   ## Dynamic a rolling motor model

This model is usually built in a number of the following assumptions:

- description of the gas-dynamic processes in the engine path is performed in a one-dimensional formulation in concentrated parameters;

- when calculating transient modes, stationary characteristics of blade machines (compressors, turbines) are used;

- the equations of gas dynamics are written without taking into account mass forces and viscosity;

- processes in the mixer and the nozzle rely isentropic and other, less significant assumptions.

These assumptions do not prevent the implementation of a sufficiently accurate model identification in a wide range of operating conditions of the engine and the flight conditions.

In models of this type are taken into account the inertia of the rotating masses, unsteady gas-dynamic processes, the dependence of the adiabatic temperature and gas composition, power take-off from the rotor to drive various units, bleed air from the compressor and the external circuit for cooling the engine and the aircraft needs, variation of the completeness of combustion main and reheat combustion chambers depending on the gas composition and pressure and other factors.

If required for specific tasks model allows us to take into account the processes of unsteady heat transfer of the gas flow and the structural elements of the engine used by the respective correction characteristics.

The mathematical model uses a rolling static characteristics of nodes, that allows extensive use of experimental data and improve the accuracy of identification. Application of the basic equations of gas dynamics in the non-stationary form makes it possible to take into account the dynamic properties of the gas path in the engine and extend the frequency range of applicability of the model, which is important for some of the problems of the dynamics control (for example, the calculation processes of the FCC and the nozzle).

At the same time it allows to solve the basic equations of the model with respect to the calculated coordinate and implement a consistent solution of equations in computer calculations without using iterative methods, which significantly reduces the time of calculation of transient processes in the engine. Steady modes in this model are considered "by the establishment."

A mathematically nodal GTE model is represented by a system of algebraic and nonlinear ordinary differential equations of order 8-10. The basic relations used in it to describe processes in typical elements and engine nodes, in combination with static dependencies representing the characteristics of the nodes, and equations for calculating thermogasdynamic parameters in the path, form a complete system of model equations. The independent coordinates in the model are external conditions (I, M, Tvh) and regulatory factors (GT, GT f, rv, <k, kP, Fc, etc.). 