Modeling of Thermodynamic Properties of Diesel Fuel and In-Cylinder

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Thermodynamics Properties Modeling of the Diesel Fuel and Incylinder Gas for Diesel Engines to Combustion Investigation Yu Ding, La Xiang, Jincheng Li, Haining Cui, and Yi Zhang Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b02570 • Publication Date (Web): 28 Nov 2018 Downloaded from http://pubs.acs.org on December 1, 2018

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Energy & Fuels

1

Thermodynamics Properties Modeling of the Diesel Fuel and

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In-cylinder Gas for Diesel Engines to Combustion Investigation

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Yu Ding*, La Xiang, Jincheng Li, Haining Cui, Yi Zhang

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College of Power and Energy Engineering, Harbin Engineering University, Harbin, 150001, China *

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Corresponding author: e-mail: [email protected]

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Abstract

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The study of thermodynamics properties of the engine fuels and in-cylinder gas is involved in the

8

analysis of chemical compound reaction and the thermodynamics analysis of fuel and gas, which

9

is quite important in the engine combustion investigation cause the fuel chemical energy

10

converts into work medium internal energy during this stage. Although the researches on the

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thermodynamics properties of fuel and in-cylinder gas have experienced a few decades, with the

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development of new fuel types, how to develop general models with sufficient accuracy to

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calculate the fuels and in-cylinder gas thermodynamics properties for engines remains a

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challenge. This paper presents a model to calculate the diesel fuel and in-cylinder gas

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thermodynamics properties based on the mixture composition theory, considering the diesel fuel

16

and in-cylinder gas mixtures in terms of the chemical reaction fundamentals. The diesel fuel and

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in-cylinder gas thermodynamic properties modeling approach, for the combustion investigation,

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is then applied in the heat release calculation model of a marine diesel engine, which is validated

19

by the experimental research on heat release. According to the simulation and experimental

20

results, considering that the diesel fuel and in-cylinder gas thermodynamic properties are

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affected by the in-cylinder temperature, fuel type and air excess ratio, the engine combustion

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simulation is more accurate to predict the reality in comparison with that when setting their

23

values constant. This paper provides a general approach for the investigation and application of

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engines fuels and in-cylinder gas thermodynamic properties, in particular for the new fuel

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substitution in the engines.

26 27

Keywords: fuel; in-cylinder gas; thermodynamic properties; engine combustion; heat release

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Nomenclature Roman symbols

ak

fitting coefficient of specific heat

s

specific entropy(J/kg)

sda

specific entropy of each species

at constant pressure(-)

ak , j

fitting coefficient of specific heat at constant pressure of each

(J/kg)

species (-) BDC

Bottom Dead Centre(-)

ref sda

reference specific entropy of dry air(J/kg)

cp

specific

heat

constant

at

sj

pressure(J/kg/K)

cp,da

entropy

of

each

species(J/kg)

specific heat at constant pressure

sref j

of dry air(J/kg/K)

cp , j

specific

reference specific entropy of each species(J/kg)

specific heat at constant pressure

sref

reference specific entropy(J/kg)

ssg

specific entropy of stoichiometric

of each species (J/kg/K)

cv

specific

heat

at

constant

volume(J/kg/K)

cv ,air

gas(J/kg)

Specific heat at constant volume

ssgref

of fresh air(J/kg/K)

cv ,da

reference specific entropy of stoichiometric gas(J/kg)

specific heat at constant volume

SOI

Start of injection(-)

T

Temperature(K)

Tf,inj

fuel injection temperature(K)

Tnorm

normalized temperature(K)

of dry air(J/kg/K)

cv , f ,liquid

specific heat at constant volume of liquid fuel(J/kg/K)

cv , j

specific heat at constant volume of each species(J/kg/K)

cv , sg

specific heat at constant volume of stoichiometric gas(J/kg/K)

CFD

Computational Fluid Dynamics(-)

Tref

reference temperature(K)

ef

specific energy of flow(J/kg)

Tshift

the Kelvin temperature is shifted to a non-zero point(K)

Ef

energy of flow(J)

uair

specific internal energy of fresh air(J/kg)

EO

Exhaust valve Open(-)

ucomb

heat of combustion(J)

h

specific enthalpy(J/kg)

uda

specific internal energy of dry air (J/kg)

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Energy & Fuels

hair

specific enthalpy of fresh air(J/kg)

ueff

of

heat

effective

combustion(J/kg) hcomb

enthalpy of combustion(J)

uf,gas

specific internal energy of gas fuel(J/kg)

hda

specific enthalpy of dry air (J/kg)

u f ,liquid

specific internal energy of liquid fuel(J/kg)

hf ,liquid

specific enthalpy of liquid fuel

uref f

(J/kg)

href f

of fuel(J/kg)

reference specific enthalpy of

uj

fuel(J/kg) hinf,liquid

specific enthalpy of liquid fuel ef

specific

uref j

reference Specific internal energy of each species(J/kg)

enthalpy

of

each

usg

species(J/kg)

href j

specific internal energy of each species(J/kg)

(J/kg)

hj

reference Specific internal energy

specific

internal

energy

of

stoichiometric gas(J/kg)

reference specific enthalpy of

x

air mass fraction(-)

x1

Intake coefficient(-)

x da j

the mass fraction of each species

each species(J/kg)

hsg

specific

enthalpy

of

stoichiometric gas(J/kg) HCCI

Homogeneous

Charge

Compression Ignition(-) IC

Inlet valve Closed(-)

dry air(-)

xgj

the mass fraction of each species gas(-)

m1

Initial mass in-cylinder(kg)

x sg j

the mass fraction of each species stoichiometric gas(-)

p

pressure(bar)

y

the mole fraction (-)

pda

pressure of dry air(bar)

y da j

the mole fraction of each species dry air(-)

pref

reference pressure(bar)

ygj

the mole fraction of each species gas(-)

Q loss

heat loss flow(W)

Greek Symbols

R

molar gas constant(J/mol/K)



normalization temperature(-)

Rda

gas constant of dry air(J/kg/K)

 ref

reference temperature(-)

Rg

gas constant(J/kg/K)



fuel burn rate(kg/s)


normalization

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Rj

Page 4 of 28

each

 15 f

the fuel liquid density at 15 oC

gas constant of stoichiometric

 fref

reference density of fuel (kg/m3)

 f ,liquid

density of liquid fuel(kg/m3)



air/fuel ratio(-)

gas

constant

of

species(J/kg/K)

Rsg

gas(J/kg/K)

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Energy & Fuels

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1. Introduction

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During the diesel engines working process, the air is drawn from the environment into the

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cylinder, and the diesel fuel is burnt in combustion process inside the cylinder and finally the in-

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cylinder exhaust gas (mixture of the air and the stoichiometric gas) is expelled out of the cylinder.

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During these stages, the composition of in-cylinder gas undergoes many changes and has the

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following characteristics: due to the high temperature, the in-cylinder gas properties are quite

37

closed to those of the ideal gas. In addition, due to the fuel combustion, the chemical

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composition of the in-cylinder gas changes during the engine working process [1-3]. Therefore the

39

in-cylinder gas can be assumed as an ideal gas mixture composed of various chemical

40

components.

41

The engine in-cylinder gas and fuel thermodynamic properties investigation are involved in

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the chemical compound reaction, the thermodynamics analysis of the fuel and gas under various

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engine operating conditions. Owing to the interwork in the multidisciplinary field, some

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absolutely mind-blowing advances are being made. Frequently the experimental and simulation

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approaches are used to investigate the in-cylinder gas and fuel thermodynamic properties. In the

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experimental research, the PIV, Burnett measurements, etc., are often applied in the gas

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composition measurement together with gas pressure, temperature, etc. to investigate the fuel

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and gas properties, the gaseous pVTx properties, etc.[4-7]. Another usage of the experiments is to

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acquire the measured data in particular for the new fuel type or blends for the empirical

50

expressions, which will facilitate the future research on calculation and simulation [8, 9].

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Regarding to simulation approaches, three methods are normally used: (1) the fuel and in-

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cylinder gas thermodynamic properties are assumed to be constant according to empirical or

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experimental data [10, 11]. Some researchers use mathematical methods such as the least square

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fitting method to fit these data into a quadratic trinomial with the in-cylinder temperature [6, 10];

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(2) the in-cylinder gas is assumed consisting of water (H2O), carbon dioxide (CO2), oxygen (O2),

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and nitrogen (N2) whilst the in-cylinder gas is considered to be the mixture of the above four

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species, from which the in-cylinder gas thermodynamic properties can be obtained based on the

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four basic components properties. The parameters and mass changes can be used to calculate

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the thermal properties of the entire work medium [12, 13]. (3) The in-cylinder gas consists of pure

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air and stoichiometric gas and further the air and stoichiometric gas consist of some species, in

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other words, the in-cylinder gas is a mixture of mixtures. The properties of the air and

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stoichiometric gas mixtures are calculated separately at the beginning, and afterwards the air

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and stoichiometric gas mixture is calculated based on the engine air excess ratio and the

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combustion reaction rate [14, 15].


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The fuel and in-cylinder gas thermodynamic properties are used in most aspects of diesel

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engine simulation modeling, in particular the engine combustion process investigation[16, 17],such

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as optimal exergy-based control of diesel engines[18], thermal-hydraulic modeling and analysis [19],

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modeling and simulation of diesel engine thermal cycle [20]. The thermodynamic properties of the

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gas have also been used to predict the knocking of a diesel engine

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recently the most popular substitution of conventional diesel engines, in particular for marine

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applications. Due to the fuel (nature gas) properties difference, the in-cylinder gas behaves with

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different characteristics, so the natural gas engine simulation still needs to include the analysis of

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the nature gas and in-cylinder gas properties

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fuel and gas properties are usually used in thermodynamic analyses of plenty of power

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generation systems [26]. Aurélien Demenay [27] has used the predicted gas properties as the ideal

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gas properties of refrigerant molecules. F. Payri

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influence on spray penetration and diffusion angles. The gas thermodynamic properties are used

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for refrigerant molecules to approach the Carnot efficiency [29].

[22-25]

[21]

. Nature gas engines are

. Apart from diesel engine applications, the

[28]

has found that gas properties have a great

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The research of diesel fuel and in-cylinder gas thermodynamic properties is quite important in

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engine simulation particularly in the research of engine combustion, during which the fuel is

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burnt converting its chemical energy into the in-cylinder gas internal energy, and changing the

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composition of in-cylinder gas varying with crank angle. No matter what kinds of engine

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combustion model is used, such as zero-dimensional, quasi-dimensional or CFD model, the fuel

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and in-cylinder gas thermodynamic properties have to be determined in a suitable method.

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Morteza Fathi

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HCCI engine in order to calculate the internal energy of the in-cylinder gas. It happens in a similar

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case where Constantine D. Rakopoulos [31] calculated the internal energy of the mixture in a two-

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zone model after knowing the specific internal energy of its components (at each time). Based on

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the chemical kinetics, E. Neshat and Mirko Baratta

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models of diesel engine and natural gas engine respectively, but they both used the composition

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and average properties of the gas mixture to calculate the thermodynamics performance of the

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work medium. Peyman Nemati

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model by employing the thermodynamic properties analysis of fuel and in-cylinder gas. Stelios A.

94

et al.

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chemical properties of the mixture to calculate thermodynamic properties such as internal

96

energy, enthalpy, and Gibbs free energy [36, 37].

[34, 35]

[30]

has applied the gas properties of working medium to a single-zone model of

[33]

[32]

established the multi-zone combustion

calculated the heat release rate in a multi-zone combustion

developed CFD models for different purposes whilst they all used the physical and

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The fuel and in-cylinder gas thermodynamic properties in the previous researches are applied

98

to investigate the engine combustion phenomena. Nevertheless, in most of these researches, the

99

authors did not consider the chemical principle of the thermodynamic properties, e.g. before fuel


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Energy & Fuels

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is burnt in the combustion chamber, it is the liquid phase firstly and then the gaseous phase

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where the fuel has different properties. Without considering this, it would lead to an error of

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approximate 2% in the engine efficiency prediction. On the other hand, a modular development

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of the thermodynamic properties model will bring an efficient and fast way for the engineers to

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be more focused on the investigation of the engine side. Therefore, a generic and sufficiently

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accurate method for estimating fuel and in-cylinder gas thermodynamic properties should be still

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attractive for the engine combustion investigation.

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In this paper, the fuel and in-cylinder gas thermodynamic properties modeling approach is

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developed on the assumption of ideal mixture of the typical chemical species of fuel and in-

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cylinder gas, thus their thermodynamic properties can be calculated based on the ideal but non-

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perfect gas theory. The models, which provide the thermodynamic properties of the fuel, the air

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and the stoichiometric gas, are developed in MATLAB/SIMULINK environment. With diesel fuel

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type selection, the effect of the fuel type on the fuel and in-cylinder gas thermodynamic

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properties are investigated. Furthermore, the fuel and in-cylinder gas properties are used in the

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engine heat release calculation under different operating conditions, which verifies the

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application and accuracy of the fuel and in-cylinder gas thermodynamic properties models. Last

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but not least, in order to get engine measurements, a marine diesel engine test bed is set up,

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with which the heat release can be compared under different operating conditions to investigate

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the thermodynamic properties of fuel and in-cylinder gas in the real engine working process.

119

2. Methodology

120

2.1. In-cylinder Gas Assumptions

121

The diesel engine in-cylinder gas consists of air and stoichiometric gas. In terms of the

122

constituents, the air is a mixture of Nitrogen (N2), Oxygen (O2), Argon (Ar) and Carbon dioxide

123

(CO2), whilst the stoichiometric gas is a mixture of Nitrogen (N2), Argon (Ar), Carbon dioxide (CO2),

124

Sulphur oxide (SO2) and Water (H2O). For each species in air and stoichiometric gas, it is

125

considered to be ideal but non-perfect gases and then the mixture behaves as ideal but non-

126

perfect as well. Therefore the specific heat, enthalpy, and internal energy of air and

127

stoichiometric gas are functions of only temperature and the mixture fractions. The mixture

128

fractions of air are obtained from the definition, whilst that of stoichiometric gas can be

129

calculated based on the fuel composition and the fuel reaction mass balance. Ultimately the

130

properties of the in-cylinder gas are functions of only temperature and air fraction in the cylinder.

131

A power series of the (normalized) temperature (equation (1)) is used to fit these property

132

data for all the species in both air and stoichiometric gas and then the properties of air and


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133

stoichiometric gas can be determined on the basis of the ideal mixture. Finally, the composition x

134

is used to calculate the in-cylinder gas property.

cp  a1  a2   a3  2 ak  k 1 am  m1

135

(1)

m

 ak  k 1 k 1

T  Tshift

136

With  

137

Tshift – the Kelvin temperature is shifted to a non-zero point, usually Tshift = 0 K.

138

Tnorm – normalized temperature, usually Tnorm = 1000 K.

139

It is mentioned that Tshift is usually higher such as 273 K, 800 K or even 1000 K. In this case 0 K

140

Tnorm

was chosen for later entropy integration.

141

There are several reasons for using a power series to obtain the specific heat at constant

142

pressure. Firstly, given the power series of the specific heat at constant pressure, it is easy to

143

integrate them for the enthalpy difference relative to a certain reference according to equation

144

(3). In addition, the terms number of the power series can be selected according to the required

145

accuracy. In this case, generally 6 terms are used to cover a range between 200 – 2500K with

146

sufficient accuracy and based on data from reference [38] valid for this range. The coefficients for

147

the polynomial to calculate cp in equation (1) can be obtained according to the references [39-41].

148

du  cv  dT

(2)

149

dh  cp  dT

(3)

150

ds  cp 

151

dp dT R T p

(4)

2.2. Gas Properties calculations

152

First of all, the properties of each species in air, stoichiometric gas and fuel are calculated:

153

cv , j  cp, j  Rj  ak , j  k 1  Rj

m

(5)

k 1

m

ak. j

k 1

k

hj  hj  href  j

154

m

ak , j

k 1

k

 Tnorm  k  

 Tnorm  ref k

(6)

155

uj  uj  uref j  hj  R j  T

(7)

156

 pj  s j  s j  sref j  R j  ln  p   ref  m a      m ak. j   a1, j  ln   ref k 1   k , j  k 1       k 2 k  1  ref  k 2 k  1  

(8)

157 158

With Tref = 25 oC; pref = 0.1 Mpa. 8 ACS Paragon Plus Environment

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159 160

Energy & Fuels

href and sref are the specific enthalpy and entropy at the reference condition (Tref and pref) and their values for different species are given in reference [42].

161

Then the properties of air (in fact dry air) can be calculated summing the properties of each

162

species weighted by the mass fractions of the species (equation (9) – (11)). The expressions for

163

the stoichiometric gas are the same as for air, the index ‘sg’ (stoichiometric gas) taking the place

164

of index ‘da’ (dry air). da cv ,da  c p ,da  Rda   x da j  cp , j   x j  R j

165

j

166

(9)

j

hda   x da j  hj

(10)

uda   x da j uj

(11)

j

167

j

168

The calculation of the entropy of the mixture of air is more complicated than that of the other

169

properties above since it is, even for ideal gas, a function of not only temperature and mass

170

fraction but also pressure.

171 172 173 174 175

  pda ref sda   x da j   s j  s j  R j  ln p  j  ref 

  da da   R j   y j  ln y j    j  

(12)

In the dry air, j represents the components: N2, O2, Ar and CO2; in the stoichiometric gas, j represents the components: N2, Ar, CO2, H2O and SO2. Finally, together with the air mass fraction calculated by equation (13), the in-cylinder gas properties are calculated by equation (14) – (17): EO

x

176

m1  x1       dt IC

(13)

EO

m1     dt IC

177

cv  x  cv ,air  (1  x)  cv ,sg

(14)

178

h  x  hair  (1  x)  hsg

(15)

179

u  x  uair  (1  x)  usg

(16)

180

  p ref s  x   sda  sda  Rda  ln p   ref 

   p ref    1  x    ssg  ssg  Rsg  ln     pref 

    

(17)

Rg   y gj  ln y gj  j

181

With Tref = 25 oC [42].

182

Rg  (1  x)  Rsg  x  Rda

183

y gj  x gj 

184

Mg Mj

da xgj  (1  x)  x sg j  x  xj


(18) (19) (20)

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1 1 x x   Mg Mg Mg

185 186

y – the mole fraction [--]

187

p – in-cylinder pressure [Pa]

188 189 190

(21)

2.3. Liquid Fuel Properties calculations The calculation of the properties of liquid fuel is somewhat different from that of the gaseous fuel. The enthalpy of the liquid fuel is calculated based on the definition:

191 192

Page 10 of 28

hf ,liquid  u f ,liquid 

p

 f ,liquid

(22)

The first item in the right hand side is calculated based on: u f ,liquid  uref f  cv , f ,liquid   T  Tref 

193

(23)

194

The diesel fuel is assumed consisting of alkane (C13H28) and benzene (C13H10). The idea is that

195

the chosen species are typical for all alkanes and aromatics and that the specific heat of alkanes

196

and aromatics differ both at reference temperature and in their temperature dependence. The

197

fractions of C13H28 and C13H10 are calculated from the carbon percentage of the fuel, which is

198

known when the fuel type is determined. The cv,f,liquid can then be calculated with the fit data,

199

ref ref which for the moment is not temperature dependent. The reference value u f equals hf minus

200

ref ref the volume work ( pref  f ) at the same reference temperature. The reference enthalpy hf of

201

the fuel is used to match the effective heat of combustion with a real measured value or a value

202

determined according to reference [43]. The evaporation heat of the two typical fuel constituents

203

at reference condition can be estimated based on reference [41].

204

The density of liquid fuel can be calculated according to reference [44]：

 f ,liquid   15 f  0.68    15 

205 206 207

(24)

With  f is the liquid fuel density at 15 oC. 15

3. Experiment

208

In order to verify the simulation models of fuel and in-cylinder gas thermodynamic properties,

209

a diesel engine test bed is set up, where the heat release measurement is carried out. Heat

210

release is a simple and efficient way to acquire the engine combustion information but it is

211

difficult to be measured directly in the engine test bed. Generally, in the case where in-cylinder

212

pressure signals are known, the heat release can be calculated based on the engine working

213

principle, during which the fuel and in-cylinder gas thermodynamic properties play an important

214

role and have sensitive effects on the results.


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215

Energy & Fuels

3.1. Test Bed Installation

216

The tested engine is a MAN4L 20/27 diesel engine, which is a medium speed, direct injection

217

marine diesel engine (Figure 1(a) is the general view of the engine test bed). The general data of

218

the engine are listed in Table 1. Figure 1(b) shows the pressure signals sensor installation position

219

on the engine. The pressure sensor is difficult to be arranged due to the rugged environment of

220

engine combustion chamber. The indicator cock (top side of the engine) or the margin sides are

221

the options to mount the sensor. The latter is only available for the leftmost and rightmost

222

cylinders. If the sensor is not close enough to the combustion chamber, the channel affect

223

becomes severe. Therefore, in this research, the pressure sensor is mounted in the engine left

224

fringe side but only for cylinder 1 measurement.

225

Table 1. The specifications of the diesel engine used in the experimental investigation Parameter Model

MAN4L 20/27

Cylinder Number

4

Bore

0.20 m

Stroke

0.27 m

Connection Rod Length

0.52 m

Nominal Engine Speed

1000 rpm

Maximum Effective Power

340 kW

Compression Ratio

13.4[-] Plunger pump

Fuel injection

Direct injection

SOI

4o before TDC

IC

20o after BDC

EO

300o after BDC

226

(a) Overview of the test bed

(b) the in-cylinder pressure sensor installation (the red circle) 11

ACS Paragon Plus Environment

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

227 228

Figure 1. Engine test bed layout

3.2. Measurements Procedures

229

Figure 2 illustrates the engine test bed layout. The sensors arranged on the test bed are: in-

230

cylinder pressure sensors, inlet pressure and temperature sensors, exhaust pressure and

231

temperature sensors, air flow meters, etc. The detailed information of the sensors are presented

232

in the reference [45]. The weighing scale and clock with a two-position three-way valve instead

233

of flow meter is used for the fuel flow measurement in the test bed, which is a traditional

234

method but ensures the accuracy of the fuel flow measurement. In the oil tank, the diesel fuel

235

can be substituted to investigate the in-cylinder gas properties differences caused by fuel types.

236 237 238

Figure 2. Schematic diagram of in-cylinder pressure measurement test bed

3.3. Engine Operating Points Selection

239

The diesel engine operating conditions are indicated by engine speed and power. In order to

240

cover various levels of rotational speeds and working loads for both generator and propeller

241

applications with the least experiment times, the following three engine operating points are

242

selected for the experimental investigation:

243

(A) The nominal point: 1000 rpm, 100% power;

244

(B) A point on the generator curve: 1000 rpm, 25% power;

245

(C) A point on the propeller curve: 800 rpm, 50% power.

246

4. Results and Analysis

247

4.1 In-cylinder Gas Properties Library Setting-up

248

In Figure 3 it is obvious that the in-cylinder gas properties are used in plenty of sub-models

249

and a ‘Properties Library’ is built in the model. The inputs of ‘Properties Library’ are gas


Page 12 of 28

Page 13 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

250

composition and in-cylinder temperature while the outputs are gas properties, e.g. specific heat,

251

internal energy, entropy.

252

The gas properties sub-model is built in a ‘Library’, which is provided by SIMULINK

253

environment. After that, the SIMULINK model can use the library directly the same as modules in

254

the ‘SIMULINK Library Browser’. There are also a few modules in the ‘Properties Library’ to

255

calculate cv, cp, h, s, etc. separately or in combination depending on the purpose. Figure 3 (a) and

256

Figure 3 (b) show the specific heat modules and specific entropy modules in the ‘Properties

257

Library’.

(a)

258

(b)

Figure 3. Properties Library used in the ‘heat release calculation’ model

259

4.2 Theoretical Investigation of Fuel and In-cylinder Gas Properties

260

4.2.1 Gas and Fuel Properties simulation Results

261

In Figure 4, the gas properties simulation model is built based on the variation of in-cylinder

262

temperature and gas composition. The range of temperature is 0-3000oC and the gas

263

composition is set to be 0 or 1 to indicate air or stoichiometric gas separately. Meanwhile the

264

pressure is assumed to be constant as 100bar, which is somewhat close to the magnitude of

265

maximum in-cylinder pressure in diesel engine

266

MATLAB/SIMULINK software. T

T

[46, 47]

. The simulation is implemented in

cp

cpair cpsg

theta

cp

+

R

_

k

theta x

/

cv

xsg

xsg

* hair hsg

267 268

*

cp

h

cv _ u + R h

Figure 4. Theoretical investigation of in-cylinder gas properties simulation model


Energy & Fuels

269

The results of the in-cylinder gas properties simulation model are shown in Figure 5. The

270

specific heat at constant pressure and volume are illustrated in Figure 5(a). The cp values of air

271

and stoichiometric gas are higher than cv respectively since the isobaric process which is derived

272

by cp needs more heat for expansion to convert into the mechanical work. In Figure 5(b) enthalpy

273

(h) is the integral of cp and energy (u) is the integral of cv so that the tendency of these four

274

curves are same as Figure 5(a). For each specific heat, it varies with temperature in particular

275

within the range of 0-2000oC, for example, cv,sg varies from around 1.05 to 1.42 due to the ideal

276

but non-perfect gas definition. It can be concluded here that if cv and cp are kept constant in

277

some researches

278

entropy changing with temperature of air and stoichiometric gas at pressure 100bar.

, the simulation accuracy could not be ensured. Figure 5(c) shows the

Specific heat [kJ/kgK]

Specific energy [kJ/kg]

[10, 11]

(a) Specific heat of air and stoichiometric gas

(b) specific energy and enthalpy of air and stoichiometric gas

Specific entropy [kJ/kgK]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(c) specific entropy of air and stoichiometric gas

279

Figure 5. In-cylinder gas thermodynamic properties

280

Figure 6 illustrates the diesel fuel properties of EHV and IHV based on enthalpy and internal

281

energy separately. Both the values increase with temperature in particular after 2000oC where

282

the ascending rates are dramatical. However below 2000oC the variation with temperature is


Page 14 of 28

Page 15 of 28

somewhat steady but still not constant, which explains the low accuracy in some researches

284

when the heating value is kept constant for engine combustion investigation [48, 49].

Heating values of fuel [kJ/kg]

283

Specific energy of fuel [kJ/kg]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(b) heating value of fuel

(a) specific energy and enthalpy of fuel

285 286

Figure 6. Diesel fuel thermodynamic properties 4.2.2 Effect of Diesel Fuel Type on Gas Properties

287

According to ISO standard, there are a few definitions of diesel fuel type based on the fuel

288

refinery process, in which the top layer classification is distillate fuel and then the residual fuel. In

289

this research, four commonly used diesel fuels are chosen: DMA and DMB fuel (distillate diesel

290

fuel), RMG 35 and RMH 55 fuel (residual diesel fuel) [51]. Table 2 shows the basic specification of

291

these four fuel types. Viscosity as well as the carbon residue is quite different from distillate

292

diesel fuel to residual diesel fuel. As a consequence, during diesel engine design stage the fuel

293

adaptability of the engine has to be considered to design the fuel supply system.

294

The sulphur composition in the diesel fuel will affect the sulfide emission which is the one of

295

the main controlled engine emissions in particular in the ECA (Emission Control Area) where

296

sulphur limit is 0.10% [51]. However, in this paper the sulfide emission effect is ignored, so all the

297

sulphur mass fractions in the fuel are set larger than 0.10%, i.e. 0.2%, 0.5%, 2% and 3% for these

298

four fuel types respectively.

299

Referring to the ISO standard of diesel fuel specifications, the carbon and sulphur mass

300

fractions in fuel have to be determined in advance of the following calculation. In fact, the

301

hydrogen fraction should also be known but it can be calculated if carbon and sulphur fraction

302

are known. Cetane number is a simple but commonly used way to evaluate the diesel fuel

303

ignition characteristics. Normally the cetane number of the distillate diesel fuel is higher than the

304

residual diesel fuel, having relatively better combustion characteristics [52].

305 306 307


Energy & Fuels

308

Table 2. Basic fuel specifications according to ISO standard Diesel fuel type

DMA

DMB

RMG35

RMH55

maximum density at 15oC (kg/m3)

890

900

991

991

maximum viscosity at 50oC (cSt)

4.8

8.5

380

700

-6 win

0 win

0 sum

6 sum

30

30

0.20

0.25

18

22

1.5

2.0

5.0

5.0

carbon mass fraction in fuel

0.865

0.865

0.863

0.860

sulphur mass fraction in fuel

0.002

0.005

0.020

0.030

cetane number

35

35

25

25

pour point (oC) carbon residue (Conrad son) maximum sulphur (% mass)

Figure 7 shows the fuel properties of these four fuel types. In Figure 7(a), the specific energy

310

does not change drastically below 1500oC and from the zoom-in view, the specific energy of DMA

311

fuel is the highest. Above 1500oC especially at 2000oC, the specific energy of these four fuel types

312

increase rapidly and the discrepancies between them are obvious: DMA is the highest and RMH

313

55 is the lowest along with the large difference between distillate diesel fuel and residual diesel

314

fuel. The lower heating value (LHV) is illustrated in Figure 7(b). The differences between these

315

four fuel types appear from the beginning and varies in the same tendency when the

316

temperature is increasing: the DMA fuel is the highest while RMH 55 is the lowest. The LHVs of

317

these four fuel types increase smoothly below 2000oC and sharply after that. This is consistent

318

with the results reported by other researches in the literatures [53-55].

Lower heating value of fuel in kJ/kg

309

Specific energy of fuel in kJ/kg

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 28

(a) specific energy of fuel

319

(b) lower heating value of fuel

Figure 7. Fuel properties of different fuel type 16 ACS Paragon Plus Environment

Page 17 of 28

The air property depend on its own composition, no matter what diesel fuel is chosen the air

321

property is kept the same. Nevertheless the stoichiometric gas is the mixture of the combustion

322

products after chemical reaction between fuel and air, so the fuel types will affect the

323

stoichiometric gas properties, which are shown in Figure 8. In Figure 8(a) the specific heat at

324

constant volume (cv) of DMA and DMB almost overlap with temperature variation due to the

325

same carbon mass fraction setting. The cv of RMG 35 and RMG 55 diesel fuel are both lower than

326

those of the other two distillate fuel types whilst RMG 35 is higher. It can be concluded that the

327

cv value is influenced by carbon fraction of the fuel. The specific energy, as shown in Figure 8(b) is

328

roughly the same as these four fuel types due to the quite small differences of carbon

329

composition between these four fuel types.

Specific energy in kJ/kg

320

Specific heat in kJ/kgK

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

(a) specific heat at constant volume of

(b) specific energy of stoichiometric gas

stoichiometric gas

330

Figure 8. Stoichiometric gas properties of different fuel type

331

4.3. Diesel Engine Heat Release Calculations using Gas and Fuel Properties models

332

4.3.1 Heat Release Calculation model

333

Figure 9 illustrates the structure of the ‘heat release calculation model’, in which the prime

334

inputs of the model are the pressure and volume (in fact the crank angle) while the ultimate

335

output is one of the definitions of engine heat release - Combustion Reaction Rate (CRR). During

336

the calculation, the ‘properties library’ (with red rectangle) is used to calculate the effective

337

combustion value (ueff + ef ), the internal energy, the enthalpy and the specific heat, which are

338

important in the energy balance. As to the ‘energy of fuel’ (ef), the injection rate is assumed

339

equal to the fuel evaporation rate and the combustion rate

340

determination of the mass and composition variations by integrating the combustion reaction

341

rate. The Woschni formula is used to calculate the heat transfer coefficient for heat loss

342

estimation. The average in-cylinder temperature is obtained by employing the First Law of

343

Thermodynamics.


[14, 45]

, which enables the

Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

m  cv 

344

CRR   

dV  dT  p  Qloss dt dt ucomb  e f d dt

d dt

Page 18 of 28

[kg/s]

(24)

dV dt

dT dt



345 346 347

Figure 9. General block diagram of ‘heat release calculation model’ 4.3.2 Heat Release and engine performance

348

The CRR is quite fluctuant because it is calculated on the basis of the measured pressure

349

signals. As the integral of the CRR, the Reaction coordinate (RCO) is a monotonous increasing

350

function, which makes it suitable for analysis as most of the fluctuations are smoothed in the

351

integration process [45]. When the RCO is calculated, Figure 10(a) shows the normalized reaction

352

coordinate, which means the ‘fuel burnt percentage’.

353

The jump in the RCO curve indicates the start of combustion and just before this jump, there

354

is a short descending slope period representing the slightly negative heat release due to fuel

355

evaporation (Figure 10(b)). The start of combustion (SOC) is defined in this paper at the point

356

where RCO starts to increase again, just before TDC. Therefore the RCO just before descending

357

should be 0 to reveal that there is no fuel burnt at that time. In the model, the correction in RCO

358

is based on the fact that between 160 degree and 170 degree it should be zero. On the other

359

hand, the RCO before SOC, in particular at the beginning of the in-cylinder process, is negative,

360

resulting in an endothermic process at the beginning of the cycle, giving unrealistic values. This

361

could be caused by the heat loss model as well as by the start value of RCO. The phenomena are

362

also shown in the literatures

363

negative values.

[14, 56]

, but the authors of those literatures are not aware of the


0.06

1.2

Normalized Reaction Co-ordinate [--]

1000rpm,100%load 1000rpm,25%load 800rpm,50%load

1 0.8 0.6 0.4 0.2 0


0.05 0.04 0.03 0.02 0.01 0 -0.01 -0.02

-0.2 0 20

120 180 240 Crank angle [deg]

300

-0.03 150

360

(a) Reaction coordinate

364

160

170 Crank angle [deg]

180

190

(b) Zoom in reaction coordinate

Figure 10. Reaction coordinate under varied engine operating conditions

365

The in-cylinder pressure and temperature are important parameters of the engine

366

performance and they are shown in Figure 11 and Figure 12. The pressure signals are derived

367

from the measurement directly and the temperatures are calculated on the basis of the ‘gas law’.

368

At first sight it seems that the fluctuations in temperature are much fiercer than those in

369

pressure. Closer inspection reveals that the fluctuations relative to the instantaneous value are

370

identical for pressure and temperature as expected from the gas law. The effect is a graphical

371

effect since the order of magnitude of the temperatures is much larger relative to the maximum

372

(i.e. 400 K versus 1300 K) than for the pressures (i.e. 1bar versus 90bar). The differences between

373

the three operating conditions are clearly revealed in these two figures. 100

1800


90 80

1600 1400 Temperature [K]

70 Pressure [bar]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Normalized Reaction Co-ordinate [--]

Page 19 of 28

60 50 40 30

1000 800 600

20

400

10

200

0 0 20

60


300

0 0 20

360

Figure 11. In-cylinder pressure

374

1200

1000rpm,100%load 1000rpm,25%load 800rpm,50%load 60


300

360

Figure 12. In-cylinder temperature

4.3.3 Fuel and In-cylinder Gas properties at different engine operating conditions

375

Figure 13 illustrates the fresh air fraction in the cylinder. After revising the reaction

376

coordinate, before SOC it almost remains constant and does not fluctuate too much (x1 = 0.95),

377

and the selection of value x1 is somewhat based on the empirical formula [45]. From the point SOC

378

it (obviously) decreases. When the engine is operating at low load, the fresh air fraction

379

decreases slightly and ends at a higher value (about 0.7). Figure 14 shows the specific energy of


Energy & Fuels

380

fuel ef. Since hinf,liquid is a function of fuel injection temperature (Tf,inj = 40 oC) and uf,gas is a

381

function of in-cylinder temperature, the difference is also function of temperature and it is

382

negative, which can be considered to be the net heat loss to the fuel before combustion [45]. This

383

result is quite important for the fuel thermodynamic properties and reveals the deficiencies of

384

the constant value setting of the lower heating value 1

[11, 12, 47, 48, 57]

.

500


0.9

0 -500 -1000

0.8

-1500

0.7

-2000 -2500

0.6

-3000

0.5

-3500 -4000

0.4


-4500

0.3 0 20

60

120

180

240

300

-5000

360

0

20

60

180

120

240

300

360

Crank angle [deg]

Crank angle [deg]

Figure 13. In-cylinder air fraction

Figure 14. Specific energy of fuel

385

The cv is illustrated in Figure 15 – Figure 17 for the three operating points. The cv of air,

386

stoichiometric gas and in-cylinder gas are displayed with crank angle and in-cylinder temperature

387

respectively. In Figure 15 (b), due to the different air fraction at the same gas temperature

388

before and after Tmax, there are two different cv values of the in-cylinder gas between 1200 K and

389

1500 K. 1150 Specific heat at constant volume [J/kg/K]

1150 Specific heat at constant volume [J/kg/K]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 28

1100 1050 1000 950 900 850 800

cv,a

750

cv,sg cv,gas

700 0 20

60


300

360

(a) versus crank angle

390

1100 1050 1000 950 900 850 800

c v,a

750

c v,sg

700

c v,gas 200

400

600

800 1000 1200 Temperature [K]

(b) versus temperature

Figure 15. Specific heat at constant volume (cv, 1000 rpm, 100% power)


1400

1600

1800

Page 21 of 28

1150

cv,a

1100

Specific heat at constant volume [J/kg/K]

Specific heat at constant volume [J/kg/K]

1150

cv,sg

1050

cv,gas

1000 950 900 850 800 750 700 0 20

60


300

1100 1050 1000 950 900 850 800

c v,a

750

c v,sg

700

360

c v,gas 200


391

400

600


1400

1600

1800


Figure 16. Specific heat at constant volume (cv, 1000 rpm, 25% power) 1150 Specific heat at constant volume [J/kg/K]

1150 Specific heat at constant volume [J/kg/K]

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

1100 1050 1000 950 900 850 800

cv,a

750

cv,sg

700 0 20

cv,gas 60


300

360


392

1100 1050 1000 950 900 850 800

c v,a

750

c v,sg

700

c v,gas 200

400

600


1400

1600

1800


Figure 17. Specific heat at constant volume (cv, 800 rpm, 50% power)

393

Figure 18 – Figure 20 show the ‘heat of combustion’. As stated, due to the fact that the in-

394

cylinder process takes place in a closed system, the internal energy should be used to calculate

395

the ‘heat of combustion’ (ucomb). However, the ‘heat of combustion’ derived from enthalpy

396

(hcomb), which is smaller than ucomb, is also shown in the figures. The black solid curves in Figure

397

18(a) indicate the ‘the effective heat of combustion’ being (ucomb - ef), i.e. after subtracting the

398

heat required to evaporate and heat up the fuel (energy of fuel ‘Ef ’). It is clear that the ‘effective

399

heat of combustion’ is considerably lower than the ‘heat of combustion’, in particular at higher

400

temperature.

401


Energy & Fuels

4

4.45

4

x 10

4.45

x 10

4.4 Specific heat of combustion [kJ/kg]

Specific heat of combustion [kJ/kg]

4.4 4.35 4.3 4.25 4.2 4.15 4.1 4.05

ucomb

4

hcomb

3.95 3.9 0 20


300

4.3 4.25 4.2 4.15 4.1 4.05

ucomb

4

hcomb

3.95

ucomb,eff 60

4.35

3.9

360

ucomb,eff 200


402


1400

1600

1800

1400

1600

1800

1400

1600

1800

4

x 10

4.45

x 10



4.4 4.35 4.3 4.25 4.2 4.15 4.1 4.05

ucomb

4

hcomb

3.95 3.9 0 20


300

4.3 4.25 4.2 4.15 4.1 4.05

ucomb

4

hcomb

3.95

ucomb,eff 60

4.35

3.9

360

ucomb,eff 200


403

400

600



Figure 19. Heat of combustion (ucomb, 1000 rpm, 25% power) 4

4.45

4

x 10

4.45

4.35 4.3 4.25 4.2 4.15 4.1 4.05

ucomb

4

hcomb

3.95 3.9 0 20

x 10


4.4

60


300

4.35 4.3 4.25 4.2 4.15 4.1 4.05

ucomb

4

hcomb

3.95

ucomb,eff 360


405

600


4

4.45

404

400

Figure 18. Heat of combustion (ucomb, 1000 rpm, 100% power)


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 28

3.9

ucomb,eff 200

400

600



Figure 20. Heat of combustion (ucomb, 800 rpm, 50% power)

5. Conclusions

406

The in-cylinder gas is assumed the mixture of air and stoichiometric gas whilst the fuel is

407

regarded as the mixture of hydro carbon, which contributes to the model development of the

408

fuel and in-cylinder gas thermodynamic properties in the MATLAB/SIMULINK environment. The 22 ACS Paragon Plus Environment

Page 23 of 28 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

409

fuel and in-cylinder gas thermodynamic properties as well as the effect of diesel fuel type on gas

410

properties are theoretically investigated. An experimental investigation into engine heat release

411

calculation is carried out under three operating conditions with crank angle and temperature

412

variation. The conclusions can be drawn as following:

413

1)

The diesel fuel type affects the engine working process in particular when comparing

414

distillate fuel with residual fuel, where the lower heating values are different by more

415

than 5%.

416

2)

The fuel and in-cylinder gas thermodynamic properties vary significantly with

417

temperature, thus the simulation errors are not acceptable if the properties are set

418

constant.

419

The fuel and in-cylinder gas thermodynamic properties models in this paper are verified by a

420

conventional marine diesel engine. Nevertheless, they are also suitable for other energy

421

conversion machines when the fuels are not typical or blended, which provides a generic way for

422

the energy conversion process research.

423

Acknowledgments

424

We gratefully acknowledge the financial support of ‘International Science & Technology

425

Cooperation Program of China’, 2014DFG72360 and the ‘National Key R&D Program of China’,

426

2016YFC0205203.

427

References

428

[1]

Kazerooni H, Rouhi A, Khodadadi A A, et al. Effects of Combustion Catalyst Dispersed by a

429

Novel Microemulsion Method as Fuel Additive on Diesel Engine Emissions, Performance,

430

and Characteristics. Energy & Fuels, 2016, 30(4): 3392-3402.

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[2]

Kasumba J, Holmén B A. Nonpolar Organic Compound Emission Rates for Light-Duty Diesel

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Engine Soybean and Waste Vegetable Oil Biodiesel Fuel Combustion. Energy & Fuels, 2016,

433

30(11): 9783-9792.

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[3]

Dale J G, Cox S S, Vance M E, et al. Transformation of Cerium Oxide Nanoparticles from a

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Diesel Fuel Additive during Combustion in a Diesel Engine. Environmental Science &

436

Technology, 2017, 51(4): 1973-1980.

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[4]

Li M, Tong Y, KLINGMANN J, et al. Experimental Study of Hydrogen Addition Effects on a Swirl-Stabilized Methane-Air Flame. Energies, 2017, 10(11): 1769.


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[5]

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Tu C, Yin Z, Lin J, et al. A Review of Experimental Techniques for Measuring Micro- to NanoParticle-Laden Gas Flows. Applied Sciences, 2017, 7(2): 120.

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Feng X, Liu Q, Zhou M, et al. Gaseous pvTx Properties of Mixtures of Carbon Dioxide and

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Propane with the Burnett Isochoric Method. Journal of Chemical & Engineering Data, 2010,

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55(9): 3400-3409.

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Modeling of Thermodynamic Properties of Diesel Fuel and In-Cylinder

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