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A Return Stroke NOx Production Model

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  • 1 NASA Marshall Space Flight Center, Huntsville, Alabama
  • | 2 Chicago State University, Chicago, Illinois
  • | 3 Universities Space Research Association, Huntsville, Alabama
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Abstract

A model is introduced for estimating the nitrogen oxides (NOx = NO + NO2) production from a lightning return stroke channel. A realistic modified transmission line model return stroke current is assumed to propagate vertically upward along a stepped leader channel of 0.1-cm radius. With additional assumptions about the initial radial expansion rate of the channel, the full nonlinear differential equation for the return stroke channel radius r(z, t) is solved numerically using Mathematica V9.0.1.0. Channel conductivity and channel air density are adjustable constants, and the model employs typical atmospheric profiles of temperature, pressure, and density. The channel pressure is modeled by a dynamic pressure expression. Channel temperature is extracted from the pressure by a minimization technique that involves a generalized gas law appropriate for high temperatures where dissociation and ionization are important. The altitude and time variations of the channel energy density are also obtained. Three model runs, each with different input parameters, are completed. Channel radii at sea level range from about 1.7 to 6.0 cm depending on the model inputs and are in good agreement with other investigators. The NOx production from each 1-m segment of the channel is computed using conservation of energy and equilibrium freeze-out-temperature chemistry. Because the NOx per meter of channel is computed as a function of altitude, extensions of the results to tortuous and branched channels are possible and lead to preliminary estimates of total return stroke NOx. These estimates are found to be smaller than the return stroke NOx values obtained from the NASA Lightning Nitrogen Oxides Model (LNOM).

Denotes Open Access content.

Corresponding author address: William Koshak, Earth Science Office, Mail Stop ZP11, NASA Marshall Space Flight Center, 320 Sparkman Drive, Huntsville, AL 35805. E-mail: william.koshak@nasa.gov

Publisher’s Note: This article was revised on 17 March 2015 to include the open access designation that was missing when originally published.

Abstract

A model is introduced for estimating the nitrogen oxides (NOx = NO + NO2) production from a lightning return stroke channel. A realistic modified transmission line model return stroke current is assumed to propagate vertically upward along a stepped leader channel of 0.1-cm radius. With additional assumptions about the initial radial expansion rate of the channel, the full nonlinear differential equation for the return stroke channel radius r(z, t) is solved numerically using Mathematica V9.0.1.0. Channel conductivity and channel air density are adjustable constants, and the model employs typical atmospheric profiles of temperature, pressure, and density. The channel pressure is modeled by a dynamic pressure expression. Channel temperature is extracted from the pressure by a minimization technique that involves a generalized gas law appropriate for high temperatures where dissociation and ionization are important. The altitude and time variations of the channel energy density are also obtained. Three model runs, each with different input parameters, are completed. Channel radii at sea level range from about 1.7 to 6.0 cm depending on the model inputs and are in good agreement with other investigators. The NOx production from each 1-m segment of the channel is computed using conservation of energy and equilibrium freeze-out-temperature chemistry. Because the NOx per meter of channel is computed as a function of altitude, extensions of the results to tortuous and branched channels are possible and lead to preliminary estimates of total return stroke NOx. These estimates are found to be smaller than the return stroke NOx values obtained from the NASA Lightning Nitrogen Oxides Model (LNOM).

Denotes Open Access content.

Corresponding author address: William Koshak, Earth Science Office, Mail Stop ZP11, NASA Marshall Space Flight Center, 320 Sparkman Drive, Huntsville, AL 35805. E-mail: william.koshak@nasa.gov

Publisher’s Note: This article was revised on 17 March 2015 to include the open access designation that was missing when originally published.

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