Generalized source term multiflux method coupled with Runge-Kutta ray tracing technique for arbitrary radiative intensity of graded-index media

The generalized source term multiflux method (GSMFM) combined with Runge-Kutta ray tracing technique is developed to calculate arbitrary directional radiative intensity of graded-index media. In this method, the finite volume method is employed to solve source terms along the curved ray path determined by the Fermat principle. Runge-Kutta ray tracing technique is adopted to obtain the ray trajectory numerical solution in graded-index media. And the GSMFM is used to solve radiative intensity to be expected. One-dimensional and two-dimensional radiative heat transfer problems are investigated to verify the performance of this method. The numerical results show that the accuracy of the GSMFM is close to that of backward Monte Carlo (BMC) method, while the efficiency of GSMFM is much higher than that of the BMC. Therefore, the GSMFM developed can be considered as a promising method to solve arbitrary radiative intensity in graded-index media.

Figure 1

The physical model of light transmission in medium with GRI.

Figure 2

The physical model in Cartesian coordinate system.

Figure 3

The flowchart of GSMFM for calculating radiative intensity.

Figure 4

Physical geometry of one-dimensional slab medium.

Figure 5

The radiative intensity with different step sizes of Runge-Kutta ray tracing.

Figure 6

The radiative intensity of different optical thicknesses.

Figure 7

The temperature distributions in semitransparent medium with GRI.

Figure 8

The radiative intensity of different temperature distributions.

Figure 9

The radiative intensity of different scattering albedos.

Figure 10

The radiative intensity for anisotropic scattering medium.

Figure 11

Physical geometry of two-dimensional medium with GRI.

Figure 12

The radiative intensity of different optical thicknesses.

Figure 13

The radiative intensity along different zenith angles.

Figure 14

The radiative intensity of different scattering albedos.

Figure 15

Temperature distributions: (a) $T=T_g+\frac{T_g}{4}\sqrt{{\left(x/H\right)}^2+{\left(y/H\right)}^2}$, (b) $T=T_g+\frac{T_g}{4}\sqrt{{{\left(\frac{x}{H}-\frac{1}{2}\right)}^2+{\left(\frac{y}{H}-\frac{1}{2}\right)}^2}^{\phantom{\int }}}$, and (c) $T=T_g+\frac{T_g}{4}sin\left(\frac{\pi x}{H}\right)cos\left(\frac{\pi y}{H}-\frac{1}{2}\right)$.

Figure 16

The radiative intensity of different temperature distributions.