Article Design and Thermodynamic Analysis of a Steam Ejector / System for Naval Surface Ship Applications

Cüneyt Ezgi * and Ibrahim Girgin

Received: 8 September 2015; Accepted: 7 December 2015; Published: 11 December 2015 Academic Editor: Kevin H. Knuth

Mechanical Engineering Department, Turkish Naval Academy, Istanbul 34942, Turkey; [email protected] * Correspondence: [email protected]; Tel.: +90-530-6065-395; Fax: +90-216-3952-658

Abstract: Naval surface ships should use thermally driven heating and cooling technologies to continue the Navy’s leadership role in protecting the marine environment. Steam ejector refrigeration (SER) or steam ejector heat pump (SEHP) systems are thermally driven heating and cooling technologies and seem to be a promising technology to reduce emissions for heating and cooling on board naval surface ships. In this study, design and thermodynamic analysis of a seawater cooled SER and SEHP as an HVAC system for a naval surface ship application are presented and compared with those of a current typical naval ship system case, an H2O-LiBr absorption heat pump and a vapour-compression heat pump. The off-design study estimated the coefficient of performances (COPs) were 0.29–0.11 for the cooling mode and 1.29–1.11 for the heating mode, depending on the pressure of the exhaust gas at off-design conditions. In the system operating at the exhaust gas boiler pressure of 0.2 MPa, the optimum area ratio obtained was 23.30.

Keywords: ship; engine; sea water; ejector system; refrigeration; heat pump

1. Introduction The International Maritime Organization’s [1] Marine Environment Protection Committee published its final third IMO greenhouse gas (GHG) study report in 2014 providing updated estimates for GHG emissions from ships. In that report, for the year 2012, total shipping emissions were approximately 949 million tonnes CO2 and 972 million tonnes CO2e for GHGs combining CO2, CH4 and N2O. International shipping emissions for 2012 were estimated to be 796 million tonnes CO2 and 816 million tonnes CO2e. International shipping thus accounted for approximately 2.2% and 2.1% of global CO2 and GHG emissions on a CO2 equivalent (CO2e) basis, respectively. In addition, and gas released from shipping contributed an additional 15 million tons in CO2 equivalent emissions. In the study, military forces were excluded from the total and international shipping calculations. To reduce the emission of greenhouse gases, specifically CO2 emissions, emitted by ships, the Energy Efficiency Design Index (EEDI) for new ships and the Ship Energy Efficiency Management Plan (SEEMP) for all ships entered into force on 1 January 2013. New ships are ships that enter the fleet from 2013. Implementing CO2 reduction measures will result in a significant reduction in fuel consumption, leading to a significant saving in fuel costs to the shipping industry. The main and auxiliary engines are used to propel the ship, and to drive generators to produce electricity, respectively. Despite the great technological development of engines, the maximum efficiency is still less than 50%. The main and auxiliary engines onboard ships produce significant quantities of heat. The primary source of waste heat of main and auxiliary engines is the exhaust

Entropy 2015, 17, 8152–8173; doi:10.3390/e17127869 www.mdpi.com/journal/entropy Entropy 2015, 17, 8152–8173 gas heat dissipation, which accounts for about half of the total waste heat, i.e., about 25% of the total fuel energy. For naval ships, the environment (decreased emissions), stealth demands (hydrodynamic, acoustic, magnetic, infrared, radar signatures) and efficiency (decreased fuel costs) are of importance. The required precautions to achieve the specified level of stealth features should be taken during both the design and operating phase. CO2 reduction measures as well as reduction and management of ship signatures must also be implemented by naval ships. To continue the Navy’s leadership role in protecting the marine environment, the search for new energy conservation methods that can be applied on board naval ships is necessary. Thermally driven heat pumps for heating and cooling can be promising solutions. Today, heating, cooling and refrigeration systems onboard ships are based on mechanical vapour compression. These cycles are powered by electrical energy generated by the combustion of fossil fuels, and the process contributes to an increase in greenhouse gases and the generation of air pollutants. One way to find a new solution to this problem is to apply an absorption refrigeration (AR)/heat pump (AHP) system to provide the required heating and cooling loads for the HVAC system instead of the traditional vapour-compression heat pump. The main problem with absorption systems is that they are more bulky than conventional vapour-compression systems. This is because an AR/AHP has more components and as the heat and mass transfer of absorption equipment is poor, large surface areas are required. Ezgi [2] presented design and thermodynamic analysis of a water-lithium bromide AHP as an HVAC system for a naval surface ship application and compared with those of a vapour-compression heat pump. Ezgi [2] performed calculations for diesel engine loads of 50%, 75%, 85%, 100%. The temperatures of , condenser, absorber are 4 ˝C, 50 ˝C, 35 ˝C, respectively, and generator temperatures were 90 ˝C, 95 ˝C, 100 ˝C, 105 ˝C and 110 ˝C. At the end of 1000 operating hours a year of a naval surface ship, it was stated that the AHP system could save 22,952–81,961 L of diesel fuel in the heating cycle and 21,135–75,477 L of diesel fuel in the cooling cycle and would reduce its annual CO2 emissions by 60.41–215.74 tons in the heating cycle and 55.63–198.67 tons in the cooling cycle, depending on the engine load and COP of the vapour-compression heat pump. Another type of system is known as an ejector refrigeration/heat pump. Riffat et al. [3] and Ma et al. [4] stated that ejector refrigeration is one of the most promising technologies because of its relative simplicity and low capital cost when compared to an . This is a heat-operated cycle capable of utilising solar energy, waste energy, natural gas or hybrid sources (e.g., solar/gas). The ejector heat refrigeration/heat pump has no moving parts and so is simple and reliable. In addition, it has the potential of long life and, unlike vapour compression systems, produces no noise or vibration. Chen et al. [5] provided a literature review on the recent developments in ejectors, applications of ejector refrigeration systems. Ejector refrigeration systems (ERS) are more attractive compared with traditional vapour compression refrigeration systems, with the advantage of simplicity in construction, installation and maintenance. Moreover, in an ERS, compression can be achieved without consuming mechanical energy directly. Furthermore, the utilization of low-grade thermal energy (such as solar energy and industrial waste heat) in the system can help mitigate the problems related to the environment, particularly by reduction of CO2 emissions from the combustion of fossil fuels. An ejector is a simple device in which high pressure stream (the primary fluid) is used to compress low pressure stream (the secondary fluid) to a higher pressure (discharge pressure). A number of experimental studies involving ejectors have been reported in the literature. Hsu [6] investigated by analytical methods the efficiency of an ejector heat pump with the 11, 113, and 114. Huang et al. [7] carried out a 1-D analysis for the prediction of the ejector performance at critical mode operation. El-Dessouky et al.[8] developed semi-empirical models for the design and rating of steam jet ejectors. Alexis [9] modelled the steam-ejector refrigeration system and estimated the maximum flow entrainment ratio for constant generator pressure (6–8 bar), condenser (40–50 ˝C) and evaporator

8153 Entropy 2015, 17, 8152–8173 temperature (4–10 ˝C). Sanaye and Niroomand [10] presented the modelling and optimization of a ground-coupled steam ejector heat pump with a closed vertical ground . Steam-ejector refrigeration systems are used in food processing plants, gas plants, breweries, the rubber and vulcanizing, paper and pulp, paints and dyes, pharmaceutical and chemical industries, and edible oil refineries. In the literature, although the ejector refrigeration cycle is most commonly used for refrigeration in land-based plants, there has been no report that an ejector heat pump system has been installed on board ships. The most important difference between land and marine refrigeration is the need for a in land-based applications and seawater in marine applications to eject heat from the condenser to ambient air. Cooling towers increase the initial system costs, and require regular maintenance and require extra space for their installation. The development of seawater-cooled steam-ejector refrigeration technology can effectively eliminate these disadvantages. Also, no investigation has been conducted yet on a seawater-cooled steam ejector refrigeration/heat pump system for a naval ship application. One possible reason why steam ejector refrigeration systems have never been applied in ships before is the lower COP—0.2~0.3—compared to vapour compression systems and other thermally driven technologies. The COP also drops significantly at operation away from the design point. Another is the lack of performance data from commercial applications to provide confidence in the ship applications of the technology and the need for uninterrupted cooling and heating on ships, especially in naval ships. Therefore, this study focuses on the dual use of steam ejector technology to produce heating and cooling onboard a naval ship. A theoretical study of the possibilities for application of steam ejector refrigeration/heat pump systems for cooling and heating of naval surface ships is presented. Waste heat from the main diesel engine exhaust gas is utilized. The technical characteristics of the system are analyzed and its economical and environmental benefits are discussed.

2. System Selection for Naval Surface Ships In general, the details of merchant ship air conditioning also apply to warships. However, all ships are governed by their specific ship specifications, and naval ships are usually governed by military specifications, which require an excellent air-conditioning system and equipment performance in the extreme environment of naval ship duty. Design conditions for naval surface ships have been established as a compromise. These conditions consider the large cooling plants required for internal heat loads generated by machinery, weapons, electronics and personnel. Today, heat pumps for heating and cooling on board naval ships are mechanically driven. Seawater is used for condenser cooling. The equipment described for merchant ships also applies to naval surface ships. Fans, cooling coils, heating coils with steam or electric heaters and air handling units (AHU) which are used to regulate and circulate air as part of an HVAC system are used on board naval ships. Steam ejector refrigeration (SER) and steam ejector heat pump (SEHP) systems are a good choice for naval surface ships because of their lower energy consumption, CO2 emissions, EEDI, infrared and acoustic signature, simple, compact construction and corrosion resistance and because they can be used with water, which is the most environment friendly refrigerant. The SER/SEHP system can be fitted into the machinery space of a ship. The system serves by supplying in cooling mode and hot water in heating mode to coil units located in various parts of the naval ship.

3. The Case Naval Ship The case naval surface ship has two main internal combustion engines that propel the ship. The specification of the each diesel engine on the naval ship is given in Table1[ 11]. The propeller demand data are presented in Table2[11].

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Table 1. Specification of a diesel engine on a naval ship.

Engine Maximum Continuous Output 3000 kW Engine speed 750 rpm Cylinder bore 320 mm Stroke 400 mm Cylinder configuration 6, in-line Backpressure, max. 4.0 kPa

Table 2. Propeller demand data.

Fuel Consumption, Exhaust Gas Temperature Exhaust Gas Flow Engine % Load g¨ (kW¨ h)´1 after Turbocharger, ˝C kg¨ s´1 50 191 315 3.71 75 182 345 4.43 85 181 336 4.96 100 185 380 5.40

The total heating and cooling loads of the case naval surface ship are 144 kW and 116 kW, respectively. The case naval surface ship has two marine diesel generator sets for auxiliary power production, each with a generator power of 240 kVA. Heating load (144 kW) is met by electric duct heaters. Cooling load (116 kW) is met by a seawater cooled unit.

4. System Design This study focuses on the dual use of ejector technology to produce heating and cooling on board a naval ship. The design criteria are given in Table3, which is determined according to Loydu’s Rules for the Classification of Naval Ships and based on the naval distillate fuel (NATO symbol F-76) used on power systems by the navies of NATO countries.

Table 3. The design criteria.

Type of Heat Pump Steam Ejector Energy source Diesel engine exhaust gas Diesel engine fuel type NATO F-76 Diesel Heating Mode Hot water temperature flows through the condenser 45 ˝C–40 ˝C Evaporator Seawater (´2 ˝C–+32 ˝C) Cooling Mode Chilled water temperature flows through the evaporator 7 ˝C–12 ˝C Condenser Seawater (´2 ˝C–+32 ˝C)

The working fluid is water in SER/SEHP system. Water is a natural working fluid. It is an excellent working fluid for high-temperature industrial heat pumps because of its favourable thermodynamic properties and the fact that it is neither flammable nor toxic. Water is inexpensive and has no environment impact (zero ozone depletion and global warming potential). Water has an extremely high heat of vaporization that causes a low circulation rate for given heating and cooling capacity. At low temperatures the saturation pressures are low (0.008129 bar at 4 ˝C) and the specific volumes are high (157.3 m3¨ kg´1 at 4 ˝C) at typical evaporator conditions. Therefore, low mechanical power is required for the pump. The system is not considered under the diesel engine load of 50% as long term operation at lower loads, typically below 50% of its maximum rated load, reduces engine service life. If the engine of the

8155 Entropy 2015, 17, 8152–8173 naval ship is in standby or under very low engine loads (below 50%), the heating and cooling load forEntropy the naval 2015, 17 surface, 1–22 ship will be met from a vapour compression heat pump. In addition, vapour compression heat pumps onboard naval ship are operated as reserves in emergency situations, at naval basecompression or during periodicheat pumps engine onboard overhauls naval in ship naval are shipyards. operated as reserves in emergency situations, at navalThe base expansion or during tanks periodic are designed engine overhauls to compensate in naval for shipyards. the changing volume of the water in the SER/SEHPThe systemexpansion to maintaintanks are thedesigned static pressureto compensate created for by the the changing pump at volume the utilisation of the water level inin waterthe SER/SEHP system to maintain the static pressure created by the pump at the utilisation level in water production and to compensate for any changes in the water flow rate. production and to compensate for any changes in the water flow rate. A SER/SEHP system design for naval ship application is presented in Figure1. The SER/SEHP is A SER/SEHP system design for naval ship application is presented in Figure 1. The SER/SEHP driven by the thermal energy of a diesel engine and consists of an ejector, a boiler, an evaporator, a is driven by the thermal energy of a diesel engine and consists of an ejector, a boiler, an evaporator, condenser, an expansion valve and a circulation pump. In the shown system, high-pressure steam a condenser, an expansion valve and a circulation pump. In the shown system, high-pressure steam expandsexpands while while flowing flowing through through the the nozzle. nozzle. The The expansionexpansion causes a a drop drop in in pressure pressure and and an an enormous enormous increaseincrease in in velocity. velocity. Due Due to to the the high high velocity, velocity, vapourvapour from the evaporator evaporator is is drawn drawn into into the the swiftly swiftly movingmoving steam steam and and the the mixture mixture enters enters the the diffuser. diffuser. The Th velocitye velocity is is gradually gradually reduced reduced in in the the diffuser diffuser but thebut pressure the pressure of the steamof the steam at the at condenser the condenser is increased is increased 5–10 times5–10 times more more than than that atthat the at entrancethe entrance of the ˝ diffuser.of the diffuser. This pressure This pressure value corresponds value corresponds to a condensation to a condensation temperature temperature of 50 ofC. 50 The °C. latent The of condensationheat of condensation is transferred is transferred to the condenser to the condenser water. The water. condensate The condensate is pumped is backpumped to the . to the The cooledboiler. water The iscooled pumped water as is the pumped refrigeration as the carrierrefrigeration to the carrier fan-coil to unit. the fan-coil The heated unit. waterThe heated is pumped water as theis heating pumped carrier as the to heating the fan carrier coil unit. to the fan coil unit.

FigureFigure 1. 1.SER/SEHP SER/SEHP system design for for a a naval naval ship. ship.

The evaporator temperature has to be designed at 4 °C to cool water of 12 °C for the air The evaporator temperature has to be designed at 4 ˝C to cool water of 12 ˝C for the air conditioning of the space to be maintained between 24 °C and 27 °C. conditioning of the space to be maintained between 24 ˝C and 27 ˝C. The condenser temperature depends on the seawater temperature. According to Loydu’s [12] The condenser temperature depends on the seawater temperature. According to Loydu’s [12] Rules for the Classification of Naval Ships, the selection, layout and arrangement of all shipboard Rules for the Classification of Naval Ships, the selection, layout and arrangement of all shipboard machinery, equipment and appliances should ensure faultless continuous operation under the machinery,seawater equipmenttemperature and of − appliances2 °C to +32 should°C and the ensure air temperature faultless continuous outside the operation ship of − under25 °C to the +45 seawater °C. ˝ ˝ ˝ ˝ temperatureThe exhaust of ´2 gasC to boiler +32 isC used and to the recover air temperature exhaust waste outside heat thefrom ship the ofdiesel´25 engine.C to +45 EachC. engine hasThe a separate exhaust exhaust gas boiler gas is boiler. used Th toe recover pressure exhaust drop of waste the gas heat side from of the the exhaust diesel engine. gas boiler Each is set engine to has3 akPa separate maximum exhaust and the gas back boiler. pressure The pressureof the exha dropust gas of thesystem gas sideis 4 kPa of themaximum. exhaust Fresh gas boilerwater is setconservation to 3 kPa maximum onboard anda naval the backship is pressure very important. of the exhaust Seawater gas is systemthe main is 4 kPa maximum.on board naval Fresh waterships, conservation like in other onboard ships. aSeawater naval ship is a is free very and important. renewable Seawater source isfor the cooling main coolantonboard on ships. board navalTherefore, ships, likethe condenser in other ships. and evaporator Seawater isused a free in this and system renewable are seawater-cooled source for cooling heat onboard exchangers. ships. Therefore,However, the seawater-cooled condenser and heat evaporator exchangers used are inprone this to system fouling, are which seawater-cooled causes the thermohydraulic heat exchangers. However,performance seawater-cooled of heat equipment exchangers to decrease are prone with to fouling, time [13]. which Design causes fouling the resistances thermohydraulic must performancealso be taken of heatinto account transfer when equipment dimensioning to decrease the exhaust with time gas [ 13boiler]. Design and heat fouling exchangers resistances because must alsothe be boiler taken and into heat account exchangers when are dimensioning subject to foulin theg exhaustand must gas operate boiler for and long heat periods exchangers without becausebeing thecleaned. boiler andThus, heat the exchangers design fouling are subjectresistances to foulingof the engine and must exhaust operate gas forand longseawater periods are withoutset to Rf,exh = 1.761 m2·K·(kW)−1, Rf,s = 0.088 m2·K·(kW)−1, respectively [14].

8156 5 Entropy 2015, 17, 8152–8173 being cleaned. Thus, the design fouling resistances of the engine exhaust gas and seawater are set to 2 ´1 2 ´1 R f ,Entropyexh = 1.761 2015, 17 m, 1–22¨ K ¨ (kW) , R f ,s = 0.088 m ¨ K¨ (kW) , respectively [14]. Seawater flows through the evaporator during the heating mode, through the condenser during the coolingSeawater mode flows all thethrough time. the To evaporator achieve this during flow, the two heating 4-way, mode, 3-position through (4/3) the condenser rotary valves during (also calledthe cooling CEFS valves) mode areall the used time. for heatingTo achieve and this cooling flow in, two the 4-way, system. 3-position One of the (4/3) 4/3 rotary valves valves is the (also supply andcalled the otherCEFS isvalves) the return are used valve. for heating The three and positions cooling in of the the system. rotary One valve of are the the4/3 heatingvalves is mode,the supply closed andand cooling the other mode. is the A return fan coil valve. system The isthree integrated position withs of the CEFS rotary valves valve in are a SEHPthe mode, as shown closed in and cooling mode. A fan coil system is integrated with CEFS valves in a SEHP system as shown in Figure2. Heat produced with the SER or SEHP system is transferred to the fan-coil units. The heat is Figure 2. Heat produced with the SER or SEHP system is transferred to the fan-coil units. The heat is mainly consumed in fan coil units. A heat meter is used to measure the heat returning from fan coil mainly consumed in fan coil units. A heat meter is used to measure the heat returning from fan coil units. The residual heat is sent to hot water production in heating mode or to machine room cooling units. The residual heat is sent to hot water production in heating mode or to machine room cooling in cooling mode. An analog-to-digital converter (ADC) is used that converts a continuous physical in cooling mode. An analog-to-digital converter (ADC) is used that converts a continuous physical quantityquantity (usually (usually voltage) voltage) to to a a digital digital numbernumber thatthat represents the the quantity's quantity' samplitude. amplitude. A Aservo servo valve valve is usedis used to to control control flow flow through through the the heat heat meter. meter.

Figure 2. Integration of fan coil and CEFS valves design for a naval ship. Figure 2. Integration of fan coil and CEFS valves design for a naval ship. 5. Thermodynamic Analysis 5. Thermodynamic Analysis The thermodynamic design of the ejector heat pump system by the first law only is usually based onThe given thermodynamic or assumed steady-state design of operating the ejector condit heat pumpions. The system condenser by the and first evaporator law only istemperatures usually based onare given fixed. or The assumed system steady-state boiler heat operatingtransfer rates conditions. are also known. The condenser and evaporator temperatures are fixed.The The fundamental system boiler simplifications heat transfer assumed rates are for alsothe model known. are as follows: The fundamental simplifications assumed for the model are as follows:  Steady state of the SER/SEHP ‚ Steady No state radiation of the SER/SEHPheat transfer ‚ No radiationThe primary heat transfer and secondary fluids are saturated and have the same molecular weight and ‚ The primaryratio of and specific secondary heats. fluids are saturated and have the same molecular weight and ratio of  Water at the condenser outlet is saturated liquid specific heats.  Water at the evaporator outlet is saturated vapour ‚ Water at the condenser outlet is saturated liquid  Pressure losses in the pipes and all heat exchangers are negligible ‚ Water atThe the primary evaporator fluid outletexpands is saturatedthrough the vapour nozzle from the boiler pressure to the evaporator ‚ Pressurepressure. losses in the pipes and all heat exchangers are negligible ‚ The primaryThe pressure fluid expands drop and through momentum the nozzle of the from secondary the boiler flow pressure are negligible. to the evaporator pressure. ‚ The pressureThere is drop no wall and friction. momentum of the secondary flow are negligible. ‚ There isAll no fluid wall properties friction. are uniform over the cross section after complete mixing at section 2.

‚ All fluidPotential properties energy are is uniform negligibly over small the in cross the sectionenergy equations. after complete mixing at Section2.  The exit velocity at the ejector outlet is ignored. ‚ Potential energy is negligibly small in the energy equations. ‚ TheThe exit T-s velocity diagram at of the the ejector steam outlet ejector is heat ignored. pump cycle is shown in Figure 3. Saturated motive steam enters the ejector at a high pressure P0, temperature T0 and zero velocity corresponding to state

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The T-s diagram of the steam ejector heat pump cycle is shown in Figure3. Saturated motive Entropy 2015, 17, 1–22 steam enters the ejector at a high pressure P0, temperature T0 and zero velocity corresponding to state (0) and(0) expands and expands to a pressure to a pressure at state at (1).state The (1). saturated The saturated secondary secondary vapour vapour enters enters the ejectorthe ejector at pressure at P4 andpressure zero velocity P4 and zero corresponding velocity corresponding to state (4). to state (4).

Figure 3. T-s diagram of the steam ejector refrigeration and heat pump cycle. Figure 3. T-s diagram of the steam ejector refrigeration and heat pump cycle. 5.1. Nominal Heat Balance 5.1. Nominal Heat Balance The conservation of mass principle is expressed as: The conservation of mass principle is expressed as: dmcv mmie (1) dmcvdt . . “ mi ´ me (1) To obtain a control volume at steady state,dt the equation is reduced to: To obtain a control volume at steady state, themm equation is reduced to:  ie  (2) ie. . mi “ me (2) The energy rate balance is expressed as: e ÿi ÿ dE V22 V The energy rate balancecv is expressed  as: i e QWcv cv mh i i  gzmh i  e e  gz e (3) dt ie22 . . 2 2 dEcv . Vi . Ve To obtain a “controlQcv ´ volumeWcv ` at msteadyi hi state` and` gztoi disregard´ me theh echanges` ` ingz thee kinetic and (3) dt ˜ 2 ¸ e ˜ 2 ¸ potential energies of the flowing streamsÿi from inlet to exit, theÿ equation is reduced to: To obtain a control volume at steady0 stateQW and to disregard mhmh the changes in the kinetic and potential cv cv i i  e e (4) energies of the flowing streams from inlet to exit, theie equation is reduced to:

Momentum equation is: . . . . 0 “ Qcv ´ Wcv ` mihi ´ mehe (4)  PAii mV iii PA ee mVe ee (5) ÿ ÿ Momentum equation is: . . 5.2. Main Engine Pi Ai ` miVi “ Pe Ae ` meVe (5) The heat transfer rate from the engineÿ exhaust gas to theÿ exhaust gas boiler is expressed as: 5.2. Main Engine   Qmhhexh exh exh,, in exh out (6) The heat transfer rate from the engine exhaust gas to the exhaust gas boiler is expressed as: where m exh is the engine exhaust gas mass flow rate, hexh, in is the engine exhaust gas specific . at the entrance of the exhaust gas. boiler and h is the engine exhaust gas specific Qexh “ mexh hexh,in ´ hexhexh,, outout (6) enthalpy at the exit of the exhaust gas boiler. . ` ˘ where mexh is the engine exhaust gas mass flow rate, hexh,in is the engine exhaust gas specific enthalpy at the entrance of the exhaust gas boiler and hexh,out is the engine exhaust gas specific enthalpy at the exit of the exhaust gas boiler. 7

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5.3. Exhaust Gas Properties The exhaust gas properties, which include specific heat at constant pressure, dynamic viscosity and thermal conductivity, should be determined for the heat transfer analysis. The main components of the exhaust gas of a diesel engine are CO2,H2O, N2 and O2. The mass fractions of these components vary with the operating conditions of the engine. When the engine operates at steady state, the injected fuel quantity and the intake air amount can be measured on the engine test bench. Except for very low engine loads, the exhaust temperature of a marine engine is between 300 ˝C and 380 ˝C, and the exhaust pressure is slightly higher than the atmospheric pressure. Therefore, exhaust gas can be treated as a mixture of ideal gases. The specific enthalpy, specific heat and density of exhaust gas can be calculated as follows [15]:

4 hm “ m fihi (7) iÿ“1 4 cp,m “ m ficp,i (8) iÿ“1 4 m fi Mi i“1 ρm “ (9) 4ř m fi Mi{ρi i“1 ř 5.4. Exhaust Gas Boiler The heat transfer rate of the exhaust gas boiler is expressed as: . . Qexh “ QB (10) The mass flow rate of the steam is: . . QB m0 “ (11) h0 ´ h9

5.5. Steam Ejector The thermodynamic properties at initial states for steam are calculated from the saturation property. At 50 ˝C, the saturation pressure of water is 12.350 kPa. At pressures below this value, water vapour can be treated as an ideal gas with negligible error (under 0.2 percent), even when it is a saturated vapour [16]. The performance of an ejector is measured by its entrainment ratio w which is the mass flow rate ratio of the secondary flow to that of the primary flow. It is given as [6]: . m4 w “ . (12) m0 The efficiency of an ejector can be defined by [6]:

wa ηE “ (13) wi The ejector structure is normally characterised by the area ratio ξ which is defined as the cross-section area of the constant area section divided by that of the primary nozzle throat. It is given as [17]: A ξ “ 2 (14) At For inlet and outlet conditions, the conservation of energy is given as: . . . . m0h0 ` m4h4 “ m0 ` m4 h3 (15) ` ˘

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5.5.1. Nozzle Section Nozzle efficiency is given as [16]: h0 ´ h1 ηn “ (16) h0 ´ h1s Assuming zero entrance velocity, the velocity of the primary fluid at the nozzle exit is:

0.5 V1 “ r2ηn ph0 ´ h1sqs (17)

The Mach number, M, is the ratio of the actual velocity of the fluid to the velocity of sound at the same state. The properties of a fluid at a location where the Mach number is unity (the throat) are called critical properties, and the above ratios are called critical ratios. When steam enters the nozzle as a saturated vapour, the critical-pressure ratio becomes [16]:

P˚ 2 k{pk´1q “ “ 0.576 (18) P k ` 1 o ˆ ˙ Since the ratio of the exit-to-inlet pressure (P4/P0) is less than the critical pressure ratio, the flow is choked at the nozzle. Then the velocity at the throat, Vt, is the sonic velocity, and the throat pressure, Pt, is the critical pressure.

5.5.2. Mixing Section Conservation of mass is: . . A2V2 m0 ` m4 “ (19) v2 Conservation of energy is:

2 . . . . V2 m0h0 ` m4h4 “ m0 ` m4 h2 ` (20) ˜ 2 ¸ ` ˘ Conservation of momentum is [6]: . . . m0V1 ` P4 A2 “ m0 ` m4 V2 ` P2 A2 (21)

Including mixing efficiency for the mixing chamber,` ˘ the momentum equation reduces to: . . . ηm m0V1 ` P4 A2 “ m0 ` m4 V2 ` P2 A2 (22) ` ˘ ` ˘ 5.5.3. Constant Area Section A normal shock wave occurs if the velocity of the mixing fluid entering the constant area section is supersonic. In this case, a sudden reaction in the mixture velocity and a rise in the pressure take place [18]. Also, that the primary and secondary streams mix in the mixing chamber and enter a normally choked (sonic flow conditions at the throat) secondary converging-diverging nozzle was stated by [19]: A2i “ A2e “ A2 (23) Conservation of mass is: V V 2i “ 2e (24) v2i v2e Conservation of energy is: V2 V2 h ` 2i “ h ` 2e (25) 2i 2 2e 2 Conservation of momentum is: . . A2 pP2i ´ P2eq “ mo ` m4 pV2e ´ V2iq (26) ` ˘ 8160 Entropy 2015, 17, 8152–8173

The Mach number of the mixed flow at Section2 after the shock wave is

V2 M2 “ ? (27) kRT2

V2 M2 “ 0.5 (28) pkP2v2q

From Equations (19), (22) and (28), the cross-sectional area, A2, is solved by: . moV1ηm A2 “ 2 (29) P2 kM2 ` 1 ´ P4ηm ASHRAE [20] proposes that the constant area` throat˘ section be typically 3–5 throat diameters long to accommodate the shock pattern and its axial movement under load.

5.5.4. Diffuser Conservation of energy is: V 2 h ` 2 “ h (30) 2 2 3 The performance of a diffuser is usually expressed in terms of the diffuser and is given as Çengel and Boles [16]: h3s ´ h2 ηd “ (31) h3 ´ h2

5.5.5. The Optimum Mixing Constant Area . The optimum mixing constant section area, A2, can be found by maximizing m4. Hsu [6] calculated six simultaneous equations containing six unknown differentials, ds2, dV2, dh2, dv2, dA2 and dP2. The optimum criterion to operate an ejector for given conditions is given as: T d ln 2 T2 v k M2 »1 ` p1 ´ η q ¨$ ˆ 2 ˙, ` ˛fi “ 1 (32) 2 d T d plnv q P 3s ’ 2 / 1 ´ 4 — ˚& . P ‹ffi — ˚ s 2 ‹ffi – ˝’ / ‚fl Finally, M2 and P2 values for the optimum%’ mixing constant-/ section area are calculated as: k ´ 1 k M2 1 ` p1 ´ η q pP {P q k ´ k “ 1 (33) 2 » d 2 3 1 ´ P {P fi ˆ 4 2 ˙ – fl k ´ 1 2 pP3{P2q k ´ ηd M2 pk ´ 1q {2 “ 1 (34)

5.6. Condenser The rate of heat transfer from the condenser is: . . QC “ m3 ph3 ´ h5q (35)

5.7. Expansion Valve The throttling model yields the result that:

h6 “ h7 (36)

5.8. Evaporator The rate of heat transfer to the evaporator is:

8161 Entropy 2015, 17, 8152–8173

. . QE “ m4 ph4 ´ h7q (37)

5.9. Feed Water Pump The power input to the pump is: . . W p “ m0 ph9 ´ h8q (38) The following is an alternative to Equation (38) for evaluating the pump work:

. 9 W p . “ vdP (39) m ˜ 0 ¸ ż8 Then: h9 “ h8 ` pP9 ´ P8q v8 (40) The work input to the system in the pump is small and neglected in the calculation of the coefficient of performance (COP) and efficiency. However; in practice, it is usually estimated to size the driving motor: . . v∆P Wdm “ (41) ηp

5.10. Overall Mass and Energy Balance of the System The energy rate balance at steady state is: . . Qcv ´ Wcv “ 0 (42) . . . . QC “ QB ` QE ` W p (43) The mass flow rates are: . . . . . m2i “ m2e “ m2 “ m3 “ m5 (44) . . . m8 “ m9 “ m0 (45) . . . m4 “ m6 “ m7 (46)

5.11. COP The performance of refrigerators and heat pumps is expressed in terms of the COP, which is defined for a vapour-compression refrigeration/heat pump as: . coolingef fect QE COP “ “ . (47) R work input Wnet;in

. heatingef fect QC COP “ “ . (48) HP work input Wnet;in The COP of the SER is: coolingcapacity obtained atevaporator COP “ (49) R heatinput forthe boiler ` workinput forthe pump

. QE COPR “ . . (50) QB ` W p

8162 Entropy 2015, 17, 8152–8173

The COP of the SEHP is: heating capacity obtained atcondenser COP “ (51) HP heatinput forthe boiler ` workinput forthe pump . QC COPHP “ . . (52) QB ` W p

5.12. Solution Procedure . ‚ Define the design parameters, which include the heat input for the boiler (QB), pressures of the primary motive steam (P0), secondary suction vapour (P4), condenser (P3) ‚ Define the efficiencies of the nozzle, mixing and diffuser (ηn, ηm, ηd) . ‚ Calculate the mass flow rate of steam (m0) ‚ Calculate the primary flow velocity (V1) ‚ Calculate the Mach number (M2) and pressure (P2) at Section2 for optimum mixing constant area (A 2) ‚ Calculate the optimum mixing constant cross-sectional area (A2) ‚ Assume value of the entropy (s2) with pressure (P2) ‚ Calculate the enthalpy (h2) and specific volume (v2) ‚ Calculate the enthalpy (h3s) at state 3s from entropy (s2) and pressure (P3) ‚ Calculate the enthalpy (h3) ‚ Calculate the velocity (V2) . ‚ Calculate the secondary mass flow rate (m4) . . A V ‚ Check convergence m ` m ´ 2 2 ď ε 0 4 v ˇ 2 ˇ ‚ Assume a new valueˇ` of the entropy˘ (s )ˇ and carry out the above calculations again, if tolerance of ˇ 2 ˇ convergence is no. ˇ ˇ ‚ Calculate cooling and heating capacities and COP for SER/SEHP system, if tolerance of convergence is yes.

For off-design study:

‚ Calculate the Mach number (M2) and pressure (P2) with known values of A2, k, ηd,P3 and P4, if the boiler pressure is lower than boiler operating pressure

‚ Calculate the pressure (P2) with the Mach number (M2 = 1), if the boiler pressure is higher than boiler operating pressure ‚ Calculate COP for cooling and heating of SER/SEHP.

6. Results and Comparison In this study, calculations were performed for diesel engine loads of 50%, 75%, 85% and 100%. ˝ ˝ The parameters were taken as evaporator temperature TE = 4 C, condenser temperature TC = 50 C, and boiler pressures PB = 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8 and 0.9 MPa. Efficiencies are assumed to be 0.90, 0.85 and 0.90 for the nozzle, mixing and diffuser processes, respectively. Tolerance of convergence is set to 1%. Specific heat ratio, k, for superheated steam is assumed to be 1.3 in the superheated steam region. Figure4 shows that the variation of Mach number and pressure versus diffuser efficiency for the optimum mixing section area at Section2. The results indicate that the pressure decreases as the diffuser efficiency increases at Section2. For diffuser efficiency, ηd “ 0.90, solving Equations (33) and (34) simultaneously yields M2 = 0.7887 and P2 = 8.697 kPa.

8163 Entropy 2015, 17, 1–22 Entropy 2015, 17, 1–22 6. Results and Comparison 6. Results and Comparison In this study, calculations were performed for diesel engine loads of 50%, 75%, 85% and 100%. The parametersIn this study, were calculations taken as evaporatorwere performed temperature for diesel TE engine= 4 °C, loadscondenser of 50%, temperature 75%, 85% TandC = 50100%. °C, Theand boilerparameters pressures were P takenB = 0.2, as 0.3, evaporator 0.4, 0.5, 0.6, temperature 0.7, 0.8 and T 0.E 9= MPa.4 °C, Efficienciescondenser temperature are assumed T toC =be 50 0.90, °C, and0.85 boilerand 0.90 pressures for the nozzle,PB = 0.2, mixing 0.3, 0.4, and 0.5, diffuser0.6, 0.7, 0.8processes, and 0.9 respectively.MPa. Efficiencies Tolerance are assumed of convergence to be 0.90, is 0.85set to and 1%. 0.90 Specific for the heat nozzle, ratio, mixing k, for and superheate diffuser prd ocesses,steam is respectively. assumed to Tolerance be 1.3 in ofthe convergence superheated is setsteam to region.1%. Specific heat ratio, k, for superheated steam is assumed to be 1.3 in the superheated steamFigure region. 4 shows that the variation of Mach number and pressure versus diffuser efficiency for the optimumFigure mixing 4 shows section that the area variation at Section of Mach 2. The number results and indicate pressure that versus the pressure diffuser efficiencydecreases foras the 0.90 Entropyoptimumdiffuser2015, 17 efficiency, 8152–8173mixing sectionincreases area at Seatction Section 2. For 2. diffuserThe results efficiency, indicate  dthat the, solvingpressure Equations decreases (33) as andthe diffuser(34) simultaneously efficiency increases yields M at2 Se= 0.7887ction 2. and For P diffuser2 = 8.697 efficiency, kPa. d  0.90 , solving Equations (33) and (34) simultaneously yields M2 = 0.7887 and P2 = 8.697 kPa.

13 12 13 11 12 10 11 9 10 8 9 7 Pressure (kPa) 8 6 Mach number 7 Pressure (kPa) 5 6 Mach number 4 5 3 4 2

Mach number and Pressure (kPa) and Pressure number Mach 3 1 2 Mach number and Pressure (kPa) and Pressure number Mach 0 1 00.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05

0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00 1.05 Diffuser efficiency

Diffuser efficiency

FigureFigure 4. Mach 4. Mach number number and and pressure pressure versus diffuserdiffuser efficiency efficiency at Section at Section 2. 2. Figure 4. Mach number and pressure versus diffuser efficiency at Section 2. The boiler heat transfer rates depend on the engine load. As the engine load increases, the boiler Theheat boilerTheincreases. boiler heat Theheat transfer boiler,transfer ratescondenser rates depend depend and on onevaporator thethe engine heat load. load. transfer As As the the rates engine engine increase load load increases, as increases,the engine the boiler theload boiler heat heatincreases. increases. Figure The The boiler, 5 shows boiler, condenser the condenser COPs versus and andevaporator theevaporator boiler pressure heat heat transfer transfer for heating rates rates andincrease increase cooling as thegiven as theengine the engine boiler load load increases.increases.heat transfer Figure Figure 5rate. shows 5 shows the the COPs COPsversus versusthe the boilerboiler pressure pressure for for heating heating and and cooling cooling given given the boiler the boiler heat transferheat transfer rate. rate.

1.6

1.61.4

1.41.2

1.21 Heating 0.81

COP Cooling Heating 0.80.6

COP Cooling 0.60.4

0.40.2

0.20 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Boiler Pressure (MPa)

Boiler Pressure (MPa) Figure 5. COPs versus boiler pressure. FigureFigure 5. 5.COPs COPs versusversus boilerboiler pressure. pressure. Figure 6 depicts the effect of boiler pressure on entrainment ratio for fixed evaporator and condenserFigure temperatures. 6 depicts the Theeffect entrainment of boiler pressure ratio of thone entrainmentsystem increases ratio withfor fixed the increasing evaporator boiler and Figurecondenserpressure6 atdepicts temperatures.given evaporator the effect The and ofentrainment boilercondenser pressure ratio temp oferatures onthe entrainmentsystem since increasesthere is ratio more with for motive the fixed increasing energy. evaporator boiler and condenserpressure temperatures. at given evaporator The entrainmentand condenser ratio temp oferatures the system since there increases is more with motive the energy. increasing boiler pressureEntropy at 2015 given, 17, 1–22 evaporator and condenser temperatures13 since there is more motive energy. 13

0.6

0.5

0.4

0.3

0.2 Entrainment Ratio

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler Pressure (MPa)

FigureFigure 6. 6.Effect Effect of of boiler boiler pressurepressure on on entrainment entrainment ratio. ratio.

Figure 7 depicts the effect of boiler pressure on area ratio for fixed evaporator and condenser temperatures. The area ratio of the system increases with the increasing boiler pressure at given 8164 evaporator and condenser temperatures.

120

100

80

60 Area Ratio Ratio Area 40

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler Pressure (MPa)

Figure 7. Effect of boiler pressure on the area ratio.

Figures 8 and 9 show the variation of cooling and heating capacity with change in entrainment ratio at a given engine load. The cooling and heating capacities of the system increase with the increase in entrainment ratio because the latter is directly proportional to the mass flow rate given to the evaporator.

Of course the mass flow rate of the steam, m 0 , decreases with the decreasing boiler heat transfer rate at a constant boiler pressure, condenser and evaporator temperatures. Therefore, COP, heating and cooling capacity decrease but the entrainment ratio and optimum mixing area ratio do not change. In this case, the exhaust gas boiler operating pressure is increased to achieve the needed heating and especially cooling capacity. The minimum recommended exhaust gas temperature can be kept as high as 285 °C depending on the sulphur content of the fuel oil in order to avoid any risk of hydrocarbon and ammonium sulphate condensation. Therefore, the boiler heat transfer rate decreases. For example, Figures 10 and 11 show the cooling and heating capacity and COP versus boiler pressures for a boiler heat transfer rate of 488 kW,. For a boiler pressure of 0.2 MPa and the boiler heat transfer rate of 488 kW at given evaporator and condenser temperatures, the heating and cooling capacity are calculated to be 630.51 kW and 142.34 kW, respectively. COP is calculated to be 1.29 and 0.29 for the heating and cooling, respectively. The heating and cooling capacities can meet heating and cooling loads of the case naval surface ship. The residual heat, 486.51 kW in heating mode and

14 Entropy 2015, 17, 1–22

0.6

0.5

0.4

0.3

0.2 Entrainment Ratio

0.1

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler Pressure (MPa) Entropy 2015, 17, 8152–8173

Figure 6. Effect of boiler pressure on entrainment ratio.

FigureFigure7 depicts 7 depicts the effectthe effect of boilerof boiler pressure pressure onon areaarea ratio ratio for for fixed fixed evaporator evaporator and andcondenser condenser temperatures.temperatures. The The area area ratio ratio of of the the system system increasesincreases with with the the increasing increasing boiler boiler pressure pressure at given at given evaporatorevaporator and condenserand condenser temperatures. temperatures.

120

100

80

60 Area Ratio Ratio Area 40

20

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler Pressure (MPa)

FigureFigure 7. 7.Effect Effect of ofboiler boiler pressure on on the the area area ratio. ratio.

Figures 8 and 9 show the variation of cooling and heating capacity with change in entrainment Figuresratio at8 anda given9 show engine the load. variation The cooling of cooling and and heating heating capacities capacity of the with system change increase in entrainment with the ratio at a givenincrease engine in entrainment load. The ratio cooling because and the heating latter is capacities directly proportional of the system to the increase mass flow with rate thegiven increase to in entrainmentthe evaporator. ratio because the latter is directly proportional to the mass flow rate given to the evaporator. Of course the mass flow rate of the steam, m. , decreases with the decreasing boiler heat transfer Of course the mass flow rate of the steam, m00, decreases with the decreasing boiler heat transfer rate at a constant boiler pressure, condenser and evaporator temperatures. Therefore, COP, heating rate at a constant boiler pressure, condenser and evaporator temperatures. Therefore, COP, heating and cooling capacity decrease but the entrainment ratio and optimum mixing area ratio do not and coolingchange. capacity In this case, decrease the exhaust but the gas entrainment boiler operat ratioing pressure and optimum is increased mixing to areaachieve ratio the do needed not change. In thisheating case, the and exhaust especially gas cooling boiler operatingcapacity. The pressure minimum is increased recommended to achieve exhaust the gas needed temperature heating and especiallycan be cooling kept as capacity. high as 285 The °C minimum depending recommendedon the sulphur content exhaust of gasthe fuel temperature oil in order can to avoid be kept any as high as 285 risk˝C dependingof hydrocarbon on theand sulphur ammonium content sulphate of the cond fuelensation. oil in order Therefore, to avoid the anyboiler risk heat of transfer hydrocarbon rate decreases. and ammonium sulphate condensation. Therefore, the boiler heat transfer rate decreases. For example, Figures 10 and 11 show the cooling and heating capacity and COP versus boiler Forpressures example, for a Figures boiler heat 10 andtransfer 11 showrate of the488 kW,. cooling For anda boiler heating pressure capacity of 0.2 MPa and and COP theversus boiler boiler pressuresheat fortransfer a boiler rate of heat 488 kW transfer at given rate evaporator of 488 kW,. and condenser For a boiler temperatures, pressure the of heating 0.2 MPa and and cooling the boiler heat transfercapacity rate are calculated of 488 kW to at be given 630.51 evaporator kW and 142.34 and kW, condenser respectively. temperatures, COP is calculated the heating to be 1.29 and and cooling capacity0.29 are for calculated the heating to and be cooling, 630.51 kWrespectively. and 142.34 The kW,heating respectively. and cooling COP capacities is calculated can meet toheating be 1.29 and 0.29 forand the cooling heating loads and of cooling,the case naval respectively. surface ship. The The heating residual and heat, cooling 486.51 kW capacities in heating can mode meet and heating and coolingEntropy 2015 loads, 17, 1–22 of the case naval surface ship. The residual heat, 486.51 kW in heating mode and 26.34 kW in cooling mode, is sent to hot water production14 in heating mode or to machine room cooling 26.34 kW in cooling mode, is sent to hot water production in heating mode or to machine room in cooling mode, respectively. cooling in cooling mode, respectively.

900

800

700

600 100%

500 85%

400 75% 50% 300

Cooling capacity (kW) capacity Cooling 200

100

0 0.3 0.4 0.4 0.5 0.5 0.6

Entrainment ratio

FigureFigure 8. 8.Effect Effect of ofentrainment entrainment ratio ratio on on cooling cooling capacity. capacity.

3,000 8165 2,500

2,000 100%

85% 1,500 75%

50% 1,000 Heating (kW) capacity 500

0 0.3 0.35 0.4 0.45 0.5 0.55

Entrainment ratio

Figure 9. Effect of entrainment ratio on heating capacity.

800

700

600

500 Heating 400 Cooling 300

200

100 Coolingand heating capacity (kW) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler pressure (MPa)

Figure 10. Cooling and heating capacity versus boiler pressure.

15 Entropy 2015, 17, 1–22

26.34 kW in cooling mode, is sent to hot water production in heating mode or to machine room coolingEntropy in cooling2015, 17, 1–22 mode, respectively.

26.34900 kW in cooling mode, is sent to hot water production in heating mode or to machine room

cooling800 in cooling mode, respectively.

700 900 600 100% 800 500 85% 700 400 75% 600 100% 50% 300 500 85%

Cooling capacity (kW) capacity Cooling 200 400 75% 50% 100 300

0 (kW) capacity Cooling 200 0.3100 0.4 0.4 0.5 0.5 0.6

0 Entrainment ratio 0.3 0.4 0.4 0.5 0.5 0.6

Entrainment ratio Figure 8. Effect of entrainment ratio on cooling capacity. Entropy 2015, 17, 8152–8173 Figure 8. Effect of entrainment ratio on cooling capacity.

3,000

3,000 2,500

2,500 2,000 100% 2,000 100% 85% 1,500 85% 75% 1,500 75% 50% 1,000 50% 1,000 Heating (kW) capacity 500Heating (kW) capacity 500

0 0 0.30.3 0.35 0.35 0.4 0.4 0.45 0.45 0.5 0.5 0.55 0.55

EntrainmentEntrainment ratioratio

FigureFigure 9. 9.Effect Effect of of entrainment entrainment ratio ratio on on heating heating capacity. capacity.

800 800 700 700 600 600 500 Heating 500 400 CoolingHeating 400 300 Cooling 300 200

200 100 Coolingand heating capacity (kW) 0 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Coolingand heating capacity (kW) 0 Boiler pressure (MPa) 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Boiler pressure (MPa) Figure 10. Cooling and heating capacity versus boiler pressure.

Entropy 2015, 17, 1–22 Figure 10. Cooling and heating capacity versus boiler pressure.

1.6 15 1.4

1.2 15 1 Heating 0.8

COP Cooling 0.6

0.4

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler pressure (MPa)

Figure 11. COP versus boiler pressure.

6.1. Verification Verification of the Results The entrainment ratios computed in thethe SER/SEHPSER/SEHP system system are are compared with the theoretical results presentedpresented inin referencesreferences [ 9[9,10].,10]. The The numerical numerica resultsl results for for the the entrainment entrainment ratios ratios are are compared compared in in Table 4. The difference in this comparison is acceptable. There is no experimental study based on the same working conditions of this study or similar ones.

Table 4. Comparison between the entrainment8166 ratios of presented system and the references.

Boiler Pressure (P0), Temperatures of This Study Ref. [10] Ref. [9]

Condenser (TC) and Evaporator (TE) Entrainment Ratio

P0 = 0.6 MPa, TC = 50 °C, TE = 4 °C 0.430 0.43 0.45

P0 = 0.8 MPa, TC = 50 °C, TE = 4 °C 0.482 - 0.48

6.2. Off-Design Study

There is an optimum mixing constant section area A2 for each operating condition, yet an ejector heat pump doesn’t always operate at the design conditions. Therefore, an off-design study should be performed to determine the effect on COP for the SER/SEHP system. Heating and cooling capacity are calculated to be 1332.58 kW and 300.83 kW, respectively, for a boiler pressure of 0.2 MPa and engine load of 50% at given evaporator and condenser temperatures.

1.4

1.2

1

0.8 Heating

COP 0.6 Cooling

0.4

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler pressure (MPa)

Figure 12. COP versus boiler pressure for off-design.

16 Entropy 2015, 17, 1–22

1.6

1.4

1.2

1 Heating 0.8

COP Cooling 0.6

0.4

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler pressure (MPa)

Figure 11. COP versus boiler pressure.

6.1. Verification of the Results The entrainment ratios computed in the SER/SEHP system are compared with the theoretical Entropy 2015, 17, 8152–8173 results presented in references [9,10]. The numerical results for the entrainment ratios are compared in Table 4. The difference in this comparison is acceptable. There is no experimental study based on Tablethe same4. The working difference conditions in this comparisonof this study is or acceptable. similar ones. There is no experimental study based on the same working conditions of this study or similar ones. Table 4. Comparison between the entrainment ratios of presented system and the references. Table 4. Comparison between the entrainment ratios of presented system and the references. Boiler Pressure (P0), Temperatures of This Study Ref. [10] Ref. [9] This Study Ref. [10] Ref. [9] Condenser (TBoilerC) and Pressure Evaporator (P0), Temperatures (TE) of Entrainment Ratio Condenser (TC) and Evaporator (TE) Entrainment Ratio ˝ ˝ P0 = 0.6 MPa,P 0T=C 0.6= 50 MPa, °C, TCE = 4 50 °CC, TE = 4 C 0.430 0.430 0.43 0.43 0.45 0.45 P = 0.8 MPa, T = 50 ˝C, T = 4 ˝C 0.482 - 0.48 P0 = 0.8 MPa, 0TC = 50 °C, TCE = 4 °C E 0.482 - 0.48

6.2. Off-Design Study

There is an optimum mixing constant section area A22 for each each operating operating condition, yet an ejector heat pump doesn’t always operate at the design cond conditions.itions. Therefore, an off-design study should be performed toto determinedetermine the the effect effect on on COP COP for for the th SER/SEHPe SER/SEHP system. system. Heating Heating and and cooling cooling capacity capacity are calculatedare calculated to be to 1332.58 be 1332.58 kW andkW 300.83and 300.83 kW, respectively,kW, respectively, for a boilerfor a boiler pressure pressure of 0.2 MPaof 0.2 and MPa engine and loadengine of load 50% atof given50% at evaporator given evaporator and condenser and condenser temperatures. temperatures.

1.4

1.2

1

0.8 Heating

COP 0.6 Cooling

0.4

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Boiler pressure (MPa)

Figure 12. COP versus boiler pressure for off-design.

16 In the system operating at the exhaust gas boiler pressure of 0.2 MPa, the optimum area ratio is determined to be ξ “ 23.30. With the designed the area ratio (ξ “ 23.30), the COP values for heating and cooling are calculated and plotted in Figure 12 for different boiler pressures.

6.3. Comparison Between an SER/SEHP System and Current System of Naval Ship The electric power inputs for heating and cooling of the case naval ship are 37.5% and 15.1% of the naval ship’s installed diesel generator power, respectively. The saved F-76 diesel fuel consumption (SFC) for heating and cooling can be calculated as: . W SFC “ net (53) Hu.ηDG

The electrical efficiency (ηDG) for the diesel generator is 95%. Some values of the logistic fuel NATO F-76 are presented in Table5[2,21,22].

8167 Entropy 2015, 17, 1–22

In the system operating at the exhaust gas boiler pressure of 0.2 MPa, the optimum area ratio is determined to be   23.30 . With the designed the area ratio (  23.30 ), the COP values for heating and cooling are calculated and plotted in Figure 12 for different boiler pressures.

6.3. Comparison Between an SER/SEHP System and Current System of Naval Ship The electric power inputs for heating and cooling of the case naval ship are 37.5% and 15.1% of the naval ship’s installed diesel generator power, respectively. The saved F-76 diesel fuel consumption (SFC) for heating and cooling can be calculated as: Entropy 2015, 17, 8152–8173 W SFC  net (53) HuDG.

The electrical efficiencyTable (D 5.G )Values for the ofdiesel the logistic generator fuel is NATO 95%. So F-76.me values of the logistic fuel NATO F-76 are presented in Table 5 [2,21,22]. Molecular Formula (Average) C14.8H26.9 Table Molecular5. Values of weight the logistic fuel NATO F-76. 205 Sulphur content, wt.% (max) 0.1 C14.8H26.9 MolecularDensity, at 15Formula˝C, kg¨ m (Average)´3 (max) 876 Fuel price,Molecular US$¨ gallon weight´1, (2015) 2053.69 ´1 LowerSulphur heating content, value, wt.% Hu, kJ(max)¨ kg 42,7000.1 Density, at 15 °C, kg·m−3 (max) 876 Fuel price, US$·gallon−1, (2015) 3.69 If an SEHP system is used instead of electric duct heaters in heating mode, 14,550 L of diesel fuel Lower heating value, Hu, kJ·kg−1 42,700 (US$14,511) can be saved and 38.30 tons of CO2 emissions reduced at the end of 1000 operating hours a year of a navalIf an surfaceSEHP system ship. is If used an SERinstead system of electric is used duct instead heaters in of heating seawater mode, cooled 14,550 chiller L of diesel unit fuel in cooling mode,(US$14,511) 5837 L of diesel can be fuel saved (US$5822) and 38.30 cantonsbe of CO saved2 emissions and 15.36 reduced tons at of the CO end2 emissions of 1000 operating reduced hours at the end of 1000a operatingyear of a naval hours surface a year ship. of a If naval an SER surface system ship. is used instead of seawater cooled chiller unit in cooling mode, 5837 L of diesel fuel (US$5822) can be saved and 15.36 tons of CO2 emissions reduced at the end of 1000 operating hours a year of a naval surface ship. 6.4. Comparison Between an SER/SEHP System and an H2O-LiBr AHP System

The6.4. referenceComparison system Between consistsan SER/SEHP of an System H2O-LiBr and an H AHP2O-LiBr system AHP System driven exhaust heat of a 3000 kW diesel engine [2]. Figures 13 and 14 show cooling and heating capacities versus engine load for the SER The reference system consists of an H2O-LiBr AHP system driven exhaust heat of a 3000 kW and SEHPdiesel system engine and[2]. Figures an H2 O-LiBr13 and 14 AHP show system. cooling Theand coolingheating capacities and heating versus capacities engine load of for the the SER and SEHP andSER and H2O-LiBr SEHP system AHP and system an H increases2O-LiBr AHP with system. the increasing The cooling engine and heating load capacities at given of evaporator the SER and condenserand SEHP temperatures. and H2O-LiBr The AHP cooling system capacities increases of with H2 O-LiBrthe increasing AHP systemengine load are at higher given thanevaporator SER but the heatingand capacities condenser are temperatures. lower than The SEHP cooling for thecapacities same engineof H2O-LiBr with AHP the samesystem load. are higher than SER but the heating capacities are lower than SEHP for the same engine with the same load.

1,600 AHP (90 oC) 1,400 AHP (95 oC) AHP (100 oC) 1,200 AHP (105 oC) 1,000 AHP (110 oC) SER (0.2 MPa) 800 SER (0.3 MPa) 600 SER (0.4 MPa) SER (0.5 MPa) 400 SER (0.6 MPa) Cooling capacity (kW) 200 SER (0.7 MPa) SER (0.8 MPa) 0 SER (0.9 MPa) 50 75 85 100

Engine load (%)

Figure 13. Cooling capacity versus engine load. Entropy 2015, 17, 1–22 Figure 13. Cooling capacity versus engine load.

17

3,000 SEHP (0.9 MPa) SEHP (0.8 MPa) 2,500 SEHP (0.7 MPa) SEHP (0.6 MPa) 2,000 SEHP (0.5 MPa) SEHP (0.4 MPa) 1,500 SEHP (0.3 MPa) SEHP (0.2 MPa) 1,000 AHP (110 oC) AHP (105 oC) Heating capacity (kW) 500 AHP (100 oC) AHP (95 oC)

0 AHP (90 oC) 50 75 85 100

Engine load (%)

FigureFigure 14. 14.Heating Heating capacitycapacity versusversus engineengine load. load.

6.5. Comparison between an SER/SEHP System and a VCHP System The reference system in this case consists8168 of a conventional diesel generator, which provides electricity and heat, and a vapour-compression heat pump (VCHP), which produces heating and cooling. VCHPs generally have COPs of 2–4 and deliver 2–4 times more energy than they consume. The electric motor of the in a VCHP is fed by a diesel generator set on board the ship. As the energy for the entire naval ship’s electrical load is produced from diesel generator sets, each electrical load directly affects the overall fuel economy and emissions. Fuel consumption and CO2 emissions decrease to produce the same amount of power given by a VCHP system when an SER/SEHP system is used. As the SER/SEHP system is assumed to replace the VCHP system, the results of the system studies will depend on the COP of the VCHP. Based on the engine load, the heating demand is assumed to be 1332.58, 1774.36, 1916.14 and 2379.16 kW, the cooling demand is assumed to be 300.83, 400.56, 432.57 and 537.10 kW, and the COP is assumed to be 2, 3 and 4 for the VCHP. The amounts of cooling and heating produced by the SER/SEHP in each system can be regarded to correspond to electricity saving. The saving is calculated by estimating fuel and the electricity input needed to produce the same heating and cooling effect using the VCHP. The calculations are performed with COPs of 2, 3 and 4 for the VCHP. Figures 15 and 16 present the SFC versus heating and cooling capacities for a boiler pressure of 0.2 MPa.

120 ) -1

100

80 VCHP of COP=2 60 VCHP of COP=3 VCHP of COP=4 40

20 The fuel saved consumption (kgh 0 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600

Heating capacity (kW)

Figure 15. SFC versus heating capacity.

18 Entropy 2015, 17, 1–22

3,000 SEHP (0.9 MPa) SEHP (0.8 MPa) 2,500 SEHP (0.7 MPa) SEHP (0.6 MPa) 2,000 SEHP (0.5 MPa) SEHP (0.4 MPa) 1,500 SEHP (0.3 MPa) SEHP (0.2 MPa) 1,000 AHP (110 oC) AHP (105 oC) Heating capacity (kW) 500 AHP (100 oC) AHP (95 oC)

0 AHP (90 oC) 50 75 85 100 Entropy 2015, 17, 8152–8173 Engine load (%)

6.5. Comparison between an SER/SEHPFigure 14. System Heating and capacity a VCHP versus System engine load.

The6.5. Comparison reference between system an in SER/SEHP this case System consists and of a VCHP a conventional System diesel generator, which provides electricity and heat, and a vapour-compression heat pump (VCHP), which produces heating and The reference system in this case consists of a conventional diesel generator, which provides cooling. VCHPs generally have COPs of 2–4 and deliver 2–4 times more energy than they consume. electricity and heat, and a vapour-compression heat pump (VCHP), which produces heating and The electric motor of the compressor in a VCHP is fed by a diesel generator set on board the ship. cooling. VCHPs generally have COPs of 2–4 and deliver 2–4 times more energy than they consume. As theThe energy electric for motor the entireof the compressor naval ship’s in a electrical VCHP is fe loadd by is a produceddiesel generator from set diesel on board generator the ship. sets, As each electricalthe energy load directly for the affectsentire naval the overall ship’s electrical fuel economy load is and produced emissions. from diesel generator sets, each Fuelelectrical consumption load directly and affects CO2 theemissions overall fuel decrease economy to produceand emissions. the same amount of power given by a VCHP systemFuel consumption when an SER/SEHP and CO2 emissions system isdecrease used. Asto produce the SER/SEHP the same systemamount isof assumedpower given to by replace the VCHPa VCHP system, system the when results an SER/SEHP of the system system studies is used will. As the depend SER/SEHP on the system COP is of assumed the VCHP. to replace Basedthe VCHP on system, the engine the results load, theof the heating system demandstudies will is depend assumed on tothe be COP 1332.58, of the VCHP. 1774.36, 1916.14 and 2379.16 kW,Based the on cooling the engine demand load, isthe assumed heating todemand be 300.83, is assumed 400.56, to 432.57 be 1332.58, and 537.101774.36, kW, 1916.14 and theand COP 2379.16 kW, the cooling demand is assumed to be 300.83, 400.56, 432.57 and 537.10 kW, and the COP is assumed to be 2, 3 and 4 for the VCHP. The amounts of cooling and heating produced by the is assumed to be 2, 3 and 4 for the VCHP. The amounts of cooling and heating produced by the SER/SEHP in each system can be regarded to correspond to electricity saving. The saving is calculated SER/SEHP in each system can be regarded to correspond to electricity saving. The saving is calculated by estimatingby estimating fuel andfuel theand electricitythe electricity input input needed needed to produceto produce the the same same heating heating and and cooling cooling effect effect using the VCHP.using the The VCHP. calculations The calculations are performed are performed with COPs with COPs of 2, 3of and 2, 3 4and for 4 thefor VCHP.the VCHP.Figures Figures 15 15and 16 presentand the 16 present SFC versus the SFCheating versus and heating cooling and capacitiescooling capacities for a boiler for a boiler pressure pressure of 0.2 of MPa. 0.2 MPa.

120 ) -1

100

80 VCHP of COP=2 60 VCHP of COP=3 VCHP of COP=4 40

20 The fuel saved consumption (kgh 0 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600

Heating capacity (kW)

Figure 15. SFC versus heating capacity. Entropy 2015, 17, 1–22 Figure 15. SFC versus heating capacity.

25 18 ) -1

20

15 VCHP of COP=2 VCHP of COP=3 10 VCHP of COP=4

5 The saved fuel consumptionThe saved (kgh 0 270 320 370 420 470 520 570

Cooling capacity (kW)

FigureFigure 16. 16.SFC SFC versusversus coolingcooling capacity. capacity.

At the end of 1000 operating hours a year of a naval surface ship, the SER/SEHP system can use more than 99.5% less electricity compared with the vapour-compression heat pump for HVAC. It can save 33,712–120,447 L of diesel fuel in the heating cycle and 7581–27,139 L of diesel fuel in the cooling cycle depending on the engine load and COP of8169 the vapour-compression heat pump. Figures 17 and 18 show the reduced CO2 emission versus heating and cooling capacities for a boiler pressure of 0.2 MPa. At the end of 1000 operating hours a year of a naval surface ship, the AHP system can improve the ship’s green profile because it will reduce its annual CO2 emissions by 88.74–317.05 tons in the heating cycle and 19.95–71.43 tons in the cooling cycle depending on the engine load and COP of the vapour-compression heat pump. Figures 19 and 20 show the profitability plotted against the heating and cooling capacities, respectively. The fuel price is set to US$3.69 gallon−1 and the operating hours are 1000 h a year. In this case, the COPs used for the VCHP are 2, 3 and 4. The SEHP system can provide an annual energy savings of US$33,621–US$120,122 and the SER system can provide an annual energy savings of US$7561–US$27,065.

350 ) -1 300

250

200 VCHP of COP=2 emission (kgh emission

2 VCHP of COP=3 150 VCHP of COP=4

100

50 The reducedCO 0 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600

Heating capacity (kW)

Figure 17. Reduced CO2 emissions versus heating capacity.

19 Entropy 2015, 17, 1–22

25 ) -1

20

15 VCHP of COP=2 VCHP of COP=3 10 VCHP of COP=4

5 The saved fuel consumptionThe saved (kgh 0 270 320 370 420 470 520 570

Cooling capacity (kW)

Entropy 2015, 17, 8152–8173 Figure 16. SFC versus cooling capacity. At the end of 1000 operating hours a year of a naval surface ship, the SER/SEHP system can use At the end of 1000 operating hours a year of a naval surface ship, the SER/SEHP system can use more than 99.5% less electricity compared with the vapour-compression heat pump for HVAC. It can more than 99.5% less electricity compared with the vapour-compression heat pump for HVAC. It can save 33,712–120,447 L of diesel fuel in the heating cycle and 7581–27,139 L of diesel fuel in the cooling save 33,712–120,447 L of diesel fuel in the heating cycle and 7581–27,139 L of diesel fuel in the cooling cycle depending on the engine load and COP of the vapour-compression heat pump. cycle depending on the engine load and COP of the vapour-compression heat pump. Figures 17 and 18 show the reduced CO2 emission versus heating and cooling capacities for a Figures 17 and 18 show the reduced CO2 emission versus heating and cooling capacities for a boiler pressure of 0.2 MPa. At the end of 1000 operating hours a year of a naval surface ship, the boiler pressure of 0.2 MPa. At the end of 1000 operating hours a year of a naval surface ship, the AHP AHP system can improve the ship’s green profile because it will reduce its annual CO2 emissions system can improve the ship’s green profile because it will reduce its annual CO2 emissions by by 88.74–317.05 tons in the heating cycle and 19.95–71.43 tons in the cooling cycle depending on the 88.74–317.05 tons in the heating cycle and 19.95–71.43 tons in the cooling cycle depending on the engine load and COP of the vapour-compression heat pump. engine load and COP of the vapour-compression heat pump. Figures 19 and 20 show the profitability plotted against the heating and cooling capacities, Figures 19 and 20 show the profitability plotted against the heating and cooling capacities, respectively. The fuel price is set to US$3.69 gallon´1 and the operating hours are 1000 h a year. respectively. The fuel price is set to US$3.69 gallon−1 and the operating hours are 1000 h a year. In this In this case, the COPs used for the VCHP are 2, 3 and 4. The SEHP system can provide an annual case, the COPs used for the VCHP are 2, 3 and 4. The SEHP system can provide an annual energy energy savings of US$33,621–US$120,122 and the SER system can provide an annual energy savings of savings of US$33,621–US$120,122 and the SER system can provide an annual energy savings of US$7561–US$27,065. US$7561–US$27,065.

350 ) -1 300

250

200 VCHP of COP=2 emission (kgh emission

2 VCHP of COP=3 150 VCHP of COP=4

100

50 The reducedCO 0 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600

Heating capacity (kW)

Entropy 2015, 17, 1–22 Figure 17. Reduced CO 2 emissionsemissions versusversus heatingheating capacity. capacity.

80 )

-1 70

60

50 19 emission (kgh emission

2 40

30 VCHP of COP=2 20 VCHP of COP=3

10 VCHP of COP=4 The reducedCO

0 270 320 370 420 470 520 570

Cooling capacity (kW)

Figure 18. Reduced CO2 emissions versus cooling capacity. Figure 18. Reduced CO2 emissions versus cooling capacity.

140,000

120,000 )

-1 8170 100,000

80,000 VCHP of COP=2 VCHP of COP=3 60,000 VCHP of COP=4

40,000 Profitability (US$year 20,000

0 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600

Heating capacity (kW)

Figure 19. Profitability of the SEHP system as a function of heating capacity.

30,000

25,000 ) -1

20,000 VCHP of COP=2 15,000 VCHP of COP=3 VCHP of COP=4 10,000 Profitability (US$year 5,000

0 270 320 370 420 470 520 570

Cooling capacity (kW)

Figure 20. Profitability of the SER system as a function of cooling capacity.

20 Entropy 2015, 17, 1–22 Entropy 2015, 17, 1–22

80 80 ) -1 ) 70

-1 70

60 60

50 50 emission (kgh emission 2

emission (kgh emission 40

2 40

30 30 VCHP of COP=2 20 VCHP of COP=2 20 VCHP of COP=3 VCHP of COP=3 10 VCHP of COP=4 The reducedCO 10 VCHP of COP=4 The reducedCO

0 0 270 320 370 420 470 520 570 270 320 370 420 470 520 570 Cooling capacity (kW) Cooling capacity (kW)

Entropy 2015, 17, 8152–8173 Figure 18. Reduced CO2 emissions versus cooling capacity. Figure 18. Reduced CO2 emissions versus cooling capacity.

140,000 140,000

120,000

) 120,000 -1 ) -1 100,000 100,000

80,000 VCHP of COP=2 80,000 VCHP of COP=2 VCHP of COP=3 VCHP of COP=3 60,000 60,000 VCHP of COP=4 VCHP of COP=4 40,000 40,000 Profitability (US$year Profitability (US$year 20,000 20,000

0 0 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 1,200 1,400 1,600 1,800 2,000 2,200 2,400 2,600 Heating capacity (kW) Heating capacity (kW)

Figure 19. Profitability of the SEHP system as a function of heating capacity. Figure 19. ProfitabilityProfitability of the SEHP system as a function of heating capacity.

30,000 30,000

25,000 ) 25,000 -1 ) -1 20,000 20,000 VCHP of COP=2 VCHP of COP=2 15,000 VCHP of COP=3 15,000 VCHP of COP=3 VCHP of COP=4 VCHP of COP=4 10,000 10,000 Profitability (US$year

Profitability (US$year 5,000 5,000

0 0 270 320 370 420 470 520 570 270 320 370 420 470 520 570 Cooling capacity (kW) Cooling capacity (kW)

Figure 20. ProfitabilityProfitability of the SER system as a function of cooling capacity. Figure 20. Profitability of the SER system as a function of cooling capacity. 7. Conclusions

A seawater cooled SER/SEHP system20 for a naval surface ship was designed and thermodynamically analysed. The SER/SEHP system was compared with those of a current system in a case naval ship, an H2O–LiBr AHP system and a VCHP system in a case naval surface ship. The dual use of ejector technology to produce heating and cooling on board a naval ship was investigated. The off-design study estimated the COPs were 0.29–0.11 for the cooling mode and 1.29–1.11 for the heating mode, depending on the pressure of the exhaust gas boiler at off-design conditions. In the system operating at the exhaust gas boiler pressure of 0.2 MPa, the optimum area ratio obtained was 23.30. The results show that the seawater-cooled SER/SEHP system not only meets the actual cooling and heating and loads of the case naval surface ship, but also provides more. The SER system is particularly attractive in applications that have a cooling demand and a source of heat, such as naval surface ships. The SEHP system is needed for the HVAC as waste heat from a running ship engine may be sufficient to provide enough heat to meet the heating load. The results show that SER/SEHP is an environmentally friendly way to produce heating and cooling as it reduces the use of an electrically driven heat pump in the energy system and thus global

8171 Entropy 2015, 17, 8152–8173

CO2 emissions. Moreover, as water can be used as the refrigerant in SER/SEHP, the problem of environmentally harmful refrigerants used in VCHP is avoided. Compared with current system of a case naval ship, SER and SEHP system have the advantages of lower energy consumption, CO2 emissions and EEDI. Despite the low COP values obtained in this study, the SEHP operating in the heating mode offers better performance than electrical resistance type heating. Compared with an AHP system, SER and SEHP system have the advantages of lower cost, simplicity, and minimal maintenance, even though its efficiency is still relatively low. More importantly, an absorption heat pump is prone to corrosion and occupies a large installation space, while an ejector heat pump is convenient and compact. Compared with a VCHP system, SER and SEHP system have the advantages of lower of energy consumption, CO2 emissions and EEDI. More importantly, the naval ship's susceptibility can be dramatically reduced by lowering infrared and acoustic signature. In future studies, variable area ejectors for seawater-cooled SER/SEHP system application should be investigated.

Acknowledgments: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing official policies or endorsements, either expressed or implied, of any affiliated organisation or government. We wish to thank Mech. Eng. Azize Ezgi for helpful suggestions and critical comments. Author Contributions: Cüneyt Ezgi conceived and designed the research, analysed the data. Cüneyt Ezgi and Ibrahim Girgin worked out the theory, and wrote the manuscript. Both authors have read and approved the final manuscript. Conflicts of Interest: The authors declare no conflict of interest.

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