# Mathematical model for calculating the mass of a heat exchanger in problems of optimizing the parameters of the working process of aircraft gas turbine engines

## Abstract

Despite the fact that aviation gas turbine engines (GTE) have reached a high degree of sophistication, requirements for the improvement of their efficiency are constantly increasing. Reduction of specific fuel consumption and specific weight of the engine unit makes it possible to improve aircraft performance. One of the effective means of reducing specific fuel consumption and obtaining high thermal efficiency of a gas turbine engine is the use of heat recovery, so the interest in it holds throughout the period of development of gas turbine engines. However, the use of heat recovery in aircraft gas turbine engines is faced with a contradiction: on the one hand, heat recovery allows reducing specific fuel consumption, but, on the other hand, it increases the weight of the power plant due to the presence of a heat exchanger. Moreover, with the increase in the degree of regeneration, specific fuel consumption decreases, whereas the mass of the power plant increases.To obtain the desired effect, it is necessary to optimize simultaneously both the parameters of the engine work process and the degree of regeneration of the heat exchanger according to the criteria of evaluating the engine unit in the aircraft system. For this purpose, it is necessary to have a mathematical model for estimating the weight of a highly efficient aircraft heat exchanger. The article presents a developed mathematical model for calculating the weight of a compact plate heat exchanger used to increase the efficiency of a gas turbine engine due to the heating of compressed air entering the combustion chamber by the hot gas that enters the combustion chamber from behind the turbine. We chose a rational pattern of relative motion of the working media in the heat exchanger, the optimal type of plate-type heat transfer surface in terms of minimizing the weight of the heat exchanger and the hydraulic losses in the air and gas ducts. For the selected surface type, the dependence of the specific weight of the heat exchanger on the degree of regeneration is determined for different nozzle exhaust velocities on the basis of a computational algorithm. To assess the reliability of the obtained model, comparative analysis of the effect of the degree of regeneration on the specific weight of the heat exchanger was carried out, based on the comparison of the results of calculations for the developed model with the data of other authors and with the data for the produced regenerators.

## Keywords

### V. S. Kuz'michev

Samara National Research University

Author for correspondence.
Email: kuzm@ssau.ru

Doctor of Science (Engineering), Professor
Professor of the Department of Theory of Aircraft Engines

Russian Federation

### H. Omar

Samara National Research University

Email: dr.hewa.omar@gmail.com

Graduate Student of the Department of Theory of Aircraft Engines

Russian Federation

### A. Yu. Tkachenko

Samara National Research University

Email: tau@ssau.ru

Candidate of Science (Engineering), Associate Professor
Assistant Professor of the Department of Theory of Aircraft Engines

Russian Federation

### A. A. Bobrik

Samara National Research University

Email: bobrik000al@mail.ru

Graduate Student of the Department of Theory of Aircraft Engines

Russian Federation

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