On one efficient method for calculating three-dimensional turbulent jets of reacting gases

This paper presents a method and algorithm for calculating the outflow of a multicomponent chemically reacting gas mixture flowing out of a rectangular nozzle with different aspect ratios and propagating into a cocurrent (flooded) flow. To describe the turbulent flow, the three-dimensional parabolic system of Navier-Stokes equations for multicomponent chemically reacting gases is used. Justified initial and boundary conditions are given. The system of equations is given after non- dimensionalization of spatial coordinates and physical parameters, as well as with the help of mathematical transformations, allowing the inlet section of the nozzle to be reduced to a unit square. To calculate the turbulent viscosity, a modified algebraic turbulence model is used that takes into account temperature inhomogeneity and velocity effects in spatial coordinates. For the numerical integration of the system of equations, a two-layer ten -point implicit finite-difference scheme was used. The continuity equation is used to calculate the mass imbalance in each computational grid. The calculation algorithm and the method for determining the boundary of jet displacement are given in detail. A number of numerical experiments have been carried out to refine the empirical Karman constant included in the turbulence moduli. Poisson's difference equation, relative to the potential function for calculating the correction for three velocities at each point in space, is solved by introducing reasonable assumptions, allowing to have a tridiagonal system of equations. This allows efficient computation. The reliability of the results was verified by comparing the numerical results with the experimental works of other authors.

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