# Potentials for Pressure Gain Combustion in Advanced Gas Turbine Cycles
## Materials and Methods
### Optimization Setup  
The optimizations were run on the in-house software IPSM (Interface for performance and SAS modeling [31]) and identified the optimum gas turbine designs for predefined constraints. For this study, the first constraint was shaft power, which was held constant at 6.63 MW. The second constraint was the turbine blade temperature calculated by Equation (1). For this study, three different temperatures were investigated: a very conservative blade temperature of 1000 K, a reasonable 1100 K, and a high 1200 K. The temperature range was identified based on data provided by [32]. Additionally, the secondary air mass flow was limited to a maximum of 35% of the engine inlet mass flow. The three constraints are listed in Table 3.  
Depending on the gas turbine cycle, the optimization had two or three variables. For the simple and recuperated cycle, engine mass flow and compressor pressure ratio were the degrees of freedom. For the intercooled and intercooled-recuperated engine, the second compressor pressure ratio was an additional variable. The parameter spaces were {2, 50} kg/s for engine mass flow and {2, 50} for the compressor pressure ratio. Here, the overall compressor pressure ratio was limited to 50 for intercooled setups. Engine mass flow as a variable was selected because it represented the engine size. Furthermore, engine mass flow directly provided the specific work, because the power output was held constant. Compressor pressure ratios were selected as the main thermodynamic parameter of influence. Since blade metal temperature and power output were selected as constraints, this setup calculated TET, which delivered the required power output and did not exceed the blade temperature margin. The objective function of the optimization was thermal efficiency, defined as follows:  
\[\eta_{th}=\frac{PW_{output}}{\dot{m}_{fuel}\cdot LHV} \tag{12}\]  
\begin{table}
\begin{tabular}{c c c} \hline \hline Output power & \(=\) & 6.63 MW \\ Turbine blade temperature & \(\leq\) & 1000 K, 1100 K, 1200 K \\ Cooling mass flow/engine mass flow & \(\leq\) & 35\% \\ \hline \hline \end{tabular}
\end{table}
Table 3: Constraints for optimizations.  
Figure 2: Pressure ratio as a function of the temperature ratio for the analyzed PGC models [19]. opt, optimistic; pes, pessimistic.  
The workflow applied for the optimizations is sketched in Figure 3. It included the optimization loop providing the degrees of freedom to the gas turbine performance model in order to maximize the thermal efficiency \(\eta_{th}\) and an embedded iterative process. The latter ensured the coolant flow matched the defined metal temperature. The required cooling flow was calculated using Equation (1). The input parameters were directly taken from the performance simulation results. The calculated mass flow was used as a new input to the performance model. This loop was iterated till convergence was reached. The optimization combined two different types of algorithms sequentially. First, an in-house-developed evolutionary algorithm was applied to the optimization problem in order to browse the parameter space for promising regions. Subsequently, a gradient-based algorithm continued the optimization on a set of the best solutions found by the evolutionary algorithm.