A.L., Losev S.A., Macheret S., Fridman A. 1997. Selection of two-temperature chemical reaction models for nonequilibrium flows. AIAA-Paper, 1997-2580.
26
References
• [9] Millikan R.C., White D.R. Systematics of vibrational relaxation. 1963. J. Chem. Phys. 39:3209-3213.
• [10] Losev S.A. and Generalov N.A. 1962. On study of excitation of vibrations and decay of oxygen molecules at high temperatures. Soviet Phys. – Dokl. 6:1081-1085
• [11] Landau L., Teller E. 1936. Theory of sound dispersion. Phys. Zs. Sow. 10:34-43.
• [12] Ibraguimova L.B., Smekhov G.D., Shatalov O.P. 2004. On the correct representation of vibrational relaxation time of diatomic molecules at high temperatures. In book "Physics of Extrem States of Matter - 2004". Chernogolovka, p. 97-98.(In Russian).
• [13] N.G. Bykova, I.E. Zabelinskii, L.B. Ibraguimova et al. Numerical and experimental study of kinetic processes in atmospheric plasma. Report No 4736. 2004. Institute of Mechanics of Moscow State University, Moscow. 66 p. (In Russian).
• [14] Ch. Park. Thermochemical relaxation in shock tunnels. AIAA Paper 2006-0585.
27
Спектры полных сечений поглощения в системе Шумана-Рунге молекулы О2 для равновесных условий (T = Tv = Tr ): 1 - T = 1000 K; 2 -
T = 2000 K; 3 - T = 3000 K; 4 - T = 10000 K.
1 2 0 1 6 0 2 0 0 2 4 0 , n m
0
4 e-0 1 8
8 e -0 1 8
1 .2 e -0 1 7
1 .6 e -0 1 7
, cm 2
1
2
3
4
28
Degree of oxygen dissociation
0,0 0,5 1,0 1,5 2,0
0,0
0,1
0,2
0,3
T0=10400K T
0=9410K
T0=6470K
T0=8620K
T0=10820 K
t, s
29
Degree of oxygen dissociation
0,0 0,2 0,4 0,6 0,8 1,0
0,0
0,1
0,2
0,3
0,4
experiment
Kuznetsov model, kd
Kuznetsov model, kd/ 5
2
1
T0=9410K
t, s
30
Absorption oscillogramm, λ=230 nm, 100%
O2; P1=1 Torr; V =4.13 km/s; T0= 9410 K.
Radiation signals:
1 - I0 is a radiation signal of light source in absence of shock wave,
2 – I is a radiation signal changed by absorption in heated gas behind the shock front.
320 325 330 3350,01
0,02
0,03
0,04
2
tm
I
I0
4
2
31
I, V
t,s
)),(exp(0
lnTTII
v
Time resolution Δt = ΔS / V ~ 0.1 μs
31
Comparison of measured and calculated absorption cross-sections σ=f(T,Tv) for
thermal equilibrium conditions
Bykova N.G., Zabelinskii I.E., Ibraguimova L.B., Shatalov O.P. // Optics and Spectrosc. 2008. V.105. № 5. P. 674.
Absorption cross-sections measured in thermal equilibrium conditions (Т=Тк)
at T0 ≤6000 K were compared with theoretical ones.
Bykova N.G., Kuznetsova L.A. // Optics and Spectrosc. 2008. V.105. № 5. P. 668.
Theoretical absorption spectra of O2 molecules was simulated for Schumann-Runge system (λ=130-270 нм) in cases of both equal (T=Tv) and unequal vibrational and translational (rotational) temperatures (T≠Tv) at range 1000-10000K.
32
Determination of vibrational temperature
ti → σ1 /σ2 = 2.6 → Tv =3610 K3000 3500 4000 45002,0
2,2
2,4
2,6
2,8
3,0
3,2
Tv=3610 K
Parameter T: 3000K 4000К 5000K 6000K
Tv, K
v
calc
TII
II
lNI
I
2
1
exp
2
1
20
10
0
21
ln
)(ln
,ln
,
The method of determination of vibrational temperature was described in following works:
1. Zabelinskii I.E., Ibraguimova L.B., Shatalov O.P., Fluid Dynamics, 2010, v. 45( 3). P.485-492.
2. I.E. Zabelinskii, L.B. Ibraguimova, O.P. Shatalov, Yu.V. Tunik. CD Proceedings of 3th European Conference for Aero-Space Sciences (EUCASS), 6-9 July 2009, Versailles, France.