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Similarity theory principles are widely applied in gas dynamic design. But completely new solutions must be realized on a base of engineering approaches to predict performances. The heart of the Universal modeling engineering method is the physical model that is based on flow visualization and measurements inside rotating impellers. The math model is a sum of algebraic equations for calculation of head losses. Normalized velocity gradients along and normal to blade surfaces are arguments. Empirical coefficients values are established in a course of the identification — calculated performances are compared with the measured ones for several dozens of model stages tests with wide range of design parameters. The 4th version of the TU SPb modeling method (the set of the several computer programs) was applied in design practice in 1993–2010. Some Russian and foreign manufacturers realized several dozens of designed compressors with power up to 25 MW. The level of design point parameters prediction was so satisfactory that the manufacturers do not prove designs by model tests anymore. The whole performance prediction was not so good. The other difficulty — to predict design point efficiency with accuracy about 0.5% the very careful choice of empirical coefficients is necessary. The difficulties have been overcome in the new 5th and 6th versions. Most effective multistage compressors plant test performances were modeled successfully by 5th version program with the single set of empirical coefficients. Calculated performances and geometry of several dozens of stages of these compressors can be are applied in designs as usual model stages. The current designs are executed by the 5th and 6th version computer programs. The single stage 32 MW pipe line compressor was recently designed for the Ukrainian partner who offered high-RPM drive and favorable single-stage scheme. The test of the model at the 1:2 scale validated project parameters. Design pressure ratio and efficiency curves have matched completely. The predicted maximum efficiency 90% was proven.

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To calculate the efficiency of a centrifugal compressor, it is sufficient to know the design parameters and similarity criteria: flow rate coefficient, loading factor, relative hub ratio, Mach number. The effect of the inlet nozzle and the diffuser type is also taken into account. The original simplified model was successfully used for calculation of compressors' candidates in computer programs of the Universal Modelling Method. Recently, the model has undergone significant revision and been remade. The modernized model is used in the program for primary design of centrifugal compressors. The authors verified the new model, comparing the calculated efficiency with the measured efficiency of several dozens of model stages 21CV family and low flow rate model stages. In total, calculations were carried out for more than thirty model stages. The range of design parameters of analysed model stages is quite wide: flow rate coefficient 0.00564 -0.0676; loading factor 0.384 -0.742; hub ratio 0.258 -0.466.

Various engineering techniques are used to calculate and design centrifugal compressors, one of which is the Universal Modelling Method developed at SPbPU. Variants’ of centrifugal compressors analysis is the first step in gas-dynamic design. Brief information on the simplified mathematical model of efficiency is presented. It is possible to compare the variants of compressors with different number of shafts, shafts RPM, the number and location of intercoolers, the type of impellers and diffusers. Examples of a variants’ calculation of a pipeline compressors, a compressor for underground gas storage and a general-purpose air compressor are presented. It is shown that single-shaft compressors for underground gas storages should be optimized by selecting the maximum possible number of stages, by selecting the ratio of loading factors and the diameters of the impellers. It is shown that the single-shaft scheme of a general-purpose air compressor is inferior in efficiency to a two-shaft scheme with larger number of intercoolers. The presented samples have demonstrated that computer program based on a simplified mathematical model for industrial centrifugal compressors provides reliable and sufficient information for different compressors variants’ analysis.