Abstract. The study presents the simulation results of the viscid gas flow in low flow coefficient centrifugal compressor stages. The problem is solved in a stationary formulation using the Ansys CFX software package. The numerical simulation is carried out on three ultrahigh-pressure model stages; two stages have blades of the classical type impeller and one stage is of the bodily type. The value of the conditional flow coefficient is 0.0063 to 0.015. As part of the study, block-structured design meshes are used for all gas channel elements, with their total number being equaled as 13–15 million. During the calculations a numerical characteristic was validated with the results of tests carried out at the Department of Compressor, Vacuum and Refrigeration Engineering of Peter the Great St. Petersburg Polytechnic University. With an increase of inlet pressure as a result of a numerical study, it was found that for a given mathematical model the disk friction and leakage coefficient (1 + βfr + βlk) is overestimated. The analysis of flow in labyrinth seals has shown an increase of total temperature near the discs by 30–50 °С, nevertheless this fact did not influence gas parameters in the behind-the-rotor section. The calculation data obtained with finer design mesh (the first near-wall cell was 0.001 mm) is identical to those obtained with the first near-wall cell 0.01 mm mesh.

Abstract. A new mathematical model has been developed to determine the coefficient of internal and theoretical head in the variant design of the low-flow rate centrifugal compressors impellers. A parametric study of the flow part of the impeller is carried out. In total 1620 impellers are numericaly simulated. As a result, a numerical database of gas dynamic and geometric parameters was developed. Due to an a priori analysis, the relations of parameters with the geometric shape of the flow part are determined. The mathematical model is developed using gas-dynamic parameters and relations determined from numerical database. Using centrifugal compressor stage digital twins, a generalizing relationship has been developed to determine the complex of friction and leakage losses.The reliability of the math model is validated by the comparison with experimental data and the results of numerical experiment in digital twins, which are not involved in the model. The application of the head math model is determined in the range of the conditional flow coefficient 0.006<Φd<0.02 and the theoretical head coefficient 0.60 <ψt<0.72.

Abstract. In this paper, various real gas state equations are considered and their comparative analysis is carried out. The following state equations are studied in the work: Benedict-Webb-Rubin modification equation, Ridlich-Kwong Real Gas equation, Peng-Robinson Real Gas equation, and the modified Ridlich-Kwong real gas state equations proposed by Barsuk S.D. We have made a direct comparison of these calculation methods with most accurate identification. In addition, the paper analyzes the equations features, with applicability limits definition of each state equations. For the chosen one, as the most universal and exact equation, the calculations were made for the liquid phase and the real gas two-phase state. Based on the data obtained, polynomials were developed for various parameters depending on the gas temperature, which can later be used to build various mathematical models. Our conclusions show main advantages of selected equation for real gases and the reasons for choosing it for modeling low-temperature heat and mass transfer processes.

Abstract. In the course of the work, the results of estimating the error in the numerical calculation of two-element 3D impeller stages of centrifugal compressors were obtained. Gas dynamic characteristics of 6 computational models of two-element stages of a centrifugal compressor are simulated. Based on available experimental data, models of validation characteristics have been performed. A parametric model has been developed for carrying out multi-criteria and multi-parametric studies.

Abstract. To carry out research, a complex of gas-dynamic design and profiling of a two-stage centrifugal compressor with an axial-radial impeller has been developed. It is a continuous process of solving the inverse and direct problem of gas-dynamic design, profiling the flow section with subsequent analysis of the rational velocity distribution of an inviscid flow on the impeller blades on axisymmetric streamline surfaces.