## 4 Results and Discussion
### Thermodynamic Parameter Characteristic of CRD Combustors  
For modern gas turbines, the combustion thermal efficiency and pressure ratio of combustors are very important indexes for improving the thermal cycle performance. Based on the following equations and the average outlet parameters of the CRD combustor under stable operating conditions (during the three periods shown in Figure 5), it was calculated that the combustion thermal efficiency \(\eta_{r}\) and pressure ratio \(\pi\) of the CRD combustor was 99.715% and 2.0664, respectively. However, for the traditional approximate constant pressure method used in the present gas turbine, the corresponding values were only 99.5% and 0.95%, respectively, using the same inlet parameters. The comparison results indicated that the CRD combustor had a significant advantage in pressure gain compared to the approximate constant pressure combustor. \[h_{r}=\frac{\overline{H}_{t,out}-\overline{H}_{t,in}}{Q_{in}} \tag{9}\]  
\[\pi=\overline{P}_{t,out}/P_{t,in} \tag{10}\]  
where \(\overline{H}_{t,out}\) and \(\overline{H}_{t,in}\) are the average outlet total enthalpy and the average inlet total enthalpy of the CRD combustor; and \(Q_{in}\) represent the heat release of fuel. In an open system of combustion processes, the steady flow energy equation is usually defined as:  
\[Q_{in}=\Delta H_{s}+\Delta W_{m}+W_{i} \tag{11}\]  
For ideal constant pressure or constant volume combustion, it can be simplified to the following, due to the internal work of 0:  
\[Q_{in}=H_{t,out}-H_{t,in} \tag{12}\]  
where \(\Delta H_{s}\) represents the variation of static enthalpy; \(\Delta W_{m}\) represents the variation in mechanical energy; \(W_{i}\) represents the internal work; and \(H_{t,out}\) and \(H_{t,in}\) represent the outlet total enthalpy and the inlet total enthalpy of the combustor. According to the above equations, we can see that for the combustors using different combustion processes (including approximate constant pressure, CRD, ideal constant pressure, and ideal constant volume) but the same inlet parameters, there will be little difference in outlet total temperature or combustion thermal efficiency. For gas turbines, combustor performance (potential power of outlet working fluid) is usually directly reflected by the output power of the turbine, which can be calculated using Equations (13) and (14). These equations show that when other parameters are consistent, the average outlet total pressure or the pressure ratio effectively reflects the potential power of the combustors. Figure 6 compares the pressure ratio of combustors using four typical combustion processes under the present numerical condition parameters. As shown in Figure 6, although both the ideal constant volume-based combustor and the CRD-based combustor have similar pressure gain characteristics, the latter obtains a much smaller pressure gain than that of the former. \[W_{T}=\overline{m}\frac{k}{k-1}R\overline{T}_{t,out}\left(1-\frac{1}{\pi_{T}^ {\frac{k-1}{k}}}\right)\eta_{T}^{*} \tag{13}\]  
\[\pi_{T}=\overline{P}_{t,  
In terms of thermodynamics, entropy generation leads to the loss of available energy, and Gibbs free energy is the available part in the system inner energy decrement. Therefore, Gibbs free energy loss directly affects the potential power of combustors. As mentioned above, the potential power of the different combustors can be effectively reflected by the pressure ratio. This means that Gibbs free energy and the pressure ratio are related. In order to understand the pressure gain characteristics of CRD combustors, Figure 7 compares the entropy generation \(\Delta S\) and Gibbs free energy increment \(\Delta G\) of different combustors. It is clearly shown in Figure 7a that the \(\Delta S\) of the CRD combustor (2080.6 J/kg\(\cdot\)K) was higher than that of the ideal constant volume-based combustor (1782.6 J/kg\(\cdot\)K). However, compared to the other two types of combustors, the CRD combustor had a low \(\Delta S\) and the decrement was about 10.0%.