Participating Media Radiation (Non-Grey)

Non-Grey Gas Radiation

Unlike grey solids, triatomic gases like $\text{CO}_2$ and $\text{H}_2\text{O}$ absorb and emit radiation selectively in discrete bands of the infrared spectrum.

Mean Beam Length ($L_e$): Characterizes the spatial scale of gas-wall radiation paths. Calculated as $L_e = 3.6 V / A_w$.
Leckner Model: Calculates total gas emissivity $\varepsilon_g(T_g)$ and gas absorptivity $\alpha_g(T_w)$ at wall temperatures.
Grey Wall Flux: Evaluates net radiation heat transfer ($q_{net, w}$) considering wall reflectivity.

📝 Configuration

🔥 Gases & Fuel Preset

Fuel Combustion Preset:

CO₂ Mole Fraction ($x_{\text{CO}_2}$):

H₂O Mole Fraction ($x_{\text{H}_2\text{O}}$):

Gas Temperature ($T_g$) [°C]:

Total Pressure ($P_{total}$) [bar]:

🧱 Enclosure Walls & Geometry Preset

Geometry Preset:

Gas Volume ($V$) [m³]:

Total Wall Area ($A_w$) [m²]:

Wall Temperature ($T_w$) [°C]:

Wall Emissivity ($\varepsilon_w$):

📊 Results & Gas Properties

Configure properties and click "Compute Gas-Wall Heat Exchange" to view results.

📘 Calculation Methodology & Hottel Enclosure Formulation

Leckner Mixture Emissivity & Absorptivity

The total emissivity of H₂O/CO₂ gas mixtures is formulated by evaluating Leckner's spectral correlations:

$$\varepsilon_g = \varepsilon_{CO_2} \cdot C_c + \varepsilon_{H_2O} \cdot C_w - \Delta\varepsilon_{overlap}$$

For gas absorptivity ($\alpha_g$), the spectral emission of the walls must be accounted for. Since the walls are at $T_w$, Leckner modifies the path lengths and temperature dependencies using the following scaling rules:

$$\alpha_{CO_2} = C_c' \cdot \varepsilon_{CO_2}\left(T_w, \ p_{CO_2} L_e \frac{T_w}{T_g}\right) \cdot \left(\frac{T_g}{T_w}\right)^{0.65}$$ $$\alpha_{H_2O} = C_w' \cdot \varepsilon_{H_2O}\left(T_w, \ p_{H_2O} L_e \frac{T_w}{T_g}\right) \cdot \left(\frac{T_g}{T_w}\right)^{0.45}$$

Net Radiation Exchange (Grey Walls)

For a combustion gas surrounded by a gray, diffuse bounding surface of area $A_w$ and emissivity $\varepsilon_w$, the multiple reflections of rays between the wall and the participating gas are represented by Hottel's network equation:

$$q_{net, w} = \frac{\sigma \left( \varepsilon_g T_g^4 - \alpha_g T_w^4 \right)}{\frac{1}{\varepsilon_w} + \alpha_g - 1}$$ $$Q_{total} = q_{net, w} \cdot A_w$$

Where $\sigma = 5.670374 \times 10^{-8} \ \text{W/m}^2\cdot\text{K}^4$. If $q_{net, w} > 0$, the wall gains net thermal energy from the hot gas core. If $q_{net, w} < 0$, the wall radiates net energy back to the gas.