# Analytical Calculation Model of the TV3-117 Turboshaft Working Regimes Based on Experimental Data
## 4 Analytical Calculation Model
\[F_{f}=\frac{P\times 0.736\times SFC}{3600}\ \ \Rightarrow\ \ M_{af}=\frac{F_{f}}{ff_{c}}\ \ \ \Rightarrow\ \ G_{f}=\ \ M_{af}+F_{f} \tag{19}\]  
\[p_{2.t.id}=p_{2.t}\ \ \Rightarrow\ \ s_{a}(T_{2.t.id})=s_{1.t}+R_{a}\times ln \Big{(}\frac{p_{2.t}}{p_{0}}\Big{)}\ \ \ \Rightarrow\ \ T_{2.t.id} \tag{20}\]  
\[l_{C.t.id}=h_{a}(T_{2.t.id})-h_{a}(T_{0})\ \ \Rightarrow\ \ l_{C.t}=\frac{l_{C.id}}{\eta_{C.t}} \tag{21}\]  
\[l_{T{\rm G.}t}=\frac{M_{af}}{G_{f}}\times\frac{l_{C.t}}{\eta_{m}};\ \ \ l_{T{\rm P.}t}=\frac{P\times 0 736}{G_{f}};\ \ \Rightarrow\ \ l_{T.t}=l_{T{\rm G.}t}+l_{T{\rm P.}t} \tag{22}\]  
\[h_{g}(T_{4.t})=h_{g}(T_{3.t})-l_{T{\rm G.}t}\ \ \Rightarrow\ \ T_{4.t} \tag{23}\]  
\[H_{R}\Big{(}T_{2,t},T_{f}\Big{)}=H_{P}(T_{3,t}) \tag{15}\]0  
Following the application of the above calculation model, in Table 15 are presented the calculated values of the similarity parameters from the takeoff regime. \begin{table}
\begin{tabular}{c c c c c c c} \hline \(p_{3.t}\) [bar] & \(G_{f}\) [kg/s] & \(T_{3.t}\) [K] & \(T_{4.t}\) [K] & \(\frac{N}{\sqrt{T_{3.t}}}\) [-] & \(\frac{G_{f}\times\sqrt{T_{3.t}}}{p_{3.t}}\) [-] & \(\frac{l_{C.t}}{N^{2}}\) [-] & \(\frac{T_{3.t}}{T_{4.t}}\) [-] \\ \hline
9.630 & 7.794 & 1248 & 803 & 0.028 & 29.478 & 325.8 & 1.553 \\ \hline \end{tabular}
\end{table} 
Table 15: Calculated values of the similarity parameters at the takeoff regime. From this point, the engine working regimes lower than takeoff can be calculated. In the current case, the calculation of the TV3-117 MT engine operating regimes starts by using the same regime speed of the gas generator, N = 96.1, 94.7, 93.5, 91.5, and 73.0 [%], as is specified in the engine manual. In this way, it a comparison method of the calculated regimes is performed with the operating regimes shown in the engine manual. Therefore, the engine main parameters and performance for the other regimes, from the idle to nominal regime, are calculated by using the next set of equations in the following order. The compressor total adiabatic efficiency:  
\[\left(\eta_{C\,t}\right)_{R}=\left(0.96\div 1\right)\times\left(\eta_{C\,t} \right)_{\text{TO}}\ \ \Rightarrow\ \ \left(\eta_{C\,t}\right)_{R} \tag{25}\]  
The compressor total specific actual work:  
\[\left(\frac{I_{C\,t}}{N^{2}}\right)_{R}=\left(0.85\div 1\right)\times\left( \frac{I_{C\,t}}{N^{2}}\right)_{\text{TO}}\ \ \Rightarrow\ \ \left(I_{C}\right)_{R}. \tag{26}\]  
The ideal compressor outlet total temperature:  
\[\left(I_{C\,t\,id}=\eta_{C\,t}\times I_{C\,t}\right)_{R}\ \ \Rightarrow\ \ \left(I_{C\,t\,id}\right)_{R}\ \ ; \tag{27}\]  
\[\left(h_{2\,id}=I_{C\,t\,id}-h_{0}\right)_{R}\ \ \Rightarrow\ \ \left(h_{2\,id}\right)_{R}\ \ ; \tag{28}\]  
\[\left(h_{2\,id}\right)_{R}=h_{a}\left(T_{2\,t\,id}\right)_{R}\ \ \Rightarrow\ \ \left(T_{2\,t\,id}\right)_{R}. \tag{29}\]  
The compressor outlet total pressure:  
\[\left(s_{1,t}=s_{2\,t\,id}=s_{a}\left(T_{2\,t\,id}\right)-R_{a}\times ln\left( p_{2\,t}/p_{0}\right)\right)_{R}; \tag{30}\]  
\[\left(p_{2\,t}\right)_{R}=p_{0}\circ e^{\left(\frac{s_{a}\circ\left(T_{2\,t\, id}\right)-s_{1\,t}}{R_{a}}\right)}\ \ \Rightarrow\ \ \left(p_{2\,t}\right)_{R}. \tag{31}\]  
The turbine inlet total pressure:  
\[\left(\sigma_{\alpha\,t}\right)_{R}=\left(0.96\div 1\right)\times\left(\sigma_{ \alpha\,t}\right)_{\text{TO}}\ \ \Rightarrow\ \ \left(\sigma_{\alpha\,t}\right)_{R}; \tag{32}\]  
\[\left(p_{3\,t}=p_{2\,t}\times\sigma_{\alpha\,t}\right)_{R}\ \ \Rightarrow\ \ \left(p_{3\,t}\right)_{R}. \tag{33}\]  
The turbine inlet total temperature:  
\[\left(\eta_{C\,t}\right)_{R}=\left(0.96\div 1\right)\times\left(\eta_{C\,t} \right)_{\text{TO}}\ \ \Rightarrow\ \ \left(\eta_{C\,t}\right)_{R} \tag{25}\]0  
The gases flow:  
\[\left(\eta_{C\,t}\right)_{R}=\left(0.96\div 1\right)\times\left(\eta_{C\,t} \right)_{\text{TO}}\ \ \Rightarrow\ \ \left(\eta_{C\,t}\right)_{R} \tag{25}\]1  
From this point, the analytical model, continues with the calculation of air excess [22] at each regime by applying the same method described for the takeoff.