5.2.2. Effect of the Turbine Inlet Pressure of the SRC

The parameters based on the first and second laws of thermodynamics are clear indicators of a system's performance, providing conclusive information about the current state of the system. Both exergy and thermal analyses are required to accurately represent the system's behavior as a function of the working pressure and temperature. In this section, the parametric optimization of the SRC is carried out in depth based on the turbine inlet pressure and temperature.

The turbine inlet pressure is a critical factor affecting the SRC performance. Figure 6 demonstrates the variation in the energy and exergy efficiency and power output of the SRC as a function of the turbine inlet pressure. The figure shows that the power output of the expander and the energy and exergy efficiency of the system fluctuate with the increasing evaporation pressure in the SRC in the range of 10,000 kPa to 30,000 kPa, whereas the power required form the SRC pump increases with an increase in evaporation pressure. In the observed range of evaporation pressures, the change in power output of SRC expander, energy, and exergy efficiency varies from 85.5 kW to 181.9 kW, 63.23% to 64.62%, and 59.91% to 61.23%, respectively.

It is noteworthy that the power output, energy efficiency, and exergy efficiency of the SRC decrease to a minimum at a turbine inlet pressure of 14,000 kPa; however, they reach a maximum at a turbine inlet pressure of 18,000 kPa. At a constant turbine inlet temperature, when the turbine inlet pressure is 14,000 kPa, liquid is formed at the inlet of the expander, influencing the results negatively. As the SRC uses two heat exchangers, it is important to consider the effects of turbine inlet pressure on the LMTD of the heat exchanger, as shown in Equations (36) and (37). Taking this into account, an evaporation pressure of 19,000 kPa was selected for this simulation.

**Figure 6.** Effect of evaporator pressure on the SRC power output and efficiency.

5.2.3. Effect of the Evaporation Temperature of the SRC

The evaporation temperature of the SRC varies with the mass flow rate of the flue gas of the SOFC, the current density of the SOFC, and the compressor ratio of the exhaust gas turbine. Different superheat temperatures of the SRC working fluid were simulated, and the results are presented in Figure 7.

**Figure 7.** Effect of superheat temperature on SRC performance and heat exchanger efficiencies.

Figure 7 shows the effect of the superheat temperature, in the range 250 ◦C to 450 ◦C, on the SRC performance indicators and the temperature difference in the heat exchangers. With an increase in the superheat temperature, the power output of the SRC significantly increases, and the energy and exergy efficiency of the SRC are improved. The power output of the SRC changes from 38.46 kW to 221.9 kW with a superheat temperature increase from 250 ◦C to 450 ◦C. However, the temperature difference (LMTD) of the heat exchangers tends to decrease with an increase in the superheat temperature. As shown in Equations (36) and (37), with a decrease in LMTD, the temperature difference between the hot and cold sources

of the heat exchangers decreases. This necessitates an increase in the heat-contacting area (A), which increases the cost of the design and operation. In contrast, a high value of LMTD necessitates a smaller heat exchange area with inherent manufacturing inefficiency. Therefore, the LMTD value selected must balance the heat exchange efficiency and cost of manufacturing.

The above analysis demonstrates the significant effect of the SRC superheat temperature on the SRC performance as well as the performance of heat exchangers (HEX-3, HEX-4, and EGB). Therefore, the selection of the stack cooling passage needs to be optimized to ensure that the SRC fluid can fully exchange heat and reach the desired superheat temperature.

#### 5.2.4. Effect of the Fuel Utilization Factor

The performance of the SOFC system has been studied for fuel utilization factors (Uf) of 65%, 75%, and 85%, respectively. Figures 8 and 9 demonstrate the influence of Uf on the efficiency of the SOFC and the integrated system. It is observed that system efficiency increases with the fuel utilization ratio, if the concentration polarization is not significantly higher than that of other polarizations. When cells operate at a low current density, the influence of the fuel usage ratio becomes increasingly significant. When the SOFC-GT operates at lower current densities, the energy efficiency of the combined cycle improves. This is because the incoming fuel mass flow rate decreases faster than the output power. The calculated values for the energy efficiency of SOFC-GT are in agreement with the thermodynamic modeling results presented in References [7,54].

When the Uf value is 0.85, the energy efficiency of the system reaches a maximum value. This is because increasing the Uf further results in the consumption of more hydrogen in the SOFC stack, which simultaneously increases the current density and reduces the voltage due to internal irreversibility. In addition, the outlet temperature of the SOFC and afterburner is reduced, which further results in a decrease in the inlet temperature and power output of the GT.

**Figure 8.** Effect of fuel utilization factor on the SOFC energy efficiency.

**Figure 9.** Effect of fuel utilization factor on the integrated system efficiency.

#### **6. Conclusions**

The energy and exergy performances of the system were assessed using the first and second laws of thermodynamics. The first law evaluates power, power density, current density, voltage, and electrical efficiency; the second law evaluates exergy efficiency and exergy losses.

In the present study, an SRC and EGB are employed to recover waste heat from an SOFC/GT system. A thermodynamic analysis predicted an increase of 175.8 kW of power due to the SRC, with energy and exergy efficiencies of 25.58% and 41.21%, respectively. Hot water and steam are generated for use in machinery and seafarer accommodation.

In addition, a parametric study showed the current density, fuel utilization factor, and turbine inlet pressures of the SRC to be the key variables affecting the system performance. Additional findings include:

As the current density increases, the exergy efficiency of the cycle decreases due to increased fuel consumption by the SOFC. As efficiency decreases, a greater amount of unconverted chemical energy is converted into heat, increasing the requirement for inlet air cooling to maintain the operating temperature of the cells.

For SRC, optimal turbine inlet pressures exist at which the net output power and exergy efficiency of the combined cycles can be maximized. The SRC is maximized for a power output of 178.5 kW, and the energy and exergy efficiencies of the entire system are 64.53%, and 61.14%, respectively. However, this results in a reduction in steam production and EGB efficiency due to the increase in the heat dissipation requirement in HEX-3.

The system efficiency increases with increasing fuel utilization factor. Within the testing range, at a Uf value of 0.85, the exergy efficiency of the hybrid system and combined cycles is maximized. On the other hand, the net output power of the cycles decreases as the fuel utilization factor increases.

Compared with the SOFC/GT system, combined cycles offer better exergy efficiency and provide an incentive to use the suggested combined cycles.

Utilizing the EGB, steam is produced at 175 ◦C, 781.1 kPa, and 725 kg/h. It is supplied to machinery and provides heating for seafarer accommodation.

**Author Contributions:** Formal analysis, P.A.D.; Investigation, B.R., C.K. and J.L.; Methodology, P.A.D.; Supervision, H.K.; Writing—original draft, P.A.D.; Writing—review and editing, H.K. All authors have read and agreed to the published version of the manuscript.

**Funding:** This work was supported by the project "Development of guidance for prevention of leaks and mitigation of consequences in hydrogen ships" (Grant No. 20200520), and the project "Test evaluation for LNG bunkering equipment and development of test technology (Grant No. 20180048)" funded by the Ministry of Oceans and Fisheries (Korea). This research was supported by BB21plus, funded by Busan Metropolitan City and Busan Institute for Talent and Lifelong Education (BIT).

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

