# Thermodynamic Analysis of Partitioned Combined Cycle using Simple Gases
## 3 Model Description
### Heat Transfer Rates in Combustion Chamber  
There are 16 Dry Low NOx (DLN) type combustion chambers being used in H-class series turbines. These chambers are designed so that all the compressed air does not pass through the chambers directly and most of the air is diffused to cool the flame adiabatic temperature. However, in the proposed PCGT all of the air must pass through the chamber. Excess air of 15% was allowed to ensure complete combustion. Furthermore, the PCGT partitioned fluid must cool the flame indirectly. Therefore, a shell and tube heat exchanger replaced each combustion chamber. Flow was equally divided. Average velocities of the gases were maintained at 25 m/s. The velocities of the gases were maintained to ensure the momentum heat transfer within the combustion and partitioned zone. Flame length must be calculated to determine the heat release pattern in the combustor tube. Many factors influence its length and Computational Fluid Dynamics (CFD) calculations are required to exactly solve the 3D heat balance equation. However, using a 1D approach in heat transfer with an estimation of the flame length may provide the dimensions/heat distribution in the combustor and partitioned fluid space within a reasonable error range (well-stirred lumped model cannot provide a rational estimate of the required length of combustor chambers due to a high adiabatic temperature). Figure 5 shows the algorithm used for calculations. The main (T\({}_{\rm m,i}\)) and partitioned fluid inlet temperatures (T\({}_{\rm p,i}\)) were obtained by the compression calculations with different adiabatic efficiencies discussed earlier. The main fluid outlet temperature (T\({}_{\rm m,o}\)) was fixed at 1435 \({}^{\circ}\)C by manipulating the partitioned fluid flow rate (m\({}_{\rm p}\)). The main fluid flow rate (m\({}_{\rm m}\)) is adjusted to keep the gas turbine output at 755 MW. The partitioned fluid outlet temperature (T\({}_{\rm p,o}\)) was obtained by an iterative convergence of the problem. Complete heat transfer was considered at the seed value (1435 \({}^{\circ}\)C). The heat transfer and heat of reaction were balanced with temperatures by adjusting the flow rates before any further calculations. This exercise was essential to obtain the boundary conditions. In the 1D model (plug flow, Equation (4)), rapid combustion in a differential length (temperature) was considered and the mixture  
Figure 4: Efficiency versus pressure for the Rankine cycle at temperatures from (370–450 \({}^{\circ}\)C), with adiabatic efficiency of 89.9%. The turbine exit pressure is 10 kPa. Dotted line represents the optimum pressure. achieved the partial adiabatic temperature instantaneously with no radial heat distribution. Only convective heat transfer was assumed to hold across the surface (although, radiation is important on hot side but it is not considered to give maximum disadvantage to the PCGT in order to reduce model errors). The solution was obtained by a code written in MATLAB. The step length was adjusted to keep the error less than \(\Delta\)T \(<\) 0.1\({}^{\circ}\)C for both partitioned and main fluid. As the mixture was changing both chemically and physically because of the combustion reaction and temperature, respectively, the properties in each differential length were calculated using the thermodynamic model as used in ASPEN HYSYS. The information was then transferred to MATLAB for each discretized step. \[\frac{dq}{dL}=Q_{generated}-Q_{Exchanged} \tag{4}\]  
One-dimensional flame length for various fuels can be estimated by the ratio 'F\({}_{\rm L}\)/d\({}_{\rm j}\)', where 'F\({}_{\rm L}\)' is the flame length and d\({}_{\rm j}\) is the jet injection diameter. A range of 'F\({}_{\rm L}\)/d\({}_{\rm j}\)' ratio can be found for different fuels. A value of 'F\({}_{\rm L}\)/d\({}_{\rm j}\)\(\approx\) 200' for natural gas is usually reported [61]. Furthermore, the effect of swirl must be accounted for at high velocities. Various formulas are reported in the literature to account for the swirl.