## 2 Materials and Methods
### Combustion Chamber
#### 2.2.2 Advanced Combustion  
In order to achieve a significant reduction in exhaust gas emissions in the future forecast, the FLOX (Flameless Oxidation) based combustion concept was chosen for the gas turbine. Here, the DLR institute of combustion technology has a deep expertise in the development, system integration, and operating behaviour in FLOX-based gas turbine combustion systems for stationary power supply [9; 10; 11; 12; 13]. The FLOX-based technology was chosen as it showed in many projects [14; 15; 16; 17] advantages in NO\({}_{x}\) emission levels, robustness towards thermo-acoustics, lean blow-off limits as well as fuel flexibility compared to swirls-stabilized concepts. Even though this technology is not yet present in aircraft gas turbines, recent projects aim to transfer this technology into the aircraft application to utilize these benefits [18]. As much more experience and experimental data of the FLOX-based technology is available in a can combustor setup, a cannular combustion chamber concept was chosen for the simulations to improve the confidence in the results. A predesign of the setup was completed resulting in a setup with three separate cans comprising of a single staged FLOX-based combustor with 16 individual air and fuel nozzles each. The layout of one of the cans is shown in Figure 2. The power density of each can was chosen as 0.5 kW/(m\({}^{3}\).Pa) with a liner volume of approximately 5.6 L. The concept of a single stage combustor simplifies the numeric modelling and validation by experimental data. Numerical analyses of the combustion in the complete given gas turbine operating range have shown that a single FLOX-based stage is feasible to stabilize the combustion in the operational envelope; however, at ignition and gas turbine ramp-up, a second stabilizing stage would be needed. These operating conditions are neglected in the following analysis. A reactor network validated to several FLOX-based combustion experiments is used as the numeric model of the combustion chamber [11]. This model takes pressure, temperature, and mass flow of both fuel and air as input parameters from the turbo fan engine performance simulation, and it delivers exhaust gas emission indices (NO\({}_{\rm{x}}\), CO, CO\({}_{2}\), and H\({}_{2}\)O) to the combustion chamber. Soot emission calculations are not included in the model, but these are approximated in a postprocessing step (see Section 2.2.3). Additionally, the load point depending total pressure loss of the combustion chamber is derived from scaled experimental results and delivered to the further tool chain. The fuel composition is a further boundary condition which also defines the selected kinetic reaction model. The split between primary (\(\dot{m}_{air,c}\)) and secondary air (\(\dot{m}_{air,d}\)) is a free model parameter and serves as an optimization variable regarding emission levels and combustion stability. In the following sections the air split S\({}_{\rm{D}}\) is defined as:  
\[S_{D}=\frac{\dot{m}_{air,c}}{\dot{m}_{air,c}+\dot{m}_{air,d}}\cdot 100\% \tag{6}\]  
The reactor network is based on a previously applied design [11] and consists of two homogeneous reactors, as delineated in Figure 2. The main recirculation zone of the FLOX based combustor is modelled with a perfectly stirred reactor (PSR). The burnout zone is represented by a plug flow reactor (PFR). In the FLOX based combustion process, gas from the burnout zone is partially recirculated to the main combustion zone. To model this recirculation, half of the mass flow from the PFR is diverted to the inflow of the PSR (Figure 2). This mass flow is diverted at the distance of 90% of the total length of the PFR. The size of the recirculation zone is dependent on various boundary conditions.