AIAA JOURNAL, VOL. 34, NO. 8: TECHNICAL NOTES 1745 3 Srinivasan, R., and Mongia, H. C., "Numerical Computation of Swirling Recirculating Flows," NASA CR 165197, Sept. 1980. 4 Hogg, S., and Leschziner, M. A., "Computation of Highly Swirling Confined Flow with a Reynolds Stress Turbulence Model," AIAA Journal, Vol. 27, No. 1, 1989, pp. 57-63. 5 Jones, W. P., and Pascau, A., "Calculation of Confined Swirling Flows with a Second Moment Closure," Journal of Fluids Engineering, Vol. Ill, Sept. 1989, pp. 248-255. 6 Gibson, M. M., and Launder, B. E., "Ground Effects on Pressure Fluc- tuations in the Atmospheric Boundary Layer," Journal of Fluid Mechanics, Vol. 86, April 1978, pp. 491-511. 7 Yakhot, V., Orszag, S. A., Thangam, S., Gatski, T. B., and Speziale, C. G., "Development of Turbulence Models for Shear Flows by a Double Expansion Technique," Physics of Fluids A, Vol. 4, No. 7, 1992, pp. 1510-1520. 8 Launder, B. E., and Spalding, D. B., "The Numerical Computation of Turbulent Flows," Computer Methods in Applied Mechanics and Engineer- ing, Vol. 3, May 1974, pp. 269-289. 9 Nejad, A. S., Favaloro, S. C., Vanka, S. P., Samimy, M., and Langenfeld. C., "Application of Laser Velocimetry for Characteristics of Confined Swirling Flow," Journal of Engineering for Gas Turbines and Power, Vol. Ill, No. 1, 1989, pp. 36^45. 1() van Doormal, J. P., and Raithby, G. D., "Enhancement of the SIM- PLE Method for Predicting Incompressible Fluid Flows," Numerical Heat Transfer, Vol. 7, No. 2, 1984, pp. 147-163. H Lai, Y. G., So, R. M. C., and Przekwas, A. J., "Turbulent Transonic Flow Simulation Using a Pressure-Based Method," International Journal of Engineering Science, Vol. 33, No. 4, 1995, pp. 469-483. l2 Lai, Y. G., "Computational Method of Second-Moment Turbulence Clo- sures in Complex Geometries," AIAA Journal, Vol. 33, No. 8, 1995, pp. 1426-1432. 13 Favaloro, S., Nejad, A., Ahmed, S., Miller, T., and Vanka, S., "An Ex- perimental and Computational Investigation of Isothermal Swirling Flow in an Axisymmetric Dump Combustor," AIAA Paper 89-0620, Jan. 1989. 14 Speziale, C. G., and Thangam, S., "Analysis of an RNG Based Turbu- lence Model for Separated Flows," NASA CR 189600, Jan. 1992. lonizational Nonequilibrium Induced by Neutral Chemistry in Air Plasmas Christophe O. Laux,* Richard J. Gessman,^ and Charles H. Kruger* Stanford University, Stanford, California 94305-3032 Introduction I ONIZATIONAL nonequilibrium in plasmas can greatly affect the reactivity, transport properties (thermal and electrical con- ductivity), and radiative phenomena because of collisional coupling between the populations of bound and free electrons. Normally, departures from equilibrium in the population of free electrons are attributed to either (or both) differences between electron and gas ki- netic temperatures or finite ionization/electron recombination rates. In contrast, the computational study reported here for a recombining air plasma suggests that under appropriate circumstances ioniza- tional nonequilibrium may be caused instead by finite dissociation/ recombination rates for neutral species. Thus we find the unex- pected result that nonequilibrium populations of neutral species can cause ionizational nonequilibrium in molecular plasmas. The Received May 25, 1994; revision received Feb. 2, 1996; accepted for publication April 22,1996. Copyright © 1996 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. * Research Associate, High Temperature Gasdynamics Laboratory. Mem- ber AIAA. * Graduate Student, High Temperature Gasdynamics Laboratory. Student Member AIAA. * Professor, Vice-Provost, and Dean of Research and Graduate Policy, High Temperature Gasdynamics Laboratory. Member AIAA. consequences of this effect on the radiative power of NO in air plasmas are examined. Model This study considers ionizational nonequilibrium in a recombin- ing air plasma assumed to be thermal (equal electron and heavy particle temperatures). Although the phenomena described herein are by no means limited to thermal plasmas, they can be described more clearly with a single temperature plasma. The Chemkin solver 1 was used for one-dimensional kinetics modeling with specified ini- tial concentrations and with imposed temperature variations. Three air reaction mechanisms [Dunn and Kang, 2 Gupta et al. (GYTL), 3 and Park 4 ' 5 ] were considered. Reverse reaction rates were obtained by detailed balance using the equilibrium thermodynamic proper- ties computed by Liu and Vinokur. 6 The air plasma was assumed to be initially in chemical equilibrium at 7500 K and 1 atm. A linear temperature drop from 7500 to 4500 K within 0.6 ms was then imposed on the plasma, and the concentration evolution of the major neutral and charged species was computed with Chemkin. At each time, concentrations were normalized to their chemical equilib- rium values at the corresponding temperature. The resulting normal- ized concentrations, or nonequilibrium factors, are shown in Fig. 1. Observations derived from these results are discussed in the next section. To check the thermal plasma assumption, we have calculated the differences between the electron kinetic temperature T e , the gas kinetic temperature 7),, and the vibrational temperature T v and found that they are negligible for the conditions of this Note. For molecular plasmas with no applied external field, the electron energy equation 7 is (D 3 body—recombination where n e ,m e , and m s represent the electron number density, the electron mass, and the mass of heavy species s, respectively; S s is the so-called nonelastic energy loss factor, used as a multiplier to the rate of energy transferred by elastic collisions to model the effect of nonelastic collisions; and the term on the right-hand side represents the net rate of energy transferred to the electrons by three-body ion Temperature (K) 7500 6500 5500 4500 7500 6500 5500 4500 7500 6500 5500 4500 0.01 0.2 0.4 0.6 Time (ms) 0.2 0.4 0.6 Fig. 1 Nonequilibrium factors predicted with the reaction mechanisms of a) Dunn and Kang, b) GYTL, and c) Park. The validity of Eqs. (2), (4), and (5) for t > 0.3 ms can be verified from these figures. For instance, that the electron overpopulation factor varies as the square root of the N overpopulation factor [Eq. (4)] can be seen most easily in the logarithmic plots (a and b), where the electron overpopulation curve lies half the distance from the equilibrium line (x/x* = 1) to the N overpopulation curve.