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.