# A Study on Combined Variable Geometries Regulation of Adaptive Cycle Engine during Throttling
## 2 Structural Analysis and Modeling of ACE
### ACE Modeling  
The performance model of ACE is a zero-dimensional (0D) engine model controlled by multiple variables which provides a platform suitable for parametric cycle analysis, performance analysis and control schedule study at different ACE working modes. To calculate the engine thermodynamic and performance parameters, specific parameters such as engine cycle parameters and component parameters should be given in advance via the combination of theoretical analysis and balance equations.  
To guarantee work of the ACE in triple bypass mode and double bypass mode, the related gas components are coupled together through the balance equations. The equations considered included the power-balance equations for each rotor, respectively, flow compatibility equations between the connected gas components and static pressure balance equations at the flow mixed zone.  
More details about general 0D engine performance simulation can be found in the literature [21; 22; 23]. As the analysis of ACE is still in the conceptual stage of research, performance simulation of ACE is developed based on the modeling of a mixed flow turbofan engine. The modeling theory and method has been tested and verified accurately as shown in Figures 5 and 6. Consequently, the accuracy of the performance model of ACE can satisfy requirements about the study of concept design in this paper.  
Figure 4: The gas paths diagram of ACE in double bypass mode.  
Figure 3: The gas paths diagram of ACE in triple bypass mode.  
The working condition of ACE is set as 0 km, 0 Ma, which is the design point's working condition in triple bypass mode to calculate the engine key geometry parameters. Some important design parameters at design point are shown in Tables 1 and 2. The losses in the bypass ducts and the variable bypass are transformed into total pressure recoveries which are calculated during engine performance simulation. For most of the time, the aircraft gas turbine engine works at appropriate power which is less than the maximal thrust, to cut down SFC. Conventional turbojets or turbofans modulate thrust by reducing airflow along with declined LPRS. The main characteristic of ACE is maintaining engine airflow as power is reduced to decrease spillage drag, and increase installed thrust during throttling. Based on the optimized design parameters and an optimized control of variable geometry regulation, it is possible to study the route and method of combined variable geometry regulation during throttling.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Parameters** & **Wa (kg/s)** & **B\({}_{\mathbf{t}}\)** & **B\({}_{\mathbf{3}}\)** & **B\({}_{\mathbf{2}}\)** & **B\({}_{\mathbf{1}}\)** \\ \hline value & 125 & 1.028 & 0.25 & 0.33 & 0.22 \\ \hline \end{tabular}
\end{table}
Table 1: Design point parameters of ACE (1). \(W_{a}\): total airflow.  
Figure 5: The demonstration of fuel consumption during throttling.NI: low pressure rotor speed.  
Figure 6: The demonstration of high pressure rotor speed (Nh) during throttling.  
The bypass ratio is defined as below: \(\mathrm{B_{t}}\): total bypass ratio; \(\mathrm{B_{3}}\): third bypass ratio; \(\mathrm{B_{2}}\): front bypass ratio; \(\mathrm{B_{1}}\): core bypass ratio; \(\mathrm{W_{af}}\): airflow of front fan; \(\mathrm{W_{av}}\): airflow of variable fan; \(\mathrm{W_{acdf}}\): airflow of CDFS; \(\mathrm{W_{ahpc}}\): airflow of HPC.  
\[\mathrm{B_{t}}=(\mathrm{W_{af}}-\mathrm{W_{ahpc}})/\mathrm{W_{ahpc}}, \tag{1}\]  
\[\mathrm{B_{3}}=(\mathrm{W_{af}}-\mathrm{W_{av}})/\mathrm{W_{av}}, \tag{2}\]  
\[\mathrm{B_{2}}=(\mathrm{W_{av}}-\mathrm{W_{acdf}})/\mathrm{W_{acdf}}, \tag{3}\]  
\[\mathrm{B_{1}}=(\mathrm{W_{acdf}}-\mathrm{W_{ahpc}})/\mathrm{W_{ahpc}}, \tag{4}\]