Estimated electric conductivities of thermal plasma for air-fuel combustion and oxy-fuel combustion with potassium or cesium seeding

Abstract

A complete model for estimating the electric conductivity of combustion product gases, with added cesium (Cs) or potassium (K) vapor for ionization, is presented. Neutral carrier gases serve as the bulk fluid that carries the seed material, as well as the electrons generated by the partial thermal (equilibrium) ionization of the seed alkali metal. The model accounts for electron-neutral scattering, as well as electron-ion and electron-electron scattering. The model is tested through comparison with published data. The model is aimed at being utilized for the plasma within magnetohydrodynamic (MHD) channels, where direct power extraction from passing electrically conducting plasma gas enables electric power generation. The thermal ionization model is then used to estimate the electric conductivity of seeded combustion gases under complete combustion of three selected fuels, namely: hydrogen (H₂), methane (CH₄), and carbon (C). For each of these three fuels, two options for the oxidizer were applied, namely: air (21 % molecular oxygen, 79 % molecular nitrogen by mole), and pure oxygen (oxy-combustion). Two types of seeds (with 1 % mole fraction, based on the composition before ionization) were also applied for each of the six combinations of (fuel-oxidizer), leading to a total of 12 different MHD plasma cases. For each of these cases, the electric conductivity was computed for a range of temperatures from 2000 K to 3000 K. The smallest estimated electric conductivity was 0.35 S/m for oxy-hydrogen combustion at 2000 K, with potassium seeding. The largest estimated electric conductivity was 180.30 S/m for oxy-carbon combustion at 3000 K, with cesium seeding. At 2000 K, replacing potassium with cesium causes a gain in the electric conductivity by a multiplicative gain factor of about 3.6 regardless of the fuel and oxidizer. This gain factor declines to between 1.77 and 2.07 at 3000 K. Based on the findings of this research study, the four analyzed factors to increase the electric conductivity of MHD plasma can be listed by their significance (descending order) as (1) type of additive seed type (cesium is better than potassium), (2) temperature (the higher the better), (3) carbon-to-hydrogen ratio of the fuel (the higher the better), and finally (4) the oxidizer type (air is generally better than pure oxygen). The relative size of the two electric conductivity components (due to neutrals scattering and Coulomb scattering) at various plasma conditions are discussed, and a threshold of 10^-5 (0.001 %) electrons mole fraction is suggested to safely neglect Coulomb scattering.

Keywords: Cesium; Electric conductivity; MHD; Potassium; Seeded plasma; Thermal ionization.

Fig. 1

Illustration of Maxwell-Boltzmann speed probability distribution of electrons at four absolute temperatures: 300 K, 1000 K, 2000 K, and 3000 K.

Fig. 2

Performance of the eighth-degree polynomial fitting of the natural logarithm of the electron-neutral collision cross-section of argon in Ų, as a function of the natural logarithm of the electron energy in eV.

Fig. 3

Performance of the eighth-degree polynomial fitting when the fitting curve and the discrete data points are compared after counterbalancing the logarithmic transformation through an opposite exponential detransformation

Fig. 4

Comparison of how the number density of electrons changes with the temperature for different seeding pressures of cesium, as published with the Frost model and as computed here.

Fig. 5

Comparison of how the electric conductivity of seeded plasma changes with the temperature for different noble gases with specified seeding pressures of cesium, as published with the Frost model and as computed here.

Fig. 6

Chemical composition used here for representing potassium-seeded (1 % mass fraction) oxygen-methane combustion products at 3040 K before ionization (top: mole fractions, bottom: mass fractions). The sum of listed mole fractions or mass fractions is adequately 1.000000.

Fig. 7

Gain in the electron density or degree of ionization over the temperature range from 2000 K to 3000 K, if cesium (Cs) is used instead of potassium (K) as the seeded vapor.

Fig. 8

Degree of ionization and electrons mole fraction over the temperature range from 2000 K to 3000 K, with either cesium (Cs) or potassium (K) used as the seeded vapor.

Fig. 9

Demonstration of the nearly exponential correlation between the degree of ionization and the electrons mole fraction with the absolute temperature, with either cesium (Cs) or potassium (K) used as the seeded vapor. The fitting curves have a dotted pattern. The corresponding repression equations are displayed.

Fig. 10

Electric conductivity over the temperature range from 2000 K to 3000 K for the case of stoichiometric oxygen-hydrogen-based plasma composition, with either cesium (Cs) or potassium (K) used as a seed vapor. The ratio of both electric conductivities is also shown.

Fig. 11

Electric conductivity over the temperature range from 2000 K to 3000 K for the case of stoichiometric oxygen-methane-based plasma composition, with either cesium (Cs) or potassium (K) used as a seed vapor. The ratio of both electric conductivities is also shown.

Fig. 12

Electric conductivity over the temperature range from 2000 K to 3000 K for the case of stoichiometric oxygen-carbon-based plasma composition, with either cesium (Cs) or potassium (K) used as a seed vapor. The ratio of both electric conductivities is also shown.

Fig. 13

Electric conductivity over the temperature range from 2000 K to 3000 K for the case of stoichiometric air-hydrogen-based plasma composition, with either cesium (Cs) or potassium (K) used as a seed vapor. The ratio of both electric conductivities is also shown.

Fig. 14

Electric conductivity over the temperature range from 2000 K to 3000 K for the case of stoichiometric air-methane-based plasma composition, with either cesium (Cs) or potassium (K) used as a seed vapor. The ratio of both electric conductivities is also shown.

Fig. 15

Electric conductivity over the temperature range from 2000 K to 3000 K for the case of stoichiometric air-carbon-based plasma composition, with either cesium (Cs) or potassium (K) used as a seed vapor. The ratio of both electric conductivities is also shown.

Fig. 16

Mean electron-neutral collision cross-section for carbon dioxide (CO₂) and molecular nitrogen (N₂) over the temperature range from 2000 K to 3000 K, according to the analytical expressions used here.