# Analytical Calculation Model of the TV3-117 Turboshaft Working Regimes Based on Experimental Data
## 3 Similarity Parameters and Experimental Data  
The concept of the analytic model calculation is based on the analysis of experimental data from the working regimes of several engines. This analysis aims to determine a series of ratio parameters that have an approximately constant variation from the idle to the takeoff regime. These parameters are called similarity parameters [1; 2; 3; 4; 5] and are used in the analytical calculation model as reference parameters. Usually, the engine regimes are defined through the engine shaft speed. The current analytic calculation model used experimental data from three different types of engines: the TV2-117A turboshaft, AI-20K turboprop, and Viper 632-41 turbojet. These engines were involved in testing applications following the run on the test bench [14; 15]. The data results presented in the current paper are the post processing results of raw experimental data from our own previous research papers [14; 15]. Based on this, the percentage variation in the engine's main parameters (\(\Delta{prm_{i}}\)) is determined by reporting to the takeoff regime in order to observe the variation limits of each parameter and to identify certain parameters or ratio parameters that have variations within close limits. These can be used as similarity parameters. \[\Delta{prm_{i}}=\frac{{prm_{i}}}{{prm_{(TO)}}}\times 100 \tag{1}\]  
For a valid analysis, it is essential to use corrected parameters because the experimental data were acquired under various atmospheric conditions. Thus, it needs to be reported to standard atmospheric condition. Typically, the fundamental corrected parameters involve speed, temperatures, and pressures in the engine main stations, as well as air mass flow and fuel flow. These parameters are defined by the following formulas:  
\[N_{co}=N\times\sqrt{\frac{{288}}{{T_{1}}}};T_{ico}=T_{i}\times\frac{{288}}{{T_{ 1}}};p_{ico}=p_{i}\times\frac{{1.01325}}{{p_{1}}} \tag{2}\]  
\[M_{af}=M_{af,co}\times\frac{{1.01325}}{{p_{1}}}\times\sqrt{\frac{{T_{1}}}{{288 }}};F_{f,co}=F_{f}\times\frac{{1.01325}}{{p_{1}}}\times\sqrt{\frac{{288}}{{T_{ 1}}}} \tag{3}\]  
The corrected values of the main engine parameters are different than actual values, but the percentage variation is the same. The percentage values of certain corrected main engine parameters are grouped into a series of tables. In Table 2 are shown the percentage values of inlet turbine total temperature (\(T_{3t}\)) and overall total pressure ratio (\(\pi_{ct}\)). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**TV2** & **AI-20** & **Viper** & **TV2** & **AI-20** & **Viper** & **TV2** & **AI-20** & **Viper** \\ \hline  & \(N_{co}\) [\%] & & & & \(T_{3t,co}\) [\%] & & & \(\pi_{CLo}\) [\%] & \\ \hline
64.1 & - & 50.6 & 68.46 & - & 64.46 & 33.03 & - & 26.07 \\
83.3 & 59.3 & 61.4 & 77.27 & 86.68 & 66.16 & 52.08 & 32.88 & 33.08 \\
85.5 & 64.8 & 71.5 & 79.05 & 86.0 & 67.52 & 56.68 & 38.31 & 42.88 \\
88.3 & 72.5 & 76.9 & 82.51 & 87.23 & 69.88 & 64.62 & 47.67 & 49.44 \\
90.5 & 76.0 & 81.5 & 85.75 & 88.84 & 72.88 & 72.6 & 52.46 & 55.88 \\
92.5 & 79.3 & 87.1 & 89.84 & 83.84 & 76.42 & 81.57 & 60.73 & 65.63 \\
94.2 & 84.0 & 92.2 & 92.65 & 86.84 & 82.31 & 86.55 & 70.56 & 76.13 \\
95.6 & 89.4 & 97.1 & 96.0 & 92.04 & 90.44 & 92.21 & 83.58 & 89.24 \\
96.9 & 93.8 & 100.4 & 99.11 & 98.12 & 96.38 & 97.67 & 96.58 & 96.18 \\
97.5 & 95.0 & 102.4 & 100 & 100 & 100 & 100 & 100 & 100 \\ \hline \end{tabular}
\end{table} 
Table 2: Percentage variation in corrected inlet turbine temperature (\(T_{3t,co}\)) and overall pressure ratio (\(\pi_{CLo}\)) with engine speed (\(N_{co}\)). In Table 3 are grouped the percentage values of the air mass flow (_Ma\(\beta\)_) and fuel flow (_Ff_). The Table 4 shows the compressor total adiabatic efficiency (\(\eta_{CI}\)) and turbine total adiabatic efficiency (\(\eta_{TI}\)). In Table 5 are shown the percentage values of combustor chamber total pressure loss (\(\sigma_{cat}\)) and burn efficiency (\(\eta_{cch}\)).