## 2 Gas Turbine
### Gas Turbine Model
#### 2.2.1 Physical Model  
The physical model has been applied for the specific mechanical study in gas turbine components (compressor [47], turbines [48], combustors [49]) and thermodynamic behavior as in [50,51]. It implies the application of Brayton cycle thermodynamic laws as in Figure 6. Entropy in the figure is the unavailability of a system's thermal energy for mechanical work conversion. In an irreversible cycle, the air is drawn at point 1 and compressed by the compressor to point 2 at constant entropy (isentropic). Then, the combustor raises the air temperature to point 3 and the heat of combustion, \(Q_{in}\), from the burned fuel is obtained. The compressed air and combustor fuel mixture are expanded to point 4 in the isentropic process. Lastly, the released heat, \(Q_{out}\), from 4 to 1 is utilized to generate power. The process at 2-3 and 4-1 is assumed as isobaric or equal in barometric pressure. These optimal conditions are implemented into differential equations of total mass balance conservation in Equation (1) and conservation energy in Equation (2). \[\frac{dm}{dt}=\dot{m}_{in}-\dot{m}_{out} \tag{1}\]  
\[\frac{dE}{dt}=\dot{m}_{in}i_{in}^{*}-\dot{m}_{out}i_{out}^{*}+Q+W \tag{2}\]  
where \(\dot{m}\) refers to the mass flow and \(E\) represents the total energy, \(i\) represents the specific enthalpy, \(Q\) refers to the heat input into the system, and \(W\) is the work produced. The phys \begin{table}
\begin{tabular}{c c c c c c c} \hline  & **TVC** & **RQL** & **COSTAIR** & **MILD/Flameless** & **NanoSTAR** & **DLE** \\ \hline \multirow{4}{*}{**Technology**} & Recirculation zone & Three section of front rich & \multirow{4}{*}{Continuously staged air} & \multirow{4}{*}{Milled} & \multirow{4}{*}{Milled/Flameless} & Introduction of \\  & Recirculation zone & burnfoldle & & & & & **multiplicity valve and** \\  & introduction to quick & & & & & & **LPM area for** \\  & trap turbulence & quenchlast lean & & temperature & & & **rich-burn** \\  & & burn & & & & & **intensity** \\ \hline \multirow{2}{*}{**Pressure Drop**} & \multirow{2}{*}{Low [17]} & \multirow{2}{*}{Moderate [29]} & \multirow{2}{*}{Low} & \multirow{2}{*}{Medium} & Very Low (2 4\% & \multirow{2}{*}{**Very Low**} \\  & & & & & & & **reduction** \\ \hline \multirow{2}{*}{**Fuel**} & Liquid/Gas [18] & Liquid/Gas [28] & Liquid/Gas & Liquid/Gas [25] & Natural Gas & **Liquid/Gas** \\ \hline \multirow{2}{*}{**Stability**} & High [16] & Moderate & Low [31] & High [22,23] & Very High & **High** \\ \hline \multirow{4}{*}{**Drawbacks**} & Too dependant & Increase & \multirow{2}{*}{\begin{tabular}{} \end{tabular} } & \multirow{4}{*}{\
\begin{tabular}{} \end{tabular} } & \multirow{4}{*}{
\begin{tabular}{} \end{tabular} } \\  & on geometric & & & & & \\ design [19] & complexity [30] & & & & & \\ \hline \end{tabular}
\end{table} 
Table 1: _Cont._ical model uses thermodynamic equations, which calculate any process inputs into an output. This method aims for the model to be robust to different sets of data without any modifications. The problem with this method is that the derivation is very extensive and challenging, especially for a larger system. Moreover, mechanical engineering backgrounds are needed in deriving the parameter [52; 53]. Thus, the physical model is not heuristic enough to aid the personnel in the decision-making process for the gas turbine operation. [PERSON]'s model is the first developed physical model for gas turbine dynamics, as illustrated in Figure 7. The model established by [PERSON] in [54] is based on the simplified mathematical model to overcome the physical model complexity. A few assumptions were made for the model, which are; (i) the model is for simple cycle, single-shaft, and generator drive only, (ii) the speed of the turbine must be constant and maintained at 97-100%, (iii) the ambient temperature and pressure are at 15 \({}^{\circ}\)C and 1 atm, respectively, and (iv) no heat recovery is considered in the model.