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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

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2 Content Measurement of time histories of vibrational temperature Т v and concentration of oxygen molecules behind a front of shock wave. Determination of O 2 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.

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3 Experiment : Spectral region and technique: Measurement of light absorption in region =210-260 nm (electronic transitions X 3 -g →B 3 -u (Schumann-Runge system)). Experimental setup : Shock tube; gas in high pressure section is O 2 / H 2 / Не; gas in low pressure section is undiluted O 2. Quantities measured : Initial gas pressure in low pressure section P 1 (1 - 2 Torr); velocity of shock wave front V (3 - 4.5 km/s), absorbance in gas behind the front of shock wave– I/I 0. Gas parameters behind the shock front: Temperature range: 4000-10800 К, Gas pressure: 0.2 - 1 atm

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4 Damper tank Pumping system Filling system О2О2 H2H2 O2O2 VM-1 U Power of PMP PT Pulsed lamp Spectrograph Ajilent 54624A; Ajilent DSO-5014A PMP Ar He HPC M LPC Experimental setup

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5 The light absorption and absorption cross sections The Beer law describes the ratio I/I 0 as: where I 0 and I are the intensities of source radiation past through the test section before and after the shock wave arrival, respectively; σ(T v,T) is the spectral absorption cross-section per molecule (cm 2 ), l is the length of optical path (cm), n is the concentration of absorbing molecules (cm -3 ); T v is the vibrational temperature of molecules, T is gas temperature. In the present work that corresponds to optically thin layer of gas studied.

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6 Initial conditions in gas: 100% O 2, P 1 = 1 Torr, V=4.4 km/s, T 0 =10670K; А - λ=260 nm; В - λ=250 nm; С - λ=230 nm; D - λ=220 nm. Absorption oscillogramms

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7 Measured and calculated absorption cross-sections of oxygen

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8 Profiles of absorptions I/I 0 and vibrational temperature behind the shock wave front. 100% O 2, P 1 = 2 Torr, V =3.07 km/s, T 0 = 5300 K.

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9 Time histories of vibrational temperature including equilibrium region (Т 0 =8620 и 9410 К)

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10 T v -time histories of vibrational temperatures at different initial conditions. A B C D A – 100% O 2, p 1 =2 Torr, V=3.07 km/s, T 0 =5300 K; B - 100% O 2, p 1 =1 Torr, V=3.4 km/s, T 0 =6470 K; C - 100% O 2, p 1 =1 Torr, V=3.95 km/s, T 0 =8620 K; D - 100% O 2, p 1 =0.8 Torr, V=4.44 km/s, T 0 =10820 K.

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11 Fig. a. Black points are measured maximal vibrational temperature. Line 1 is an equilibrium vibrational temperature calculated on the assumption T v =T before dissociation onset, 100% О 2. Dependence of maximum vibrational temperatureon initial gas temperature

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12 Scheme of experimental data handling for determination of kinetic coefficients

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13 Determination of T 2, p 2, ρ 2, γ O2, γ O - parameters behind the shock front Conservation equations system on the shock discontinuity Known quantities Molar-mass concentration of О 2 molecules (mole/g )

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14 Vibrational relaxation of oxygen at T>6000 K Millikan&White systematics: Landau&Teller theory, harmonic oscillator, one-quantum transitions: For oxygen: Park model: state-to-state transition rate coefficients are based on the forced harmonic oscillator model.

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15 Profiles of temperatures, density and O 2 concentration (Т 0 =10820К) The kinetic equation for the O 2 - concentration can be presented in the form: Here k d = k d (O 2 -O 2 ) is a rate constant of dissociation near the shock front.

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16 Dissociation rate constant Curves: 1 is the data [1], 2 is the value k 0 recommended in [2] for conditions T v =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 Black and white points are the rate constants measured in conditions of thermal non-equilibrium (T v ≠T) and thermal equilibrium (T v =T), respectively.

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17 Numerical modeling Baulch et al., 1976; Millikan R.C., White D.R., 1963. Ibraguimova L.B., Smekhov G.D., Shatalov O.P., 2004 In our calculations the following values were used as initial version: is coupling factor. - Treanor&Marrone model, 1962

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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.

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19 Testing Kuznetsov model at Т≤6000К 100% O 2. Fig. A: P 1 =2 Torr, V = 3.07 km/s; Fig. B: P 1 =1.5 Torr, V = 3.22 km/s; Fig. С: P 1 = 1.5 Torr, V=3.4 km/s. The curve 1 is calculation using Kuznetsov model.

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20 Testing Kuznetsov and Macheret-Fridman models at Т>6500K 100% O 2 ; P 1 =1 Torr, V = 4.13 km/s, Т 0 =9410 К. Points are measured values T v and T. Calculations using Kuznetsov model, curves: 1 -, k 0 ; 2, 2a –, 0.2∙k 0 (0.2∙Z ) Calculation using Macheret-Fridman model, curve 3:, k 0.

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21 Vibrational relaxation of oxygen Millikan&White systematics: Landau&Teller theory, harmonic oscillator, one-quantum transitions: For oxygen: Park model: state-to-state transition rate coefficients are based on the forced harmonic oscillator model.

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22 Temperature dependence of vibrational relaxation time. 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.

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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.

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24 Thank you for your attention!

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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.

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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.

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27 Спектры полных сечений поглощения в системе Шумана-Рунге молекулы О 2 для равновесных условий (T = T v = T r ): 1 - T = 1000 K; 2 - T = 2000 K; 3 - T = 3000 K; 4 - T = 10000 K.

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28 Degree of oxygen dissociation

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29 Degree of oxygen dissociation

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30 Absorption oscillogramm, λ=230 nm, 100% O 2 ; P 1 =1 Torr; V =4.13 km/s; T 0 = 9410 K. Radiation signals: 1 - I 0 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. Time resolution Δt = ΔS / V ~ 0.1 μs

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31 Comparison of measured and calculated absorption cross-sections σ=f(T,T v ) 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=Т к ) at T 0 ≤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 O 2 molecules was simulated for Schumann-Runge system (λ=130-270 нм) in cases of both equal (T=T v ) and unequal vibrational and translational (rotational) temperatures (T≠T v ) at range 1000-10000K.

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32 Determination of vibrational temperature t i → σ 1 /σ 2 = 2.6 → T v =3610 K 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.

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