Propagation of three-dimensional turbulent jet from lobar nozzle through surrounding stream

Propagation of the jet through the surrounding stream, after discharge from a lobar nozzle in a two-flow turbojet engine, is analyzed on the basis of an approximate mathematical model which describes mixing of two substances and facilities numerical calculations. The static pressure in the cylindrical mixing chamber is assumed to remain constant, with negligible molecular and thermal diffusion in the direction of flow so that the two equations of the boundary layer become parabolic. The one-parametric equation of turbulence is also parabolic. Mixing is assumed to occur at a low Mach number and the equation of state reduces to that for a perfect gas. The system is closed by an equation of continuity which, upon inclusion of the transverse velocity of secondary potential flow, becomes an elliptic Poisson equation. The initial conditions are characterized by the ratio of velocities and the ratio of densities at the nozzle throat as well as by the geometry of the boundary layer and the distribution of eddy viscosity. The corresponding boundary value problem, formulated in dimensionless variables, is solved by numerical integration according to the method of false positions.