Energy efficiency analysis of marine high-powered medium-speed diesel engine base on energy balance and exergy

Energy 176 (2019) 991e1006

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Energy efficiency analysis of marine high-powered medium-speed diesel engine base on energy balance and exergy Zhi-Min Yao a, b, *, Zuo-Qin Qian a, Rong Li b, Eric Hu c a

Key Laboratory of Marine Power Engineering and Technology, School of Energy and Power Engineering, Wuhan University of Technology, Wuhan, 430063, China b Faculty of Engineering and Information Technologies, University of Sydney, Sydney, 2006, Australia c School of Mechanical Engineering, The University of Adelaide, Adelaide, SA, 5005, Australia

a r t i c l e i n f o

a b s t r a c t

Article history: Received 10 September 2018 Received in revised form 15 March 2019 Accepted 6 April 2019 Available online 11 April 2019

High-powered, medium-speed diesel engines are widely used in merchant ships. Improving energy efficiency by using energy rationally is critical to reducing both environmental pollution and transport charges. In this paper, the energy efficiency of marine high-powered, medium-speed diesel engine is investigated. A new thermal cycle model of the marine engine is developed using AVL-Boost software. The thermodynamic data of the engine thermal cycle are obtained from the AVL-Boost software. The energy efficiency of the marine diesel engine is evaluated using both energy balance and exergy analysis. From the energy balance analysis, about 25% of the total energy is lost through exhaust heat. This forms the largest energy loss. However, using exergy analysis the largest energy loss originates from the irreversible exergy loss produced during the combustion process. This represents about 36% of the total energy loss. To explore ways to reduce energy loss and improve the energy efficiency, the effects of critical combustion parameters in the thermal cycle (combustion quality index, combustion starting angle and combustion duration angle) on energy distributions are discussed. The decrease in the combustion quality index, combustion starting angle and combustion duration angle (within a reasonable range) all contribute to reduce the total energy loss, increasing the indicated work and improving energy efficiency. © 2019 Elsevier Ltd. All rights reserved.

Keywords: Marine diesel engine Energy efficiency Energy balance Exergy analysis

1. Introduction Diesel engines are widely used in transportation as the primary items of equipment for generating power. They are reliable and have a wide power and speed range. Over the coming decades, they will continue to occupy a dominant position in mobile power generation [1,2]. Improving energy efficiency is an ongoing goal of diesel engine engineering, primarily due to the attention directed towards exhaust emissions [3,4]. Energy efficiency analysis can clarify the law of energy conversion, distribution and use, identify the unreasonable and wasteful use of energy, and provide a reference for the rational use of energy [5,6]. The shipping industry is the major mode of transport for the

* Corresponding author. Key Laboratory of Marine Power Engineering and Technology, School of Energy and Power Engineering, Wuhan University of Technology, 1178 Hepin Road, Wuhan, Hubei, 430063, China. E-mail address: [email protected] (Z.-M. Yao). https://doi.org/10.1016/j.energy.2019.04.027 0360-5442/© 2019 Elsevier Ltd. All rights reserved.

world trade [1]. High-powered, medium-speed diesel engines have been widely used as main engines and diesel generators [1,4]. More than 90% of merchant ships use diesel engines as their main engines and almost all generators are diesel driven [7]. Although powerful, the marine diesel engine has large fuel consumption e.g. a marine engine with a power output of 10,000 kW consumes approximately 5000 g/kWh of fuel. Fuel costs account for 30e55% of the total vessel operational cost [8,9]. Furthermore, the power output generated from the engine accounts for only 30e45% of the total fuel energy with the remainder being discharged as waste heat. Recently, depressed shipping markets caused by global economic risks have forced shipping companies to focus on cost savings, resulting in an increased need to reduce energy consumption [10]. Considerable research into the energy efficiency of diesel engines already exists [11,12]. Taymaz et al. [13,14] employed a thermal balance method to analyze the energy efficiency of diesel engine. They evaluated the heat losses at different engine loads and speeds in diesel engines with the effect of ceramic coating and

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reported a reduction in heat loss to the coolant between 5 and 25%. Models of engine thermal balance and engine body heat transfer were introduced by Yu et al. [15] to evaluate the engine heat dissipation and to determine the engine coolant requirements. They used a lumped parameter model and their stable-state analysis results showed that the combustion heat distribution in subsystems can be the basis of improved engine design. Using energy balance analyses, Yuksel et al. investigated the effects on the heat distribution and performance of a four-stroke engine by adding constant quantity hydrogen to the gasoline-air mixture [16]. Their results showed a significant reduction in heat loss to the cooling water and unaccounted losses by about 36% and 30% (respectively) of the average values could be achieved by using hydrogen supplementation. Simultaneously, heat loss through the exhaust gases was nearly the same as that of gasoline. The exergy analysis method has also been used in assessing the energy efficiency analysis of the internal combustion engine [17e19]. Caliskan et al. [20] reviewed exergetic efficiency analysis and assessed various types of engines. Their results show that exergetic efficiency is best achieved using four-stroke, four-cylinder, turbocharged diesel engines at about 30% excepting to stationary diesel engine. Exergetic efficiency can be higher at lower speeds: between 1140 rpm/min and 2200 rpm/min. Azoumah et al. [21,22] calculated the exergy efficiency and engine performance of a direct injection compression ignition engine using a variety of biofuels. Their results proposed a tradeoff zone of engine load (based on the second law of thermodynamics) that could accommodate environmental concerns and engine efficiency. This tradeoff zone lay between 60% and 70% of the maximum engine load (6 kW in this case). Muammer et al. [23] conducted the exergy analyses of a diesel engine, analyzing the effect of pre-injection timing on engine performance. Yamegueu et al. [21,24] used exergy analysis combined with gas emissions analysis to optimize the performance of a compression ignition (CI) engine using biofuels. They showed that this combination of exergy and gas emissions analyses is a very effective tool for evaluating the optimal loads that can be supplied by CI engines. In summary, thermal energy is supplied to the internal combustion engine by the combustion reaction of the fuel and transformed into work, heat in exhaust and heat in cooling water. There are two main methods to analyze and evaluate the energy efficiency of the diesel engine; thermal balance (energy balance) and exergy analysis [25,26]. The energy balance analyses of internal combustion engines can determine the heat distribution and provide theoretical guidance and reference data for quantifying the reduction in heat loss. Energy balance analysis deals with energy conservation whereas the exergy analysis focuses on the availability of energy, which determines the ability of a system to do work in a specific environment [27,28]. Exergy can be destroyed by irreversible processes during combustion, heat transfer, friction and mixing in the thermodynamic cycles of internal combustion engines. This is in contrast to energy, which is neither created nor destroyed. Identifying sources of exergy destruction and reducing the exergy loss in an internal combustion engine is also crucial to enhance the engine efficiency [25,28]. Therefore, it is necessary to analyze the energy efficiency of internal combustion engines by comprehensively using both the energy balance and the exergy analysis. However, in the past, researchers have evaluated the energy efficiency of internal combustion engines only using either energy balance analysis or exergy analysis. There is limited research that combines both energy balance and exergy analysis to assess the energy efficiency of the diesel engine [29,30]. In addition, compared with the internal combustion engines used in other fields (such as cars, trucks, engineering vehicles and trains), the

marine diesel engines have high manufacturing cost, large size (some are more than ten meters high), high power requirements, a range of auxiliary equipment and complex operations. Concomitantly, the experiment conditions required by the marine engines are much higher than in other fields. Energy consumption and other costs in the experimental process are also quite high [8,10]. A number of factors combine to make the experimental study of highpowered medium-speed marine diesel engine difficult; they require high manpower, large material resources and considerable technical support. Therefore, to date there are few studies and references on the energy efficiency of marine high-powered medium-speed diesel engine. The establishment of thermodynamic cycle model, energy balance analysis and exergy analysis are necessary to improve the energy efficiency of marine diesel engine. In this paper, the energy efficiency of high-powered, mediumspeed marine diesel engine is investigated using a new approach combining both energy balance and exergy analyses. The software AVL-Boost is employed to analyze the thermal cycle of the diesel engine and the simulation results are validated by comparing output with experimental results. Combined with results from the thermal cycle model of the diesel engine, the energy efficiency of the marine diesel engine is analyzed using both energy balance and exergy. The amount of heat energy and exergy in the processes of conversion, transmission, utilization and losses are identified and quantified, and the largest losses of heat energy and exergy are found. To explore ways to reduce energy loss and improve the energy efficiency, the effects of critical combustion parameters in the thermal cycle (i.e. combustion quality index, combustion starting angle and combustion duration angle) on energy distributions are discussed. The results provide theoretical guidance and reference data for improving the energy efficiency and decreasing energy consumption of diesel engine from the point of both “energy quantity” view and “energy quality” view. Moreover, this study also provides a theoretical foundation for studying the energy efficiency of diesel engine by both energy balance and exergy analysis method. 2. Models An inline eight-cylinder, four-stroke, intercooled exhaust turbocharged high-powered, medium-speed marine diesel engine is used to demonstrate the process proposed. Specific parameters of the diesel engine are given in Table 1. The diesel engine thermodynamic system includes: (a) compressor, (b) intercooler, (c) intake pipe, (d) cylinder, (e) exhaust pipe and (f) turbine (Fig. 1). 2.1. The model of the diesel engine 2.1.1. Equation of thermodynamic process The thermodynamic cycle process of the diesel engine is complex. The mathematical development and analysis for the incylinder thermodynamic cycle of the diesel engine require a number of assumptions and simplifications [30,31]. The state of each part in cylinder is assumed to remain the same; the differences of thermodynamic parameters at various points in the

Table 1 Parameters of the diesel engine. Number of cylinders Number of strokes Rated power Rated speed Crank radius Cylinder bore

8 4 1520 kW 900 rpm 155 mm 210 mm

Piston displacement Compression rate Connecting rod length Firing order Maximum cylinder pressure Fuel consumption

310 mm 15.5 693 mm 1-2-4-6-8-7-5-3 200bar 186 g/kWh±5%

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Fig. 1. The diesel engine thermodynamic system.

cylinder including pressure, temperature and concentration of substances are ignored. During the intake process, the fresh air and the residual exhaust gas in the cylinder are assumed to be instantaneously and uniformly mixed. The working substance in the cylinder is considered to be an ideal gas, in which thermodynamic parameters are only related to the gas temperature and gas composition. The gas leakage loss at the cylinder boundary is ignored. The combustion and exothermic processes are simplified and the in-cylinder working substance is heated according to the existing heat release rules. A schematic for the in-cylinder working process of the diesel engine is shown in Fig. 2. In the mathematical simulation, the cylinder working volume is defined as the control volume. The law of conservation of energy, the law of conservation of mass and the ideal gas law are employed. The model equations of the in-cylinder thermodynamic process are given by Equation (1) [31,32].

  1 dQB dQW dV dms dme dm vu 9 > þ  m þ  p h h þ  u s e
vu d4 > d4 d4 d4 vl > d4 d4 > > m > = vT dm dmB dms dme > > > ¼ þ þ > > d4 d4 d4 d4 > ; dT ¼ d4

pV ¼ mRT

(1) where f is the crank angle; p, V and T are pressure, volume and temperature, respectively, of the in-cylinder gas; Q is the heat exchange between the working volume of the cylinder and the region outside the cylinder; m is the mass of the working substance; u is the specific energy of the working substance; h is the specific enthalpy; R is the gas constant; l is the instantaneous excess air coefficient in the cylinder. Subscripts s and e represent the gas flow into the cylinder through the inlet valves and the gas flow out through exhaust valves, respectively. B is the combustion fuel and w is the heat exchange between the boundary of cylinder and the cooling medium. For consistent calculations, the energy or mass entering the system is defined as positive while the energy or mass leaving the system is defined as negative. 2.1.2. Boundary condition 1) Cylinder working volume [31,33]. The relationship between the cylinder volume and the crank angle is given by Equation (2),

V¼

  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi  Vs 2 1 þ 1  cos f þ 1  1  l2s sin2 f 2 εc  1 ls

(2)

and the change rate of the cylinder volume with the crank angle is shown by Equation (3).

0

1

dV Vs B sin f,cos f C ¼ @sin f þ ls qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiA df 2 1  l2s sin2 f

(3)

For Equations (2) and (3), Vs ¼ p4D2 ,S is the working volume of the cylinder; D is the cylinder diameter; S is the piston stroke; εc is the compression ratio; ls ¼ S=2l is the crank link ratio; l is the connecting rod length. Fig. 2. The working process of diesel engine.

2) Flow equation

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The actual mass flow of the gas flowing through the intake and exhaust valve can be obtained by multiplying the corresponding coefficient with the theoretical mass flow, as shown in Equations (4) and (5) [32,34],

pffiffiffiffiffiffiffiffiffiffi dms;e 1 ¼ ms;e As;e 4s;e p1 r1 6n df

(4)

8 vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > " # > k  >u u 2k p 2k p kþ1 k k1 > pII 2 > II II t > > ;  > > k1 < kþ1 p p p I

fs;e ¼

I

I

> >  k sffiffiffiffiffiffiffiffiffiffiffiffi k   > k1 k1 > 2 2k pII 2 > >  ; > > : kþ1 k þ 1 pI kþ1

(

aw ¼

 



2 kþ1

k k1

c1 cm

#)0:8   VTDC 2 0:2 IMEP 1þ2 V (8)

where D is the diameter of the cylinder; pc is the in-cylinder gas pressure; Tc is the in-cylinder gas temperature; C1 is the velocity coefficient; calculated by C1 ¼ 2:28 þ 0:308,cu =cm, in which cu is the circumferential velocity, cm is the average velocity of the piston; VTDC is the combustion chamber volume; V is the actual cylinder volume; IMEP is the average indicating effective pressure. In the ventilation process, the heat transfer coefficient is described by Equation (9) [32,37].

(9)

where C3 ¼ 6:18 þ 0:417cu =cm .

3) Heat exchange

5) Characteristics of working substance

The heat exchange between the working mass and the outside occurs through the cylinder wall and is calculated using Equation (6) [35,36]. 3 dQw 1 X ¼ KF ðT  TÞ 6n i¼1 i wi d4

(6)

where i ¼ 1, 2, and 3, which corresponds to the cylinder wall, piston top and cylinder head respectively; K is the heat transfer coefficient which can be determined according to empirical formulas, half empirical formulas and experimental results. Fi is the heat exchange area of each region where the heat transfer area of the cylinder wall varies with the crank angle; Twi is the average temperature of the surface acquired by experiment and empirical formulas.

The combustion process of a diesel engine contains complex physical and chemical reactions, which are extremely difficult to accurately describe. Substitution exothermic regularity is the most widely used method of exothermic regularity in the cylinder of a diesel engine. It essentially adjusts the corresponding parameters in the empirical formula to ensure the modelled results are consistent with experimental results. The widely used Viber substitution exothermic regularity formula is used here and is given by Equation (7) [31,32],

 
ff mþ1 0 m þ 1 f  f0 m  e6:908 fz fz fz

The thermodynamic characteristics of the working substance have a direct effect on the energy transfer and conversion. Characteristics of the in-cylinder gas differ for different thermodynamic processes. In simulating the diesel engine, the working substance gas is assumed to be an ideal gas, and its composition can be expressed by the instantaneous excess air coefficient, the specific internal energy of which can be expressed as Equation (10) [31,37].

u ¼ uðT; lÞ

(10)

The Justi specific internal energy formula is shown in Equation (11).

   0:0485 u ¼ 0:14455  0:0975 þ 0:75 ðT  273Þ3  106

l

    3:36 46:4 þ 7:768 þ 0:8 ðT  273Þ2  104 þ 489:6 þ 0:93

l

4) Exothermic regularity

¼ Hu gb hu 6:908

"

0:53 aw ¼ 130D0:2 p0:8 ðC3 cm Þ0:8 c Tc

, the flow is in the supercritical flow state.

dQB dx ¼ Hu gb hu df df

0:53 130D0:2 p0:8 c Tc

(5)

where m is the flow coefficient; A is the geometric flow crosssectional area; I and II are import and export parameters respectively; f is flow function, when the pressure difference is small,  k k1 pII 2 , the flow is in the subcritical flow state; when pI > kþ1 pII pI

the combustion exothermic regularity of the diesel engine can be accurately determined. For the in-cylinder combustion process, heat transfer in the gas occurs simultaneously with combustion and heat release. The Woschni 1990 in-cylinder heat transfer model provides the most accurate prediction for the engine load, and is selected in this investigation. The formula is given by Equation (8) [32,37].

(7)

where m is the quality index of the fuel which is also known as the shape coefficient with different values of m governing the shape of the exothermic curve; fz is the combustion duration angle; f0 is the combustion starting angle. By adjusting these three parameters,

2

ðT  273Þ  10

 þ 1358:6

l

(11)

2.1.3. Analysis of in-cylinder thermodynamic process Utilization and transfer of energy of a range of processes can be analyzed using the thermodynamic process differential Equation (1) and boundary conditions, the in-cylinder thermodynamic processes and the changes in the thermodynamic characteristics. The thermodynamic cycle of a diesel engine consists of a compression process, a combustion process, an expansion process, an exhaust process, a valve opening stage, and a suction process. The final three of these processes can be combined to form a ventilation process. These processes are described below. 1) Compression process In the compression process, the inlet and exhaust valves are closed, with no intake and exhaust gases present. As there is no fuel

Z.-M. Yao et al. / Energy 176 (2019) 991e1006

in the cylinder, the gas quality in the cylinder and the physicochemical properties of the gas are constant. This process is represented by Equations (12) and (13) [32,34].

dm dl ¼ 0; ¼0 df df m1 l¼ l0 mBr

dQb ¼0 d4

(20)

(13)

2.1.4. Parameters setting for simulation In this paper, the software AVL Boost [40] is employed to simulate a diesel engine. The settings of the model include parameters for the control component, the turbocharger, the intercooler, the cylinder and the pipes. These are described below. (1) Parameter setting for the control component

In the combustion process, the inlet and exhaust valves are still closed, with no intake and exhaust gases present. The quality change of the in-cylinder working substance occurs when fuel is injected into the cylinder. Assuming that the exothermic law of combustion process follows the Weber substitution exothermic law function, the mass conservation equation at the combustion process can be expressed as [32,38]:

(14)

and l can be calculated using Equation (15),

m1 l0 mB

(19)

In the whole ventilation process, there is no combustion, so that

2) Combustion process

l¼

dms dme dl s0; ¼ 0; s0 d4 d4 d4

(12)

where m1 is the quality of intake air in the inlet process; mBr is the fuel quality converted from the quality of in-cylinder exhaust gas, and its physical meaning can be expressed as the quality of the exhaust gas in the cylinder which is formed by the complete combustion of mBr kilograms of fuel. If there is no exhaust gas recirculation, and the scavenging process is complete, mBr ¼ 0.

dm dmB 1 dQB ¼ ¼ df Hu df df

995

(15)

In the basic parameters setting, the single calculation mode is selected; the engine speed is set as 900 rpm; the lower heating value is 42,700 kJ/kg; the theoretical air-fuel ratio is 14.7; the reference temperature and pressure are 21  C and 1 bar, respectively. The piston firing order is set as1-2-4-6-8-7-5 3, and the ignition time is shown in Table 2. In the model, setting of average mechanical loss pressure shown as Equation (21) is employed [36,40].

pm ¼ D0:1778 ð0:0855Cm þ 0:0789pe  0:214ÞðbarÞ

(21)

where pe is the average effective pressure of the diesel engine; D is the diameter of the cylinder; Cm is the average velocity of the piston. (2) Parameter setting for the turbocharger

3) Expansion process During the expansion process, the quality of the working substance has not been changed and the instantaneous excess air coefficient is constant which equals to the value of l at the end-point of combustion [33,36],

l¼

m1 ¼ const l0 ðmBr þ gb Þ

(16)

4) Ventilation process The ventilation process includes an exhaust process, a scavenge process and a suction process, where the mass of the working substance transfers through the boundary of the system [32,39]. In the exhaust process, there is no change of the gas composition, so that

dms dme dl s0; s0; s0 d4 d4 d4

(17)

In the scavenge process the fresh air entering is mixed with the exiting exhaust gases, such that

dms dme dl ¼ 0; s0; ¼0 d4 d4 d4

(18)

In the suction process, only fresh air enters the cylinder, so that

The model allows for two types of turbocharger modes; full and simplified. Full mode is adopted in those cases where the turbocharger characteristics change over time, such as the starting condition and the variable working condition. Simplified mode is used in the steady operation condition where the booster ratio of the compressor, the efficiency of compressor and turbine, and the flow capacity of the turbine are all assumed constant. The simplified mode includes three calculation modes; a boost pressure calculation mode, a turbine layout calculation mode and a waste gate calculation mode. In this paper, the turbine layout calculation mode is selected [40,41]. The turbine size is calculated by the target supercharging ratio and turbocharger efficiency. The equivalent turbine discharge coefficient is 0.15, the turbo charger overall efficiency is 0.66, the compressor efficiency is 0.7, the mechanical efficiency is 0.98, the compressor pressure ratio is 3.83. (3) Parameter setting for the intercooler An intercooler is a type of heat exchanger that uses water as a coolant. Using the intercooler results in a decrease in the temperature of the intake air and an increase in the air quality of the intake. The outlet temperature is calculated by Equation (22) [40,42],

Table 2 Ignition time for each cylinder. Number of cylinders Ignition interval (deg)

1 0

2 90

3 630

4 180

5 540

6 270

7 450

8 360

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Ts ¼

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T  Two  þ Twi  k Csw ðTk Ts þT wi Two Þ exp dmw dt

(22)

,cpw ðTwo Twi Þ

The water coolant temperature of the intercooler is calculated using Equation (23): dms dt Two ¼ Twi þ dm

w

dt

,cps ,cpw

ðT k Ts Þ

(23)

where Tk is the inlet air temperature, Ts is the outlet air temperature, Twi is the inlet coolant temperature, Two is the outlet coolant s w temperature, dm is the air flow through the intercooler, dm is the dt dt coolant flow through the intercooler. The parameter settings of the intercooler include geometrical parameters and working conditions. In the geometrical parameters, the volume of the intercooler is 90 L, the volume of the intake chamber is 15 L, the volume of the exhaust chamber is 15 L and the length of the cooling core is 400 mm. In the working conditions, the mass flow is 8645 kg/h, target pressure drop is 3  103 MPa, target venting temperature is 45  C, inlet temperature is 200  C, inlet pressure is 3.83 bar and cooling temperature is 38  C.

2.2. The model verification To verify the accuracy of the numerical simulation model, simulation results under different loads are compared with experiment results. The measured indicator diagrams of different loads are provided by the Key Laboratory of Marine Power Engineering & Technology (Wuhan University of Technology), Ministry of Transport. The indicator diagram is the direct description of the in-cylinder working process of the diesel engine. It shows the in-cylinder pressure variation as a function of the crank angle. Fig. 3 indicate that the simulated results of the in-cylinder pressure are consistent with the experimental results under 100%, 90%, 75% and 50% load. The high correlation between the simulation of the in-cylinder process and experimental results suggests the model well reflects the actual working process of the diesel engine. In addition, the thermodynamic parameters of the diesel engine under different loads are compared for the simulation and the experimental results. From Fig. 4, it is clear that the deviations are small, with the largest deviation of fuel consumption being 3.86%, the largest deviation of output power being 4.21%, the largest deviation of exhaust temperature being 4.3%, the largest deviation of temperature in inlet of the turbocharger being 1.54% and the largest deviation of temperature in the outlet of the turbocharger being 3.11%. To conclude, the analyses of the in-cylinder pressure and thermodynamic parameters indicate that the simulation results are consistent with the experiment results, verifying the accuracy of the simulation model and the reliability of the simulation results.

Fig. 3. Comparison of indicator diagram.

dQin dQE dU dW dQw dQout dQs þ þ þ ¼ þ þ df df df df df df df

(24)

E in where dQ is the energy carried into the system by air intake, dQ is df df

dU is the df dW is the df

the heat release of fuel combustion,

internal energy vari-

ation of the working substance,

output work of the

working substance,

dQw df

is the heat transfer of the working sub-

stance through the cylinder boundary, dQs df

dQout df

is the exhaust energy,

is the remainder heat loss and f is crank angle.

Making the work cycle the object of calculation, the variation of internal energy is zero. Taking 100% load as an example, the heat release of the fuel combustion QE is given by Equation (25).

3. Energy balance analysis and exergy analysis

QE ¼ HL ,ME

3.1. Energy balance analysis

where HL is the low calorific value of fuel, and ME is the amount of fuel injected into the cylinder. The output work of the working substance W is given by

The energy balance of the diesel engine, also called the heat balance, investigates the distribution of heat generated by fuel combustion during the work cycle of the diesel engine [32,36,43]. The in-cylinder energy balance formula of the diesel engine is given by Equation (24).

W ¼ 3600Pe where Pe is the effective power of the diesel engine.

(25)

(26)

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Fig. 4. Comparison of thermodynamic parameters.

In calculating the heat equivalent of the effective work in a working cycle, the following Equation (27) can be used,

W¼

3600Pe t 60ni

(27)

where n is the rotational speed of the diesel engine, i is the number of cylinders, t is 2 for four stroke diesel engines and 1 for two stroke diesel engines. The heat transfer of the working substance through the cylinder wall Qw is given by Equation (6) and shown in Fig. 5. Energy taken away from the system by the exhaust is given by Equation (28).

Qp ¼ ðME þ Min ÞCout Tout  Min Cin Tin

(28)

where Min is the quality of the air intake, Cout is the average specific heat at constant pressure of exhaust gas, Cin is the average specific heat at constant pressure of the intake gas, Tout is the gas temperature in the exhaust pipe and Tin is the air temperature of the intake pipe. From the simulation results, data on the related thermal parameters for the energy balance analysis can be extracted. The relationships between mass flux of intake air and crank angle, temperature of air intake and crank angle, mass flux of exhaust and crank angle and temperature of exhaust and crank angle are shown in Fig. 6. The remainder heat loss energy Qs is given by

Qs ¼ QE  ðW þ Qw þ QP Þ

(29)

Fig. 5. Heat transfer between working substance and cylinder wall.

3.2. Exergy analysis Exergy analysis investigates the thermodynamic cycle process of a diesel engine with respect to energy quality [21,25,36]. The exergy balance equation of the system is defined in Equation (30).

dEin dEQE dEw dEQW dEout dEs dED þ ¼ þ þ þ þ df df df df df df df in where dE is the exergy carried into the cylinder by intake air, df

the exergy of the fuel combustion, dEQW df

dEw df

(30) dEQE df

is

is the exergy of piston work,

is the exergy taken away from the system by heat transfer

through the cylinder wall, system by exhaust,

dEs df

dEout df

is the exergy taken away from the

is the exergy increment of internal energy of

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Fig. 6. Temperature and mass of intake air and exhaust gas.

D in-cylinder working substance, dE is the irreversible exergy loss of df

the system in the actual process. Taking the thermodynamic work cycle as the analysis object, the exergy variation of the working substance is zero. Taking 100% load as an example, the exergy carried into the cylinder by air intake Ein is given by

dEin dm1 ¼ ½h1  h0  T0 ðs1  s0 Þ df df

(31)

where h1 is the instantaneous specific enthalpy of air intake, h0 is the initial specific enthalpy of air intake, T0 is the environment

Fig. 7. Relationships between energy distribution and load.

temperature, s1 is the instantaneous specific entropy of air intake, 1 s0 is the initial specific entropy of air intake, and dm is the change in df

mass of the air intake with the crank angle. The exergy of the fuel combustion EQE is given by Equation (32).

dEQE ¼ HL ð1:0038 þ 0:1365H=C þ 0:0308O=C df dx þ 0:0104S=CÞME df

(32)

where H; C; O; S are the element qualities of hydrogen, carbon, oxygen and sulfur, respectively, in the fuel; and

dx df

is burning rate.

Fig. 8. Relations between Exergy distribution and load.

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The exergy of piston work Ew is given by Equation (33).

dEw dV ¼ ðp  p0 Þ df df

999

  dEQW dQw T ¼ 1 0 df df T

(33)

where p is the instantaneous in-cylinder pressure, p0 is the air

(34)

where T is the in-cylinder temperature. The exergy taken away from the system by exhaust Eout is given by Equation (35).

is the change of volume pressure on the bottom of the piston and dV df

dEout dmE ¼ ½hE  h0  T0 ðsE  s0 Þ df df

with the crank angle. The exergy removed from the system by heat transfer through the cylinder wall EQW is given by Equation (34).

exhaust gas, s0 is the initial entropy of ambient air and

(35)

where hE is the enthalpy of exhaust gas, sE is the specific entropy of

Fig. 9. Variations of thermodynamic parameters with combustion quality index m.

dmE df

is the

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change of exhaust gas mass with the crank angle. The irreversible exergy loss of the system in the actual process ED ¼ EQE  Ew  EQW  ðEout  Ein Þ is given by Equation (36).

ED ¼ EQE  Ew  EQW  ðEout  Ein Þ

(36)

3.3. Results and discussion The energy balance and exergy analysis of the diesel engine under different loads are investigated using simulated results from the thermal cycle process. Results of the energy balance analysis are given in Fig. 7. The figure shows the relationship between heat energy distributions and different loads. The results indicate that the heat of the fuel combustion transfers to the heat of indicated work, heat dissipation through the cylinder wall, heat loss through exhaust, with the remainder being heat loss. The quantity of the heat of indicated work, the heat dissipation through the cylinder wall, heat loss through the exhaust and the remainder heat loss all increase with load. However, changes to the relative proportions are only small. For the working process of the diesel engine, the largest energy loss is through the exhaust. Heat loss increased from 8 kJ to 15.34 kJ as the load increased from 50% to 100% load. This represents a percentage change of up to 26.62% of heat for fuel combustion under 50% load. With increasing load, more fuel is injected into the cylinder for combustion. Then, temperature and pressure of the gas in the cylinder increases, causing the indicated work to increase from 14.42 kJ to 27.88 kJ. Simultaneously, the increase of gas temperature in the cylinder leads to an increase of heat dissipation through the cylinder wall (from 4.74 kJ to 7.5 kJ). This also leads to a rise in exhaust temperature, increasing the heat loss through the exhaust (from 8 kJ to 15.34 kJ). With increasing load, the indicated work in the proportion of the total heat only changes by a small percentage (remaining close to 48%). The percentage of heat loss of heat dissipation through the cylinder wall decreases from 15.77% to 12.75%. The change of exhaust heat loss is not obvious, increasing 2% when the load increases from 75% load to 100% load; meanwhile the remainder heat loss increases from 9.62% to 13.77%. The results of the exergy analysis are summarized in Fig. 8. The figure shows the relationships between exergy distributions and different loads. The results indicate that the exergy of the fuel combustion, the exergy of indicated work, the exergy loss of heat transfer through the cylinder wall, the exergy loss of exhaust and the irreversible exergy loss all increase with load. Based on the exergy analysis, the largest exergy loss is the irreversible exergy loss, which increases from 10.92 kJ to 22.57 kJ, representing up to 37.43% of exergy of the fuel combustion. This due to the exergy loss in the combustion process, which is about 80% of the irreversible exergy. As load increases, more fuel and air are injected into the cylinder, the mixing becomes more vigorous and the temperature difference between the flame and working substance becomes larger. This causes an increase of the exergy loss in the combustion process and the irreversible exergy. With increasing load, more fuel is injected into the cylinder and more exergy is produced by the system. The increased temperature and pressure of the gas in the cylinder will cause the exergy of indicated work to increase from 14.42 kJ to 27.88 kJ. Simultaneously, the exergy of heat dissipation through the cylinder wall increases from 2.72 kJ to 4.42 kJ. The increase in the temperature of the gas in the cylinder also causes a rise in the temperature of the exhaust. This results in increased exergy loss through the exhaust from 2.73 kJ to 5.54 kJ. As the load increases, the change in exergy of indicated work as a proportion of total exergy is small. The percentage of

exergy loss of heat transfer through the cylinder wall decreases from 8.83% to 7.13%. The percentage of the exergy of exhaust increases by a small amount only, and the irreversible exergy loss increases from 35.47% to 37.44%. Based on the energy efficiency analysis, the largest heat energy loss is through the exhaust. This represents about 25% of total heat energy. The largest heat energy loss in the exergy analysis is the irreversible exergy loss which is about 36% of the total energy. This result demonstrates that both thermal balance analysis and exergy analysis are necessary to assess the total energy efficiency of a diesel engine. To improve the energy efficiency of the diesel engine, both the heat loss and irreversible exergy loss need to be examined. The result should be reasonable suggestions and methods of recovering heat energy and optimizing the work process of a diesel engine to reduce irreversible processes. In marine engineering, the heat loss of exhaust can be used by the exhaust boilers to recover the energy in the exhaust gas. Heat from the exhaust gas may also be used as heat source to generate electricity. The energy lost through the cylinder wall is mainly absorbed by cooling water, which is a source of low-grade energy with relatively low temperature. According to the principle of

Fig. 10. Energy distribution with different m.

Fig. 11. Exergy distribution of different m.

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energy level matching, it is ideal to use it as an energy source for heating or in water distillation equipment to recover the energy. The largest exergy loss, the irreversible exergy loss, is mainly produced during the combustion process. To reduce the energy loss, one needs to identify the influencing factors, then target adjustments to the combustion process. Furthermore, this paper investigated ways to reduce the irreversible exergy loss according to exothermic regularity. 4. Effects of combustion parameters on energy efficiency

1001

combustion process affects the largest exergy loss (the irreversible exergy loss). This warrants a closer examination of the combustion process. Viber exothermic is used in the combustion process model. Combustion quality index, m, combustion starting angle, 4b, and combustion duration angle, 4d are the three main combustion parameters used in the Viber exothermic regularity function. The effects on energy efficiency of these three combustion parameters are investigated to reduce energy loss and improve energy efficiency.

Based on the analysis of results presented in section 3.3, the

Fig. 12. Variations of thermodynamic parameters with combustion starting angle 4b.

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4.1. Effects of combustion quality index m Energy balance and exergy distributions are analyzed with the work conditions of speed at 900 rpm/min and 100% load and combustion quality index m values of 1.25, 1.1, 0.95, 0.8 and 0.65. Relationships between the energy efficiency of the diesel engine and combustion quality index are found. Variations of thermodynamic parameters with different values for the combustion quality index, m are shown in Fig. 9. The variations of cylinder pressure, heat transfer through the cylinder wall, intake air mass flow, intake air temperature, exhaust mass flow and exhaust gas temperature with crank angle at different values of the combustion quality index are presented in Fig. 9 (a)-(f). The combustion quality index affects the shape of the indicator diagram. The maximum cylinder pressure increases with a decrease in m. As the value of m becomes smaller, the combustion becomes more intense and the explosion pressure of each cylinder increases gradually. The smaller the value of m, greater heat is released in the initial stage, and the rate of pressure increases in the cylinder. The process is more volatile. As the value of m increases, the rate of pressure rise tends to ease, the diesel engine works more smoothly, and the exothermic curve gradually shifts to the right. The energy distribution for different values of m is shown in Fig. 10, which the exergy distribution for different values of m is shown in Fig. 11. From Fig. 10 it can be observed that heat dissipation increases by a small amount with decreasing values of m while heat loss through the exhaust and the remainder heat loss both reduce. As the value of m decreases, exergy loss of heat dissipation increases, exergy loss of the exhaust and irreversible exergy loss reduce and its proportion decreases from 36.44% to 34.64% (Fig. 11). Figs. 10 and 11 show that heat and exergy of the indicated work increase, which means the energy efficiency increases as the combustion quality index decreases. With decreasing values of m, more heat is released at the early stage of the combustion process, the cylinder pressure rises faster and combustion becomes more violent. This optimizes the process of combustion, and more heat and exergy are converted into the indicated work.

loss reduced (Fig. 13). As the value of the combustion start angle 4b increases, the exergy of indicated work reduces from 27.88 kJ to 26.41 kJ, a percentage reduction from 46.24% to 43.80% (Fig. 14). Heat dissipation through the cylinder wall reduces. The exergy loss through the exhaust increases and the irreversible exergy loss increases from 21.97 kJ to 23.42 kJ, proportionally from 36.44% to 38.85%. Heat and exergy of the indicated work both increase as 4b decreases, increasing the energy efficiency (Figs. 13 and 14). As 4b decreases, the maximum cylinder pressure increases and more energy is produced in the combustion process, resulting in more heat and exergy being converted into the indicated work. 4.3. Effects of combustion duration angle 4d Energy balance and exergy distribution are analyzed with the work conditions of speed at 900 r/min and 100% load for combustion duration angles, 4d of 53 , 58 , 63 , 68 and 73 . The relationship between the energy efficiency of the diesel engine and combustion duration angle is found.

4.2. Effects of combustion starting angle 4b Energy balance and exergy distributions are analyzed using the work conditions of speed at 900r/min and 100% load and combustion starting angles 4b of 718.21, 716.2 , 714.2 , 712.2 and 710.2 . Relationships between energy efficiency and combustion starting angle are found. Variations of thermodynamic parameters with the combustion starting angle are shown in Fig. 12. Variations of cylinder pressure, heat transfer through the cylinder wall, intake air mass flow, intake air temperature, exhaust gas mass flow, and exhaust gas temperature with crank angle at different values of the combustion starting angle are presented in Fig. 12(a)e(f). The results indicate that, as the combustion starting angle increases, the corresponding angle of the detonation pressure advances and the detonation pressure gradually decreases. When the combustion starting angle was adjusted from 710.2 to 718.2 , the in-cylinder detonation pressure decreased by a significant amount, 38.52 bar. It can be seen from Fig. 12(a) that the maximum cylinder pressure increases significantly and the maximum cylinder pressure appears later as a decrease in 4b. Figs. 13 and 14 are the energy distribution and the exergy distribution at different 4b, respectively. As 4b decreases, the indicated work reduces from 27.88 kJ to 26.41 kJ, proportionally from 47.40% to 44.90%, while heat dissipation increased and the heat loss of exhaust and remainder heat

Fig. 13. Energy distribution of different 4b.

Fig. 14. Exergy distribution of different 4b.

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Variations of thermodynamic parameters with the combustion duration angle 4d are presented in Fig. 15. Variations of cylinder pressure, heat transfer through the cylinder wall, intake air mass flow, intake air temperature, exhaust gas mass flow, and exhaust gas temperature with crank angle at different values of combustion duration angle 4d are given in Fig. 15(a)e(f). As the value of 4d decreases, the explosion pressure gradually increases. The energy distribution and exergy distribution at different 4d are shown in Figs. 16 and 17, respectively. As the combustion angle 4d increases, the indicated work decreases from 28.96 kJ to 27.88 kJ, a percentage reduction from 49.23% to 47.40% (Fig. 16). Heat loss by dissipation through the

1003

cylinder increases, and the heat loss through exhaust and remainder heat loss reduce. As the value of the combustion duration angle 4d increases, the exergy of indicated work reduces from 27.88 kJ to 26.41 kJ, a percentage reduction from 48.03% to 46.24% (Fig. 17). The exergy loss of heat dissipation through the cylinder wall is reduced. The exergy loss from gas and fire increases and the irreversible exergy loss increases from 20.44 kJ to 21.97 kJ, proportionally from 33.90% to 36.44%. Heat and exergy of the indicated work increases as the combustion duration angle 4d increases (Figs. 16 and 17), which reduces the energy efficiency. With increasing values of 4d, the

Fig. 15. Variations of thermodynamic parameters with combustion duration angle 4d.

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Fig. 16. Energy distribution of different 4d.

Fig. 17. Exergy distribution of different 4d.

maximum cylinder pressure decreases, and less energy is produced in the combustion process. Less heat and exergy are converted into the indicated work.

5. Conclusions In this paper, the energy efficiency of diesel engine is studied. The new model of the thermodynamic process is established. Both the energy balance analysis and the exergy analysis are applied to comprehensively evaluate the energy efficiency of a marine highpower medium-speed engine. Furthermore, the effects of the combustion parameters on energy efficiency are discussed. Below are the major findings of this research. 1) Heat of indicated work, heat transfer through the cylinder wall, heat loss of exhaust and remainder heat loss all increase with an increase in load. When the load increases, the ratio of the indicated work heat to the total heat of the fuel combustion varies only by a small amount. The proportion of heat dissipation through the cylinder wall reduces, and the proportion of

heat loss of exhaust increases. The exergy of the indicated work, the exergy loss of the heat dissipation through the cylinder wall, the exergy loss of exhaust and the irreversible exergy loss all increase with the load. When the load was increased, the ratio of the exergy of indicated work to the total exergy of the fuel changes little, the proportion of exergy of heat dissipation through the cylinder wall reduces, while the proportion of the exergy loss through the exhaust and the irreversible exergy loss both increase. The main reason is that as the load increases, the quantity of injected fuel and intake air increase, leading to the mixing of fuel and air becoming more intense, and the temperature difference between the flame and the working substances becoming greater. The result is an increase in the proportion of irreversible exergy loss. 2) As the combustion quality index increases, the explosion pressure in the cylinder decreases, power decreases, fuel consumption rate increases; the heat of indicated work reduces, heat loss of heat dissipation reduces, and heat loss of exhaust increases; the exergy of indicated work reduces, exergy loss of heat dissipation decreases, exergy loss through exhaust increases, and irreversible exergy loss increases from 20.89 kJ to 21.97 kJ a percentage increase from 34.64% to 36.44%. 3) As the combustion start angle increases, the explosion pressure in the cylinder decreases, the power decreases, the fuel consumption rate increases; indicated work reduces, heat loss of heat dissipation reduces, heat loss of the exhaust increases; exergy of indicated work decreases, exergy loss of heat dissipation through the cylinder wall decreases, exergy loss of exhaust increases, and irreversible exergy loss increases from 21.97 kJ to 23.42 kJ which proportion increases from 36.44% to 38.85%. 4) As the combustion duration angle increases, the explosion pressure in the cylinder decreases, the power decreases, the fuel consumption rate increases; the heat of indicated work decreases, heat loss of heat dissipation through the cylinder wall decreases and heat loss of exhaust increases; the exergy of indicated work reduces, exergy loss of heat dissipation through cylinder wall decreases, exergy loss of exhaust varies little and irreversible exergy loss increases from 20.44 kJ to 21.97 kJ which proportion rise from 33.90% to 36.44%. Based on the energy balance and exergy analysis results, the heat loss of exhaust is the largest heat energy loss, while it is the second largest energy loss in the exergy analysis. The largest energy loss in the exergy analysis is the irreversible exergy loss. These results show that both thermal balance analysis and exergy analysis are necessary in assessing the energy efficiency of diesel engines. To improve the energy efficiency of the diesel engine, both the heat loss and irreversible exergy loss need to be considered. This involves the recovery of heat energy and optimizing the work process of diesel engine to reduce irreversible process. This may include using the exhaust boilers to recover the heat of exhaust gas, using the heat of exhaust gas as a heat source to generate electricity and using heat loss through the cylinder wall as an energy source for heating or in water distillation equipment to recover the heat energy. Irreversible exergy loss occurs mainly during the combustion process. To reduce the energy loss, one needs to identify out the influencing factors and target adjustment of the combustion process. The investigation in this paper found that the decrease in the combustion quality index, combustion starting angle and combustion duration angle are all beneficial to reducing the exergy loss, increasing the indicated work and improving energy efficiency. The information presented in this study provides a new method to investigate the energy efficiency of diesel engines with comprehensive use of both energy balance analysis and exergy

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analysis. The results provide a theoretical reference and data for the designers and operators of the marine diesel engine.

p0 hE sE

1005

air pressure on the bottom of the piston enthalpy of exhaust gas specific entropy of exhaust gas

Acknowledgment The Project is supported by “the Fundamental Research Funds for the Central Universities (2017IVA025)”, “the Key Laboratory of Marine Power Engineering & Technology (Wuhan University of Technology), Ministry of Transport” and “China Scholarship Council (No. 201706955097)”. Nomenclature 4 p V T Q m u h R

l Vs D S εc

ls

l

m A Ⅰ Ⅱ

f

K Fi 4z 40 m1 mBr pe Tk Ts Twi Two pc Tc C1 cu cm VTDC IMEP pe n i Cout Cin Tout Tin h1 h0 T0 s1 s0

crank angle pressure volume temperature heat mass specific energy specific enthalpy gas constant instantaneous excess air coefficient working volume of the cylinder cylinder diameter piston stroke compression ratio crank link ratio connecting rod length flow coefficient geometric flow cross-sectional area import parameters export parameters flow function heat transfer coefficient heat exchange area of each region combustion duration angle combustion starting angle quality of intake air fuel quality converted from the quality of in-cylinder exhaust gas average effective pressure temperature of inlet air temperature of outlet air temperature of inlet coolant temperature of outlet coolant pressure of in-cylinder gas temperature of in-cylinder gas velocity coefficient circumferential velocity average velocity of piston combustion chamber volume average indicating effective pressure effective power rotational speed of diesel engine Number of cylinders average specific heat at constant pressure of exhaust gas average specific heat at constant pressure of intake gas exhaust gas temperature in the exhaust pipe air temperature of the intake pipe instantaneous specific enthalpy initial specific enthalpy temperature of environment instantaneous specific entropy initial specific entropy

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