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Stable combustion is one of the main requirements for combustion chambers of gas turbine engines. Therefore, the prediction of combustor stable operation limits during the design stage is an important task. The stable operation limits with a sufficient degree of accuracy can be determined by experiments or using computational fluid dynamics. The present paper describes a numerical and experimental investigation of swirled premixed flame stabilization in a modular swirled burner (MSB). The burner has a vane swirler and a diffuser with a cylindrical tube downstream of the swirler. This design has several advantages. First, the cylindrical tube protects the flame from external disturbances and acts as the pre-chamber in which combustion efficiency can reach high values. Secondly, the swirled flow of the fresh mixture passes along the walls of the tube and prevents them from overheating. The influence of the swirler vanes angle on MSB lean blow out (LBO) was experimentally and numerically investigated. The results of the experiments were also used to validate the simulation results. All studies were conducted under atmospheric conditions in an open-space laboratory environment. Three-dimensional modeling was carried out using the large eddy simulation (LES) with a Smagorinsky–Lilly subgrid model. Combustion was described within the Flamelet Generated Manifold model. Initially, the influence of the size and shape of outlet boundary, the mesh resolution and turbulent-chemistry interaction models was investigated. As a result the configuration of the model was received, which allows simulating LBO with sufficient accuracy. Stable operation limits for several types of MSB geometries and different fuels (methane and propane) were subsequently established. It was found that in the case of swirler vane angle equal to 45 degrees the range of stable operation limits is wider than in the case of 60 degrees. The influence of pre-chamber length on LBO was studied only numerically. It was discovered that with increasing pre-chamber length, the LBO limits become wider, but the possibility of the tube walls overheating becomes higher too.