Thermo-Economic Study of a Regenerative Dual-Loop ORC System Coupled to the Main Diesel Engines of a General Support Vessel

A thermo-economic analysis of a regenerative dual-loop organic Rankine cycle (ORC) is conducted, which will be coupled with the main diesel engines of a general support vessel. An energy and exergy analysis of the regenerative dual-loop ORC is conducted. The energy and exergy analysis results of the regenerative dual-loop ORC are compared with pertinent results for a simple dual-loop ORC without regeneration. A mission analysis that was based on a vessel speed profile with the proposed ORC was conducted. A heat transfer analysis was performed for dimensioning the heat exchangers of both ORC loops. Finally, an economic analysis is conducted to calculate the total capital cost and the payback period of the proposed ORC. The results showed that the proposed ORC is thermodynamically superior in both energetic and exergetic terms compared to the simple dual-loop ORC. The total fuel cost saving is 337,493 Euros, the total CO2 emission saving is 1,153,416.4 kg, and the SO2 emission saving is 36,044.3 kg. The total capital cost of the proposed ORC is 2,546,000 Euros. Finally, the installation of the proposed ORC in the examined vessel is economically feasible because it results in a reasonable payback period, which is less than nine years.


Introduction
Contemporary marine diesel engines that are currently used in naval vessels as main engines or auxiliary engines are characterized by high efficiency, which is higher when compared to marine gas turbines and marine steam turbines [1]. Specifically, the brake efficiency of a modern four-stroke marine diesel engine is close to 50% of the fuel heating power, whereas almost the 30% of the fuel heating power is rejected to the ambient through hot exhaust gases [2]. The remaining fuel heating power, which is not converted to useful brake power and exhaust gas heating power, is rejected to the engine coolant, to the cooling medium of the intercooler, and to the lubricant oil cooler, whereas a small percentage of the fuel heating power is rejected to the ambient through radiative heat transfer thermal losses [3].
Various technologies have been proposed in the literature for the utilization of waste heat from marine diesel engines [3]. Specifically, Singh and Pedersen [4] have analyzed the specifications and the advantages and disadvantages of a water steam Rankine cycle, a subcritical Rankine cycle, and a supercritical organic Rankine cycle. They have also examined the use of a secondary Kalina cycle with the ammonia-water mixture as working medium as an alternative thermodynamic cycle for the waste The thermal efficiency of the dual-loop ORC system varies from 8.97 to 10.19% at the entire engine operational range.
Another interesting study was performed by Scardigno et al. [19], which adopted a genetic algorithm for performing a multi-objective optimization of a hybrid organic Rankine cycle for solar and low-grade energy sources. The main objectives of the genetic optimization method were the maximization of the first and second law efficiencies of the cycle and the minimization of the levelized energy cost. The theoretical results of this analysis showed that the lowest energy cost and the highest first law efficiency were attained using cyclopropane, whereas the highest second law efficiency was achieved by employing R143a.
Hence, from the detailed examination and analysis of the available literature regarding the implementation of the dual-loop ORC in internal combustion engines, the following observations can be made: • The use of a dual-loop ORC for the recovery of waste heat from exhaust gases, engine coolant, and intercooler of the main engines of a naval vessel, such as a general support vessel, has not been examined up to now.

•
The simple dual-loop ORC with a regenerative dual-loop ORC has not compared up to now in order to determine the deviations between the two cycles in both energetic and exergetic performance parameters.

•
It has not examined up to now the fuel, CO 2 and SO 2 savings during a mission analysis of a general support vessel equipped with a regenerative dual-loop ORC coupled to its main engines. • It has not been implemented up to now a detailed thermal analysis for dimensioning the heat exchangers of the regenerative dual-loop ORC, which is coupled with the main engines of a general support vessel. • It has not been implemented up to now an economic analysis to predict the capital cost of the ORC installation, the cost of generated electric energy, and the payback period of the regenerative dual-loop ORC investment.
Hence, in the present study, an energy and exergy analysis are performed for a dual-loop ORC coupled to the main diesel engines of a general support vessel. Additionally, an energy and exergy analysis of a regenerative dual-loop ORC equipped with an Open Feed Organic Heater (OFOH) in both HT and LT loop, which is also coupled to the main engines of a general support vessel, is conducted. The energetic and exergetic performance results of the simple dual-loop ORC and the regenerative dual-loop ORC are compared in order to specify the optimum thermodynamic cycle to be used for the waste heat recovery from the exhaust gases, engine coolant, and intercooler of the main engines of the examined general support vessel. R245fa and R600 are examined as organic fluids of the HT loop of both simple and regenerative dual-loop ORCs due to their improved thermal stability at high exhaust gas temperatures, whereas R245fa, R600, R1234yf, and R1234ze are examined as working mediums of the LT loop of both examined dual-loop ORCs. A parametric study considering the effect of various thermodynamic parameters of the HT and the LT loop for all possible combinations of the organic fluids considered in the present study is performed. A mission analysis of the general support vessel equipped with the combined system of the main engines and the regenerative dual-loop ORC is performed in order to predict the economic benefit from the fuel savings and also the predict the CO 2 and SO 2 savings. A detailed heat transfer analysis is conducted for dimensioning the exhaust gas heat exchanger of the HT loop and the heat exchangers that harvest waste heat from the HT loop organic fluid at the preheater, the engine supplied air at the LT loop intercooler, the engine coolant at the LT loop, and the LT loop condenser. Finally, an economic analysis is conducted in order to estimate the cost of the ORC system components, the cost of generated electric energy, and the overall investment cost of the regenerative dual-loop ORC while taking the mission analysis revenues from fuel savings and the maintenance and insurance cost of the regenerative dual-loop ORC into consideration.

Brief Description of the General Support Vessel and its Main Propulsion and Electric Power Generation System
In the present investigation, the installation of a regenerative dual-loop ORC with OFOH in a general support vessel of the Greek Navy is proposed. The deadweight of the examined general support vessel is 13,400 tones and it is equipped with two main turbocharged direct injection (DI) twelve-cylinder diesel engines [20]. The Maximum Continuous Rating (MCR) of each main diesel engine is 8640 kW at 510 rpm [21]. More details regarding the main diesel engine performance characteristics cannot be released due to confidentiality reasons. The maximum speed of the specific general support vessel is 21.5 knots [20]. It is proposed the installation of the regenerative dual-loop ORC system in the engine room of the examined general support vessel due to space availability. It is also proposed that the regenerative dual-loop ORC system to operate at constant vessel speed and at steady operating conditions in order to avoid potential back pressure problems to the main engines turbocharging system from excess fouling of the exhaust gas heat exchanger during transient engine operation. The examined general support vessel is equipped with three auxiliary diesel generators. The generated power of each diesel generator is 872 PS and its corresponding sfc is 224 g/PSh [21].

Organic Fluid Description and Selection
The proper selection of the organic medium plays a very important role in the design of the ORC system. Organic fluids with low evaporation temperature are often preferred for the waste heat recovery from medium and low-grade thermal sources, such as the ones of internal combustion engines (mean temperature of exhaust gases and low temperature of engine coolant and charged air) [22]. Refrigerants and hydrocarbons are two commonly used working fluids for ORC systems. The organic fluid that will be selected for an ORC system should not be corrosive, flammable, and toxic when considering the ORC installation safety limitations and the environmental repercussions of the organic fluid [21]. Hence, chlorofluocarbons (CFCs) and hydrochlorofluorocarbons (HFCs) are not considered as candidate working mediums for ORC systems due to their high Global Warming Potential (GWP) and their high Ozone Depletion Potential (ODP) [22]. In addition, the present study does not examine the use of a "wet" working medium such as water/steam, which expands in the two-phase area as a liquid/steam mixture because the high-pressure ratio expansion of liquid droplets in the expander might result in the corrosion of the rotating expander blades [22]. Recent detailed studies have shown that R245fa [9,[22][23][24][25][26][27][28] and R600 [9,26] have been utilized as working mediums in a broad range of ORC system applications. In addition, traditional refrigerants are replaced by hydrofluoroolefins (HFOs), which are new and environmentally friendly refrigerants with zero ODP and very low GWP, according to the current practice. Hence, based on all aforementioned reasons, four organic fluids, namely: R245fa, R600, R1234yf, and R1234ze, were chosen to be used in the dual-loop ORCs, which are examined in the present study. Table 1 presents the critical pressure and temperature, the ODP, and the GWP of the previously mentioned organic fluids. Table 1. Critical pressure and critical temperature, Ozone Depletion Potential (ODP) and Global Warming Potential (GWP) of the four working fluids that are examined in the present study [18].

Description of the Regenerative Dual-Loop Organic Rankine Cycle
In Figure 1 the schematic view of the regenerative dual-loop ORC with OFOH is shown, which includes the HT and LT loop, and it was considered in the present study. The HT loop has been designed to recover waste heat from the exhaust gases of the diesel engine, whereas the LT loop is used to recover rejected heat from the engine coolant network, the engine intercooler and the condenser of the HT loop, which is used as preheater for the organic fluid of the LT loop.
Energies 2020, 13, x FOR PEER REVIEW 6 of 46 designed to recover waste heat from the exhaust gases of the diesel engine, whereas the LT loop is used to recover rejected heat from the engine coolant network, the engine intercooler and the condenser of the HT loop, which is used as preheater for the organic fluid of the LT loop. The HT loop of the regenerative dual-loop ORC comprised of an evaporator (evaporator 1), where the organic medium utilizes waste heat from the hot exhaust gases, an expander (expander 1), a preheater, two circulation pumps (pump 1 and pump 2), and an OFOH, where the hot stream and the cold stream of the organic fluid are mixed. The superheated organic steam expands up to an intermediate pressure in the expander 1 and, then, part of the expanded organic fluid flow rate is extracted from the expander 1 and is transferred to the OFOH to preheat the "cold stream" of the organic fluid, which comes out of the preheater and goes in the evaporator 1, whereas the remaining organic fluid flow rate expands up to low condensation pressure of the HT loop.
The LT loop of the regenerative dual-loop ORC comprised of an evaporator (Evaporator 2), where the organic fluid utilizes rejected heat from the engine coolant, an expander (Expander 2), a condenser, where the organic fluid rejects heat to the cooling seawater, two circulation pumps (pump 1 and pump 2), the engine intercooler, where the organic fluid recovers waste heat from the charged air, and an OFOH, where the hot stream and the cold stream of the organic fluid are mixed. Additionally, in the expander of the LT loop the saturated organic steam is expanded up to an The HT loop of the regenerative dual-loop ORC comprised of an evaporator (evaporator 1), where the organic medium utilizes waste heat from the hot exhaust gases, an expander (expander 1), a preheater, two circulation pumps (pump 1 and pump 2), and an OFOH, where the hot stream and the cold stream of the organic fluid are mixed. The superheated organic steam expands up to an intermediate pressure in the expander 1 and, then, part of the expanded organic fluid flow rate is extracted from the expander 1 and is transferred to the OFOH to preheat the "cold stream" of the organic fluid, which comes out of the preheater and goes in the evaporator 1, whereas the remaining organic fluid flow rate expands up to low condensation pressure of the HT loop. The LT loop of the regenerative dual-loop ORC comprised of an evaporator (Evaporator 2), where the organic fluid utilizes rejected heat from the engine coolant, an expander (Expander 2), a condenser, where the organic fluid rejects heat to the cooling seawater, two circulation pumps (pump 1 and pump 2), the engine intercooler, where the organic fluid recovers waste heat from the charged air, and an OFOH, where the hot stream and the cold stream of the organic fluid are mixed. Additionally, in the expander of the LT loop the saturated organic steam is expanded up to an intermediate pressure and at this pressure part of the organic mass flow rate is extracted from the expander and then transferred to the OFOH as "hot stream" and it is used to preheat the "cold stream" of the organic medium that comes out of the condenser of the LT loop. The remaining organic mass flow rate is expanded up to the low condensation pressure of the LT loop. Figure 2 shows the thermodynamic processes that undergoes the organic fluid in the HT loop in a temperature-entropy diagram. In the HT loop, the subcooled organic fluid at state H8 that enters evaporator 1, where it recovers waste heat from engine's exhaust gases and it is heated until it becomes superheated steam at the exit of evaporator 1 at state H1. Subsequently, the superheated organic fluid at high evaporation pressure enters the expander 1, where it expands initially up to an intermediate pressure at state H2, where a portion of the organic fluid flow rate is extracted from the expander 1 and transferred to the OFOH whereas, the remaining organic fluid flow rate expands up to the low condensation pressure of the HT loop. Both expansions in the expander 1 of the HT loop generate useful mechanical power, which is converted to useful electrical power since the expander 1 is connected to an electric generator. The organic fluid that has been expanded in expander 1 up to intermediate pressure and it is at superheated condition that H2 enters the OFOH, where it preheats the low temperature organic fluid stream that exits the circulation pump 1. The remaining organic fluid in the expander 1 is expanded up to low condensation pressure and exits the expander 1 as low condensation pressure superheated steam H3 and then enters the condenser of the HT loop, which operates as preheater of the organic fluid at the LT loop. At the condenser of the HT loop, the organic medium rejects heat to the organic fluid of the LT loop and it is condensed at the low condensation pressure of the HT loop. The organic fluid exits the condenser i.e., preheater of the HT loop as saturated liquid at state H5 and then enters pump 1, where it is compressed at the intermediate pressure of the HT loop and exits from the pump 1 as subcooled organic liquid at state H6. Subsequently, the subcooled organic liquid at state H6 is mixed with superheated steam of state H2, where it has been extracted from the first expansion at expander 1 and then the entire organic mass flow rate exits at state H7 as saturated liquid. The saturated organic liquid of state H7 is compressed by the circulation pump 2 at high evaporation pressure of the HT loop and it comes out from the pump 2 as subcooled liquid at state H8.
Energies 2020, 13, x FOR PEER REVIEW 7 of 46 intermediate pressure and at this pressure part of the organic mass flow rate is extracted from the expander and then transferred to the OFOH as "hot stream" and it is used to preheat the "cold stream" of the organic medium that comes out of the condenser of the LT loop. The remaining organic mass flow rate is expanded up to the low condensation pressure of the LT loop. Figure 2 shows the thermodynamic processes that undergoes the organic fluid in the HT loop in a temperature-entropy diagram. In the HT loop, the subcooled organic fluid at state H8 that enters evaporator 1, where it recovers waste heat from engine's exhaust gases and it is heated until it becomes superheated steam at the exit of evaporator 1 at state H1. Subsequently, the superheated organic fluid at high evaporation pressure enters the expander 1, where it expands initially up to an intermediate pressure at state H2, where a portion of the organic fluid flow rate is extracted from the expander 1 and transferred to the OFOH whereas, the remaining organic fluid flow rate expands up to the low condensation pressure of the HT loop. Both expansions in the expander 1 of the HT loop generate useful mechanical power, which is converted to useful electrical power since the expander 1 is connected to an electric generator. The organic fluid that has been expanded in expander 1 up to intermediate pressure and it is at superheated condition that H2 enters the OFOH, where it preheats the low temperature organic fluid stream that exits the circulation pump 1. The remaining organic fluid in the expander 1 is expanded up to low condensation pressure and exits the expander 1 as low condensation pressure superheated steam H3 and then enters the condenser of the HT loop, which operates as preheater of the organic fluid at the LT loop. At the condenser of the HT loop, the organic medium rejects heat to the organic fluid of the LT loop and it is condensed at the low condensation pressure of the HT loop. The organic fluid exits the condenser i.e., preheater of the HT loop as saturated liquid at state H5 and then enters pump 1, where it is compressed at the intermediate pressure of the HT loop and exits from the pump 1 as subcooled organic liquid at state H6. Subsequently, the subcooled organic liquid at state H6 is mixed with superheated steam of state H2, where it has been extracted from the first expansion at expander 1 and then the entire organic mass flow rate exits at state H7 as saturated liquid. The saturated organic liquid of state H7 is compressed by the circulation pump 2 at high evaporation pressure of the HT loop and it comes out from the pump 2 as subcooled liquid at state H8.  Figure 3 shows the thermodynamic processes that the organic fluid undergoes in the HT loop in a T-s diagram. In the LT loop, the subcooled organic fluid at state L8 enters the engine intercooler, where it recovers rejected heat from the charged air and it is heated under the constant evaporation pressure of the LT loop and it exits the intercooler as saturated organic liquid at state L9. Then the saturated organic liquid state L9 enters the preheater where it receives rejected heat from the   Figure 3 shows the thermodynamic processes that the organic fluid undergoes in the HT loop in a T-s diagram. In the LT loop, the subcooled organic fluid at state L8 enters the engine intercooler, where it recovers rejected heat from the charged air and it is heated under the constant evaporation pressure of the LT loop and it exits the intercooler as saturated organic liquid at state L9. Then the saturated organic liquid state L9 enters the preheater where it receives rejected heat from the condensed organic fluid of the HT loop and is converted to organic two-phase mixture, which exits the preheater at state L11. The two-phase mixture at state L11 enters the evaporator 2, where it receives the rejected heat from the engine coolant and it is heated under constant high evaporation pressure of the LT loop until it becomes saturated steam at state L1. The organic saturated steam state L1 enters the expander 2, where it expands up to intermediate pressure at state H2 and this state a portion of the superheated steam is extracted from the expander 2 and is transferred to the OFOH and the remaining organic mass flow rate continues to expand at low condensation pressure of the LT loop. The organic fluid exits the expander 2 as superheated steam at low condensation pressure at state L3. Subsequently, the superheated organic steam at state L3 enters the condenser of the LT loop, where the organic medium rejects heat to the seawater and exits the condenser as saturated organic liquid at state L5 and then it enters the circulation pump 1, where it compressed from the low condensation pressure to the intermediate pressure of the LT loop and exits the circulation pump 1 as subcooled organic liquid at state L6. The subcooled organic liquid state L6 enters the OFOH where is mixed with the superheated organic steam at state L2, which has been extracted from expander 2 at intermediate pressure and then the total organic mass flow rate exits the OFOH as saturated liquid state L7. Saturated liquid state L7 is compressed in the circulation pump 2 from the intermediate pressure to the high evaporation pressure of the LT loop and it exits the circulation pump 2 at state L8 as subcooled liquid to go again in the intercooler.

Energy and Exergy Analysis of the Regenerative Dual-Loop ORC
In the following section the energy and exergy analysis of the regenerative dual-loop ORC is described in detail. The corresponding energy and exergy analysis terms of the thermodynamic processes of the pertinent dual-loop ORC without the OFOH have been described in detail in Refs. [18,22], and they are not included in the present study for the sake of brevity of space.

Thermodynamic Processes of the HT Loop
The following thermodynamic processes take place in the HT loop of the regenerative dual-loop ORC, according to the Figure 2.
Process H1-H2-H3 (Expander 1): the generated power of the expander 1 of the HT loop taking into consideration both the expansion of the total flow rate of the superheated organic fluid from high

Energy and Exergy Analysis of the Regenerative Dual-Loop ORC
In the following section the energy and exergy analysis of the regenerative dual-loop ORC is described in detail. The corresponding energy and exergy analysis terms of the thermodynamic processes of the pertinent dual-loop ORC without the OFOH have been described in detail in Refs. [18,22], and they are not included in the present study for the sake of brevity of space.

Thermodynamic Processes of the HT Loop
The following thermodynamic processes take place in the HT loop of the regenerative dual-loop ORC, according to the Figure 2.
Process H1-H2-H3 (Expander 1): the generated power of the expander 1 of the HT loop taking into consideration both the expansion of the total flow rate of the superheated organic fluid from high evaporation pressure to intermediate pressure and the expansion of the remaining organic fluid flow rate after the extraction of a portion a from intermediate pressure to low condensation pressure of the HT loop is given in the following Equation (1). The isentropic efficiency of the expander 1 is given in Equation (2): The mechanical generated power P exp1 is converted to electrical power after multiplication with the efficiency of the electric generator, which is assumed to be equal to 99%.
The extraction rate α of the HT loop is defined, as follows: The irreversibility rate of expander 1 is calculated, as follows: Process H3-H5 (Preheater): The heat transfer rate from the organic medium of the HT loop to the preheater is given by the following relation: The irreversibility rate of the organic medium in the preheater is calculated according to the following relation: Process H5-H6 (Pump 1): The mechanical power consumption of the circulation pump 1 at the HT loop and the corresponding isentropic efficiency of the circulation pump 1 are given by the following relations: The irreversibility rate of the circulation pump 1 is calculated from the following relation: Process H2-H6-H7 (OFOH of the HT loop): the heat transfer rate from the hot organic stream that is extracted at the intermediate pressure of the HT loop is used to preheat the subcooled organic fluid state H6 that exits the circulation pump 1, according to the following relation: Energies 2020, 13, 2991 10 of 45 The irreversibility rate of the organic fluid in the OFOH is calculated, as follows: .
Process H7-H8 (Pump 2): The mechanical power consumption of the circulation pump 2 at the HT loop and its corresponding isentropic efficiency are calculated, as follows: The irreversibility rate of the organic medium in the circulation pump 2 is given by the following relation: Process H8-H1 (Evaporator 1): in the evaporator 1 of the HT loop exhaust gas heat is used for the heating of the organic fluid up from the subcooled to the superheated state, as described below: m gas h gas,a − h gas,d (15) The irreversibility rate of the evaporator 1 is calculated, as follows: .
m gas s gas,a − s gas,d

Thermodynamic Processes of the LT Loop
The organic medium undergoes the following thermodynamic processes in the LT loop in accordance with Figure 3.
Process L1-L2-L3 (Expander 2): the total power generated in the expander 2 comprised of the power generated from the total organic fluid mass flow rate that expands from the high evaporation pressure of the LT loop to its intermediate pressure and the power generated by the organic fluid flow rate that remains in expander 2 and it expands to the low condensation pressure of the LT loop after the extraction of portion "α" of total fluid flow rate at intermediate pressure. The total power generated in the expander 2 and the isentropic efficiency of expander 2 are given below: The mechanical generated power P exp2 is converted to electrical power after multiplication with the efficiency of the electric generator, which is assumed to be equal to 99%.
The portion "α" of organic fluid that is extracted from the LT loop expander and is transferred to the OFOH is: The irreversibility rate of the organic fluid expansion in the expander 2 is given in the following relation: Process L3-L5 (Condenser of the LT loop): the heat transfer losses of the organic medium in the condenser of the LT loop are transferred to the seawater and, thus, the energy balance in the LT loop condenser is: m sw · c p,sw (T sw,in − T sw,out ) (21) where c p,sw is the isobaric heat capacity of the seawater, which is calculated as function of the temperature, salinity, and pressure, as follows: c p,sw t, S kg/kg , p, p 0 = c p,sw t, S kg/kg + where temperature "t" is given in Celsius, salinity "S kg/kg " is given in kg/kg, pressure p, and reference pressure p 0 is given in MPa.
The irreversibility rate of the condensation process in the LT loop is calculated, as follows: where T mc is the average condensation temperature of the working medium. Process L5-L6 (Pump 1): the power consumption and the isentropic efficiency of circulation pump 1 are given by the following relations: The irreversibility rate of the compression process in the circulation pump 1 is calculated, as follows: Process L2-L6-L7 (OFOH of the LT loop): the heat transfer rate from the hot organic stream state L2 that is extracted at the intermediate pressure of the LT loop is used to preheat the subcooled organic fluid state L6 that exits the circulation pump 1, according to the following relation: The irreversibility rate of the OFOH of the LT loop is calculated according to the following relation: .
Process L7-L8 (Pump 2): the power consumption and the isentropic efficiency of the circulation pump 2 at the LT loop are calculated according to the following relations: The irreversibility rate of the circulation pump 2 is estimated by the following relation: Process L8-L9 (Intercooler): in the intercooler, the organic fluid harvests portion of the heat rejected by the engine charged air according to the following relation: The irreversibility rate of the process that takes place in the intercooler of the LT loop is calculated, as follows: Process L9-L11 (Preheater): in the preheater the organic medium of the LT loop receives a percentage of the heat that is rejected from the condensed organic medium of the HT loop. This percentage is determined by the effectiveness ε pre of the preheater according to the following relation: Process L11-L1 (Evaporator 2): in evaporator 2, the organic medium of the LT loop receives a percentage of the heat rejected by the engine coolant according to the effectiveness ε eva2 of the evaporator 2, as described below: The irreversibility rate of the evaporator 2 is calculated, as follows: (36) where T me is the average evaporation temperature of the organic medium at evaporator 2.

Performance Indices of the Regenerative Dual-Loop ORC
The net generated power of the HT loop is the difference between the power generated in the expander 1 and the power consumed by the circulation pumps 1 and 2 of the HT loop: The net generated power of the LT loop is the difference between the power generated in the expander 2 and the power consumed by the circulation pumps 1 and 2 of the LT loop: P LT,net = P exp2 − P p1 − P p2 (38) Hence, the overall net generated power of the both the HT and LT loop is given by the following relation: P tot,net = P HT,net + P LT,net The thermal efficiency of the dual-loop ORC is given by the following relation: Q int is the heat transfer rate of the intercooler of the LT loop, and . Q eva2 is the heat transfer rate between the engine coolant of the main diesel engine and the organic fluid in the evaporator 2 of the LT loop.
The main assumptions adopted for the examination of the regenerative dual-loop ORC are the following: 1.
The combined installation of the marine four-stroke diesel engine and the regenerative dual-loop ORC system operates under steady state conditions. 2.
Pressure drops in the pipelines are neglected.

3.
The isentropic efficiency of the expanders is 0.85.

4.
The isentropic efficiency of the circulation pumps is 0.75. 5.
The effectiveness of the LT loop intercooler was considered equal to 0.7, the effect of the preheater was considered equal to 0.5, and the effectiveness of the LT loop evaporator 2 was assumed equal to 0.5.

Modelling of the HT and LT Loop Heat Exchangers of the Regenerative ORC
Two different types of heat exchangers are considered in the present study having the waste heat transfer characteristics of the diesel engines in mind. A fin-and-tube heat exchanger is selected as evaporator 1 due to the high temperature of the exhaust gas, whereas a plate heat exchanger is used as intercooler, condenser, preheater, and evaporator 2. A heat transfer analysis for the fin-and-tube heat exchanger of the HT loop and the plate heat exchangers of the LT loop is essential in calculating the main dimensions, the heat transfer area, and the overall heat transfer coefficient of the heat exchangers and, then, in a following section, to calculate the capital cost of the heat exchangers based on their calculated heat transfer area. Heat exchanger analysis is also essential, since pure thermodynamics cannot provide the main dimensions, the heat transfer area, and the overall heat transfer coefficient of each heat exchanger. The calculation of area of heat exchanger is based on the logarithmic mean temperature difference (LMTD). According to this method, the heat transfer rate is: ∆T LMTD = ∆t max − ∆t min ln ∆t max ∆t min (42)

Fin-and-Tube Heat Exchanger Thermal Analysis
The evaporator 1, which is considered to be a fin-and-tube heat exchanger is divided into three zones: the single-phase liquid zone (state H8-state H9), the two-phase zone (state H9-state H10), and the single-phase vapor zone (state H10-state H1), as observed from Figure 2. Figure 4 provides a schematic view of the fin-and-tube internal geometry.
The overall heat transfer coefficient in each section is given by the following relation: The fouling resistance of organic fluid r in in the fin-and-tube heat exchanger was set equal to 0.0002, which corresponds to refrigerants liquids, as defined in Cao [30]. The fouling resistance of the external exhaust gas flow r out in the fin-and-tube heat exchanger was set equal to 0.002, which corresponds to diesel engine exhaust gases, as defined in Cao [30].

Fin-and-Tube Heat Exchanger Thermal Analysis
The evaporator 1, which is considered to be a fin-and-tube heat exchanger is divided into three zones: the single-phase liquid zone (state H8-state H9), the two-phase zone (state H9-state H10), and the single-phase vapor zone (state H10-state H1), as observed from Figure 2. Figure 4 provides a schematic view of the fin-and-tube internal geometry. The overall heat transfer coefficient in each section is given by the following relation: The fouling resistance of organic fluid rin in the fin-and-tube heat exchanger was set equal to 0.0002, which corresponds to refrigerants liquids, as defined in Cao [30]. The fouling resistance of the external exhaust gas flow rout in the fin-and-tube heat exchanger was set equal to 0.002, which corresponds to diesel engine exhaust gases, as defined in Cao [30].
The Nusselt number for the exhaust gas is given by the Zukauskas correlation [31]: When 1000 < Re:   The Nusselt number for the exhaust gas is given by the Zukauskas correlation [31]: When 1000 < Re: In the single-phase liquid zone [18]: In the single-phase vapor zone [18]: The wall temperature at the external exhaust gas flow is calculated from the following relation [30]: The wall temperature of the internal organic fluid flow is calculated, as follows [30]: For the liquid and the vapor phase zone inside the tube, the heat exchanger is divided into N parts according to the progressive variation of the vapor quality. The thermodynamic properties in Energies 2020, 13, 2991 15 of 45 each part can be considered as constant. The convective heat transfer coefficient is given by the Liu and Winterton correlation [33]: The forced convective heat transfer enhancement factor can be determined, as follows [18]: The suppression factor is [18]: The film boiling convective heat transfer coefficient can be calculated using Dittus-Boelter correlation [18]: The convective heat transfer coefficient for the nucleate boiling is given by the Cooper's pool boiling correlation [18]: The overall heat transfer coefficient of the plate heat exchanger can be calculated, as follows:

Plate Heat Exchanger Thermal Analysis
The fouling resistance of internal organic fluid flow rin in all plate heat exchangers was set equal to 0.0002, as dictated by Cao [30]. The fouling resistance of external air flow rout in the plate heat exchanger of intercooler was set equal to 0.0002 [30]. The fouling resistance of the external engine coolant flow rout in the LT loop evaporator was set equal to 0.0002 [30] and the external organic fluid flow rout of the HT loop in the plate heat exchanger of the preheater was also set equal to 0.0002 [30]. The fouling resistance of the external seawater flow in the LT loop condenser was set equal to 0.00009 [30].
The Nusselt number for the single-phase working fluid can be calculated from the Chisholm and Wanniarachchi [18,34]: Re Pr (59) The overall heat transfer coefficient of the plate heat exchanger can be calculated, as follows: The fouling resistance of internal organic fluid flow r in in all plate heat exchangers was set equal to 0.0002, as dictated by Cao [30]. The fouling resistance of external air flow r out in the plate heat exchanger of intercooler was set equal to 0.0002 [30]. The fouling resistance of the external engine coolant flow r out in the LT loop evaporator was set equal to 0.0002 [30] and the external organic fluid flow r out of the HT loop in the plate heat exchanger of the preheater was also set equal to 0.0002 [30]. The fouling resistance of the external seawater flow in the LT loop condenser was set equal to 0.00009 [30]. The Nusselt number for the single-phase working fluid can be calculated from the Chisholm and Wanniarachchi [18,34]: The Reynolds number is given from the following relation [18]: The mass flux can be expressed, as follows [18]: The hydraulic diameter of the flow channel can be calculated, as follows [18]: The two-phase heat transfer zone of the plate heat exchanger is divided into N parts according to the variation of vapor quality in the two-phase region. The Nusselt number for the condensation process is [35]: The Nusselt number for the evaporation process can be determined from the following relation [36]: The equivalent Reynolds number can be calculated, as follows [18]: The equivalent boiling number can be expressed as [18]: where:

Exhaust Gas Pressure Drop at the HT Loop Evaporator 1
The calculation of the exhaust gas pressure drop at the HT loop evaporator is that the highest portion of diesel engine exhaust gases is air since marine diesel engines always operate with excess air and with a high air to fuel ratio, which is considerably higher than the stoichiometric. Hence, according to Cao [30], the pressure drop of the air through heat exchanger bundle of tubes is: where f is the friction factor and G S is the mass flow density, which is defined as [30]: Additionally, L p is the length of path, which is defined as [30]: The geometrical parameters S L , S T and S F are defined in the following Figure 6. In Equation (66), parameter D e' is the equivalent diameter for friction and it is defined, as follows [30]: Energies 2020, 13, x FOR PEER REVIEW 17 of 46 The net free volume is the volume between the central plates of two consecutive rows minus the portion of that volume occupied by the tubes and fins [30]: The friction factor f can be expressed as function of the Reynolds number, as follows [30]: where the Reynolds number Re'S is defined, as follows:

Economic Analysis-Calculation of the Total Capital Cost and Electricity Production Cost
The dual-loop ORC is comprised from many different components. All direct and overhead costs should be taken into consideration for each part of the installation. The Module Costing Technique (MCT) is a commonly used method for calculating the bare module cost of chemical plants [37]. Based on the MCT, the capital cost of the heat exchanger can be calculated while using the following relation:  The net free volume is the volume between the central plates of two consecutive rows minus the portion of that volume occupied by the tubes and fins [30]: The friction factor f can be expressed as function of the Reynolds number, as follows [30]: where the Reynolds number Re' S is defined, as follows:

Economic Analysis-Calculation of the Total Capital Cost and Electricity Production Cost
The dual-loop ORC is comprised from many different components. All direct and overhead costs should be taken into consideration for each part of the installation. The Module Costing Technique (MCT) is a commonly used method for calculating the bare module cost of chemical plants [37].  [36].
The bare module cost of the heat exchanger is: where K 1,HX , K 2,HX , and K 3,HX are the constants that depend from heat exchanger type and A HX is the heat exchanger area. The values of K 1,HX , K 2,HX , and K 3,HX are 4.66, −0.1557, and 0.1547, respectively [36]. The pressure factor of the heat exchanger is [37]: where C 1,HX , C 2,HX , and C 3,HX are the constants that depend on the type of heat exchanger and P HX is the design pressure of the heat exchanger. The values of C 1,HX , C 2,HX , and C 3,HX are all zero. The capital cost of the circulation pump is [37]: where C PP 0 is the bare module cost of the circulation pump, B 1,PP and B 2,PP are the constants that depend from the type of the circulation pump, and F M,PP and F P,PP are the material and pressure factors, respectively. The values of B 1,PP and B 2,PP are 1.89 and 1.35, respectively, and the value of F M,PP is 2.20 [36]. The bare module cost of the circulation pump is [37]: where K 1,PP , K 2,PP , and K 3,PP are the constants that depend from the type of the circulation pump and . W PP is the power consumption of the circulation pump. The values of K 1,PP , K 2,PP , and K 3,PP are 3.389, 0.536, and 0.1538, respectively [36]. The pressure factor of the circulation pump can be determined, as follows: where C 1,PP , C 2,PP , and C 3,PP are the constants that depend on the type of the circulation pump and P PP is the design pressure of the circulation pump. The values of C 1,PP , C 2,PP , and C 3,PP are −0.3935, 0.3957, and −0.00226, respectively [36].
The capital cost of the expander can be expressed, as follows: where C 0 EXP is the bare module cost of the expander and F MP is the additional expander factor, which is equal to 3.5 [36].
The bare module cost of the expander is: where K 1,EXP , K 2,EXP , and K 3,EXP are the constants that depend on the type of the expander, and . W EXP is the power output of the expander. The values of K 1,EXP , K 2,EXP , and K 3,EXP are 2.2659, 1.4398, and −0.1776, respectively [36].
According to Imran et al. [28], the cost of the feed heater is: where B 1,FH and B 2,FH are constants for feed heater type, which are equal to 1.12 and 0.87, respectively, and F M,PH is the additional material factor, F P,PH is the pressure factor for the OFOH, and C' FH is the basic cost of the OFOH. The basic cost of the OFOH is [28]: where K 1,FH , K 2,FH , and K 3,FH are the constants for the OFOH type, which are equal to 4.2, −0.204, and 0.1245, respectively. The pressure factor of the OFOH is [28]: where the constant C 1,FH is equal to 0.0, constant C 2,FH is equal to 10, and constant C 3,FH is equal to 0.0. The total investment cost (TIC) of the system is the sum of the capital cost of each component of the installation: The Capital Recovery Factor (CRF) is [38]: where i is the interest rate and LT pl is the plant lifetime. The value of interest rate i is 0.1 and the value of LT pl is 15 [36]. The Electricity Production Cost (EPC) is: where f k is the maintenance and insurance cost factor, which is equal to 0.0165 [35] and h full_load is the full load operation hours, which is 4000.

Parametric Investigation to Determine the Optimum Regenerative Dual-Loop ORC and the Optimum Organic Fluids for the HT and LT Loops
In this section, a parametric study is performed for examining the effect of various combinations of the organic fluids examined in the present study under different thermodynamic parameters on the thermodynamic performance and cost indices of the regenerative dual-loop ORC. The purpose of this For each one of the previously mentioned pairs of organic mediums, it is examined the effect of the following thermodynamic parameters on the total generated electric power, the thermal cycle efficiency, the total irreversibility rate, the total investment cost, and the cost of generated electrical energy: • In this section, the effect of HT loop evaporation pressure on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electricity production cost (EPC) is examined for all the pairs of organic fluids considered in this study. The variation of generated power of the regenerative dual-loop ORC with HT loop evaporation pressure for all of the combinations of organic mediums considered in this study is shown in Figure 7a. As observed, the increase of HT loop evaporation pressure results, as expected, in the increase of the generated power at all cases of organic fluid pairs. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 7b shows the variation of the regenerative dual-loop ORC thermal efficiency with HT loop evaporation pressure for all organic medium combinations considered in this study. As witnessed, the thermal efficiency of the regenerative dual-loop ORC increases with increasing HT loop evaporation pressure due to the corresponding of the generated electrical power for the same waste heat transfer rates from the main diesel engine. The highest values of thermal efficiency are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of thermal efficiency are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 7c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with HT loop evaporation pressure for all organic fluid pairs considered in the present analysis. As observed, the increase of the HT loop evaporation pressure results in an increase of the total irreversibility rate of the regenerative dual-loop mainly due to the increase of irreversibility rates in the HT loop expander, which was the result of the increase of its pressure ratio. The highest values of total irreversibility rate are observed for the organic medium pairs R245fa (HT loop) and R600 (LT loop) and R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).
is examined for all the pairs of organic fluids considered in this study. The variation of generated power of the regenerative dual-loop ORC with HT loop evaporation pressure for all of the combinations of organic mediums considered in this study is shown in Figure 7a. As observed, the increase of HT loop evaporation pressure results, as expected, in the increase of the generated power at all cases of organic fluid pairs. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).  Figure 7b shows the variation of the regenerative dual-loop ORC thermal efficiency with HT loop evaporation pressure for all organic medium combinations considered in this study. As witnessed, the thermal efficiency of the regenerative dual-loop ORC increases with increasing HT loop evaporation pressure due to the corresponding of the generated electrical power for the same waste heat transfer rates from the main diesel engine. The highest values of thermal efficiency are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of thermal efficiency are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 7c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with HT loop evaporation pressure for all organic fluid pairs considered in the present analysis. As observed, the increase of the HT loop evaporation pressure results in an increase of the total irreversibility rate of the regenerative dual-loop mainly due to the increase of irreversibility rates in the HT loop expander, which was the result of the increase of its pressure ratio. The highest values  for all organic fluid pairs considered in the present study. The increase of the HT loop evaporation pressure results in the increase of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 8a. The highest values of total investment cost are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of total investment cost are evidenced for the two organic medium pairs R600 (HT loop) and R1234ze (LT loop) and R600 (HT loop) and R1234yf (LT loop).  In this section, the influence of HT loop superheating degree on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all the pairs of organic fluids considered in this study.
The variation of generated power of the regenerative dual-loop ORC with HT loop superheating degree for all the combinations of organic mediums considered in this study is shown in Figure 9a. As observed, the increase of HT loop superheating degree does not provide noticeable change of the generated power in all cases of organic fluid pairs. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).
Total Investment Cost (kEuro) In this section, the influence of HT loop superheating degree on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all the pairs of organic fluids considered in this study.
The variation of generated power of the regenerative dual-loop ORC with HT loop superheating degree for all the combinations of organic mediums considered in this study is shown in Figure 9a. As observed, the increase of HT loop superheating degree does not provide noticeable change of the generated power in all cases of organic fluid pairs. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).
The variation of thermal efficiency of the regenerative dual-loop ORC with HT loop superheating degree for all of the combinations of organic mediums considered in this study is shown in Figure 9b. As observed, the increase of HT loop superheating degree does not provide noticeable change of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 9c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with HT loop superheating degree for all the combinations of organic mediums considered in this study. As observed, the increase of HT loop superheating degree results in a small increase of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 10a shows the variation of the total investment cost with the HT loop superheating degree for all of organic fluid pairs considered in the present study. The increase of the HT loop superheating degree results in small increase of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 10a. The highest values of total investment cost are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of total investment cost are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). The variation of thermal efficiency of the regenerative dual-loop ORC with HT loop superheating degree for all of the combinations of organic mediums considered in this study is shown in Figure 9b. As observed, the increase of HT loop superheating degree does not provide noticeable change of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 9c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with HT loop superheating degree for all the combinations of organic mediums considered in this study. As observed, the increase of HT loop superheating degree results in a small increase of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 10a shows the variation of the total investment cost with the HT loop superheating degree for all of organic fluid pairs considered in the present study. The increase of the HT loop superheating degree results in small increase of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 10a. The highest values of total investment cost are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of     Figure 10b shows the variation of the EPC with the HT loop superheating degree for all organic medium pairs considered in the present analysis. The cost of the produced electricity is slightly reduced at all cases of organic medium pairs with increasing HT loop superheating degree. The highest values of EPC are observed for the organic medium pair R600 (HT loop) and R1234yf (LT loop), whereas the lowest values of EPC are evidenced for the two organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop).

Effect of the Condensation Temperature of the HT Loop
In this section the influence of HT loop condensation temperature on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all the pairs of organic fluids considered in this study.
The variation of generated power of the regenerative dual-loop ORC with HT loop condensation temperature for all of the combinations of organic mediums considered in this study is shown in Figure 11a. As observed, the increase of HT loop condensation temperature results in a reduction of the generated power at all cases of organic fluid pairs due to the reduction of the pressure ratio in the HT loop expander. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). The variation of thermal efficiency of the regenerative dual-loop ORC with HT loop condensation temperature for all of the combinations of organic mediums considered in this study is shown in Figure 11b. As observed, the increase of HT loop condensation temperature results in a linear reduction of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair  The variation of thermal efficiency of the regenerative dual-loop ORC with HT loop condensation temperature for all of the combinations of organic mediums considered in this study is shown in Figure 11b. As observed, the increase of HT loop condensation temperature results in a linear reduction of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 11c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with HT loop condensation temperature for all the combinations of organic mediums considered in this study. As observed, the increase of HT loop condensation temperature results in a reduction of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 12a shows the variation of the total investment cost with the HT loop condensation temperature for all organic fluid pairs considered in the present study. The increase of the HT loop condensation temperature results in the reduction of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 12a. The highest values of total investment cost are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of total investment cost are evidenced for the two organic medium pairs R600 (HT loop) and R600 (LT loop) and R600 (HT loop) and R1234ze (LT loop). The variation of the EPC with the HT loop condensation temperature for all organic medium pairs considered in the present analysis is shown in Figure 12b. The cost of the produced electricity is increased at all cases of organic medium pairs with increasing HT loop condensation temperature. The highest values of EPC are observed for the organic medium pair R600 (HT loop) and R1234yf (LT loop), whereas the lowest values of EPC are evidenced for the two organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop).

Effect of the Evaporation Temperature of the LT Loop
In this section, the influence of the LT loop evaporation temperature on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all the pairs of organic fluids considered in this study.
The variation of generated power of the regenerative dual-loop ORC with the LT loop evaporation temperature for all of the combinations of organic mediums considered in this study is shown in Figure 13a. As observed, the increase of LT loop evaporation temperature results in the linear increase of the generated power at all cases of organic fluid pairs due to the increase of the pressure ratio in the LT loop expander. The highest values of generated power are observed for the The variation of the EPC with the HT loop condensation temperature for all organic medium pairs considered in the present analysis is shown in Figure 12b. The cost of the produced electricity is increased at all cases of organic medium pairs with increasing HT loop condensation temperature. The highest values of EPC are observed for the organic medium pair R600 (HT loop) and R1234yf (LT loop), whereas the lowest values of EPC are evidenced for the two organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop).

Effect of the Evaporation Temperature of the LT Loop
In this section, the influence of the LT loop evaporation temperature on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the Energies 2020, 13, 2991 26 of 45 regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all the pairs of organic fluids considered in this study.
The variation of generated power of the regenerative dual-loop ORC with the LT loop evaporation temperature for all of the combinations of organic mediums considered in this study is shown in Figure 13a. As observed, the increase of LT loop evaporation temperature results in the linear increase of the generated power at all cases of organic fluid pairs due to the increase of the pressure ratio in the LT loop expander. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).  Figure 13b shows the variation of thermal efficiency of the regenerative dual-loop ORC with LT loop evaporation temperature for all combinations of organic mediums considered in this study. As observed, the increase of LT loop evaporation temperature results in a linear increase of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 13c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with LT loop evaporation temperature for all of the combinations of organic mediums considered in this study. As observed, the increase of LT loop evaporation temperature results in the increase of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 14a shows the variation of the total investment cost with the LT loop evaporation  Figure 13b shows the variation of thermal efficiency of the regenerative dual-loop ORC with LT loop evaporation temperature for all combinations of organic mediums considered in this study. As observed, the increase of LT loop evaporation temperature results in a linear increase of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 13c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with LT loop evaporation temperature for all of the combinations of organic mediums considered in this study. As observed, the increase of LT loop evaporation temperature results in the increase of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 14a shows the variation of the total investment cost with the LT loop evaporation temperature for all organic fluid pairs considered in the present study. The increase of the LT loop evaporation temperature results in the increase of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 14a. The highest values of total investment cost are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of total investment cost are evidenced for the two organic medium pairs R600 (HT loop) and R600 (LT loop) and R600 (HT loop) and R1234ze (LT loop).  Figure 14b shows the variation of the EPC with the LT loop evaporation temperature for all organic medium pairs considered in the present analysis. The cost of the produced electricity is decreased at all cases of organic medium pairs with increasing LT loop evaporation temperature. The highest values of EPC are observed for the organic medium pair R600 (HT loop) and R1234yf (LT loop), whereas the lowest values of EPC are evidenced for the two organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop).

Effect of the Condensation Temperature of the LT Loop
In this section, the influence of the LT loop condensation temperature on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all of the pairs of organic fluids considered in this study.
The variation of generated power of the regenerative dual-loop ORC with the LT loop condensation temperature for all combinations of organic mediums considered in this study is shown in Figure 15a. As observed, the increase of LT loop condensation temperature results in the linear reduction of the generated power at all cases of organic fluid pairs due to the reduction of the pressure ratio in the LT loop expander. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).  Figure 14b shows the variation of the EPC with the LT loop evaporation temperature for all organic medium pairs considered in the present analysis. The cost of the produced electricity is decreased at all cases of organic medium pairs with increasing LT loop evaporation temperature. The highest values of EPC are observed for the organic medium pair R600 (HT loop) and R1234yf (LT loop), whereas the lowest values of EPC are evidenced for the two organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop).

Effect of the Condensation Temperature of the LT Loop
In this section, the influence of the LT loop condensation temperature on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all of the pairs of organic fluids considered in this study.
The variation of generated power of the regenerative dual-loop ORC with the LT loop condensation temperature for all combinations of organic mediums considered in this study is shown in Figure 15a. As observed, the increase of LT loop condensation temperature results in the linear reduction of the generated power at all cases of organic fluid pairs due to the reduction of the pressure ratio in the LT loop expander. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).  Figure 15b shows the variation of thermal efficiency of the regenerative dual-loop ORC with LT loop condensation temperature for all combinations of organic mediums considered in this study. As observed, the increase of LT loop condensation temperature results in a linear reduction of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 15c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with LT loop condensation temperature for all combinations of organic mediums considered in this study. As observed, the increase of LT loop condensation temperature results in the increase of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 16a shows the variation of the total investment cost with the LT loop condensation temperature for all organic fluid pairs considered in the present study. The increase of the LT loop condensation temperature results in reduction of the total investment cost of the regenerative dualloop ORC installation, as witnessed from Figure 16a. The highest values of total investment cost are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest  Figure 15b shows the variation of thermal efficiency of the regenerative dual-loop ORC with LT loop condensation temperature for all combinations of organic mediums considered in this study. As observed, the increase of LT loop condensation temperature results in a linear reduction of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 15c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with LT loop condensation temperature for all combinations of organic mediums considered in this study. As observed, the increase of LT loop condensation temperature results in the increase of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 16a shows the variation of the total investment cost with the LT loop condensation temperature for all organic fluid pairs considered in the present study. The increase of the LT loop condensation temperature results in reduction of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 16a  In this section, the influence of the exhaust gas temperature at HT loop evaporator 1 outlet on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all of the pairs of organic fluids considered in this study. Figure 17a shows the variation of generated power of the regenerative dual-loop ORC with the exhaust gas temperature at HT loop evaporator 1 outlet for all of the combinations of organic mediums considered in this study. As observed, the increase of exhaust gas temperature results in the linear reduction of the generated power at all cases of organic fluid pairs due to the reduction of the exhaust gas heat transferred to the organic fluid at the HT loop evaporator 1. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).  In this section, the influence of the exhaust gas temperature at HT loop evaporator 1 outlet on the generated power and the thermal efficiency of the regenerative dual-loop ORC, on the total irreversibility rate of the regenerative dual-loop ORC, on the total investment cost, and on the electrical power cost (EPC) is examined for all of the pairs of organic fluids considered in this study. Figure 17a shows the variation of generated power of the regenerative dual-loop ORC with the exhaust gas temperature at HT loop evaporator 1 outlet for all of the combinations of organic mediums considered in this study. As observed, the increase of exhaust gas temperature results in the linear reduction of the generated power at all cases of organic fluid pairs due to the reduction of the exhaust gas heat transferred to the organic fluid at the HT loop evaporator 1. The highest values of generated power are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 17b shows the variation of thermal efficiency of the regenerative dual-loop ORC with the exhaust gas temperature at HT loop evaporator 1 outlet for all combinations of organic mediums considered in this study. As observed, the increase of the exhaust gas temperature at HT loop evaporator 1 outlet results in reduction of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop).  Figure 17b shows the variation of thermal efficiency of the regenerative dual-loop ORC with the exhaust gas temperature at HT loop evaporator 1 outlet for all combinations of organic mediums considered in this study. As observed, the increase of the exhaust gas temperature at HT loop evaporator 1 outlet results in reduction of the thermal efficiency at all cases of organic fluid pairs. The highest values of the thermal efficiency of the regenerative dual-loop ORC are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of generated power are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 17c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with the exhaust gas temperature at HT loop evaporator 1 outlet for all combinations of organic mediums considered in this study. As observed, the increase of the exhaust gas temperature at HT loop evaporator 1 outlet results in the linear reduction of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 18a shows the variation of the total investment cost with the exhaust gas temperature at HT loop evaporator 1 outlet for all organic fluid pairs considered in the present study. The increase of the exhaust gas temperature at HT loop evaporator 1 outlet results in the reduction of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 18a. The  Figure 17c shows the variation of the total irreversibility rate of the regenerative dual-loop ORC with the exhaust gas temperature at HT loop evaporator 1 outlet for all combinations of organic mediums considered in this study. As observed, the increase of the exhaust gas temperature at HT loop evaporator 1 outlet results in the linear reduction of the total irreversibility rate at all cases of organic fluid pairs. The highest values of the total irreversibility rate of the regenerative dual-loop ORC are observed for the organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop), whereas the lowest values of the total irreversibility rate are evidenced for the organic medium pair R600 (HT loop) and R1234yf (LT loop). Figure 18a shows the variation of the total investment cost with the exhaust gas temperature at HT loop evaporator 1 outlet for all organic fluid pairs considered in the present study. The increase of the exhaust gas temperature at HT loop evaporator 1 outlet results in the reduction of the total investment cost of the regenerative dual-loop ORC installation, as witnessed from Figure 18a. The highest values of total investment cost are observed for the organic medium pair R245fa (HT loop) and R245fa (LT loop), whereas the lowest values of total investment cost are evidenced for the organic medium pairs R600 (HT loop) and R1234yf (LT loop) and R600 (HT loop) and R1234ze (LT loop). However, it should be noted that the variation of the total investment cost between all organic fluid pairs are not significant and, thus, the deviation between the highest and lowest values are not considerable. Figure 18b shows the variation of the EPC with the exhaust gas temperature at HT loop evaporator 1 outlet for all organic medium pairs considered in the present analysis. The cost of the produced electricity increases at all cases of organic medium pairs with increasing exhaust gas temperature at HT loop evaporator 1 outlet. The highest values of EPC are observed for the organic medium pair R600 (HT loop) and R1234yf (LT loop), whereas the lowest values of EPC are evidenced for the two organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop). Hence, from the parametric investigation performed regarding the effect of various thermodynamic parameters and pairs of organic mediums on the performance characteristics and the cost parameters of the regenerative dual-loop ORC, it can be concluded that the optimum dualloop ORC with OFOH should operate with the following organic fluids and it should have the following settings: 1. The optimum organic fluid of the HT loop is R245fa and the optimum organic fluid of the LT loop is R600. This is the best organic fluid pair solution compared to all others examined, because it provides the maximum electrical power with the lowest cost per kWh and it also provides the highest thermal efficiency despite the fact that it does not provide the lowest total investment cost and it has the highest total irreversibility rate. 2. The optimum superheating degree of the HT loop is 20 °C. 3. The minimum and, thus, optimum condensation temperature of the HT cycle was found to be equal to 76.85 °C. The maximum and, thus, optimum evaporation temperature of the LT cycle was found to be equal to 70 °C and the minimum and, thus, optimum condensation temperature of the LT cycle was found to be equal to 35 °C. The condensation temperature of the LT cycle was selected based on the fact that the condenser of the LT cycle will be cooled with seawater. The seawater temperature does not exceed over 27 °C, according to the historic data of average monthly seawater surface temperature of Greek seas from 1850 to 2006 [39]. Hence, the minimum and, thus, optimum LT loop condensation temperature of 35 °C is 8 °C higher when compared to the highest possible inlet seawater temperature at the LT loop condenser and, thus, it satisfies the heat transfer ability from the organic fluid to the seawater  Figure 18b shows the variation of the EPC with the exhaust gas temperature at HT loop evaporator 1 outlet for all organic medium pairs considered in the present analysis. The cost of the produced electricity increases at all cases of organic medium pairs with increasing exhaust gas temperature at HT loop evaporator 1 outlet. The highest values of EPC are observed for the organic medium pair R600 (HT loop) and R1234yf (LT loop), whereas the lowest values of EPC are evidenced for the two organic medium pairs R245fa (HT loop) and R245fa (LT loop) and R245fa (HT loop) and R600 (LT loop).
Hence, from the parametric investigation performed regarding the effect of various thermodynamic parameters and pairs of organic mediums on the performance characteristics and the cost parameters of the regenerative dual-loop ORC, it can be concluded that the optimum dual-loop ORC with OFOH should operate with the following organic fluids and it should have the following settings: 1.
The optimum organic fluid of the HT loop is R245fa and the optimum organic fluid of the LT loop is R600. This is the best organic fluid pair solution compared to all others examined, because it provides the maximum electrical power with the lowest cost per kWh and it also provides the highest thermal efficiency despite the fact that it does not provide the lowest total investment cost and it has the highest total irreversibility rate.

2.
The optimum superheating degree of the HT loop is 20 • C.

3.
The minimum and, thus, optimum condensation temperature of the HT cycle was found to be equal to 76.85 • C. The maximum and, thus, optimum evaporation temperature of the LT cycle was found to be equal to 70 • C and the minimum and, thus, optimum condensation temperature of the LT cycle was found to be equal to 35 • C. The condensation temperature of the LT cycle was selected based on the fact that the condenser of the LT cycle will be cooled with seawater. The seawater temperature does not exceed over 27 • C, according to the historic data of average monthly seawater surface temperature of Greek seas from 1850 to 2006 [39]. Hence, the minimum and, thus, optimum LT loop condensation temperature of 35 • C is 8 • C higher when compared to the highest possible inlet seawater temperature at the LT loop condenser and, thus, it satisfies the heat transfer ability from the organic fluid to the seawater 4.
The lowest temperature of the exhaust gas at the exit of evaporator 1 of the HT cycle is set to 150 • C in order to be 30 • C higher than the dew point temperature of exhaust gas in case the fuel burned in the engine contains sulphur [5].

Comparative Evaluation of the Simple Dual-Loop ORC with the Regenerative Dual-Loop ORC
This section comparatively evaluates the main thermal performance parameters of the simple dual-loop ORC without OFOH and the regenerative dual-loop ORC with OFOH. Figure 19a presents the comparatively evaluated variation of generated electrical power of the simple dual-loop ORC and the regenerative dual-loop ORC with engine load. As observed, the generated electrical power increases with engine load and it is higher in the case of the regenerative dual-loop ORC when compared to simple dual-loop ORC for all engine loads. The difference in generated power between the two examined cycles is progressively increasing with increasing load. The generated power of the regenerative dual-loop ORC varies from 156.5 kW at 40% of MCR to almost 636 kW at 100% of MCR. Figure 19b presents the comparatively assessed variation of the bsfc improvement of the simple dual-loop ORC and the regenerative dual-loop ORC with engine load. As observed, the bsfc improvement increases with engine load and the values of bsfc improvement of the regenerative dual-loop ORC are higher as compared to the corresponding values of the simple dual-loop ORC at all engine loads, because, as evidenced in Figure 19a, the regenerative dual-loop ORC generates more power when compared to the simple dual-loop ORC at all engine loads. Specifically, the bsfc improvement of the regenerative dual-loop ORC varies from 3.3% at 40% of MCR to 6.7% at 100% of MCR. Overall, it can be concluded that the regenerative dual-loop ORC generates more power and it results in higher bsfc improvement when compared to the simple dual-loop ORC at all cases of engine load examined.
Energies 2020, 13, x FOR PEER REVIEW 32 of 46 4. The lowest temperature of the exhaust gas at the exit of evaporator 1 of the HT cycle is set to 150 °C in order to be 30 °C higher than the dew point temperature of exhaust gas in case the fuel burned in the engine contains sulphur [5].

Comparative Evaluation of the Simple Dual-Loop ORC with the Regenerative Dual-Loop ORC
This section comparatively evaluates the main thermal performance parameters of the simple dual-loop ORC without OFOH and the regenerative dual-loop ORC with OFOH. Figure 19a presents the comparatively evaluated variation of generated electrical power of the simple dual-loop ORC and the regenerative dual-loop ORC with engine load. As observed, the generated electrical power increases with engine load and it is higher in the case of the regenerative dual-loop ORC when compared to simple dual-loop ORC for all engine loads. The difference in generated power between the two examined cycles is progressively increasing with increasing load. The generated power of the regenerative dual-loop ORC varies from 156.5 kW at 40% of MCR to almost 636 kW at 100% of MCR. Figure 19b presents the comparatively assessed variation of the bsfc improvement of the simple dual-loop ORC and the regenerative dual-loop ORC with engine load. As observed, the bsfc improvement increases with engine load and the values of bsfc improvement of the regenerative dual-loop ORC are higher as compared to the corresponding values of the simple dual-loop ORC at all engine loads, because, as evidenced in Figure 19a, the regenerative dual-loop ORC generates more power when compared to the simple dual-loop ORC at all engine loads. Specifically, the bsfc improvement of the regenerative dual-loop ORC varies from 3.3% at 40% of MCR to 6.7% at 100% of MCR. Overall, it can be concluded that the regenerative dual-loop ORC generates more power and it results in higher bsfc improvement when compared to the simple dual-loop ORC at all cases of engine load examined.
(a) (b) Figure 19. Comparison of (a) generated electric power and (b) bsfc improvement between the simple dual-loop ORC and the regenerative dual-loop ORC. Figure 20a illustrates the comparatively evaluated variation of the cycle thermal efficiency of the simple dual-loop ORC and the regenerative dual-loop ORC with engine load. As evidenced, the variation of thermal efficiency with engine load is limited for both examined bottoming cycles. Additionally, the values of thermal efficiency for the regenerative dual-loop ORC are higher when compared to the corresponding values of the simple dual-loop ORC at all engine loads examined. Specifically, the thermal efficiency of the regenerative dual-loop ORC ranges from 12.5% at 40% of MCR to 12.3% at 100% of MCR. The higher values of thermal efficiency for the regenerative dualloop ORC as compared to the values of the simple dual-loop ORC can be ascribed to the fact that the regenerative dual-loop ORC generates more electrical power as compared to the simple dual-loop ORC at each engine load for the same waste heat transfer rates. Figure 20b Figure 20a illustrates the comparatively evaluated variation of the cycle thermal efficiency of the simple dual-loop ORC and the regenerative dual-loop ORC with engine load. As evidenced, the variation of thermal efficiency with engine load is limited for both examined bottoming cycles. Additionally, the values of thermal efficiency for the regenerative dual-loop ORC are higher when compared to the corresponding values of the simple dual-loop ORC at all engine loads examined. Specifically, the thermal efficiency of the regenerative dual-loop ORC ranges from 12.5% at 40% of MCR to 12.3% at 100% of MCR. The higher values of thermal efficiency for the regenerative dual-loop ORC as compared to the values of the simple dual-loop ORC can be ascribed to the fact that the regenerative dual-loop ORC generates more electrical power as compared to the simple dual-loop ORC at each engine load for the same waste heat transfer rates. Figure 20b presents the comparatively assessed values of combined main engine-ORC efficiency of the regenerative dual-loop ORC and the simple dual-loop ORC with engine load. The values of the combined engine-ORC efficiency are compared with the corresponding values of main engine efficiency. As observed, the combined systems of engine and simple dual-loop ORC and engine and regenerative dual-loop ORC both have higher efficiencies when compared to the main engine efficiency. The efficiency of the combined diesel engine-regenerative dual-loop ORC is higher when compared to the corresponding efficiency of the combined diesel engine-simple dual-loop ORC at all engine loads. Specifically, the efficiency of the combined diesel engine-regenerative dual-loop ORC ranges from 45.8% at 40% of MCR to 46.9% at 100% of MCR and is 4% to 6.7% higher when compared to the brake efficiency of the main diesel engine. Obviously, the total efficiency of the combined diesel engine-regenerative dual-loop ORC system is increased as compared to the efficiency of the main engine due to the additional power generated from the ORC system for the same fuel heating power provided to the main diesel engine.
Energies 2020, 13, x FOR PEER REVIEW 33 of 46 compared with the corresponding values of main engine efficiency. As observed, the combined systems of engine and simple dual-loop ORC and engine and regenerative dual-loop ORC both have higher efficiencies when compared to the main engine efficiency. The efficiency of the combined diesel engine-regenerative dual-loop ORC is higher when compared to the corresponding efficiency of the combined diesel engine-simple dual-loop ORC at all engine loads. Specifically, the efficiency of the combined diesel engine-regenerative dual-loop ORC ranges from 45.8% at 40% of MCR to 46.9% at 100% of MCR and is 4% to 6.7% higher when compared to the brake efficiency of the main diesel engine. Obviously, the total efficiency of the combined diesel engine-regenerative dual-loop ORC system is increased as compared to the efficiency of the main engine due to the additional power generated from the ORC system for the same fuel heating power provided to the main diesel engine.     Figure 21b presents the comparatively evaluated values of the irreversibility rate of expander 2 of the LT loop of the regenerative dual-loop ORC with the corresponding values of the simple dualloop ORC with engine load. As evidenced, the irreversibility rate of the expander 2 of the LT loop increases with engine load in both bottoming cycles. The differences in the irreversibility rate of the LT loop expander between the two bottoming cycles are not significant and lower when compared to the corresponding differences of irreversibility rate of the HT loop expander between the two bottoming cycles. The irreversibility rate of the LT loop expander of the regenerative dual-loop ORC varies from 10.9 kW at 40% of MCR to 46.4 kW at 100% of MCR, whereas the corresponding variation in the simple dual-loop ORC ranges from 10.5 kW at 40% of MCR to 44.8 kW at 100% of MCR. Figure 21c illustrates the comparatively assessed values of the total irreversibility rate of the HT loop of the regenerative dual-loop ORC with the corresponding values of the simple dual-loop ORC with engine load. As observed, the total irreversibility rate of the HT loop increases with engine load in both bottoming cycles. The values of the total irreversibility rate of the HT loop of the regenerative dual-loop ORC are lower when compared to the corresponding values of the simple dual-loop ORC at all examined engine loads. Hence, an asset of the installation of the OFOH in the HT loop of the regenerative dual-loop ORC is that its operation results in the considerable reduction of the total exergy destruction rate. This is due to the fact that the OFOH results in better internal utilization of the heat transfer rates in the HT loop, since part of the high temperature organic fluid is utilized for the preheating of the low temperature organic fluid in the OFOH and this operation results in a reduction of the required thermal energy for organic fluid superheating in the HT loop. Similar observations can be made for the values of the total irreversibility rate of the LT loop between the regenerative dual-loop ORC and the simple dual-loop ORC in Figure 21d. Specifically, also in the  Figure 21c illustrates the comparatively assessed values of the total irreversibility rate of the HT loop of the regenerative dual-loop ORC with the corresponding values of the simple dual-loop ORC with engine load. As observed, the total irreversibility rate of the HT loop increases with engine load in both bottoming cycles. The values of the total irreversibility rate of the HT loop of the regenerative dual-loop ORC are lower when compared to the corresponding values of the simple dual-loop ORC at all examined engine loads. Hence, an asset of the installation of the OFOH in the HT loop of the regenerative dual-loop ORC is that its operation results in the considerable reduction of the total exergy destruction rate. This is due to the fact that the OFOH results in better internal utilization of the heat transfer rates in the HT loop, since part of the high temperature organic fluid is utilized for the preheating of the low temperature organic fluid in the OFOH and this operation results in a reduction of the required thermal energy for organic fluid superheating in the HT loop. Similar observations can be made for the values of the total irreversibility rate of the LT loop between the regenerative dual-loop ORC and the simple dual-loop ORC in Figure 21d. Specifically, also in the case of the LT loop, the values of total irreversibility rate of the regenerative dual-loop ORC are lower when compared to the corresponding ones of the simple dual-loop ORC at all examined engine loads. In addition, the difference in total irreversibility rate of the LT loop between the two bottoming cycles is progressively increased with increasing engine load. The total irreversibility rate of the LT loop in the case of the regenerative ORC varies from 1921 kW at 40% of MCR to 2208 kW at 100% of MCR, whereas the total irreversibility rate of the LT loop in the case of the simple dual-loop ORC varies from 2358 kW at 40% of MCR to 3902 kW at 100% of MCR.

Mission Analysis of the General Support Vessel with Regenerative Dual-Loop ORC-Calculation of the Fuel Mass and Cost Savings and CO 2 and SO 2 Savings
This section examines the effect of the regenerative dual-loop ORC system on the fuel saving, fuel cost saving, CO 2 , and SO 2 savings during a typical mission analysis of the examined general support vessel. According to the literature [40], the power consumption by the vessel propellers is provided as a function of the vessel speed according to the cube law, as follows: Hence, for a specified mechanical efficiency n M of the reduction gear equal to 0.98, the previously mentioned constant "c" can be calculated, while using the maximum speed of the examined general support vessel, which corresponds to the maximum continuous rating (MCR) of the two main diesel engines: Consequently, for MCR of each main engine equal to 8640 kW and for maximum vessel speed equal to 21.5 knots [20], the value of constant "c" that results from Equation (90) is: c = 12.515. Afterwards, for each vessel speed of the assumed speed profile is calculated from Equation (89) the corresponding required power from the propellers and through the mechanical efficiency of the reduction gear calculates the required generated power from the main diesel engines and the number of main diesel engines, which are coupled to the propellers. Subsequently, the data for exhaust gas mass flow rate, exhaust gas temperature, engine coolant temperature, boost air mass flow rate, and boost air temperature of the examined main diesel engine are fitted to polynomial relations as function of the generated power of the main diesel engine. Using this process, the values of exhaust gas flow rate and temperature, engine coolant temperature, and boost air mass flow rate and temperature are estimated that correspond to each speed of the examined general support vessel, as given in Table 2 The estimated values of exhaust gas mass flow rate and temperature, engine coolant temperature, and boost air mass flow rate and temperature for each vessel speed and generated power of the main diesel engine are then provided to the regenerative dual-loop ORC simulation model and results for the net power output of the ORC system are generated, which are given in Table 2. Hence, having calculated the generated electrical power of the ORC system for each vessel speed, it is assumed that this electrical power is provided to the electrical system of the examined general support vessel and, thus, the corresponding electrical power from the two auxiliary diesel generators (it is assumed that two of the three diesel generators are in operation whereas, the third diesel generator is a backup engine of other two diesel generators, which can be used in case of a severe malfunction or failure of one of the other two diesel generators) is reduced analogically. Hence, the fuel consumption in kg/h using this procedure, which is saved from the two diesel generators at each speed of the general support vessel is estimated. Assuming then, a vessel mission of 4000 h with the speed profile that is shown in Table 3, the fuel mass saving and the fuel cost saving at each vessel speed are calculated and the total fuel mass saving and the total fuel cost saving are also calculated for the entire mission of the general support vessel. For the calculation of the corresponding CO 2 and SO 2 savings, a simplified perfect combustion analysis of a hydrocarbon resembling to the military fuel F-76 is adopted. Specifically, the maximum sulphur content of fuel F-76 is 0.5%, its minimum hydrogen percentage is 12.5%, and its molecular weight is 205 kg/kmol, according to Ezgi and Coban [41]. Using these data, a representative composition of F-76 fuel in carbon, hydrogen, and sulphur is estimated and, then, through perfect combustion analysis shown below, it can be estimated that 1 kg F-76 fuel generates 3.2 kg CO 2 and 0.01 kg SO 2 : C n H m S z + λ α n + m 4 + z O 2 + 3.76λ α n + m 4 + z N 2 → nCO 2 + m 2 H 2 O + (λ α − 1) n + m 4 + z O 2 + 3.76λ α n + m 4 + z N 2 + zSO 2 (91) Using the aforementioned analogies for CO 2 and SO 2 and the fuel mass saving for each vessel speed, the corresponding CO 2 and SO 2 savings for each vessel speed are estimated. Table 3 provides the results for fuel mass savings, fuel cost savings, CO 2 and SO 2 savings.

Dimensioning Results of the Heat Exchangers of the HT and the LT Loop of the Regenerative Dual-Loop ORC-Calculation of the Regenerative Dual-Loop ORC Capital Cost and Payback Period
In the previous section, it was described thoroughly the mission analysis of the general support vessel that was performed to calculate the fuel mass saving, the fuel cost saving, the CO 2 emission saving, and the SO 2 emission saving. Hence, the geometrical dimensions of all heat exchangers were derived based on the heat transfer analysis of the fin-and-tube heat exchanger of the evaporator 1 of the HT loop that was described in Section 5.1 and the heat transfer analysis of the plate heat exchangers of the intercooler, the preheater, the evaporator 2 of the LT loop, and the condenser that was described in Section 5.2 and the vessel speed profile of the mission analysis. Table 4 gives the main geometrical dimensions of the fin-and-tube heat exchanger of the evaporator 1 of the HT loop. Table 5 provides the main geometrical dimensions of the plate heat exchanger of the intercooler. Table 6 provides the main geometrical dimensions of the plate heat exchanger of the preheater of the LT loop. Table 7 gives the main geometrical dimensions of the plate heat exchanger of the evaporator 2 of the LT loop. Table 8 provides the main geometrical dimensions of the plate heat exchanger of the LT loop condenser.
In addition, using the economic analysis that was previously described, the capital cost of each component of the regenerative dual-loop ORC was estimated. Additionally, the total capital cost and the EPC of the ORC system installation were estimated. The results for the capital cost of each component of the regenerative dual-loop ORC installation and the total capital cost and the EPC of the bottoming cycle are given in Table 9. The total capital cost of the ORC system installation is 2,546,000 Euros and the EPC is 0.2495 Euro/kWh, as evidenced from Table 9.      Table 10 presents the results of a payback period analysis that was performed to calculate the number of years that are required in order to recover the total capital cost of the regenerative dual-loop ORC system through the yearly revenues from the fuel cost savings and initiate obtaining net profits from the operation of the proposed bottoming cycle. Hence, Table 10 contains the total revenues per year that correspond to the yearly income from the fuel cost savings, the annual total expenses of the bottoming cycle installation, which correspond to the annual maintenance and insurance cost, which, according to [18], is equal to 1.65% of the total capital cost of the ORC installation. Additionally, Table 9 contains the difference between the total revenues per year and the total expenses per year and the net difference between the ORC system remaining capital cost per year and the net annual profit of the ORC system installation. As observed from Figure 10, at the end of the 9 th year from the initiation of the ORC system operation the total capital cost of the ORC system will be completely covered, and the installation will be profitable by 113,356 Euros. Hence, the payback period of the proposed regenerative dual-loop ORC falls into the ninth year from the commencement of the proposed bottoming cycle operation and, because it is lower than 10 years, it can be considered as a marginally reasonable payback period.

Conclusions
In the present study a regenerative dual-loop ORC system was proposed to be coupled with the main diesel engines of a general support vessel. The regenerative dual-loop ORC was comprised of two loops: one high temperature (HT) loop equipped with an evaporator for recovering waste heat from exhaust gases and an open feed organic heater (OFOH), which was fed with a high temperature organic fluid that was depreciated from the expander of the HT loop at intermediate pressure and used to preheat the low temperature organic fluid before it entered the evaporator of the HT loop. The low temperature (LT) loop of the dual-loop ORC was equipped with three heat exchangers for recovering waste heat from boost air at the intercooler, for recovering waste heat from engine coolant at evaporator 2 and recovering waste heat from the organic fluid of the HT loop at the preheater of the LT loop. The LT loop was also equipped with an OFOH and a condensation heat exchanger, where the organic fluid rejects heat to the seawater. A detailed thermodynamic model was developed to perform an energetic and exergetic analysis of both HT and LT loops of the ORC system. Additionally, a thorough heat transfer analysis was conducted for estimating the heat transfer area and the main geometrical dimensions of the fin-and-tube heat exchanger of the evaporator 1 of the HT loop and the corresponding area and dimensions of the four plate heat exchangers of the LT loop. In addition, a mission analysis of the examined general support vessel was performed based on a predefined speed profile for estimating the fuel mass saving, the fuel cost saving, the CO 2 emission, and the SO 2 emission saving for each vessel speed, and, in total, for a 4000 h mission of the examined vessel. Finally, an economic analysis was conducted based on chemical engineering plants capital cost analysis in order to calculate the capital cost of each component of the dual-loop ORC, the total capital cost of the proposed ORC system, and the electricity production cost of the ORC system. From the detailed assessment and discussion of the theoretical findings of the present study, the following conclusions can be derived:

•
The use of the OFOH in the HT loop and in the LT loop of the proposed regenerative dual-loop ORC provides higher values of the ORC system generated power and its thermal efficiency and lower values of total irreversibility rate of both HT and LT loop as compared to the simple dual-loop ORC without regeneration. Hence, the use of regeneration with OFOH in both the HT and LT loop substantially improves the energetic and exergetic performance of the dual-loop ORC.

•
The installation of the proposed regenerative dual-loop ORC in a general support vessel and its operation over a specified mission results in significant savings of fuel mass, fuel consumption cost, and CO 2 and SO 2 emissions. Hence, the installation of the proposed ORC system in a naval support vessel can provide high energy savings and can substantially reduce its carbon and sulphur footprint.
• From an economic standpoint, the installation of the proposed regenerative dual-loop ORC in a general support vessel is economically feasible because the payback period of the ORC system capital cost can be limited to less than eight years and, in any case, can further be reduced based on the total annual time of the vessel's mission and the annual time of the proposed ORC system operation. Acknowledgments: Authors wish to express their sincere gratitude to the staff of the Hellenic Navy for the donation of invaluable raw of data.

Conflicts of Interest:
The authors declare no conflict of interest. Isentropic efficiency of expander 1 n is,exp2

Nomenclature
Isentropic efficiency of expander 2 n is,p1 Isentropic efficiency of circulation pump 1 n is,p2 Isentropic efficiency of the circulation pump 2 p,p 0 Pressure (MPa) P exp1 Net power output of expander 1 of the HT loop (W) P exp2 Net power output of expander 2 (W) P HT,net Net power output of the HT loop (W) P HX Design pressure of the heat exchanger P LT,net Net power output of the LT loop (W) P p1 Power consumption of the circulation pump 1 (W) P p2 Power consumption of the circulation pump 2 (W) P PP Design pressure of the circulation pump P tot,net Net power output of the dual-loop ORC (W) Q Heat (J) . Q Heat transfer rate (W) q Heat flux (W/m 2 ) q wall Imposed wall heat flux (W/m 2 ) r in Fouling resistance of the heat exchanger internal flow (m 2 K/W) r out Fouling resistance of the heat exchanger external flow (m 2 K/W) s Specific entropy (J/kgK) S Suppression factor S kg/kg Salinity (kg/kg) T External flow (i.e., exhaust gas) mean temperature (K) t Internal flow (i.e., organic fluid) mean temperature (K) t Temperature ( • C) T 0 Reference temperature of exergy destruction rate (K) T mc Average condensation temperature of the organic fluid (K) T me Average evaporation temperature of the organic fluid at the evaporator 2 (K)