Simulation of turbulent gas flow

Background and Objectives: The purpose of the study carried out in the article is to obtain analytical expressions for calculating the gas (liquid) flow rate in the turbulent gas (liquid) flow regime. A method is presented for the mathematical description of a three-dimensional profile (hodograph) of the flow velocity in a turbulent flow regime based on two known velocity values in the pipeline cross section. The article analyzes the physical processes occurring in the turbulent flow. In the cross section of the pipeline, characteristic areas are distinguished: the core of the turbulent flow and the laminar near-wall layer. Materials and Methods: To simulate the velocity distribution in the core of the flow, a power law was used, in the near-wall region, a linear law of change in the modulus of the velocity vector. The exponent is determined depending on the value of the Reynolds number, the algorithm is given. The approach used does not require significant computational costs, in contrast to a number of well-known grid methods based on the Navier–Stokes system of differential equations. Results: Based on the analysis of physical processes, a method for mathematical modeling of the turbulent gas flow in a round pipe has been proposed in the form of fairly simple engineering formulas. The geometric view of the three-dimensional velocity hodograph is a combination of a round truncated cone and a figure of rotation formed on the basis of a power function. The boundary of the near-wall region has been determined on the basis of the Reynolds number, and an engineering formula has been obtained. The results of calculations have been presented; two-dimensional velocity profiles have been plotted for a number of velocity values. Conclusions: Analysis of the results allows us to determine the limits of applicability of the model. So, with significant deviations of the velocity modules on the axis of the pipeline and near the wall, i.e. as the Reynolds number decreases, the velocity hodograph undergoes a kink in the apex region. This is explained by the approach of the gas flow to the laminar flow regime and the need to use a parabolic velocity profile according to the Poiseuille law.