On the dynamics of hot air plasmas related to lightning discharges: 1. Gas dynamics

In this paper, we first study the dynamics of hot shocks in air in cylindrical geometry coupled to multiband radiation transport and detailed air chemistry. The wide energy and length scale ranges which are covered herein includes and exceeds the ones of first and subsequent return strokes happening during lightning discharges. An emphasis is put on the NOx production and the optical power emitted by strong shocks as the ones generated by Joule heating of the air from intense current flows. The production rate of NOx, which is useful for atmospheric global modeling, is found to be between 4.5 × 1016 and 8.6 × 1016 molecules/J for all computed cases, which is in agreement with the literature. Two different radiation transport methods are used to characterize the variability of the results according to the radiation transport method. With the exact radiation solver, we show that between 15 and 40% of the energy is lost by radiation, with a percentage between 20 and 25% for averaged lightning energies. The maximal visible peak is between 7 × 108 W/m and 3 × 107 W/m obtained for, respectively, a 19 kJ/cm and a 28 J/cm energy input. The mean radiated powers in the visible range are found between 9 × 106 W/m and 2 × 105 W/m for the energies just mentioned. We discuss the agreement of these values with previous studies.

[1]  J. Green,et al.  Optical observations of terrestrial lightning by the FORTE satellite photodiode detector , 2001 .

[2]  B. Turman.  Detection of lightning superbolts , 1977 .

[3]  M. Plooster,et al.  Shock Waves from Line Sources. Numerical Solutions and Experimental Measurements , 1970 .

[4]  A. Bourdon,et al.  Air‐density‐dependent model for analysis of air heating associated with streamers, leaders, and transient luminous events , 2010 .

[5]  John I. Castor,et al.  Radiation Hydrodynamics: List of figures , 2004 .

[6]  Dinesh K. Prabhu,et al.  Computation of Radiation in the Apollo AS-501 Reentry Using Opacity Distribution Functions , 2007 .

[7]  David M. Suszcynsky,et al.  FORTE observations of simultaneous VHF and optical emissions from lightning: Basic phenomenology , 2000 .

[8]  Joseph E. Borovsky,et al.  An electrodynamic description of lightning return strokes and dart leaders: Guided wave propagation along conducting cylindrical channels , 1995 .

[9]  M. Plooster,et al.  Numerical Model of the Return Stroke of the Lightning Discharge , 1971 .

[10]  Joseph E. Borovsky,et al.  Lightning energetics: Estimates of energy dissipation in channels, channel radii, and channel‐heating risetimes , 1998 .

[11]  John Zinn,et al.  On the dynamics of hot air plasmas related to lightning discharges: 2. Electrodynamics , 2014 .

[12]  E. Philip Krider,et al.  The optical power radiated by lightning return strokes , 1983 .

[13]  W. Borucki,et al.  Lightning: Estimates of the rates of energy dissipation and nitrogen fixation , 1984 .

[14]  T. Magin,et al.  Coarse-grain model for internal energy excitation and dissociation of molecular nitrogen , 2012 .

[15]  Joseph Hilsenrath,et al.  TABLES OF THERMODYNAMIC PROPERTIES OF NITROGEN IN CHEMICAL EQUILIBRIUM INCLUDING SECOND VIRIAL CORRECTIONS FROM 2000 K TO 15,000 K , 1964 .

[16]  Vladimir A. Rakov,et al.  Review and evaluation of lightning return stroke models including some aspects of their application , 1998 .

[17]  J. Zinn.  A finite difference scheme for time-dependent spherical radiation hydrodynamics problems , 1973 .

[18]  C. D. Sutherland,et al.  Chemical equilibria in hot air with moisture, salt, and vaporized metal contaminants , 1975 .

[19]  Marco Panesi,et al.  Rovibrational internal energy transfer and dissociation of N2(1Σg+)-N(4S(u)) system in hypersonic flows. , 2013, The Journal of chemical physics.

[20]  K. Charrada,et al.  Simulation of Expansion of Thermal Shock and Pressure Waves Inducaed by a Streamer Dynamics in Positive DC Corona Discharges , 2013, IEEE Transactions on Plasma Science.

[21]  E. I. Dubovoy,et al.  Mesurements and numerical modeling of radio sounding reflection from a lightning channel , 1995 .

[22]  G. Gisler,et al.  Coordinated observations of two large Leonid meteor fireballs over northern New Mexico, and computer model comparisons , 1999 .

[23]  J. McFadden.  Initial Behavior of a Spherical Blast , 1952 .

[24]  C. Russell,et al.  Progress in planetary lightning , 2002 .

[25]  S. A. Losev,et al.  Processes in high-temperature air involving molecules and atoms in excited electron states , 2010 .

[26]  M. Plooster,et al.  Numerical Simulation of Spark Discharges in Air , 1971 .

[27]  B. Duncan,et al.  Impact of lightning NO emissions on North American photochemistry as determined using the Global Modeling Initiative (GMI) model , 2010 .

[28]  M. Shneider.  Turbulent decay of after-spark channels , 2006 .

[29]  F. Tholin,et al.  Simulation of the hydrodynamic expansion following a nanosecond pulsed spark discharge in air at atmospheric pressure , 2013 .

[30]  A. V. Phelps,et al.  ROTATIONAL EXCITATION AND MOMENTUM TRANSFER CROSS SECTIONS FOR ELECTRONS IN H2 AND N2 FROM TRANSPORT COEFFICIENTS , 1962 .

[31]  R. L. Gardner,et al.  Reply to comments of Hill , 1987 .

[32]  Vorticity production and turbulent cooling of “hot channels” in gases: Three dimensions versus two dimensions , 2003 .

[33]  Effects of radiative transfer modelling on the dynamics of a propagating electrical discharge , 2010 .

[34]  R. Dickerson,et al.  Nitric oxide production by simulated lightning: Dependence on current, energy, and pressure , 1998 .

[35]  Olivier Chazot,et al.  Analysis of the FIRE II Flight Experiment by Means of a Collisional Radiative Model , 2008 .

[36]  M. N. Özişik,et al.  Radiation in cylindrical symmetry with anisotropic scattering and variable properties , 1990 .

[37]  E. Philip Krider,et al.  On the electromagnetic fields, Poynting vector, and peak power radiated by lightning return strokes , 1992 .

[38]  R. Anderson,et al.  Structure and luminosity of strong shock waves in air , 1973 .

[39]  E. Philip Krider,et al.  The peak electromagnetic power radiated by lightning return strokes , 1983 .

[40]  G. Stenchikov,et al.  Production of lightning NOx and its vertical distribution calculated from three‐dimensional cloud‐scale chemical transport model simulations , 2010 .

[41]  Olivier Chazot,et al.  Fire II Flight Experiment Analysis by Means of a Collisional-Radiative Model , 2009 .

[42]  F J Gordillo-V.  Air plasma kinetics under the influence of sprites , 2008 .

[43]  B. N. Turman,et al.  Analysis of lightning data from the DMSP satellite , 1978 .

[44]  A. Phelps,et al.  DETERMINATION OF MOMENTUM TRANSFER AND INELASTIC COLLISION CROSS SECTIONS FOR ELECTRONS IN NITROGEN USING TRANSPORT COEFFICIENTS. , 1964 .

[45]  C. Laux,et al.  Optical Diagnostics and Radiative Emission of Air Plasmas , 1993 .

[46]  B. Armstrong,et al.  Absorption coefficients of heated air: A tabulation to 24 000°K , 1966 .

[47]  M. A. Biondi,et al.  Measurements of the Attachment of Low-Energy Electrons to Oxygen Molecules , 1962 .

[48]  D. Hauglustaine,et al.  The global distribution of lightning NOx simulated on-line in a general circulation model , 2001 .

[49]  A. Bourdon,et al.  Consistent multi-internal-temperatures models for nonequilibrium nozzle flows , 2013 .

[50]  J. Lowke.  On the physics of lightning , 2004, IEEE Transactions on Plasma Science.

[51]  E. Philip Krider,et al.  The optical and radiation field signatures produced by lightning return strokes , 1982 .

[52]  N. Aleksandrov,et al.  Effect of continuous current during pauses between successive strokes on the decay of the lightning channel , 2000 .

[53]  Richard N. Zare,et al.  Optical diagnostics of atmospheric pressure air plasmas , 2003 .

[54]  C. Anastasi,et al.  Formation of nitrogen oxides by electrical discharges and implications for atmospheric lightning , 1996 .

[55]  R. D. Hill.  Comments on ‘‘Lightning return stroke. A numerical calculation of the optical radiation’’ [Phys. Fluids 29, 2736 (1986)] , 1987 .

[56]  T. M. E. Sherbini,et al.  Measurement of electron density utilizing the Hα-line from laser produced plasma in air , 2006 .

[57]  H. Brode.  Numerical Solutions of Spherical Blast Waves , 1955 .

[58]  Vladimir A. Rakov,et al.  Measurements of NOX produced by rocket‐triggered lightning , 2007 .

[59]  V. Rakov,et al.  On the upper and lower limits of peak current of first return strokes in negative lightning flashes , 2012 .

[60]  W. David Rust,et al.  Two‐dimensional velocity, optical risetime, and peak current estimates for natural positive lightning return strokes , 1993 .

[61]  R. Dickerson,et al.  Nitric oxide production by lightning discharges , 1993 .

[62]  Ulrich Schumann,et al.  The global lightning-induced nitrogen oxides source , 2007 .

[63]  F. J. Gordillo-Vazquez,et al.  Air plasma kinetics under the influence of sprites , 2008 .

[64]  R. Farley,et al.  Numerical modeling of lightning‐produced NOx using an explicit lightning scheme: 1. Two‐dimensional simulation as a “proof of concept” , 2003 .

[65]  B. C. Edgar,et al.  Early coincident satellite optical and ground‐based RF observations of lightning , 2004 .

[66]  V. Cooray,et al.  Efficiencies for production of NOx and O3 by streamer discharges in air at atmospheric pressure , 2005 .

[67]  A. Phelps,et al.  Elastic and Inelastic Collision Cross Sections in Hydrogen and Deuterium from Transport Coefficients , 1963 .

[68]  D. Revelle,et al.  Leonid meteor ablation, energy exchange and trail morphology , 2002 .

[69]  P. Chowdhuri,et al.  Parameters of lightning strokes: a review , 2005, IEEE Transactions on Power Delivery.

[70]  R. L. Gardner,et al.  Lightning return stroke. A numerical calculation of the optical radiation , 1986 .

[71]  Vladimir A. Rakov,et al.  Estimation of input energy in rocket‐triggered lightning , 2006 .

[72]  Olivier Chazot,et al.  Electronic Excitation of Atoms and Molecules for the FIRE II Flight Experiment , 2011 .

[73]  Philippe Rivière,et al.  Radiative transfer in LTE air plasmas for temperatures up to , 2003 .

[74]  A. Soufiani,et al.  Contributions of diatomic molecular electronic systems to heated air radiation , 2002 .

[75]  G. Brasseur,et al.  Florida thunderstorms: A faucet of reactive nitrogen to the upper troposphere , 2004 .