Electron and Vibrational Kinetics in Supersonic Nozzle Expansion

Vibrational and electron kinetics, as well as electronic excited states and ionization kinetics, have been coupled self consistently solving master and Boltzmann equation at the same time. These kinetics have been inserted in a quasi one-dimensional code for the high enthalpy nozzle expansion. INTRODUCTION The supersonic expansion through a nozzle flow is characterised by strong non-equilibrium conditions. Multitemperature approach does not describe correctly the vibrational distributions. In previous works [1-3] we have shown the non-Boltzmann character of the vibrational distributions in N2/N [1], and air mixtures [2,3], especially when atom recombination is dominant; starting with very high temperature in the reservoir, the gas is partially dissociated and during the expansion the recombination is strong, generating non-Boltzmann vibrational distributions. As a consequence, the global dissociation rates do not follow the Arrhenius dependence on the local temperature. If the reservoir temperature is high enough to have ionization degree of the order of lO'^-rlO", electron-molecule (e-M) collisions cannot be neglected. The conditions of the system during the supersonic expansion can be compared to post-discharge [4]: energy trapped in internal degrees of freedom (vibrational and electronic excited states) and electron kinetic energy are very high, therefore the system should relax to reach the equilibrium with the translational temperature of molecules. In the nozzle supersonic expansions there is a further difficulty due to the fact that gas temperature and pressure change during the expansion, while these quantities are constant in post-discharge systems. Even if ionization degree is high, electron-electron collisions, though very important, are not sufficient to overcome the effect of superelastic and inelastic collisions, and therefore non-Maxwell electron energy distributions are obtained [4]. To model non-equilibrium vibrational distributions in presence of non maxwellian electron energy distributions it is necessary to solve contemporary the master equations for the vibrational kinetics and the Boltzmann equation for free electrons (selfconsistent model). The self-consistent model has been applied in flow conditions for the boundary layers of hypersonic re-entering body [5] and for nozzle supersonic expansion [6], neglecting ionization and electronically excited state kinetics, showing strong effect of the self-consistent coupling in both vibrational and electron energy distribution functions (eedf); electronically excited states fraction as well as ionization degree have been considered constant. In recent work [7] we have applied the model to the conic nozzle adding the electronically excited states and ionization/recombination kinetics. The results have shown that as supposed in previous works ionization degree is practically constant, because the pressure is CP585, Rarefied Gas Dynamics: 22 International Symposium, edited by T. J. Bartel and M. A. Gain's © 2001 American Institute of Physics 0-7354-0025-3/01/$18.00 270 REPORT DOCUMENTATION PAGE Form Approved OMB No. 0704-0188 Public reporting burder for this collection of information is estibated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burder to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 09-07-2000 2. REPORT TYPE Conference Proceedings 3. DATES COVERED (FROM TO) 09-07-2000 to 14-07-2000 4. TITLE AND SUBTITLE Electron and Vibrational Kinetics in Supersonic Nozzle Expansion Unclassified 5a. CONTRACT NUMBER 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME AND ADDRESS Centra di Studio per la Chimica del Plasmi, CNR and Dip. di Chimica, Universitd di Bari, Bari, Italyxxxxx 8. PERFORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME AND ADDRESS AOARD Unit 45002 APO AP, xx96337-5002 10. SPONSOR/MONITOR'S ACRONYM(S) 11. SPONSOR/MONITOR'S REPORT NUMBER(S) 12. DISTRIBUTION/AVAILABILITY STATEMENT APUBLIC RELEASE , 13. SUPPLEMENTARY NOTES See Also ADM001341, Rarefied Gas Dynamics (RGD) 22nd International Symposium held in Sydney, Australia, 9-14 July 2000. 14. ABSTRACT Vibrational and electron kinetics, as well as electronic excited states and ionization kinetics, have been coupled self consistently solving master and Boltzmann equation at the same time. These kinetics have been inserted in a quasi one-dimensional code for the high enthalpy nozzle expansion. 15. SUBJECT TERMS 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT Public Release 18. NUMBER OF PAGES 8 19. NAME OF RESPONSIBLE PERSON Fenster, Lynn [email protected] a. REPORT Unclassified b. ABSTRACT Unclassified c. THIS PAGE Unclassified 19b. TELEPHONE NUMBER International Area Code Area Code Telephone Number 703767-9007 DSN 427-9007 Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39.18 very low, but electronically excited states change in a range of many orders of magnitude. Strong nonnon-equilibrium distributions are obtained, with a strong effect of superelastic collisions. In this work we have applied the model used in [7] to F4 nozzle [8] to study the effect of a different nozzle profile. NUMERICAL MODEL The model used to calculate the nozzle fluid dynamics is based on the quasi one-dimensional steady Euler equations [1-3] dpuA = 0 dx dP du — + pu— = dx dx du dh „ u— + — = 0 dx dx dpsyuA x pRT (1) sv _ d