This paper presents the results of a numerical simulation of the gas flow in the flame tube of an annular combustion chamber of a gas turbine engine. Numerical simulation was performed in the ANSYS Fluent 2022 R1 computational complex, in which the numerical solution of the Reynolds-averaged Navier-Stokes equations (RANS) was implemented, the dissipation rates were determined using the Enhanced Wall Treatment near-wall function. For numerical simulation problems, a computational polyhedral mesh was built. The purpose of the calculations was to evaluate the effect of the method for supplying igniter hot gases to the start of the combustion chamber. The article does not address the operation of the igniter itself (its ignition, combustion, and the flow in it), but only its main task is the generation of a flame (gas) with a given temperature. All calculations were carried out for two gas temperatures, 800 and 1200 °C, at the outlet of the igniter nozzle, and a temperature of minus 20 °C at the inlet to the combustion chamber. In the calculation model, at the inlet to the igniter nozzle, the gas flow rate was set with a temperature taken from the experiment. When the chamber operates in the region of low temperatures, low velocities and pressures at the inlet, the degree of fuel evaporation and the mixing of its vapors with air have a significant effect. Therefore, with an increase in air flow through the chamber, the limits of flame blow-off expand. With a further increase in air flow, the processes of fuel evaporation and its burnout in the reverse current zone are completed, and flameout is mainly determined only by the temperature in the reverse current zone, and the boundaries of stable combustion narrow with increasing flow rate, which is typical for combusting a homogeneous mixture. The calculations found that the penetration and spread of heat when using igniter nozzles with a large diameter (12 mm) in the outlet section are higher than those in holes with a smaller diameter (8 mm). In the variants where the supply of hot gases is in the plane of the nozzle, a better distribution of heat in the zone of reverse currents is shown than where the supply of hot gases is carried out between the nozzles. Also, to analyze the results of the calculation, a criterion was proposed that shows the optimal conditions for the ignition of the mixture.