# Research on Real-Time Model of Turboshaft Engine with Surge Process
## 3 Real-Time Surge Model of Turboshaft Engine
### Coupling Relationship between Extended MG Model and CLM  
The extended MG model well describes the dynamic process of the compressor instability at different rotor speeds, while the CLM can simulate the overall aero-thermal parameters of the dynamic process of the whole engine. Therefore, it is considered to estab  
Figure 7: Compressor characteristic curves cluster. lish a connection between the two models, and transfer the compressor surge characteristics to the CLM to realize the simulation of the whole engine surge behavior. In the extended MG model, the mass flow, pressure, and time are dimensionless as follows:  
\[\left\{ \begin{array}{l}\Phi=\frac{W_{a3}}{\rho A_{C}U}\\ \Psi=\frac{P_{3}-P_{2}}{\rho U^{2}}\\ \zeta=\frac{U}{K}\end{array} \right. \tag{21}\]  
Therefore, the relationship between the pressure coefficient, the flow coefficient and the actual parameters of the compressor components can be derived according to Equation (22):  
\[\left\{ \begin{array}{l}W_{a3}=\Phi\cdot\rho A_{C}U\\ P_{3}=P_{2}+\Psi\cdot\rho U^{2}\end{array} \right. \tag{22}\]  
It is obvious that the flow coefficient \(\Phi\) and the pressure coefficient \(\Psi\) calculated by the extended MG model are linearly related to the compressor's actual mass flow \(W_{a3 CLM}\) and pressure \(P_{3 CLM}\), thus the change of the pressure rise coefficient and the flow coefficient in the surge dynamic process and the change of the actual outlet pressure and flow of the compressor must be consistent. Normalize \(\Phi\) and \(\Psi\) as in Equation (23) to obtain the flow instability coefficient \(C_{\Phi}\) and the pressure rise instability coefficient \(C_{\Psi}\), which describe the changes in \(\Phi\) and \(\Psi\) compared to the steady operation when the surge occurs. Finally, the compressor outlet pressure and flow under surge conditions, \(W^{\prime}_{a3}\) and \(P^{\prime}_{3}\) can be obtained in Equation (24) and the surge process of the extended MG model is mapped to the component-level model. \[\left\{ \begin{array}{l}C_{\Phi}=\frac{\Phi}{\Phi_{0}}\\ C_{\Psi}=\frac{\Psi}{\Psi_{0}}\end{array} \right. \tag{23}\]  
\[\left\{ \begin{array}{l}W_{a3}{}^{\prime}=C_{\Phi}\cdot W_{a3}\\ P_{3}{}^{\prime}=C_{\Psi}\cdot P_{3}\end{array} \right. \tag{24}\]  
It should be noted that when the surge occurs in the engine, although the compressor outlet parameters show a large low-frequency pulsation, considering the overall rotor inertia and thermal inertia of the engine, the performance parameters such as speed and exhaust temperature do not follow the pulsation, but show a slow downward trend. After \(W_{a3}\) and \(P_{3}\) being calculated, if the pulsating flow and pressure are directly substituted into the components and subsequent components calculation of CLM, the characteristics of performance parameters such as speed and exhaust gas temperature will also show pulsation, which is not consistent with the actual surge process. Therefore, after the \(W^{\prime}_{a3}\) and \(P^{\prime}_{3}\) are calculated, they are just recorded as the mass flow and pressure at the compressor outlet, but not substituted into the subsequent calculations in CLM. Instead, the Savitzky-Golay smoothing filter is used to \(C_{\Phi}\) and \(C_{\Psi}\) to get \(C^{\prime}_{\Phi}\) and \(C^{\prime}_{\Psi}\) in Figure 8, and then calculate the actual outlet mass flow \(W_{a3 CLM}\) and pressure \(P_{3 CLM}\) of the compressor in CLM again which will be substituted into the subsequent calculation of CLM. As the engine goes through the process of stable--surge--stable, the mass flow and pressure after filtering show a slow downward trend and will slowly return to the original level before the surge when the stability is recovered, which is in line with the characteristics of the slow change of the engine performance parameters during the actual whole engine surge process. In summary, the structure of the turboshaft engine real-time surge model based on the surge mechanism model is shown in Figure 9, including two parts: the component-level model and the extended MG model.