## 2 S-CO\({}_{2}\) Bottoming Cycle Study for Diesel Generator  
### Cycle Layout and Analysis Method  
It is well known that the turbine inlet temperature and pressure ratio have great effect on the efficiency of gas Brayton cycle. However, overall cycle efficiency and a heat recovery factor should be carefully adopted for the application of waste heat recovery system because the factors are directly combined to the work recovered from the amount of transferred waste heat to the bottoming cycles. [PERSON] et al. [9] noted that to obtain the net efficiency of the heat recovery cycle (calculated by dividing net produced work by the total heat recovered through ideally cooling flue gases to ambient temperature), the product of the cycle efficiency (net produced work divided by recovered heat) and the heat recovery factor (recovered heat divided by ideally recoverable heat) should be calculated. Hence, when optimizing heat recovery cycles, instead of maximizing the cycle efficiency, maximizing the product of cycle efficiency and heat recovery factor becomes more valid. According to [PERSON] et al. [10], the performance indicator of bottoming cycles can be simply expressed by adopting the waste heat recovery index (WHRI):  
\[\mathrm{WHRI}=\mathrm{X}^{*}\mathrm{\Pi}_{\mathrm{cycle}} \tag{1}\]  
\[\mathrm{X}=\frac{\mathrm{thermal}\ power\ absorbed\ by\ the\ bottoming\ cycle}{\mathrm{total\ net\ thermal\ power\ recoverable\ due\ thermal\  
By utilizing this performance index, various bottoming cycle designs can be assessed with a more applicable framework especially for the waste heat recovery systems' performance. This indicator matches to the concept of cycle net efficiency, except that it evaluates the performance replacing the cycle heat input with maximum obtainable heat from the heat source for the bottoming cycle. The WHRI values for various S-CO\({}_{2}\) cycle layouts are obtained. Parametric sensitivity of the design variables such as turbine outlet pressure (or pressure ratio), CO\({}_{2}\) mass flow rate, first compressor outlet pressure, and flow splits, with respect to cycle performance, is summarized. Furthermore, the cycle minimum pressure is placed as a major design parameter to be optimized. An in-house code is used for the cycle optimization. The code is developed by the research team at KAIST, and it is named as KAIST-Closed Cycle Design (KAIST-CCD) code [11; 12; 13]. The code is based on MATLAB. Enthalpy and fluid properties for calculation in the code are referred from the NIST reference fluid thermodynamic and transport properties database (REFPROP) [14]. Figures 3 and 4 show the algorithm of the code structure and the partial heating cycle layout. This layout is chosen to illustrate the process of the cycle analysis. Firstly, the recuperator cold side inlet flow condition (point 5) and the heater 2 hot side inlet flow condition (point 10) are assumed. Through the component models (compressor, turbine, recuperator, heater, cooler, and mixing tee), the component inlet and outlet conditions are calculated. Then, the heat input from exhaust gas with exhaust inlet and outlet conditions is calculated. If the cycle calculation error remains above \(10^{-5}\), the assumed values are updated to the newly calculated conditions, and the cycle calculation is repeated. If the error is less than \(10^{-5}\), the code calculation terminates and prints output results. The partial heating cycle and other layouts are evaluated by the KAIST-CCD code through a similar algorithm. Figure 3: The cycle design code algorithm for the partial heating cycle. The full power of the reference four strokes diesel engine is 9 MW with 720 or 750 rpm, but around 80% of full power is used for the emergency electrical load due to safety margin. Table 5 shows the main specification of the AAC DG which influences the design of the S-CO\({}_{2}\) bottoming cycle. Table 6 displays the values of exhaust gas source, properties, and mole fraction of each species [15].