Abstract
A procedure based on two-step method is suggested to simplify time-consuming spectral radiative transfer calculations in open flames containing scattering particles. At the first step of the problem solution, the P1 approximation is used to calculate the divergence of radiative flux, and it is sufficient to determine the flame parameters. The second step of solution is necessary to obtain the radiation field outside the flame, and this can be made independently using the ray-tracing procedure and the transport source function determined at the first step. Such a splitting of the complete problem results in much simpler algorithm than those used traditionally. It has been proved in previous papers that the combined two-step method is sufficiently accurate in diverse engineering applications. At the same time, the computational time decreases in about two orders of magnitude as compared with direct methods. An axisymmetric pool fire at the initial stage of fire suppression by a water spray is considered as the case problem. It is shown that evaporating small water droplets characterised by a strong scattering of infrared radiation are mainly located in regions near the upper front of the flame and one can observe the scattered radiation. This effect can be used in probe experiments for partial validation of transient Computational Fluid Dynamics (CFD) simulations.
Highlights
Radiative transfer calculations are the most time-consuming in CFD simulation of fires
The simple box model is used for spectral absorption coefficient of molecular gases, but this choice is not critical for the present study because it is focused on a general approach for the radiative transfer calculations and on infrared scattering by evaporating water droplets outside the absorption bands of water
A comparison of two temperature fields shown in Fig. 1 indicates that the effect of thermal radiation on the flame formation is relatively small at early stages of flame development
Summary
Radiative transfer calculations are the most time-consuming in CFD simulation of fires. The P1 (the first-order approximation of the spherical harmonics method) [1,2,3,4] is the simplest method of this type, and there is a very positive long-time experience of using this approach in diverse multi-dimensional problems [1,5,6,7,8,9,10,11,12,13,14,15,16,17] It appears to be sufficiently accurate in the case when one needs only the divergence of radiative flux in the energy equation. The simple box model is used for spectral absorption coefficient of molecular gases, but this choice is not critical for the present study because it is focused on a general approach for the radiative transfer calculations and on infrared scattering by evaporating water droplets outside the absorption bands of water. A numerical solution for the conventional axisymmetric flame (after averaging the numerical results for the 3-D flow field) is considered because this simplification in the flame data is acceptable for the present study
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