Shock Waves by DSMC. D. Bruno C.N.R. - I.M.I.P. Italy

Transcription

1 Shock Waves by DSMC D. Bruno C.N.R. - I.M.I.P. Italy

2 Overview Shock Waves Rankine-Hugoniot relations DSMC simulation of shock waves The shock profile Translational nonequilibrium Rotational relaxation Vibration and dissociation

3 Shock waves The Euler description predicts the existence of singularities related to the steepening of compression waves v " c c "T 1 2

4 Rankine-Hugoniot relations ρ 1 T 1 v 1 ρ 2 " 1 u 1 = " 2 u 2 T 2 v p 1 + " 1 u 1 = p2 + " 2 u 2 h u 1 2 = h u 2 2

5 Perfect- vs. real-gas p = nkt c = " kt m Ma = u c kt h = c p m " c p = const. &# 2 = $+1 ( (# 1 ' ( p 2 ( = ) p 1 ( )Ma 2 2+ ( $%1)Ma 2 ( 2 1+$ 2Ma %1 ) $+1

6 Particle simulations " # 1 $ % Kn = " $ = f ( Ma ) Ma < 2 Typical re-entry conditions h = 80 "120 km # T = 150 " 500 K % p = 10 "2 $ "1 mtorr% u = 5 "12 km /s & % ' Ma = 2 " 25

7 DSMC simulation Shock Shocked gas Unperturbed gas

8 Shock waves in atomic gas " = " ( g) 1 Density Temperature Argon T=300 K; n=10 15 cm -3 Ma=10 Common models: HS, VHS, VSS Conclusion: shock profile determined by viscosity x, cm

9 Velocity distribution function 10 0 T=300 K T, K T=9637 K x, cm 10-3 Mach ε, ev ε/kt v, cm/s D. Bruno, M. Capitelli, S. Longo, Effect of translational kinetics on chemical rates in a Direct Simulation Monte Carlo model gas phase detonation, Chem Phys. Lett (2003).

10 Translational nonequilibrium A " B + #E 8 " = 1.2 D = D, p 0,! 0, "=0 u, p,!, ". 0 $ < E 0 th " A#B = / ' %" 0 1& E th * 0 ), $ - E ( $ + th x/x 1/2

11 Translational nonequilibrium (II) 10-8 T/T K, cm 3 s x/x 1/ ,2 0,4 0,6 0,8 1 T 1 /T J. B. Anderson, L. N. Long, Direct Simulation Monte Carlo Simulation of Chemical Reaction Systems: Prediction of Ultrafast Detonations, Journal of Chemical Physics (2003).

12 Rotational relaxation de R dt = " E R " E R 0 # R " R = Z R " 0 Z R = Z R ( T) J. G. Parker, Rotational and vibrational relaxation in diatomic gases, Phys Fluids (1959).

13 DSMC models Continuous energy Discrete energy Larsen-Borgnakke SICS QCT I. D. Boyd, Relaxation of discrete rotational energy distributions using a Monte Carlo method, Phys Fluids A (1993). K. Koura, A generalization for Parker rotational relaxation model based on variable soft sphere collision model, Phys Fluids (1996). K. Koura, Monte Carlo direct simulation of rotational relaxation of diatomic molecules using classical trajectory calculations: Nitrogen shock wave, Phys Fluids (1997).

14 Results Oxygen Mach=10; T=300 K E, ev x/! F. Robben, L. Talbot, Experimental study of the rotational distribution function of nitrogen in a shock wave, Phys Fluids (1964).

15 Vibration and chemistry O atom concentration for heat flux calculation NO properties define radiation signature Dissociation behind the shock shows delay time Dissociation rate behind shock is below thermal value

16 State-to-state vibrational model Vibrational relaxation time is comparable to chemical relaxation: vibrational nonequilibrium Nonequilibrium vibrational distribution function and chemical rates: vibration-chemistry-vibration coupling Discrete vibrational distribution VT processes VV processes A 2 ( v) + M " A 2 ( w) + M A 2 ( v) + B 2 ( w) " A 2 ( v + l) + B 2 ( w # s)

17 Vibrationally favoured chemistry Chemical reaction rates favoured by vibrational energy content Nonequilibrium vibrational distribution function affects chemical rates Dissociation Exchange Zeldovich A 2 ( v) + M " 2A + M AB( v) + C " AC( w) + B ( ) + O " NO( w) + N ( ) + N " NO( w) + O N 2 v O 2 v

18 Shock profiles Nitrogen 1, Mach = 16; T 0 = 200 K T, K! N 1, , , , Note: how to choose boundary conditions 2, , x/" D. Bruno, M. Capitelli, F. Esposito, S. Longo, P. Minelli, Direct simulation of non-equilibrium kinetics under shock conditions in nitrogen, Chem. Phys. Lett (2002).

19 Results: VT models Nitrogen flow about a sphere V = 5.1 km/s ; T = 190 K Vibrational relaxation model has influence on T v and VdF L-B model exhibits too fast relaxation Rarefied flows (Kn~0.01) exhibit strong VdF nonequilibrium VV processes reduce VdF nonequilibrium S. F. Gimelshein, I. D. Boyd, Q. Sun, M. S. Ivanov, DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows, AIAA paper (1999).

20 Results: vibrational favouring Oxygen stagnation streamline V = 5.1 km/s ; T = 180 K Dissociation model vs. equilibrium rate constant Shock tube data (QSS rate) sensitive to VT model / equilibrium rate, not to dissociation model Vibrational favouring changes with temperature Rotation is more effective than translation D. C. Wadsworth, I. J. Wysong, Vibrational favoring effect in DSMC dissociation models, Phys. Fluids (1997).

21 Results: CID model Experimental (O 2 /N 2 ): shock tube QSS dissociation, incubation time P i" f = # i" f Theoretical: QCT results # Tot Nonadiabatic effects at high energies VHS/VSS are based on IPL and matched to (low temp) transport properties (effects on reaction prob or comp cost) Adjusting parameters to match thermal rates gives no guarantee Reproducing rate coefficients relies on assumed form for cross section DSMC models developed for low vibrational levels I. J. Wysong, R. A. Dressler, Y. H. Chiu, I. D. Boyd, Direct Simulatrion Monte Carlo dissociation model evaluation: comparison to measured cross sections, JTHT (2002).

22 Results: NO formation BSUV-2 flight data provide NO and O UV emissions (5.1 km/s) Above 80 km, calculations without CVD are too low N 2 ( v) + O " NO + N ( a) O 2 v ( ) + N " NO + O ( b) Vibrational favouring improves results (over Park s) by increasing O production Excited electronic state kinetics involved in nonequilibrium UV radiation At 3 km/s the rate is determined by Nitrogen VT and (a) dominates At 9 km/s nonequilibrium is substantial but dissociation is rapid and (b) dominates D. Boyd, G. V. Candler, D. A. Levin, Dissociation modeling in low density hypersonic flows of air, Phys. Fluids (1995). C. E. Treanor, I. V. Adamovich, M. J. Williams, J. W. Rich, Kinetics of nitric oxide formation behind shock waves, JTHT (1996).

23 O 2 -O 2 VT rates O 2 (1)+O 2 -->O 2 (0)+O 2 O 2 (29)+O 2 -->O 2 (28)+O 2 k, cm 3 /s T, K Billing 2004 Billing 1992 Armenise FHO-FR Kunc MQST k, cm 3 /s Billing 2004 FHO-FR MQST T, K C. Coletti, G. D. Billing, Vibrational energy transfer in molecular oxygen collisions, Chem. Phys. Lett (2004). G. D. Billing, R. E. Kolesnick, Vibrational relaxation of oxygen. State to state rate constants, Chem. Phys. Lett (1992).

24 Multiquantum transitions S. H. Kang, J. A. Kunc, Energy dependence of vibration-translation transitions in collisions of neutral particles, AIAA paper (1994).

25 O 2 (v)+o-->3o! diss, A Oxygen T rot = 5000 K ,5 1 1,5 2 2,5 3 ", ev 46 Vibrational favouring Cross section for high vibrational levels exceeds VHS (effects on comp cost) Extension to higher energies needed F. Esposito, M. Capitelli, Quasiclassical trajectory calculations of vibrationally specific dissociation cross-sections and rate constants for the reaction O+O 2 (v)->3o, Chem. Phys. Lett (2002).

26 Conclusions Achievements DSMC is established as simulation tool for hypersonic flows in the rarefied regime Improved thermo-chemical modeling able to reproduce available data Limitations Benchmark studies at high temperature still lacking Treatment of polyatomics in its infancy Unable to treat plasma and radiation effects

27 DSMC models: vibration Larsen-Borgnakke with variable Z v Multiple Quantum Step Transition ITFITS/LCCS (monoquantum, HO) Nonperturbative semiclassical FHO-FR Quasiclassical energy transfer F. Bergemann,I. D. Boyd, New discrete vibrational energy model for the Direct Simulation Monte Carlo method, Prog. In Aero. And Astro (1994). P. Vijayakumar, Q. Sun, I. D. Boyd, Vibrational-translational energy exchange models for the direct simulation Monte Carlo method, Phys Fluids (1999). K. Koura, A set of model cross sections for the Monte Carlo simulation of rarefied real gases: Atomdiatom collisions, Phys. Fluids (1994). I. V. Adamovich, Three-dimensional analytic model of vibrational energy transfer in molecule-molecule collisions, AIAA J (2001). S. F. Gimelshein, M. S. Ivanov, G. N. Markelov, Yu. E. Gorbachev, Statistical simulation of nonequilibrium rarefied flowswith quasiclassical vibrational energy transfer models, JTHT (1998).

28 DSMC models: chemistry LCCS WVB ME Threshold line TCE VFD Semiclassical Multichannel C. Rebick, R. D. Levine, Collision induced dissociation: a statistical theory, J. Chem. Phys (1973). K. Koura, A set of model cross sections for the Monte Carlo simulation of rarefied real gases: Atomdiatom collisions, Phys. Fluids (1994). M. A. Gallis, J. K. Harvey, The modeling of chemical reactions and thermochemical nonequilibrium in particle simulation computations, Phys. Fluids (1998). S. O. Macheret, A. A. Fridman, I. V. Adamovich, J. W. Rich, Mechanisms of nonequilibrium dissociation of diatomic molecules, AIAA paper (1994); S. O. Macheret, I. V. Adamovich, Semiclassical modeling of state-specific dissociation rates in diatomic gases, J. Chem. Phys (2000). B. L. Haas, I. D. Boyd, Models for Direct Monte Carlo simulation of coupled vibration-dissociation, Phys. Fluids A (1993). M. S. Ivanov, G. N. Markelov, S. F. Gimelshein, Statistical simulation of reactive rarefied flows: numerical approach and applications, AIAA paper (1998).

29 DSMC models: assessment Vibration-Translation models S. F. Gimelshein, I. D. Boyd, Q. Sun, M. S. Ivanov, DSMC modeling of vibration-translation energy transfer in hypersonic rarefied flows, AIAA paper (1999). Vibrational favouring D. C. Wadsworth, I. J. Wysong, Vibrational favoring effect in DSMC dissociation models, Phys. Fluids (1997). Chemistry models I. J. Wysong, R. A. Dressler, Y. H. Chiu, I. D. Boyd, Direct Simulatrion Monte Carlo dissociation model evaluation: comparison to measured cross sections, JTHT (2002).

30 Experiments K. L. Wray, Shock-tube study of the coupling of the O 2 -Ar rates of dissociation and vibrational relaxation, J. Chem. Phys (1962). W. S. Watt, A. L. Myerson, Atom formation rates behind shock waves in oxygen, J. Chem. Phys (1969). K. L. Wray, E. V. Feldman, P. F. Lewis, Shock-tube study of the effect of vibrational energy of N 2 on the kinetics of the O-N 2 ->NO-N reaction, J. Chem. Phys (1970). W. D. Breshears, P. F. Bird, J. H. Kiefer, Density gradient measurements of O2 dissociation in shock waves, J. Chem. Phys (1971). H. G. Hornung, Induction time for nitrogen dissociation, J. Chem. Phys (1972). W. D. Breshears, P. F. Bird, Precise measurements of diatomic dissociation rates in shock waves, 14th Intl. Symposium on Combustion, Pittsburgh, USA, D. J Kewley, H. G. Hornung, Chem. Phys. Lett (1974). (Shock tube, N 2 ) H. Oertel, Oxygen vibrational and dissociation relaxation behind regular reflected shocks, J. Fluid Mech (1976). W. H. Wurster, C. E. Treanor, M. J. Williams, Kinetics of UV production behind shock waves in air, AIAA paper (1990). S. P. Sharma, 18th Intl. Shock Tube Symposium, Tohoku, Japan, (Shock tube, N 2 ) P. W. Erdman, E. C. Zipf, P. Espy, L. C. Howlett, D. A. Levin, R. J. Collins, G. V. Candler, Measurements of ultraviolet radiation from a 5-km/s bow shock, JTHT (1994). S. Nonaka, H. Mizuno, K. Takayama, C. Park, Measurement of shock standoff distance for sphere in ballistic range, JTHT (2000).

31 Other References K. Koura and H. Matsumoto, Variable Soft Sphere Molecular Model for Inverse-Power-Law or Lennard Jones Potential, Physics of Fluids A (1991). K. Fujita, T. Abe, Coulpled rotation-vibration-dissociation kinetics of nitrogen using QCT models, AIAA (2003). G. D. Billing, L. Wang, Semiclassical calculations of transport coefficients and rotational relaxation of nitrogen at high temperatures, J. Phys. Chem (1992). J. A. Kunc, Impact of Dissociation on Viscosity of Gases, Physics of Plasmas (1995).