# Potentials for Pressure Gain Combustion in Advanced Gas Turbine Cycles
## Materials and Methods
### Gas Turbine Model  
Different setups of a single spool stationary gas turbine will be analyzed. These are a simple cycle gas turbine, a gas turbine with intercooler, a gas turbine with a recuperator, and a gas turbine with an intercooler and recuperator. The assumptions for pressure losses and heat exchanger thermal effectiveness were all taken from (4). The gas turbine model contained a simplified secondary air system (SAS) and evaluates blade temperatures. The SAS consisted of a single bleed flow from the compressor outlet to the turbine. This bleed flow passed for PGC cycles a compressor to rise the cooling air's pressure 5% above the turbine inlet pressure, in order to overcome the additional pressure rise in the combustor. This ensured a pressure ratio inside the blades for cooling that was similar to gas turbines with conventional combustors. The additional compression increases the cooling air temperature. Here, an isentropic compressor efficiency of 90% was assumed. Gas turbine designs where the combustion air is bled from the compressor and dilution and cooling air remains in the compressor could justified this value. The cooling flow was split at the turbine, and 50% was considered in the blade temperature module for cooling of the first turbine stage. Furthermore, it was assumed that only this 50% was doing the work in the rotor. The rest did not contribute to turbine power and was simply mixed with the annulus flow. The blade temperature \(T_{mat}\) was determined using a model described by (29), which calculated the temperature as a function of hot gas flow and coolant flow properties and a tuning factor \(c\).  
\[\frac{\dot{m}_{cold}}{\dot{m}_{hot}}=c\cdot\frac{T_{hot}-T_{mat}}{T_{mat}-T_{ cold}} \tag{1}\]  
The factor \(c\) in Equation (1) was set to 0.098 throughout this study. This value was already used in a previous study (19) and remained constant for comparison. It was the outcome of the following module inputs: 10% cooling air, \(T_{hot}=\) 1355 K, \(T_{cold}=\) 639 K, and \(T_{mat}=\) 1100 K. This paper extends previous studies at a blade temperature of 1100 K for temperatures of 1000 K and 1200 K keeping the tuning factor \(c\), which lumps cooling effectiveness, material properties, and geometry, constant. For a higher \(T_{mat}\), a lower cooling mass low is required. The opposite is true for a lower \(T_{mat}\). The optimizations may result in increased cooling air flows, in order to allow higher turbine entry temperatures (TET). However, higher cooling mass flows cause higher mixing losses within the turbine. Consequently, higher cooling mass flows will lower the turbine isentropic efficiency. This was captured by a literature-based exchange rate from (30) as defined in Equation (2).  
\[\Delta\eta=0.2\cdot\left(0.1-\frac{\dot{m}_{cold}}{\dot{m}_{engine}}\right) \tag{2}\]Above 10% of cooling air, every additional percentage point (PP) resulted in 0.2 PP lower turbine isentropic efficiency. Contrarily, the efficiency was increased by 0.2 PP for every percentage point of cooling air less than 10%. The temperature and mixing loss evaluation did not distinguish between different cooling methods such as film cooling or convective cooling.