Gas turbine engines processes mathematic simulations are widely used in different steps of its living cycle. All engine simulations may be divided into different difficulty levels: higher simulation level allows doing a more pre­cise description of physical processes in main units of gas turbine engines and their elements. It gives the oppor­tunity for getting better arrangement of calculation results and experimental data, reduce the quality of factors, which are traditionally used in determine engine operational characteristics with 1-level models. The purpose of the article is to describe the thermogasdynamic parameters and maintenance perfomances cal­culation method, which based on second level mathematic simulation. Its main feature is blade-to-blade turbomachines description (multistage compressor and multistage cooling gas turbine), which allows to take into account blade and flow path geometrical parameters. Their changing during the gas turbine engine design and de­velopment processes influence its performances: thrust, fuel consumption, efficiency as functions of values of flow rate, rotational speed, engine entrance conditions and so on. All these dependences could be defined by using proposed calculation method. In distinction from methods which are noted, this method allows to concede compressor or turbine incidence angles, drag values, pressure ratio, surge margin in design and off-design  engine regimes. The opportunity to take into account by-passing and air bleeding from compressor blade channels and their engine parameters influence is very important also. The article includes calculation method main points, block-scheme, equations system, which gives the opportunity of alignment the engine units and their elements in wide range of state working regimes. Set of equations consists of flow rate balance equations through the stages of multistage compressor and turbine, combustion chamber and connected channels. Also system includes power balance equations, by-passing, air bleeding from compressor stages channels, its admission into the cooling turbine stages and ac­counts their thermodynamic parameters. Compressors and turbines maps parameters are calculated with main turbomachinery theory lows and semi-empirical dependences. This article is the first in series of articles, which considers this problem


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