Perfection of turbojet mathematical model for considering the additional criteria at a stage of its parameters choice


Аuthors

Ezrokhi Y. A.*, Kalenskii S. M.**

Central Institute of Aviation Motors named after P.I. Baranov, CIAM, 2, Aviamotornaya str., Moscow, 111116, Russia

*e-mail: yaezrokhi@ciam.ru
**e-mail: 30105@ciam.ru

Abstract

In the presented article the basic problems of the turbojet mathematical modeling at a preliminary design stage are considered. It is shown, that parameters of strength reliability can become the main limitation by selection of high parameters of a thermodynamic cycle of the created engine. Application of ways of the simplified estimation of parameters describing strength and resource characteristics on an example of the turbine rotor blade (RB) is considered.

As the most simple and widespread version of the account of strength and resource factors the selection way of cooling type and the necessary consumption of cooling air δGcool is presented. Quantity of air taken from the compressor should provide value of temperature of a surface of a RB of the turbine at an admissible level. For this purpose so-called «depth of cooling» θ blades of the turbine is determined. It depends on cooling air temperature, a gas stream temperature and as much as possible admissible temperature of the RB surface. On value of a gas stream temperature in front of the turbine the way of a RB cooling gets out. After definition of the cooling way and «depth of cooling» a RB of the turbine the demanded consumption of cooling air on an available relation δGcool=f(θ) is determined.

Other way of the approximate account of strength properties of the turbine RB is connected with an indirect estimation of tension stress in its root cross-section σр. In the basis of this approach the known relation of tension stress to parameters rotating with frequency n, radially disposed bar lays. Difference of the turbine RB from a rectangular bar is characterized by factor of form Ф=0,48…0,54. At a known material and parameters of the turbine RB stress in its root cross-section is determined by a square of a rotational speed and the area FT of ring cross-section of the vane wheel rotor (σр = const ·FT ·n2).

For an estimation of the parameter qualitatively describing resource of the turbine RB, parameter of Larson-Miller Р is used. It connects among themselves blade temperature Тbl and value of the time parameter τр describing duration of a continuous work before destruction of this element under affecting of thermal and mechanical factors Р=Тbl · (lg(τр)+20). For the chosen material of a turbine blade exists gained by practical consideration dependence between Larson-Miller's parameter and long-term strength.

It is in summary noted, that definition resource characteristic of a real product represents a challenge and can be realized only at later stages of the engine creation. However it does not remove necessity at a preliminary stage of sampling of the turbojet parameters to have some approached approaches, presented above. The given approaches allow even to spend at the earliest stages of a engine creation a preliminary comparative estimation of observed alternatives by fuller criteria.

Keywords:

mathematical model, turbojet, consumption of cooling air, rotor blading of the turbine, heat-stressed condition

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