# Analytical Calculation Model of the TV3-117 Turboshaft Working Regimes Based on Experimental Data
## 1 Introduction  
The use of an analytical calculation methodology to determine the working regimes of gas turbine engines, from the idle to maximum regime, is not commonly presented in gas turbine theory, turbomachinery books, or research papers [1, 2]. This approach, valuable for gas turbine education and practical engineering applications, needs more exposure. Generally, thermodynamic calculation models for gas turbine engines are based on a series of assumptions, which are defined by certain parameters or coefficients, which are assigned constant values, in order to generate an easier calculation algorithm [3, 4]. In the case of regime calculation, by using the calculation assumptions, mathematical relations between the parameters of the known regime with the parameters of the unknown regime can be determined. The calculation models can use dimensional or kinematic parameters, such as diameters, cross sections, velocities, blade angles, as well as thermodynamic parameters such as engine main parameters and performances. By default, these models incorporate the mathematical relations between the dimensional, kinematic, and thermodynamic parameters [5, 6].  
The models that combine dimensional or kinematic parameters with thermodynamic parameters are less accessible for use. This is because most specifications of an engine, as presented on data sheets, refer to the engine's main parameters and performance not its dimensional or kinematic parameters. Even in the engine manuals, the dimensional and kinematic parameters for the main station of the engine are not specified. Therefore, a calculation model that uses only thermodynamic parameters is more accessible and flexible for use or development. The development of an analytical calculation model requires a database with values and variations of the engine's main parameters and performance.  
In the field of gas turbine performance calculation, from the standpoint of accuracy and precision, there are specific professional software programs, such as the Gas TurbProgram [7] presented in Figure 1a, Gas Turbine Simulation Program (GSP) [8] presented in Figure 1b, and the Propulsion Object-Oriented Simulation Software (PROOSIS) [9], that are advanced tools of gas turbine engines working simulation and performance analysis. These software programs implemented mathematical calculation models using various engine parameters. Through a graphical interface, they are used to determine and simulate engine performances and working regimes.  
To use these software programs, a license is required, which you must pay for. Additionally, when using these types of software, the user becomes just an operator without understanding the equation system behind the software. The mathematical models used in the professional software [7; 8; 9] are based on a vast and valid data library from engine measurements, experiments, and tests used in order to generate a closely realistic simulation. There are specific research or work papers [10; 11; 12; 13], similar from an engineering point of view to the current paper, that study the development of a gas turbine design and off-design performance calculation models. The current paper presents a mathematical model based on a limited data library, but with valid experimental data acquired from engine testing applications presented in some of our previous research papers [14; 15].  
A simple engine modeling approach involves processing the performance data provided by the engine manufacturer. By applying basic thermodynamic relationships, it is possible to predict the performance of gas turbines in terms of the engine life cycle [16].