## 1 Introduction
An alternative approach to determining the static flow characteristics involves the use of computational fluid dynamics (CFD) tools based on the RANS (Reynolds Average Navier-Stokes) model [18], describing the flow processes in each cell of the compressed air volume of the considered volume based on the declared numerical grid. A key aspect of using CFD tools is the declaration of the boundary conditions of the model consistent with the conditions of the actual operation of the tested pneumatic assembly and the selection of a finite element mesh discretizing the spatial model of the fluid, liquid or gas volume, ensuring high-quality results at the optimal duration of the numerical simulation. In the problem under consideration, the Ansys Fluent environment was used, which provides wide possibilities for declaring lumped volume meshes and polyhedral domains [19; 20; 21] based on polyhedral spatial cells after transforming the basic tetrahedral mesh. According to the literature studies and the authors' earlier work [22], such an approach ensures the attainment of real results while maintaining the optimal duration of the simulation. Despite the fact that a number of experimental studies have been conducted on the effectiveness of pneumatic brake systems, a lack of detailed studies on the flow characteristics of the component paths of brake valves [23; 24; 25] was found. This was the basis for formulating a research gap, which indicated the need for the flow characteristics of individual paths of pneumatic brake valves to be determined. Very often, in modellingusing empirical models [26], the flow characteristics of brake valves are described by a rectangular characteristic, based on the minimum and maximum value. This results in discrepancies in the times required to reach the reference pressures during the validation of such models. Additionally, despite the significant development of computer techniques, their common use in the flow assessment of flow paths of brake valves was not found. The scientific objective of this study was to determine the capacity of the main and additional supply path of a modified pneumatic brake relay valve. The achievement of this goal was realized in experimental and model conditions. The experimental determination of the capacity of both paths depending on the degree of opening will allow the determination of the static characteristics of both paths using empirical relationships. The CFD computer simulation method based on the 3D model of the considered brake valve using the Ansys Fluent environment allows for verification, an assessment of the validity and the validation of the numerical approach to solving static problems related to pneumatic brake valves. The conclusions of the above analyses constitute an introduction to dynamic tests and valve configuration in order to obtain the dual-range operation assumed by the authors. The rest of the article is as follows. Section 2 presents the object of analysis with a detailed description of both supply tracts. The basics of the adopted experimental and numerical research methodology in the CFD Ansys Fluent environment are described. Section 3 presents the results obtained in the experimental and numerical research, taking into account both directions of compressed air flow during braking and debraking. Section 4 contains an analysis and discussion of the obtained results. Section 5 contains conclusions, and Section 6 presents further directions for research.