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The paper outlines a finite volumes refined mathematical model of the working gas flow in the flow path of the three stage modern single shaft gas turbine engine that can be used in floating power plants. Such mathematical model based on the finite volumes of hexagonal-type was constructed using the three-dimensional Navier–Stokes equations for the case of viscous working fluid flow. For the problem solution such boundary conditions as “inlet’, “outlet” and “wall” have been used. The calculation is carried out in a non-stationary setting with a time step of 1.5974 × 10−6 s, which corresponds to the angle of rotation of the rotor, relative to the stator, of 0.09°. The total number of time iterations is 350. Also, it was shown that the variation field of pressure on the blades feather surfaces and the gas flow velocity due to rotation are the critical factors, causing the blades vibration. The result was confirmed with the experiment. The obtained results would be used as a base for further investigations of gas flow pressure field on the blades surface, because the gas flow pressure are key factors, causing the rotor forced vibration, and as initial data for their fatigue strength and crack study.

The problem of turbine engines blades stress-strain state has been studied. All calculations have been provided for the cooled blades constructions, used in the turbo machinery manufacturing. The investigation’s purpose was to develop the new adaptive mathematical model of turbine engine bladed disks with circular damping links stress-strain state by means of finite elements method. The foregoing approach to the finite elements method was borrowed from the literature on finite elements method. The main mathematical models and some types of the finite elements can’t be used for the correct description of the foregoing problem. The matter is that turbine blades have constructional non-homogeneity, which hardly ever could be correctly explained, using well-known finite elements and their mathematical dependences. On the other hand the variable aerodynamic force influence has also been taken into consideration. That is why the new model, which consists of sections, including disk’s sector, the whole blade and parts of damping links, has been developed. The finite elements methodology has been used for the dynamic stresses of this section calculation. Such approach gives an opportunity to describe the stress-strain state of the whole bladed disk as the superposition of the developed sections

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In this paper the problem of gas turbine rotor impellers free vibration has been studied. For its solution, the new, more correct mathematical model on the base of the nonlinear FEM has been designed. All calculations have been held for the two types of boundary conditions (C-C and C-S) that match the most common types of the turbine rotors assembling. By the usage of the designed mathematical model several rotor impellers free vibration modes and frequencies have been calculated. The developed mathematical model adequacy has been verified by the comparison of calculated results with the experimental data.