delta_e

This script calculates delta_e for mixtures consisting of carbon dioxide, water vapor, and nonradiant components.

Excel-script included in the downloadable package.

This script calculates delta_e for mixtures consisting of carbon dioxide, water vapor, and nonradiant components. The delta_e is a correction factor which is necessary because of the overlap of the individual emission bands of the gases involved. The emissivities and absorptances for each of the components are read from the Fig. 9a-c (VDI Heat Atlas 2010, page 986) for the partial pressures at hand.

The emissivity of the mixture e_g is then calculated as follows

e_g = e_H2O + e_CO2 - delta_e(T_gas)

And the absorptance of the mixture A_v is then calculated as follows

A_v = A_v_H2O + A_v_CO2 - delta_e(T_wall)

Valid range:

• T ≥ 403 K and T ≤ 1193 K
• p_L ≥ 8 bar * cm and p_L ≤ 150 bar * cm
• x ≥ 0 and x ≤ 1

This script extrapolates the delta_e if you go above or below these boundaries but these results are not reliable after certain point.

Variables:

• T is temperature in K
• x_H2O is the mole fraction of H2O gas component in a gas mixture
• x_CO2 is the mole fraction of CO2 gas component in a gas mixture
• L is the length in cm
• p_total is the total pressure of a gas mixture in bar
• p_L is the pathlength in bar * cm
• x is the pressure fraction

Example:

e = delta_e(T, x_H2O, x_CO2, L, p_total)

e = delta_e(800,0.15,0.05,100,1)

Reference:

VDI Heat Atlas 2010. page 986. ISBN 978-3-540-77876-9.