Hydrodynamic instability of premixed tubular flame stabilized in stretched rotating flow

The paper analyzes the hydrodynamic instability of a cylindrical flame stabilized in a converging rotating gas flow simulating the flow in a cyclone combustion chamber. The analysis was carried out within the framework of a two-dimensional model describing the gas flow with radial and tangential supply of combustible gas through the walls of a cylindrical chamber. In the stationary case, the gas flow in combustion products and the combustible mixture is described by the solution for a rotating tornado-shaped vortex. The rotation of the gas creates a centrifugal force, which has a stabilizing effect on the flame perturbations. The dependences of the perturbations growth rate on the wave vector of perturbations, the radial and tangential inlet gas velocities, and other parameters of the problem are obtained. The analytical criterion of neutral stability separating regions of stable flame with respect of any perturbations and flame instability in the plane of radial and tangential velocities is obtained. In the absence of rotation and at the large flame radii, the model converts into the Landau- Darrieus model of flame hydrodynamic instability.