# Analytical Calculation Model of the TV3-117 Turboshaft Working Regimes Based on Experimental Data
## 3 Similarity Parameters and Experimental Data
\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  & \(N_{\omega}\)**[\%] & & & & \(\eta_{CI,\omega}\)**[\%] & & & \(\eta_{TC,\omega}\)**[\%] & \\ \hline
64.80 & - & 49.4 & 99.0 & - & 94.70 & 96.08 & - & 61.35 \\
84.30 & 59.7 & 60 & 95.48 & 91.59 & 96.83 & 97.83 & 90.07 & 83.94 \\
86.50 & 65.4 & 69.9 & 95.26 & 96.02 & 102.00 & 100.27 & 91.37 & 79.69 \\
89.40 & 73.1 & 75.3 & 96.79 & 98.98 & 104.44 & 101.62 & 93.07 & 78.58 \\
91.70 & 76.7 & 79.7 & 98.13 & 97.84 & 103.78 & 102.37 & 95.29 & 77.52 \\
93.80 & 80.0 & 85 & 98.44 & 98.64 & 101.49 & 101.74 & 99.08 & 109.27 \\
95.50 & 84.9 & 90 & 99.34 & 99.89 & 103.62 & 101.44 & 98.04 & 102.18 \\
97.00 & 90.2 & 94.8 & 99.54 & 99.55 & 104.23 & 100.43 & 98.95 & 100.40 \\
98.40 & 94.8 & 98 & 99.26 & 99.89 & 101.57 & 100.22 & 99.35 & 100.50 \\
99.11 & 96.0 & 100 & 100 & 100 & 100 & 100 & 100 & 100 \\ \hline \end{tabular}
\end{table} 
Table 4: Percentage variation in corrected compressor total adiabatic efficiency (\(\eta_{CI,\omega}\) [%]), and turbine total adiabatic efficiency (\(\eta_{TI,\omega}\)) with corrected engine speed (\(N\)). \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  & \(N_{\omega}\)**[\%]** & & & \(\sigma_{cat}\)**[\%]** & & & \(\eta_{cch}\)**[-]** & \\ \hline
64.80 & - & 49.4 & - & - & 101.58 & - & - & 96.16 \\
84.30 & 59.7 & 60 & - & 101.05 & 100.21 & - & 98.96 & 97.52 \\
86.50 & 65.4 & 69.9 & - & 100.63 & 99.00 & - & 96.87 & 98.27 \\
89.40 & 73.1 & 75.3 & - & 100.42 & 98.92 & - & 98.85 & 98.66 \\
91.70 & 76.7 & 79.7 & - & 100.11 & 98.90 & - & 99.48 & 98.99 \\
93.80 & 80.0 & 85 & - & 98.95 & 98.66 & - & 98.96 & 99.36 \\
95.50 & 84.9 & 90 & - & 98.95 & 99.09 & - & 100.94 & 99.65 \\
97.00 & 90.2 & 94.8 & - & 100.0 & 99.61 & - & 100.94 & 99.88 \\
98.40 & 94.8 & 98 & - & 100.0 & 99.83 & - & 100.10 & 99.96 \\
99.11 & 96.0 & 100 & - & 100 & 100 & - & 100 & 100 \\ \hline \end{tabular}
\end{table} 
Table 5: Percentage variation in combustor chamber total pressure loss (\(\sigma_{cat}\)) and burn efficiency (\(\eta_{cch}\)) with the corrected engine speed (\(N\)). Following the percentage analysis, it was found that the engine main parameters varied from idle to the takeoff between certain limits. Additionally, it is noteworthy that not all parameters have the same value variations or vary in the same way, as shown in Table 6.  
According to gas turbine theory, there are certain similarity parameters used in thermodynamics calculations as constants. These parameters are ratios of specific main engine parameters, among which the most commonly used ones are mentioned. \[\left(\frac{N}{\sqrt{T_{3,t}}}\right)_{TO}\quad\left(\frac{G_{f}\times\sqrt{T_ {3,t}}}{P_{3,t}}\right)_{TO}\quad\left(\frac{l_{CI}}{N^{2}}\right)_{TO} \tag{4}\]  
Following the percentage variation analyses, an additional coefficient is defined, namely the turbine temperature ratio, which can be used as a similarity parameter. \[\left(\frac{T_{3,t}}{T_{4,t}}\right)_{TO} \tag{5}\]  
One objective of the percentage variation analysis was to validate, through the calculation, based on measured data, that the similarity parameter indeed maintains nearly constant values as is specified in engine gas turbine theory. The percentage values of the similarity parameter are presented in the subsequent tables: Tables 7 and 8. In order to have a better view about the percentage variations of each similarity parameter of each studied engine reported to the engine speed, the data results are grouped into a series of tables form Tables 9-12. Thus, in Tables 9 and 10 are shown the percentage values of the first and secondary similarity parameter, which are the most used in gas turbine theory. In Table 11 are shown the percentage values of the third similarity parameter, which usually are used on compressor map performance calculation.