The purpose of this paper is to summarize important aspects related to the study of the mathematical model of internal flow and the nominal performance main parameters of the conical swirl atomizer similar to that used in the JT8 Pratt & Whitney engine. The mathematical proposed model is composed of the inviscid fluid theory of Abramovich and incompressible friction theory of Kliachko, applied to the complexity of the geometry of the inlet channels, such as the irregular cross-section area and nontangential nature with respect to the swirl chamber (geometric characteristics of the conical swirl atomizer). Computational fluid dynamics (CFD) provides additional information on internal flow characteristics of swirl atomizers, the main difficulty of which is the precise control of liquid/air. It was found that by using the volume of fluid (VoF) method and k-epsilon turbulence model (implemented in software Fluent 6.3.26), an understanding of physical phenomena can be obtained as well as better visualization of the air core and hollow-cone spray angle of the atomizer, where the computational domain is composed for three-dimensional structured grids. Experimental data and numerical simulation were used for validation of this mathematical model. These results provide elementary and worthwhile information for the practical design of swirl atomizers, in addition to cost reduction before the combustion testing phase.