Overall scheme design of a closed solid oxide fuel cell hybrid engine for ships

A scheme of compact closed solid oxide fuel cell hybrid engines for ship power and propulsion on ships is proposed. A zero-emission closed engine at the effective equivalence ratio of 1 is achieved by recirculating water and fuelling by liquid hydrocarbon fuel and oxygen. The adiabatic pure oxygen reforming temperature of the reformer is higher than the specified anode inlet temperature. A turbine is placed in front of the solid oxide fuel cell anode. Detailed potential distributions are considered using a two-dimensional solid oxide fuel cell model, and thermodynamic models of the hybrid engine are built. The performance of the reformer is more sensitive to the oxygen-carbon ratio rather than the steam-carbon ratio, which leads to a huge change of the pressure ratio of the turbine. Therefore, the power ratios of turbines and SOFC are also affected by the oxygen and steam carbon ratio and excess oxygen coefficient. The optimized power ratio is 1.02 – 1.13, which results in a significant change in the efficiency of the engine. Under the specified operating conditions, the engine can achieve a high efficiency of 67 %. Under the off-design conditions, with the increase of the mass flow of fuel or the current density, the power of the engine can be changed from 20 % to 160 % of the designed power.


Introduction
Carbon dioxide emissions from ships accounted for approximately 2 % of the total global anthropogenic carbon dioxide emissions in 2022, according to the International Maritime Organization (IMO) [9].The IMO has set an extremely ambitious target of a 50 % absolute reduction in emissions by 2050 compared to the 2008 level [10].Developing lowcarbon power devices is the key to mitigating the damage caused by carbon dioxide emissions [11].
Electrification and novel fuels are essential directions for the development of the shipping industry, especially for inland shipping and coastal medium-distance coastal shipping.Their user is more concerned about the economics and carbon emissions of the power and energy systems.The cost of fuel accounts for about 20-40 % of the cost of shipping companies.It can be decreased to a large degree if the novel high-efficiency engine technology is adopted.
Diesel engines are widely commonly used power suppliers for ships.However, the large amount of carbon emissions from diesel engines is not consistent with the target of developing a low-carbon society.Alternatives of power resources for ships mainly depend on thermal efficiency and specific fuel consumption [12].Engines fed by ammonia and hydrogen with low emissions have been widely researched [5,6].Technical challenges related to combustion and nitrogen oxide emissions exist when using internal combustion engines such as intercombustion engines or gas turbines, especially in the case of pure hydrogen.
Gas fuel can be used by fuel cells, which are an energy conversion technology with high efficiency and low emission [15].Results from Baldi et al. [16] show that the most cost-optimal scheme of carbon dioxide reduction in the maritime sector is the SOFC power system, which can reduce 34 % of emissions.SOFC power systems can significantly decrease the environmental influence of ships compared with existing engines [16].Strazza et al. [17] reported that the SOFC systems on board ships have a significantly lower environmental impact compared with the conventional auxiliary power system.The most commonly used metric to quantify greenhouse gas emissions is known as GWP100.For the traditional engine, the value is 747, which is only 0.99 for a methanol SOFC system.Replacing diesel engines with SOFC-assisted power systems is a promising solution for reducing fuel consumption and carbon dioxide emissions.
Previous studies on the SOFCs as power or propulsion systems for ships are briefly summarized in Table 1.It is essential to study the overall thermodynamic performance of SOFC systems to show their advantages in efficiency.Nehter et al. [18] proposed a diesel-based SOFC system for ships with a gross electrical efficiency of 55 % and fuel utilization of 73 % by using the lumped parameter model.They indicated that an adiabatic pre-reforming process is vital because it could allow the diesel to be conducted without any deep desulphurization procedures.However, air reforming decreases the concentration of hydrogen, which leads to an increase in the polarization of SOFCs and a decrease in fuel utilization.Baldasano et al. [19] proposed a hybrid propulsion system consisting of a diesel generator for thruster units and methanol-fed SOFC systems for electricity supply.Its electric efficiency is only 47 %.Ezgi et al. [20] compared a diesel-fueled SOFC system with a diesel-electric generator.The net efficiency of the diesel-fueled SOFC is 55.3 %, and the diesel-electric is 25.3 %.The carbon dioxide emission of the SOFC system is 52 % of that of the marine diesel engine [20].
However, the configuration of the SOFC power system, e.g., exhaust recycling or collection, has not been comprehensively investigated.In Ref [18], the heat of exhaust is just utilized by the heat exchanger and not used by highly efficient turbines.This would lead to a low useful power output.In Ref [19], methanol is used as the fuel where the hydrogen molar fraction is low.Because the fuel is mixed with the anode exhaust, the concentration of hydrogen is lower.In this way, the efficiency of the SOFC will not be very high unless the current density is very low.From the respective of carbon dioxide emission, even though carbon dioxide can be reduced sharply by integrating SOFC into the liquefied natural gas-fueled power and propulsion system [21], the emission is still produced.The performance potential of the SOFC system on the ship was not ultimately revealed.In addition, the compactness of engines is required [22] when they are applied for transportation.The density of liquid oxygen is about one thousand times higher than that of oxygen under atmospheric conditions.If the SOFC engines are fueled by macromolecular hydrocarbon and liquid oxygen, their volume and energy density will be meaningfully improved.
This work is motivated by the urgent need for carbon reduction and neutrality.Moreover, ship companies have a demand for power and energy systems with low fuel consumption compared with diesel engines.
The novelty of this work is that we proposed a scheme of closed solid oxide fuel cell hybrid engines for power and propulsion on ships.Zero emission is achieved by storing the solid-state carbon dioxide.The gas carbon dioxide is solidified by combining SOFC with heat exchangers to reduce the temperature of the exhaust, which is lower than the phase change temperature of solid and liquid.Moreover, by the design of the SOFC hybrid engine, the efficiency of the closed hybrid engine is up to 67 %, which is higher than the engines based on the fuel cells for the ship reported in the literature.This article is structured in the following manner.In Section 2, the closed SOFC hybrid engine scheme is introduced.Mathematical models used for simulations are presented in Section 3. Results and discussion of hydrocarbon reforming, SOFCs, and the hybrid engine are stated in Section 4. The performance coupling effects between the reforming and the electrochemical reaction are analyzed.The effects of key specified parameters on the hybrid engine and its designed and off-designed performance are discussed.The main conclusions are drawn in Section 5.

Concept of a closed solid oxide fuel cell hybrid engine
The schematic diagram of the proposed hybrid engine is shown in Fig. 1 (a), and its simplified schematic Diagram is shown in Fig. 1 (b).The engine is fed by liquid hydrocarbon fuel, and pure oxygen is used as an oxidizer.All the exhaust is recycled or collected by constructing the closed power cycle, and no emission is produced.The engine is initiated by pumping the fuel, water, and oxygen into the corresponding containers.The engine has three streams: fuel supply stream, oxygen supply stream, and exhaust stream, and four electricity generators: fuel turbine generators, oxygen turbine generators, exhaust turbine generators, and SOFCs.The hybrid engine is equipped with three storage tanks: ambient temperature fuel, water tank, and cryogenic oxygen tank.The size of each storage tank depends on the endurance and weight of the ship.The product of the hybrid engine is water and dry ice.Excess water is discharged into the seawater, and dry ice is stored for other purposes.This is a near-zero emission engine.
The fuel supply stream includes fuel tanks, fuel pumps, reformers, fuel turbines, water tanks, water pumps, and heat exchangers, which provide rich hydrogen with specified temperature T specified,SOFC,anode and pressure p specified,SOFC,anode to the anode of the SOFCs.The fuel is atomized and mixed with oxygen and steam in the reformer and produces hydrogen, carbon dioxide, methane, and carbon monoxide.All reformed gases are sent to the anode channels of the SOFCs.Part of the water in the tank is recirculated, and only a small amount of water is needed to start up the hybrid engine.
The oxygen supply stream includes oxygen tanks, oxygen pumps, exhaust heat exchangers, cathode heat exchangers, oxygen turbines, blowers, and cathode mixers, providing oxygen with specified pressure p specified,SOFC,cathode and temperature T specified,SOFC,cathde to the cathode channels of the SOFCs.SOFCs generate electricity by electrochemical reactions and inner reforming (carbon monoxide and methane react in the SOFC).The heat and gases from the SOFCs are reused through the exhaust turbines.
The exhaust stream includes anode mixers, burners, exhaust turbines, cathode heat exchangers, coolers, gas-liquid separators, dry ice storage towers, and oxygen recirculation pumps.To keep the specified outlet temperature of the SOFC T specified,SOFC,out , part of the cathode exhaust is recirculated by the blower.The burning exhaust expands in the turbines where electricity is generated by coupling the generators.The turbine exhaust is first cooled by the cathode heat exchanger.Then, the exhaust is cooled by seawater and is used to generate water.Next, the carbon dioxide in the exhaust is turned into a solid state by cooling it with oxygen from the tank, which can be stored.The gas (oxygen) is pressurized by the oxygen recirculation pump and recirculated into the oxygen tank.The electricity produced by the SOFCs and the turbines is provided to marine vehicles for power and propulsion.
If the steam of hydrocarbon fuel is directly sent to the anode channels, the electrode materials can be quickly degraded due to the high temperature [27].Therefore, the external reformer is positioned upstream of the SOFCs.The liquid oxygen tank is used to provide oxygen to the reformer and the SOFCs.This will lead to a high concentration of hydrogen or carbon monoxide in the reformer and a small polarization in the SOFC cathode.Additionally, pure oxygen adiabatic reforming will lead to a high outlet temperature, which can be far higher than the specified inlet temperature of the SOFCs T specified,SOFC,anode .Therefore, turbines are arranged downstream of the reformer.Correspondingly, the pumps are arranged upstream of the reformer to keep the atmospheric operation condition of the SOFCs p specified,SOFC,anode .

Mathematical modeling
Lumped parameter models are frequently used to model an SOFC, and most of them have been validated with experimental results [28].These models are suitable for use in low current densities.The variations in fuel and air utilization and temperature are slight in most existing model validations of the lumped parameter model SOFC models.However, we found that the results from these models did not completely agree with the results calculated by the 2D SOFC model in Fig. 2. By comparing the solved variables (e.g., voltage) using a lumped parameter model and a 2D SOFC model, the deviation of the simulation results between the lumped parameter model and 2D model increases with the increase of the current density.This is because the variations of variables along the channel direction are more significant at higher current densities.The variations of current density and temperature along the flow direction significantly affect the polarization.In this work, we integrate a 2D SOFC model into the hybrid engine to capture the changes in variables along the channel direction.
The models are developed based on the following main assumptions: [9] The closed hybrid engine is operated at a steady state.[10] The fuel is a liquid hydrocarbon fuel, and n-tetradecane was chosen as its surrogate.[11] Anode-support planar SOFC is used.[12] The dimensions and boundary conditions of SOFC units are considered the same as shown in Fig. 3. [13] SOFCs and other components are insulated without heat loss.[14] All working fluids are considered ideal gases.[15] Reforming gas is composed of methane, carbon dioxide, carbon monoxide, hydrogen, and steam.[16] The specified power of the hybrid closed cycle is 1 MW.

SOFC model
The cell has a nickel yttria stabilized zirconia (Ni-YSZ) support, a Ni-YSZ active layer, a YSZ electrolyte and a lanthanum strontium cobalt ferrite (LSCF) based oxygen electrode.A gadolinia doped ceria (CGO) barrier layer plus a contact layer are present between the electrolyte and the LSCF-based electrode.Yang [29] et al. investigated the long-term durability of the SOCs operated at 800, 750, and 700 ℃ for periods exceeding 1000 h each.The cells show different initial performance due to different operating temperatures, but all experience a significant degree of initial degradation within the first 300 h, with a degradation rate of 2.80, 1.93, and 1.77A cm − 2 kh − 1 for the cells tested at 800, 750, and 700 ℃, respectively.The relevant physical processes in the gas channels, electrodes, and electrolytes are described using energy conservation equations, momentum conservation equations, and mass conservation equations, see Table 2. Darcy's law is used to describe the momentum of transportation.Fourier's law is used to describe energy transportation.
In the mass conservation equations of electrodes and channels, D eff j,g is the effective diffusion coefficient of the gas j.C j is the molar concentration of the gas j.u is the velocity vector, and S m,j is the reaction source term of working fluid j.In the electrodes, the source term is the substances that take part in the electrochemical equation.In the gas channels, the source term is the substances related to methane and carbon monoxide reforming.In the momentum conservation equation, μ is the dynamic viscosity of the working fluids.S o,j is the source term of the momentum of working fluids of j.This value is assumed to be zero in the gas channels.In the electrode, it is μ K u.K is the permeability of the working fluids in the porous region.The energy conservation equation considers the energy from electrochemical reactions, polarization loss, and joule heat.λ is thermal conductivity, and S T is the energy source term.In the anode and cathode charge conservation equation, σ ele is the effective electron conductivity, and i is the current density.In the electrolyte charge conservation equation, σ ion is the effective ion conductivity.
Table 3 shows the voltage of SOFCs and polarization models.The voltage loss is due to the ohmic polarization in the electrodes and  electrolyte, the concentration polarization, and activation polarization, respectively, in the anode and cathode [31].The dimensions of the SOFC unit are listed in Table 4.The parameters in Ref [32] are used in the models.

Definitions of the balance of plants
The parameters of the balance of plants are listed in Table 5.The first law of thermodynamics is used to calculate the outlet temperature of burners, heat exchangers, and reformers.Non-isentropic processes are considered to be built for blowers and turbines.The efficiency of the burners η burner from Sirignano and Liu [33], the turbines η turbine , heat exchanger ε from Lv et al. [34,35], and the cathode blower η blower are from Barelli et al. [36], respectively.The efficiency of the water pump changes from 60 % to 90 % due to the influences of the mass flow and the rotation speed.In this work, an efficiency of 70 % is assumed to estimate the power of the pumps conservatively [37].The reforming temperature is considered the outlet temperature of the former.The equilibrate state of the reforming reaction is solved with the software Chemical Equilibrium with Applications (CEA) provided by the National Aeronautics and Space Administration (NASA) [38].The energy efficiency ϕ reformer is defined as the low heating value (LHV) ratio of the reforming gas (carbon monoxide, hydrogen, and methane) and the fuel (n-tetradecane).The hydrogen yield Y H2 is defined as the carbon monoxide and hydrogen molar sum ratio of reforming gas and the available maximum from fuel.Besides, the oxygen-carbon ratio R oc and the steamcarbon ratio R sc are defined to measure the ratio of the mass of steam and oxygen.The net power P hybrid of the close hybrid engine is defined as the difference between the sum of the power SOFCs P SOFC and the turbines P turbine and the sum of the power of the pumps P consume , which is the sum of the power of blowers P blower and pumps P pump .
The efficiency of the SOFCs ϕ SOFC and the power of the hybrid engine P hybrid are used to evaluate the performance of the closed hybrid engine, which is explained in Table 6.Because the coefficient of total pressure loss of SOFCs, the exhaust separators, and the SOFC mixers is lower than 5 %, the pressure differences among the pressure ratios of the fuel turbine, the oxygen compressor, and the water pump are small under the designed scheme, see Fig. 1.
The density of the liquid hydrogen, liquid oxygen, and n-tetradecane are respectively 70.85 g/L, 1141 g/L, and 770 g/L.If the energy of 142 MJ is needed for storage, the volume of the propellant for the hydrogen

Physical quantities Mathematical models
Ideal voltage

Table 4
Parameters for the single 2D SOFC unit [32].engine and the proposed hybrid engine is shown in Fig. 4. It can be seen that the propellant for the hybrid engine does not occupy more volume than the hydrogen-fuelled engine.The volume can be reduced by at least 4 %.All of the efficiency of the component is shown in Table 7.

Validation of the SOFC model
The burner models, reformer models, heat exchanger models, pump models, and blower models used in this work have been widely used in the modeling work of the hybrid power engine for electricity generation [28,39].Here, we conduct the validation of the SOFC model.Simulation results are compared with experimental data provided in [32].The boundary conditions are stated in Table 8.Fig. 5 shows the comparisons of the I − V curves from the SOFC simulations and the experiments under the different boundary conditions.We can see that the simulation results are in good agreement with the experimental data.

Calculation procedure
The calculation flow chart of the closed hybrid engine is shown in Fig. 6.Three iteration processes are performed with the same relative tolerance of 10 -3 .The calculation is initialized by inputting specified component parameters under the assumptions, which include the oxygen-carbon ratio R oc , steam-carbon ratio R sc , excess oxygen coefficient R eoc , molar flow rate of the fuel n fuel , dimensions of the SOFC units, the efficiency of each component (η pump , η blower , η turbine , η burner , ε).For the SOFC, the specified anode inlet temperature of the SOFC anode T specified,SOFC,anode , inlet temperature of the SOFC cathode, T specified,SOFC, cathode , outlet temperature of the SOFC T specified,SOFC,out are also inputted.For the cathode heat exchanger, the outlet temperature of the cold fluids of the cathode heat exchanger, T specified,HX,cathode,cold,out is inputted.Storage conditions of the oxygen tank p tank,o ,T tank,o , water tank p tank,w , T tank,w , and fuel tank p tank,f ,T tank,f are set as user-defined.The mass flows of the working fluids m tank,o , m tank,f , m tank,w are obtained in terms of the inputting parameters.Because the pressure ratio of the fuel pump π pump,f is unknown, the pressure ratios of the tanks π pump,w ,π pump,o ,π pump,f are initially guessed.
The calculation procedure is composed of the following steps: (a) outputting parameters of the oxygen pumps p pump,o ,T pump,o ,m pump,o , fuel p pump,f ,T pump,f ,m pump,f , and water p pump,w ,T pump,w ,m pump,w are calculated by the equations in Table 5.The reformer and anode turbine calculations are in progress.The outlet parameters of pressure, temperature, mass flow, and molar flow rate of the reformer (p reformer,out , T reformer,out ,m re- former,out ,n ,reformer,out ) and the anode turbine (p turbine,out , T turbine,out (T SOFC,anode ), m turbine,out n ,turbine,out,i ) are output.The above process is repeated by iterating the pressure ratio of the fuel turbine π turbine,f , oxygen pump π pump,o , and fuel pump π pump,f until the outlet temperature of the anode turbine T turbine,anode (it is the same as the anode inlet temperature of the SOFC T SOFC,anode ) is close to the specified temperature T specified,SOFC,anode (temperature boundary conditions for the anode of the SOFCs) where the relative tolerance is 10 -3 .The power of the pumps P pump,o , P pump,f , P pump,w , fuel turbine P turbine,f , and the blower P blower are calculated using the equations in Table 5. (B) the calculations of the heat exchanger and cathode turbine are underway.The outlet parameters of cathode heat exchanger p cathode,HX,cold , p cathode,HX,heat , T cathode,HX,cold,out , T cathode,HX,hot,out are output.The calculation of the cathode turbine parameters T cathode,turbine, p cathode,turbine, P cathode,turbine are followed.The outlet temperature of the cold fluid of the exhaust of the heat exchanger Fig. 4. Comparisons of sizes of the liquid hydrogen tank and size of the liquid oxygen tank, and the hydrocarbon tank when the energy 142 MJ is needed to store.

Table 7
Efficiency of the models for the balance of plants .

Components Values
Pump (η pump ) 0.7 [37] Blower (η blower ) 0.72 [36] Turbine (η turbine ) 0.82 [34] Burner (η burner ) 0.98 [33] Generator (η generator ) 0.98 [35] Heat exchanger (ε) 0.98 [35] Table 8 Boundary conditions used for the SOFC models and experiments.T specific,HX,cathode,cold,out are guessed repeatedly until the inlet temperature of the cathode of the SOFCs T SOFC,cathode is close to the specified temperature T specified,SOFC,cathode (temperature boundary conditions for the cathode of the SOFCs) where the relative tolerance is 10 -3 .(C) Under the designed conditions, the parameters of the SOFCs p SOFC,out , T SOFC,out, m SOFC,out n ,SOFC,out, i V , n ,sofc,out,i η SOFC are calculated.If the difference between the specified SOFC output temperature T specified,SOFC,out, and the calculated temperature T SOFC,out is larger than the relative tolerance (1 0 − 3 ), the last iteration needs to be recalculated by adjusting the current density i automatically by the procedure.Under the off-designed conditions, the current density are input and not iterated.(D) The calculation of the exhaust turbine p turbine,ex , T turbine,ex , m turbine,ex are in progress.Coolers, liquid separators, dry ice storage towers, exhaust heat exchangers, and oxygen recirculation pumps can be calculated.The efficiency of the SOFCs η SOFC and the hybrid engine η hybrid (in Table 6) are used to evaluate the performance of the hybrid engine.

Results and discussions
The performance of hydrocarbon reforming with pure oxygen and SOFCs is investigated, which shows the sensitivity of the reforming performance to the oxygen carbon ratio R oc and steam carbon ratio R sc , and the power density advantage of the SOFC fed by hydrocarbon fuel and pure oxygen.During the design stage, the number of the SOFC units changes by adjusting R oc and R sc , which is proportional to the designed power of the SOFC.During the off-design stage, the number of the SOFC is constant, which is determined by the former stage.SOFC units are aligned series, and the overall power of the SOFC is the power sum of the units.Moreover, we make assumptions that the adiabatic efficiency of turbines or compressors is unchanged as mass flow or pressure ratios change during the operation process.Thermodynamic evaluations of the closed hybrid engine with different operating conditions are conducted.The efficiency and carbon dioxide emission of the hybrid engine is compared with other reported engines based on the fuel cells.

Reforming fed by pure oxygen and steam
The sensitivity of the steam-carbon ratio, oxygen-carbon ratio, and reforming temperature to the reforming performance is investigated.The operating conditions are listed in Table 9. Univariate sensitivity analysis for these parameters is executed where the steam-carbon ratio, oxygen-carbon ratio, and reforming temperature respectively change within the range 0.2-1.6,0.3-0.8, and 923 K − 1223 K.The effects of these operating parameters on the hydrogen yield and energy efficiency are shown in Fig. 7 and Fig. 8.By comparing the results shown in the figures, and we can see that the oxygen-carbon ratio R oc has a more significant influence on the performance of the reforming, than the steam-carbon ratio R sc .The effects of R sc on the reforming performance are more sensitive to the reforming temperature than that of R oc .The above information will play a significant role in Section 4.3.
As can be seen in Fig. 7, the hydrogen efficiency and energy efficiency exhibit a nearly linear decrease with the increase of R oc .When R oc increased by 0.1, the hydrogen yield decreased by 0.1, and the energy efficiency decreased by 0.12.
According to the Gibbs energy minimization principle, the molecules with low Gibbs free energy have a high molar fraction.The carbon monoxide is converted into carbon dioxide with an increase of R oc .The hydrogen is oxidized and converted into water.During the process of energy conversation, the overall Gibbs energy reaches a minimum.The decrease in energy efficiency of the hydrocarbon reforming indicates that the chemical energy of the fuel is converted into heat energy.The effects of reforming temperature on the energy efficiency are minor until the oxygen-carbon ratio R oc is lower than 0.4 and the reforming temperature is lower than 1023 K.Under the specified reforming conditions, the methane is not entirely consumed, indicating that the overall Gibbs energy is influenced by the Gibbs energy of methane.When the reforming temperature is higher than 1023 K, only the water gas shift reaction occurs.There are nearly no changes in the energy efficiency and hydrogen yield because the Gibbs free energy change is lower than 5 %.
The hydrogen efficiency and energy efficiency exhibit a strong nonlinearity decrease with the change of R oc .With the increase of R sc of 0.1, the maximum decrease of the hydrogen yield is approximately 0.05, and the maximum energy efficiency change is about 0.015 in Fig. 8.
Particularly, it can be seen from Fig. 8 (a) that the rate of increase of the hydrogen yield with the increase of R sc decreased significantly at the reforming temperature of 923 K.With the increase of R sc , more steam is converted into hydrogen according to the chemical equilibrium, resulting in the increase of the hydrogen yield.When the reforming temperature is higher than 1123 K, the change of Gibbs energy is lower than 5 % with the temperature increases, and there are nearly no changes in the hydrogen yield.With the increase of reforming temperature, carbon dioxide and steam are converted into carbon monoxide and hydrogen.When the reforming temperature is lower than 1023 K, the energy efficiency increases with the increase of R sc .When the reforming temperature is higher than 1023 K, the energy efficiency decreases with the increase of R sc .This is because the water gas shift reaction changes from endothermic to exothermic.At the reforming temperature of 1023 K, the energy efficiency first increases until R sc = 0.4, and then it decreases with the further increase of R sc .
In Section 4.2, the SOFC is integrated with a reformer fed by pure oxygen, and its inputting parameters are acquired by maximizing the hydrogen yield with the 1 % limitation of the maximum molar fraction of methane.A genetic algorithm is used.In Section 4.3, the SOFC is integrated with the turbines.The hydrogen yield is set to be higher than 0.5.Correspondingly, the R oc changes from 0.32 to 0.44, and the R sc changes from 0.35 to 2.4.

SOFC unit integrated with reforming
The single SOFC unit integrated with reformers fed by oxygen and hydrocarbon fuel is simulated under the operating conditions in Table 10.Its performance is compared with that of the SOFC unit integrated with a reformer fed by air.The oxygen-carbon ratio R oc and steam-carbon ratio R sc for the air or oxygen reformer is optimized by the genetic algorithm to maximize the hydrogen yield.The maximum power density of the SOFC integrated with a reformer fed by pure oxygen and hydrocarbon fuel can improve by 13 % in Fig. 9, compared with the SOFC integrated with the reformer fed by air and hydrocarbon fuel under the same operating temperature and pressure.
OCV, operating voltage, and power density of the SOFC integrated with a reformer fed by pure oxygen are respectively higher than those integrated with a reformer fed by air in Fig. 9.The reason is that the hydrogen concentration in the reformer fed by air is low according to the Table 10.Therefore, the anode concentration polarization is high.The oxygen concentration in the cathode side of the SOFC is low and is neglected in general.With decreasing operating voltage, the power density increases.At the current density of 11450 A/m 2 , the maximum power density of the SOFC integrated with a reformer fed by oxygen is 8512 W/m 2 .At the current density of 10408 A/m 2 , the value of the SOFC integrated with the reformer fed by air is 7353 W/m 2 .At the atmosphere conditions, the difference in the maximum power density between the SOFC integrated with a reformer fed by air and oxygen is 1159 W/m 2 .The weight of the SOFC of the hybrid engine can decrease by 13 % compared with that of the hybrid engine integrated with a reformer fed by air.

Performance of the closed hybrid engines
In this section, the effects of the oxygen/steam-carbon ratios R oc /R sc on the closed hybrid engine are analyzed.The costing time ratios of container ships in the transit mode, port or anchorage model, and the Maneuvering in/out of the port reported by Wu et al. [24] are 64.6 %, 28.2 %, and 7.16 %, respectively.The performance of the hybrid engine under the designed and off-designed conditions is analyzed respectively to meet the power requirements of the ship at the cruising and port berthing stage.Moreover, the performance of the close hybrid engine is compared with that of previously proposed engines based on fuel cells.

Effects of oxygen/steam-carbon ratios on the closed hybrid engine
The performance of the closed hybrid engine is affected by the power of SOFCs and turbines P turbine pumps P pump , and blower P blower .The changing trend of the power of these components is nonlinear with the change of R oc /R sc ., the effects of the ratios R oc /R sc on the hybrid engine are analyzed to determine the thermodynamic parameters of the closed hybrid engine, and the inputting parameters are in Table 11.With the increase of R oc , the power ratio of the SOFCs and turbines decreases from 1.6 to 0.84.The engine efficiency is increased from 0.66 to a maximum of 0.68, and then it is decreased to 0.65.With the increase of R sc , the power ratio is increased from 1.0 to 1.1.The engine efficiency increases from 0.61 to 0.67, and then it decreases to 0.64.The optimized power ratio is 1.02-1.13,and the engine efficiency can be up to 67 % ~ 68 %.
The molar flow rate sum of the hydrogen and carbon monoxide decreases with the increase of R oc .More reactant is oxidized, and the temperature of the reformer outlet is increased.To decrease it, the pressure ratio of the fuel turbine π turbine,f is increased in Fig. 10 (c), which leads to an increase in the fuel turbine power P turbine,f .Owing to the increase of the mass flow and pressure ratio π turbine,f , the power produced by the exhaust turbine P turbine,ex and the oxygen turbine P turbine,o are both increased in Fig. 10 (c).On the other hand, the consumed power by the oxygen pump P pump,o and water pump P pump are also increased because of the rise of the pressure ratio π turbine,f (the synchronous change of the pressure ratios of turbines π turbine and pumps π pump are shown in section 3), but the sum of consumed power P consume is lower than 50 kW when the pressure ratio π turbine,f is lower than 5.
Owing to the decrease in the hydrogen concentration, the open circuit voltage V OCP , operating voltage V, and molar flow rate of hydrogen and Fig. 7. (A) hydrogen yield and (b) energy efficiency vary with the increase of the oxygen-carbon ratio R oc from 0.3 to 0.8 and the reforming temperature from 923 K to 1223 K at the steam carbon ratio of 1. Fig. 8. Hydrogen yield (a), and energy efficiency (b) vary with the increase of the steam-carbon ratio R sc from 0.2 to 1.6 and the reforming temperature from 923 K to 1223 K at the oxygen carbon ratio of 0.3.

Table 10
Operating conditions for the SOFC units.carbon monoxide are all reduced in Fig. 10 (c).The power produced by the SOFC P SOFC is decreased.The increased power is over than the consumed power P consume when R oc is lower than 0.37.So, the efficiency of the hybrid engine η hybrid is increased.
Water is the liquid state, and the water pump only consumes low energy P pump,w .The molar flow ratio of the oxygen and the fuel in the closed hybrid engine R eoc (the ratio is different from the ratio of oxygen carbon of the reformer R oc ) is high to decrease the temperature rise in the SOFC electrode, which causes the power of the oxygen pumps P pump, p to be high if the oxygen-carbon ratio R oc is huge.Moreover, there is exergy loss in the pumps and turbines.As the pressure ratio π turbine,f and mass flow are increased, the loss is increased.When R oc is 0.45, the consumed power is P consume over 130 kW.The energy recycling by the cathode heat exchanger is limited by the cathode mixer.If the inlet temperature of the oxygen turbine is high up to 1023 K, the outlet temperature of the cathode mixer will be higher than that of the specified inlet temperature of the SOFC cathode T specified,SOFC,cathode , particularly when the mass flow of the oxygen from the tank is low.The engine efficiency η hybrid decreases when the oxygen-carbon ratio R oc is over 0.37.Moreover, owing to the increase of energy loss caused by the nonadiabatic process of turbines P turbine and pumps P pumps , the engine efficiency η hybrid is rapidly decreased.
The molar flow rate sum of the hydrogen and carbon monoxide is increased with the increase of R sc .More carbon monoxide is converted into hydrogen by the water gas shifting reaction.The outlet temperature of the reformer is decreased in Fig. 11 (c).The pressure ratio of the fuel turbine π turbine,f is decreased to keep the anode inlet temperature unchanging, which also leads to a decrease of the power consumed by the oxygen pump π pump,o in Fig. 11 (b), the power of the oxygen turbines P turbine,o and fuel turbines P turbine,f are both decreased owing to the Fig. 9.I − V curve, OCV, and power density of the SOFC integrated with the reformer fed by air and pure oxygen with increasing current density.decreases of the pressure ratios π turbine,f .Although the pressure ratios of the turbine π turbine,f is decreased, the mass flow of the exhaust through the turbines is increased.The power of the exhaust turbine is increased.
The OCV V OCV and operating voltage V both decrease in Fig. 11 (d) because the molar concentration sum of the hydrogen and carbon monoxide decreases.Owing to the increase of the overall molar flow rate of the reforming gas, the SOFC power P SOFC is changed slightly in Fig. 11 (a).Engine efficiency η hybrid is increased when R sc is lower than 1.35.
When R sc is over 1.35, the power consumed by the oxygen pump P pump decreases with the increase of R sc .However, the turbine produces little power P turbine .The engine efficiency η hybrid is decreased.
There is no positive correlation between engine efficiency η hybrid and SOFC efficiency η SOFC .The turbines can recycle some energy that is not utilized by the SOFC.Moreover, the engine efficiency η hybrid is more sensitive to the oxygen-carbon ratio R oc rather than the steam-carbon ratio R sc because the hydrogen yield Y H2 is more sensitive to the oxygen-carbon ratio R oc in Section 4.1.As the oxygen-carbon ratio R oc or steam-carbon ratio R sc changes, the maximum efficiency η hybrid area (0.67-0.68) will be achieved in Fig. 12.In the area, the difference between the amount of hydrogen and carbon monoxide is lower than 1 %, the pressure ratios of the fuel turbine π turbine,f .are lower than 2 %.The power ratio of the SOFC and the turbines is 1.02-1.13.The maximum efficiency of the hybrid engine η hybrid is 0.68 with R sc and R oc, respectively 1.1 and 0.39 with the maximum limitation of combustion temperature of 1600 K, which is determined by the interior-point algorithm.

Performance of the closed hybrid engine under the designed conditions
Liu et al. [40] pointed out that the reforming parameters have a significant impact on the performance of the SOFC engine.Compared with the reformer fed by air in the literature [40], the molar concentration sum of the carbon monoxide and hydrogen can improve by 50 % under the same operating conditions.The reforming temperature is decreased by the fuel turbine, and the outlet temperature is 1023 K.The power ratio of SOFC and turbines is 1.09 in Fig. 13 according to the inputting parameters under the designed conditions in Table 12, and 47 % of power is output by the exhaust turbine P turbine,ex .The power ratio of the turbines to the total power is 0.47.In general, the ratio is 0.2 ~ 0.25 for the SOFC hybrid system integrated with a reformer fed by air [41].This is mainly caused by the huge pressure and temperature ratios in the exhaust turbines of closed hybrid engines.The turbine's power P turbine is increased with increasing the ratios.For the SOFC gas turbine hybrid system integrated with the reformer fed by steam, the temperature ratio is about 4. For the closed hybrid engine, the ratio is 7.2.All the pumps, blowers, and compressors consumed 4.4 % power, and the engine efficiency was 67 %.

Performance of the closed hybrid engine under the off-designed conditions
The cost-effectiveness of the power engine under the off-designed conditions is important to save fuel.The operating conditions under the conditions are shown in Table 13.The parameters that can be  Z.Ji and X.-Y.Miao adjusted are the mass flow of the fuel and current density.Fig. 14 and Fig. 15 show the performance of the close hybrid engines.With the increase of the mass flow of fuel or the current density, the power of the hybrid engine P hybrid can be changed from 20 % to 160 % of the designed power.
With the increase in the mass flow of the fuel, the molar flow rate sum of the hydrogen and carbon monoxide for every SOFC unit is increased.The OCV V OCV , and operating voltage V are both increased because of the reduction of fuel utilization in Fig. 14.Because the exergy efficiency of the SOFC is higher than that of the turbines [42], the efficiency of the close hybrid engine is decreased with the decrease of fuel utilization.In Fig. 15 the OCV V OCV , and operating voltage V are both decreased with the increase of the current density i.However, the fuel utilization of every SOFC unit is increased, and its increasing degree is greater than the decreasing degree of operating voltage.The fuel utilization average increases by 0.1 when the current density i is increased by 1000 A/m 2 .The operating voltage V just is average decreased by 0.025, which leads to an increase in SOFC efficiency η SOFC .The efficiency of the hybrid engine η hybrid is increased with the increase of the SOFC power P SOFC .If the criterion of power and efficiency are both acquired, it is better to adjust the current density instead of the mass flow of fuel.The power and efficiency of the hybrid engine can be both improved significantly, The detailed models and analysis can provide support for the performance comparisons and emissions.The efficiency of the closed hybrid engine is up to 67 %, which is higher than the engines based on the fuel cells for the ship in Table 14.The fuel, oxygen, and exhaust turbines play essential roles in achieving high efficiency.Moreover, there is no emission in the closed hybrid engine even though the fuel is hydrocarbon rather than pure hydrogen.

Conclusions
A scheme of compact closed solid oxide fuel cell hybrid engines for power and propulsion on ships is proposed.The engine can be operated at an effective equivalence ratio of 1.The product of the hybrid engine is dry ice and water.The zero-emission hybrid engine is analyzed, and the main conclusions can be obtained as follows: (1) The maximum power density of the SOFC can be improved by 13 % compared with that fed by air and hydrocarbon fuel.The power ratios of turbines and SOFC are affected by the oxygen and steam carbon ratio, as well as the excess oxygen coefficient.(2) The performance of the reformer is more sensitive to the oxygencarbon ratio rather than the steam-carbon ratio.When the oxygen-carbon ratio is increased by 0.1, the hydrogen yield is decreased by 0.1.When the steam carbon ratio is increased by 0.1, the maximum decrease in the hydrogen yield is approximately 0.05, which leads to a significant change of the power ratio of the hybrid engine.With the increase of the oxygen-carbon ratio, the power ratio of the SOFCs and turbines is decreased from 1.6 to 0.84.The engine efficiency is increased from 0.66 to a maximum of 0.68, and then it is decreased to 0.65.With the increase of the steam-carbon ratio, the power ratio is increased from 1.0 to 1.1.The engine efficiency is increased from 0.61 to 0.67, and then it is decreased to 0.64.This leads to the engine efficiency being more sensitive to the oxygen-carbon ratio rather than the steam-carbon ratio.The optimized power ratio is 1.02--1.13,and the engine efficiency can be up to 67 % ~ 68 %. (3) For a 1 MW hybrid engine, the mass flow of fuel is 0.1673 kg/s, the hybrid engine can achieve high efficiency of 67 % at the oxygen carbon ratio of 0.39 and the water-carbon ratio of 1.1.Under the off-design conditions, with the change of the mass flow of fuel or the current density, the power of the hybrid engine can be adjusted from 20 % to 160 % of the designed power.The ship

Table 12
Inputting parameters for the hybrid engine under the designed conditions.

Table 13
Inputting parameters for the hybrid engine under the off-designed conditions.

Operating conditions Values
Molar flow of the fuel 0.027 kg/s ~ 0.041 kg/s Steam-carbon ratio 1 Oxygen-carbon ratio 0.48 Current density 2,000 ~ 8,000 A/m 2 Operating pressure of the SOFC 1 bar SOFC number 3.9 × 10 ^4 Z. Ji and X.-Y.Miao powered by the hybrid engine has a small specific fuel consumption at the cruising stage and the port berthing stage.The scheme contributes to the objectives of an absolute emissions reduction of 50 % by 2050 compared with the 2008 level.

Informed consent Statement
Not applicable.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Fig. 1 .
Fig. 1.(a) Schematic diagram of the closed solid oxide fuel cell hybrid engines, (b) simplified schematic diagram of the closed hybrid engines.

Fig. 2 .
Fig. 2. Comparisons of I − V curves calculated by the lumped parameter model and the 2D model with (a) hydrocarbon fuel and (b) pure hydrogen fuel.

Fig. 10 .
Fig.10.Effects of the oxygen-carbon ratio R oc on the close hybrid engine (a) the power produced by the SOFC P SOFC and turbines P turbine , (b) the power consumed by the pumps P pump and blowers P blower , (c) SOFC voltage V and efficiency η SOFC , and (d) the pressure ratio of the fuel turbine π turbine,f and reforming temperature.

Z.
Ji and X.-Y.Miao

Fig. 11 .
Fig. 11.Effects of the steam-carbon ratio R sc on the closed hybrid engine (a) the power produced by the SOFC P SOFC and turbines P turbine , (b) the power consumed by the pumps P pump and blowers P blower , (c) SOFC voltage V and efficiency η SOFC , and (d) the pressure ratio of the fuel turbine π turbine,f and reforming temperature.

Fig. 12 .
Fig. 12. Efficiency of the hybrid engine with the change of oxygen-carbon ratio R oc and steam-carbon ratio R sc .

Fig. 13 .
Fig. 13.Performance of the close hybrid engine under the designed conditions.

Fig. 14 .
Fig. 14.Off-designed performance of the hybrid engine (a) engine efficiency and voltage, (b) efficiency and fuel utilization of the SOFC as changes the mass flow of the fuel.

Fig. 15 .
Fig. 15.Off-designed performance of the hybrid engine (a) engine efficiency and voltage, (b) efficiency and fuel utilization of the SOFC as changes current density.

Table 1
Short review of the fuel cell power system for ships.

Table 5
Definitions of the parameters of the balance of plants.

Table 6
Definitions of the closed hybrid engine.

Table 9
Inputting conditions for the hydrocarbon reforming integrated with pure oxygen.

Table 11
Inputting parameters for the hybrid engine.

Table 14
Comparison of the SOFC power engine for a ship.