# Gas turbine engine lubrication system mathematical modeling specifics

### Аuthors

Schurovskiy Y. M.

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

e-mail: shchurovsky@ciam.ru

### Abstract

The paper presents the developing principles of dynamic mathematical model of oil systems with electrically driven pumps for gas turbine engines (GTE).

The oil system with electrically driven pumps can replace the traditional system with pumps driven by gearbox. The demonstrational oil system model with adjustable electrically driven pumps was developed in the CIAM. Experimental studies of its characteristics on the workbench with the simulator oil chamber GTE demonstrated the complexity of hydro- and gas-dynamic processes occurring in it, and the need to develop dynamic models of such systems. The literature generally discusses the mathematical models for the study of oil systems based on static hydraulic ratios without considering the dynamic characteristics of pipelines, gas content changes over the path of pumping the two-phase mixture, and others.

The dynamic mathematical model of the system based on finite element with lumped parameters is designed to sel ect its characteristics and control laws. The finite element describes the part of pneumo-hydraulic circuit of oil system. Gas and hydraulic network system are divided into separate sections of working medium flow (pipelines, etc.), concentrated volumes, pumps, located on sections, are described by quasi-static characteristics. The distributed pressure losses due to friction within the pipeline are focused at the border and summed with the losses on other hydraulic resistances of this section.

It is assumed, that the pressure, temperature, mass gas content and thermal characteristics of the working mixture are constant along length of the concentrated section and vary only in time. The volumes of the type of oil cavity, where two-phase medium is formed fr om air and oil, describe the stratified flow of oil-air and air-oil mixtures. The change of thermal and thermodynamic characteristics is calculated in the acoustic volumes, where the two-phase flows merge. Calculation of two-phase mixture movement in the pipelines is made with allowance for its inertia and compressibility. Solution of the system model is carried out in a computer program by direct numerical calculation without iterations (Euler method).

Comparison of the calculated and experimental processes in the demonstration lubrication system revealed their good agreement in the area of the 1-st tone oscillations of hydraulic network system 0.2 ... 5 Hz.

### Keywords:

gas-turbine engine, lubrication system, controlled electric drive, dynamic mathematical model, two-phase flow

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