Development of an unstructured radiation model applicable for two-dimensional planar, axisymmetric, and three-dimensional geometries

Numerical simulation of the Czochralski growth process of oxide crystals with a relatively thin optical thickness

“…Therefore, the results of the simulation were compared with the following: (1) the exact solution for radiative flux along the lateral wall of a 2D axisymmetric triangular toroid, where the medium in the toroid with cold and black walls is maintained at an emissive power of unity and is assumed to be absorbing-emitting with a 0 = 1.0 m À1 [11] and (2) the exact numerical solutions of the temperature profile in a gray gas contained between infinite parallel plates, where optical thickness of the gas is 1.0 and the plates are black at the dimensionless temperatures 0.5 and 1.0 [12]. Fig.…”

“…Here, to solve the radiative transfer equation, the FVM was used [11], where the 4p angular domain at any spatial location is divided into a finite number of discrete, M, nonoverlapping solid angles by the azimuthal discretization strategy. According to [11], the FVM is the same as the discrete ordinates method (DOM), except that the azimuthal discretization was used as the angular discretization strategy instead of the Sn-type one in the DOM. With the discretization of the angular domains, the radiative transfer equation along a specified discrete direction x m can be expressed as follows,…”

Coupled simulation of heat transfer and temperature of the composite rocket nozzle wall

“…To compute the radiative heat transfer inside the nozzle, the enclosure is established and the Zone method is also adopted to divide the calculating domain [9]. The nozzle and the gases are assumed as an enclosure filled with inhomogeneous radiative gases.…”

Discrete ordinates method applied to radiative transfer equation in complex geometries meshed by structured and unstructured grids

“…This also makes the RTE problem compatible with other phenomena such as combustion, conduction and fluid dynamics. Investigations on the basis of unstructured solutions for radiation has been carried out by Sakami and coworkers [21][22][23] and Shang [24].…”