Abstract

The escalating costs of fuel, global fuel supply disruptions, and stringent international emissions regulations necessitate more efficient ship operations. A key component of environmentally sustainable, economical, and efficient marine transportation is the recovery and utilization of waste heat. This study investigates the potential of converting waste heat from ship exhaust gas into useful energy through an organic Rankine cycle and its subsequent integration into a refrigeration system. In this study, the thermodynamic performance of the refrigerants R717, R152a, R290, and R134a was investigated. The findings demonstrate that R717 exhibits superior performance in terms of utilization factor and second law efficiency (η_II), while R290 emerges as the optimal choice when minimizing total entropy generation (s_{gen_TOT}) is the primary objective. If the priorities are focused on maximizing useful work production, minimizing energy losses, and reducing environmental impacts, the advantages of the R717 refrigerant, which has the highest total ecological coefficient of performance (ECOP) and exergetic performance criteria (EPC) values, are clearly evident. The ideal operating temperatures for evaporator temperature (T_Evap) and turbine temperatures (T_Turbine) concerning EPC and ECOP, using R717 as the refrigerant, were investigated in the continuation of the study. During this investigation, changes in T_Evap and T_Turbine were observed to have affected other components. When the T_Evap is kept constant, and the T_Turbine amount is increased, an improvement was observed in EPC_TOT, ECOP_TOT, η_II, and utility factor values, while an increase in s_{gen_TOT} and exergy destruction (ExD_TOT) values. When the T_Turbine is kept constant, a decrease is observed in the EPC_TOT value. At the same time, an improvement is seen in ExD_TOT, η_II, and ECOP_TOT values, while an increase is noted in the s_{gen_TOT} value.

1. Introduction

Contemporary engineering systems must prioritize cost-effectiveness, efficiency, and environmental sustainability. To reach these objectives, various strategies for enhancing efficiency and minimizing environmental impact are implemented throughout land and marine vehicles’ design and operational phases. In the maritime domain, common approaches include resistance reduction techniques, the adoption of alternative fuels, operational optimizations, design parameters such as energy efficiency design index and energy efficiency existing index, and the recovery and utilization of waste heat [1]. Ships often generate substantial waste heat from systems like main engine cooling, lubrication, and flue gas [2]. This heat can be harnessed for various applications, including direct heating of tanks or fuel, steam generation [3], power generation, or cooling through different thermodynamic cycles [4]. However, ships also face significant cooling demands for spaces, food stores, and transported cargo [5]. To meet these cooling needs, engineers explore alternative approaches beyond traditional vapor compression refrigeration (VCR) systems. These include absorption or organic Rankine cycle (ORC) driven VCR systems utilizing waste heat, as well as hybrid methods combining both approaches.

The existing literature encompasses a diverse range of investigations into ORC-driven combined cooling systems or dual-cycle configurations for marine applications and low-temperature heat sources. Comparative performance assessments of various heat-powered refrigeration cycles, including absorption cycles, multi-stage arrangements, and combined heat-power systems, have been reported [6]. Thermodynamic analyses of ORC-VCR systems utilizing low-temperature source heat have been conducted for different working fluids and design parameters, leading to insights into optimal fluid selection and equipment [7-9]. Optimization studies have focused on refining design and operational parameters of ORC-VCR systems based on varying working fluids and heat source temperatures [10, 11]. Exergy-based performance analyses have explored the impact of different working fluids, heat sources, and system layouts on ORC-VCR system efficiency [12-14]. Experimental investigations have been conducted to evaluate the performance of ORC-VCR systems recovering waste heat from internal combustion engines [15].

Exergetic performance analysis and optimization of air refrigeration cycles based on ecological coefficient of performance (ECOP) were studied by [16]. Analyses of exergy-based performance outputs, including exergetic performance criteria (EPC) analyses, of the multipurpose refrigeration system for different design conditions were performed by [17]. A recent research study was explored the optimization of simple Brayton refrigeration models using an exergy-based approach to improve ecological function by [18]. Exergy based thermodynamic analysis and optimizations of low temperature cascade refrigeration systems applications were presented by [19, 20]. The performance analysis of the heat-powered refrigeration system using marine waste heat energy on the second law of thermodynamics was carried out depends on the different design parameters by [21]. This study will evaluate the performance of a refrigeration system driven by an ORC utilizing waste heat from a ship’s diesel engine. The analysis will focus on key performance metrics, including utility factor (U_f), second law efficiency (η_II), total entropy generation (s_{gen_TOT}), exergy destruction ratio (y), ECOP, and EPC. These metrics will be assessed under various operating conditions, considering different working fluids and different evaporator temperatures (T_Evap), condenser, and turbine temperatures (T_Turbine).

2. Thermodynamic Model

The waste heat-powered ORC-VCR system can be conceptualized as two interconnected subsystems that utilize a single working fluid, which can be applied in such as industrial waste heat recovery systems, combined cooling and power systems, data center cooling, or marine systems. The ORC is a thermodynamic cycle that converts heat energy into mechanical work, similar to a steam Rankine cycle but using an organic working fluid (e.g., R134a, R717, 290, etc) instead of water. The ORC component comprises a condenser, pump, waste heat boiler, and steam turbine. The VCR cycle is a standard refrigeration process that absorbs heat from a low-temperature or cooled source and rejects it at a higher temperature. The VCR subsystem includes an evaporator, compressor, condenser, and expansion valve. Figure 1 illustrates the flow diagram of the ORC-VCR system. The ORC effectively converts waste heat from the main engine exhaust gases into a net work, driving the pump and compressor. In cases where the main engine is not operating or cannot provide exhaust gas with sufficient thermal content, the boiler is activated and thus continuity in the cooling system is ensured. The VCR then leverages this energy to refrigerate the storage compartments.

The fundamental design parameters and associated assumptions are outlined below. The heat addition to the ORC, Q_H, is calculated based on exhaust gas properties, including mass flow rate and inlet temperature (T_exhaust,in). The specific heat capacity at constant temperature (Cp) of the exhaust gases was determined using Equation 1, considering the reference inlet and outlet temperatures.

​​Cp = 956 + ​(​​0.3389   ​T​ exhaust,in​​​)​​–​(​​2.476   ​10​​ −5​  ​T​ exhaust, in​  2 ​​)​​​​    (1)

Heat transfer (Q_Con, Q_L, and Q_H) values are calculated from the basic balance equations. The U_f, defined by Equation 2, represents the ratio of the refrigeration or cooling load of the VCR system (Q_L) to the heat input to the ORC (Q_H).

The η_II calculated with Equation 3 as the ratio of U_f and Carnot U_f (U_{f_Carnot}).

s_{gen_TOT}, as defined by Equation 6, is the sum of the entropy generations from the environment, Equation 4, (Δs_env) and the system, Equation 5, (Δs_sys). The temperature difference between relevant environments and system points is denoted by ΔT. The heat transfer from the condenser unit (Q_Con) is the combined heat transfer from the power loop (PL) and the refrigeration loop (RL). T_Con and T_avr represent the temperature of condenser for power loop and the average value between condenser inlet and outlet temperature of RL, respectively.

The exergy density (ρ_ex) is a beneficial tool to compare the size and exergetic capacity of the system point which was defined the ratio of specific exergy to the specific volume of the system point in Equation 8 by [22].

The exergy destruction (ExD) of components is calculated with Equation 9 which depends on the flow rate and physical exergy of inlet and outlet conditions of components. The total ExD_TOT is the sum of all components of ExD as in Equation 10.

The y can be defined for each component as the ratio of the ExD of components to the ExD_TOT of the system in Equation 11 [23].

ECOP is defined as ratio of power output to the loss rate of availability in Equation 12 [24] and EPC defines the ratio of total exergy output to the loss rate of availability with Equation 13 [25].

Some properties such as global warming potential, refrigerant concentration limit of working fluids (R717, R290, R134a, and R152a) according to the ASHRAE [26] were given in Table 1 Assumptions made for the analysis of the system were also shared in Table 2.

The thermodynamic analysis of the marine refrigeration system (MRS) was conducted for the following refrigerants: R717, R290, R134a, and R152a. The analysis relied on the following simplifying assumptions:

• All system components were assumed to operate under steady-state conditions.

• Chemical, kinetic, and potential energy, as well as their corresponding exergy terms, were disregarded.

• Pressure losses within the system’s pipelines were considered negligible.

• Heat transfer to or from the compressor and expansion valve was assumed to be insignificant.

• The expansion of refrigerants in the expansion valves was assumed to be isenthalpic.

3. Results and Discussion

To evaluate the performance of the system under different refrigerant conditions, a parametric study was conducted using the established model (Equations 1-13). Four commonly employed refrigerants (R717, R290, R134a, and R152a) were selected. Their corresponding performance metrics, including the U_f, the η_II, the ECOP_TOT, the EPC_TOT, the s_{gen_TOT}, and the ExD_TOT, were calculated for different turbine and T_Evap. The Python 3.11.4 programming language, in conjunction with the CoolProp 8.3 library [27], was employed for the numerical simulations.

The results of this analysis, the information presented in Figure 2 compares the performance outputs of a waste heat-driven marine refrigeration cycle using four different refrigerants. It was observed that the optimal refrigerant choice is contingent upon the specific performance objective. R717 generally exhibits higher U_f, η_II, ECOP_TOT, EPC_TOT, and ExD_TOT and lower s_{gen_TOT} compared to R290, R152a, and R134a. This suggests that R717 is more efficient in converting waste heat into refrigeration, indicating that ammonia might be a slightly more efficient refrigerant in this specific application, despite its disadvantages for human health.

Temperature (T), pressure (P), specific enthalpy (h), specific entropy (s), mass flow rate (m), specific volume (v), specific exergy (ex), and exergy density (ρ_Ex) values of system points for the R717 are presented in Table 3 as thermophysical properties. Our priorities are to maximize practical work production, minimize energy losses, and reduce environmental impacts. In this case, the advantages of R717 refrigerant, which has the highest total ECOP and EPC values, are apparent.

To evaluate the system’s overall performance, it would be helpful to calculate the performance outputs that would provide a comprehensive understanding of the system’s losses and efficiencies. Table 4 represents performance outputs such as ExD, EPC, y, and η_II for the heat-powered MRS components (steam turbine, compressor, condenser, evaporator, expansion valve, pump, and boiler). The table shows that the evaporator has the highest ExD_TOT rate and the highest y value, with an almost 41% ratio, and the lowest ExD and y values belong to the pump unit. It can also be obtained from the table that the heat-related components (condenser, evaporator, and boiler) generate more ExD_TOT. Regarding the EPC value, the highest values are for pump and turbine units; the lowest are for heat-related units. By implementing design modifications and operational adjustments to the evaporator, condenser, and boiler units, the system’s ExD_TOT can be reduced, leading to a notable increase in overall efficiency.

Figure 3 shows the effect of the T_Turbine on the system components’ EPC. As the T_Turbine increases, the overall EPC generally decreases. Nevertheless, the individual EPC contributions of different components demonstrate different trends. Significant decreases in EPC_Turbine, EPC_Boiler, and EPC_Condenser between 340 and 355 K temperature and slight decreases in EPC_Pump are also observed. EPC_Evap, EPC_Compressor, and EPC_Valve remain relatively constant, as the evaporator’s temperature does not directly affect the compressor’s and valve’s performance.

Figure 4 shows the effect of T_Evap on the EPC of the system components. As the T_Evap increases, the overall EPC generally increases. However, the individual EPC contributions of different components show different trends. EPC_Turbine, EPC_Boiler, and EPC_Pump remain relatively constant, as the turbine’s, boiler’s, and pump’s performance are not directly affected by the T_Evap. EPC_Evap and EPC_Condenser increase slightly, EPC_Compressor and EPC_Valve increases significantly with T_Evap.

Figure 5 shows the relationship between the U_f and the total EPC_TOT or EPC_TOT where the different lines represent various combinations of evaporator and T_Turbine. As the T_Evap increases, the EPC_TOT generally decrease for a given U_f, and the U_f increases for a given constant T_Turbine. However, there is a trade-off between T_Evap and cooling capacity. Higher T_Evap can reduce the cooling capacity of the system. Increasing the T_Turbine generally increases EPC_TOT and U_f for constant T_Evap. Since improving EPC_TOT is the priority, the scenario in which It reaches its maximum improvement should be considered. Therefore, when the T_Evap was set to 243.15 K and the T_Turbine to 368.15 K, an improvement of nearly 100% in EPC_TOT and almost 115% in U_f according to the values in T_Turbine is 338.15 K.

Figure 6 depicts the effects of the evaporator and T_Turbine on the relationship between ECOP_TOT or ECOP_TOT and EPC_TOT. As the T_Evap increases, the ECOP_TOT generally increases for a given EPC_TOT or at a constant T_Turbine. However, increasing in T_Evap at constant T_Turbine decreases the EPC_TOT. T_Evap and cooling capacity are inversely correlated, such that an increase in one leads to a decrease in the other. Increasing the T_Turbine generally leads to a increase in ECOP_TOT for a constant T_Evap. The ideal scenario is when the T_Evap is 258.15 K, and the T_Turbine is 368.15 K to maintain optimal improvements in both ECOP_TOT and EPC_TOT.

Figure 7 describes the relationship between EPC_TOT and η_II of the system using R717. As the T_Evap increases, η_II generally increases while EPC_TOT decreases for constant T_Turbine. Increasing the T_Turbine generally increases both EPC_TOT and η_II for a given T_Evap. Since maximizing EPC_TOT is the primary objective, the scenario yielding its highest improvement should be considered. Accordingly, when the T_Evap was adjusted to 243.15 K and the T_Turbine was 368.15 K, an enhancement of almost 170% in η_II was calculated by comparing it to the lowest scenario.

Figure 8 depicts the relationship between EPC_TOT and ExD_TOT. The different lines represent various combinations of evaporator and T_Turbine. As the T_Evap increases, the ExD_TOT generally increases for a given EPC_TOT, and EPC_TOT decreases with higher T_Evap at a constant T_Turbine value. Increasing the T_Turbine generally increases the ExD_TOT and EPC_TOT. By carefully selecting these temperatures, optimizing the system’s performance in terms of both ExD_TOT and EPC_TOT is possible. While improving EPC_TOT, to keep ExD_TOT at its lowest level, two scenarios emerge: The most optimal balance between both values occurs when the T_Evap is 243.15 K and the T_Turbine is 338.15 K. However, if the increase in ExD_TOT can be overlooked, the ideal temperature range for maximizing EPC_TOT is when the T_Evap is 243.15 K and the T_Turbine is 368.15 K.

Figure 9 shows the relationship between EPC_TOT and s_{gen_TOT} for the system according to the different T_Evap (straight lines) and T_Turbine (dotted lines). As the T_Evap increases, the s_{gen_TOT} generally increases for a given EPC_TOT. However, EPC_TOT also decreases with higher T_Evap. Higher T_Evap can lead to higher irreversibilities in the system, such as heat transfer across finite temperature differences and pressure drops in the components. Increasing the T_Turbine generally leads to an increase in s_{gen_TOT} for a given EPC_TOT. Besides, EPC_TOT also increases with higher T_Turbine. The optimal combination of evaporator and T_Turbine depends on the specific requirements of the heat-powered refrigeration system, which must balance between minimizing s_{gen_TOT} and maximizing EPC_TOT. For example, lower T_Turbine and T_Evap might be suitable if the priority is to minimize entropy generation. If the priority is to maximize EPC_TOT, a lower v and a higher T_Turbine might be better. It has been observed that the ideal scenario between EPC_TOT and s_{gen_TOT} occurs when the T_Evap is 243.15 K, and the T_Turbine is 368.15 K.

4. Conclusion

This study investigated the feasibility of converting waste heat from ship exhaust gas into helpful energy through an ORC and subsequently utilizing this converted energy in a VCR cycle. The effects of the varying evaporator and condenser temperatures and different working fluids on the U_f, η_II, and s_{gen_TOT} production were analyzed. The results indicated that ammonia (R717) is the most suitable fluid for this system. Future research endeavors will focus on conducting detailed comparative performance analyses and exploring exergy-based environmental and economic assessments. Analyses have shown that the high ECOP and EPC values of R717 (ammonia) indicate their significant potential to enhance system efficiency. These results suggest that R717 could play an effective role in energy conversion processes, particularly optimizing energy efficiency. Furthermore, the high efficiency of R717 could lead to lower emissions and more sustainable energy solutions from an environmental perspective, while economically, it could reduce operating costs by lowering energy consumption. Future studies will further explore the broader application areas of R717 and its impact on environmental and economic assessments.

The optimal combination of e T_Evap and T_Turbine depends on the specific requirements of the refrigeration system. For example, if the priority is to maximize cooling capacity, a lower T_Evap and a higher T_Turbine might be suitable. If the priority is to minimize energy consumption, a higher T_Evap and a lower T_Turbine might be better. Figures 5-9 show that the EPC_TOT of the heat-powered system using R717 is influenced by both the evaporator and T_Turbine. To optimize the total EPC, it is advantageous to operate at a lower T_Evap and a higher T_Turbine. The observations indicate that the optimal thermodynamic conditions for the EPC_TOT, occur at an T_Evap of 243.15 K and a T_Turbine of 368.15 K which have almost 100% increment according to the lowest EPC_TOT value. By carefully selecting these temperatures, optimizing the system’s performance for a given application is possible.