Modeling and algorithm for calculation the mixing and propagation of co-current flows in channels.

This paper describes in detail the method and algorithm for calculating the numerical integration of non-stationary two-dimensional systems of Navier-Stokes equations for a compressible gas using high-order implicit (explicit) difference schemes, i.e., the Beam-Warming difference scheme. A number of mathematical transformations, such as non-dimensionalization of coordinates and physical parameters, transforming the shape of the channel into a square one, as well as thickening the integration steps with large gradients of unknowns, which make it possible to bring problems to a model one for solving similar problems. In addition to the study, as convergence in the number of calculated points, the dependence of the number of iterations on the Courant number and comparison of the results obtained by different proposed models for calculating the effective viscosity, as well as a number of numerical studies as co-occurrence, temperature inhomogeneities, non-design, the ratio of the sizes of the inlet slots of cocurrent flows and the length of the channel to the height of the main flow and the degree of expansion of the channel to the process of mixing and distribution of flows in the channel. It was revealed at what ratios of the initial parameters of the cocurrent flows and the linear dimensions of the channel a recirculation zone is formed. For a channel of constant cross section at large ratios of velocities (72, 46) and temperature (2, 33), as well as small ratios of the channel length to the height of the inlet slot of the main flow (5, 31), even at the same jet pressures in the initial section, the recirculation zone occupies more than 55% of the input section, and the length along the longitudinal coordinate reaches 20 cm. [ABSTRACT FROM AUTHOR]