Xin Q. Diesel Engine System Design
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296 Diesel engine system design
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299
4
Fundamentals of dynamic and static diesel
engine system designs
Abstract: This chapter lays out the foundation of dynamic and static diesel
engine system designs by linking the theoretical governing equations of
the instantaneous engine in-cylinder cycle processes and the gas ow
network of the air system. Engine manifold lling dynamics is discussed
for dynamic system design. The chapter develops the theory of pumping
loss and engine delta P, which are key design issues for modern high-
EGR turbocharged diesel engines. The theory is used to predict engine
hardware performance or determine hardware specications to meet target
performance. Four core equations for engine air system are proposed.
Different theoretical options of engine air system design are summarized.
Key words: dynamic design, static design, engine thermodynamic cycle
simulation, manifold lling dynamics, pumping loss, engine delta P, diesel
engine air system.
4.1 Introduction to diesel engine performance
characteristics
4.1.1 Engine performance maps
Engine performance is often characterized by the engine operating behavior
in the speed–load domain, for example, the behavior of emissions, fuel
consumption, noise, mechanical and thermal loading. Engine performance maps
refer to the constant value contour plots of a given performance parameter
in the speed–torque domain. A good understanding of engine performance
maps is important to a system design engineer.
For an engine equipped with xed-geometry hardware without exible
controls (e.g., xed-geometry turbine, mechanical camshaft, mechanical
water pump), optimum system performance is a large compromise between
high-speed and low-speed operations, or between high-load and low-load
operations. The trade-off effect is especially prominent when the range of
the engine speed (or load) is wide. Mapping the operating characteristics of
engine customer applications (e.g., vehicle driving cycles, marine engine load
cycles) to the engine speed–load map and mapping the engine speed–load
characteristics to the component characteristic map (e.g., a compressor map)
are two important design techniques for a system engineer in conducting
system integration. Owing to the paramount importance of engine speed–load
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300 Diesel engine system design
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characteristics, typical examples of engine performance maps are illustrated
and discussed in this section.
For reference, engine glossary and abbreviations are provided in SAE J604
(1995). Engine testing is summarized in Martyr and Plint (2007). Engine
power test codes can be found in SAE J1995 (1995) and J1349 (2008). Engine
design details are provided in Haddad and Watson (1984a,b), Challen and
Baranescu (1999) and Basshuysen and Schafer (2004).
4.1.2 The characteristics of engine power and fuel
consumption
Figure 4.1 presents the steady-state GT-POWER simulation data of a heavy-
duty diesel engine at sea-level altitude and normal ambient temperature. The
engine brake power map has second-order contours since power is equal to
speed multiplied by torque. The operating points of a vehicle at a constant
travelling speed but different transmission gear ratios are located along a
constant-power curve.
Engine BSFC contours usually exhibit a minimum (optimum) in the low-
speed and high-load region such as at peak torque. BSFC is affected mainly
by fuel injection timing, engine delta P, mechanical friction, and heat losses.
The large increase in BSFC toward very low loads at a constant speed is
primarily because the proportion of mechanical friction power relative to
brake power is high, which means the engine mechanical efciency is low.
The increase of BSFC toward high engine speeds at a constant torque may
be partly due to the increase in mechanical friction and engine delta P.
The shape of the BSFC contours is also largely affected by the emissions
calibration strategy, especially in the region above 25% load and between
the peak-torque speed and rated speed.
4.1.3 The characteristics of engine air–fuel ratio and
exhaust gas recirculation rate
Engine air–fuel ratio is dened as the mass ow rate ratio of fresh air to fuel.
The shape of the air–fuel ratio contours is largely affected by the type of
turbocharger and EGR rate. An excessively high air–fuel ratio may produce
high pumping loss, high peak cylinder pressure, and high compressor outlet
temperature. An excessively low air–fuel ratio may produce the problems
of deteriorated combustion efciency, high smoke, and high exhaust gas
temperature. Air–fuel ratio is affected by the engine air ow rate at a given
engine speed and load mode, and the air ow rate is determined by the
intake manifold boost pressure and engine volumetric efciency. Unlike
the xed-geometry turbine or pneumatically controlled wastegated turbine,
the electronically controlled wastegated turbine and VGT in modern diesel
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301Fundamentals of dynamic and static engine system designs
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Engine brake power (hp)
Air–fuel ratio
Engine outlet coolant temperature (°F)
BSFC (lb/(hp.hr))
EGR rate (%)
Engine oil temperature (°F)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
500
450
400
350
300
250
200
150
100
50
0.8
0.7
0.6
0.5
0.4
60
55
50
45
40
35
30
25
20
30
25
20
15
10
5
202
200
198
196
194
192
190
188
230
225
220
215
210
205
4.1 Illustration of steady-state diesel engine system performance
maps.
Compressor outlet air temperature (°F)
CAC outlet air temperature (°F)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
Engine BMEP (bar)
Engine BMEP (bar)
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
400
350
300
250
200
150
100
120
115
110
105
100
95
90
85
80
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302 Diesel engine system design
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EGR cooler outlet gas temperature (°F)
Turbine inlet gas temperature (°F)
Intake manifold gas temperature (°F)
Turbine outlet gas temperature (°F)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
260
250
240
230
220
210
200
190
150
140
130
120
110
100
1200
1100
1000
900
800
700
600
500
400
1000
900
800
700
600
500
400
Intake manifold pressure (inch Hg, gauge)
Peak cylinder pressure (bar)
Exhaust manifold pressure (inch Hg, gauge)
Engine delta P (bar)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
60
50
40
30
20
10
0
80
70
60
50
40
30
20
10
160
140
120
100
80
60
0.7
0.6
0.5
0.4
0.3
0.2
0.1
4.1 Continued
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Exhaust restriction at turbine outlet (inch Hg)
DPF pressure drop (inch Hg)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
Engine BMEP (bar)
Engine BMEP (bar)
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
7
6
5
4
3
2
1
4.5
4
3.5
3
2.5
2
1.5
1
0.5
4.1 Continued
Engine coolant heat rejection (including EGR
cooler, Btu/min)
CAC heat rejection (Btu/min)
Total engine coolant and CAC heat rejection
(Btu/min)
EGR cooler heat rejection (Btu/min)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
Engine BMEP (bar)
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
14000
12000
10000
8000
6000
4000
2000
4000
3500
3000
2500
2000
1500
1000
500
0
3500
3000
2500
2000
1500
1000
500
0
18000
16000
14000
12000
10000
8000
6000
4000
2000
Percentage of engine coolant heat rejection in fuel
energy rate
Percentage of CAC heat rejection in fuel
energy rate
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
800 1000 1200 1400 1600 1800 2000
Engine speed (rpm)
Engine BMEP (bar)
Engine BMEP (bar)
20
18
16
14
12
10
8
6
4
2
20
18
16
14
12
10
8
6
4
2
0.4
0.35
0.3
0.25
0.1
0.09
0.08
0.07
0.06
0.05
0.04
0.03
0.02
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304 Diesel engine system design
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engines are able to exibly regulate or reduce air–fuel ratio to a large extent
or maintain it even at a nearly constant level, especially at medium or high
loads.
EGR rate is dened as the mass ow rate ratio of EGR to the sum of fresh
air and EGR. The shape of the EGR rate contours is determined primarily
by emissions calibration. EGR rate directly affects coolant heat rejection,
air–fuel ratio, and exhaust temperature.
4.1.4 Engine temperature characteristics
Engine outlet coolant temperature (or radiator inlet coolant temperature) is
determined by coolant heat rejection and the characteristics of radiator and
water pump. The coolant temperature usually reaches the highest value at full
load but not necessarily at the rated speed. In fact, it often occurs at the peak
torque or a medium speed. Engine oil temperature is affected by coolant ow
rate and oil cooler heat rejection, which consists of the contributions from
both mechanical friction heat and piston cooling. The highest oil temperature
may occur at a lower engine speed than the rated speed.
Compressor outlet air temperature is affected mainly by compressor pressure
ratio, ow rate, and efciency. Charge air cooler (CAC) outlet air temperature
(before mixing with EGR) is affected by cooler effectiveness and cooling
medium temperature (also called cooler sink temperature). Excessively low
CAC outlet temperature may generate water condensation problems. EGR
cooler outlet temperature is affected by EGR cooler effectiveness, coolant
temperature, and EGR ow rate. Again, excessively low EGR cooler outlet
temperature may produce condensation problems of water and sulfuric acid.
Intake manifold gas temperature (IMT) is the result of mixing between the
fresh air at the CAC outlet and the EGR gas at the EGR cooler outlet. The
required intake manifold gas temperature is determined by a compromise
between the requirement to control NO
x
emissions and the acceptable limit
to control condensation for good durability. The highest IMT may not always
occur at rated power.
Turbine inlet gas temperature (or exhaust manifold gas temperature) is
determined mainly by a charge mass-to-fuel ratio, heat release rate and intake
manifold gas temperature. The charge mass-to-fuel ratio here is dened
as the mass ow rate ratio between the sum of fresh air and EGR to fuel.
Turbine outlet temperature is affected by both turbine inlet temperature and
turbine efciency. It is important for aftertreatment performance and DPF
regeneration, especially at low speeds/loads.
4.1.5 Engine pressure characteristics
Intake manifold pressure is determined by compressor pressure ratio or
essentially turbine pressure ratio. It determines engine air ow rate through
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the relationship with volumetric efciency. It also affects peak cylinder
pressure and engine delta P. Exhaust manifold pressure is affected by turbine
area and turbine ow rate. It affects turbine pressure ratio and engine delta P.
The maximum peak cylinder pressure usually occurs at rated power. Engine
delta P is affected mainly by engine air ow rate, turbine area, turbocharger
efciency and engine volumetric efciency. Engine delta P greatly affects
pumping loss and EGR driving. It is the most important parameter in the
design of the air system of modern diesel engine. Engine delta P control is
thoroughly elaborated in this book. Exhaust restriction usually refers to the
total pressure drop from the turbine outlet to the ambient. Exhaust restriction
is affected by engine air ow rate and the ow restriction characteristics of
the exhaust and aftertreatment system. Exhaust restriction greatly affects
turbine performance and hence air–fuel ratio. DPF pressure drop is variable
with respect to time of operation, depending on the soot load in the DPF.
4.1.6 Engine heat rejection characteristics
Engine coolant heat rejection affects the coolant temperatures in the top
tank, at the radiator inlet and engine inlet. It usually has the highest value
near rated power or at a higher speed. Total engine coolant and CAC heat
rejection presents the overall challenge for the vehicle cooling system design
from the engine. Note that for engine manufacturers, the total heat rejection
usually does not include transmission cooler heat rejection, which is normally
estimated by the vehicle powertrain or drivetrain design team. However,
in vehicle cooling system design, the heat rejections from the transmission
cooler, the air conditioning and other miscellaneous sources all need to be
taken into account. CAC or EGR cooler heat rejection is proportional to
the air or gas ow rate and the gas temperature drop across the cooler. The
percentage of fuel energy rate lost to engine coolant heat rejection is generally
low at high loads and high at low loads. The reason is that at high loads the
relative proportion of engine brake power in fuel energy is high, while the
situation is opposite at low loads so that all the fuel energy primarily goes
to coolant heat rejection and exhaust gas.
4.2 Theoretical formulae of in-cylinder
thermodynamic cycle process
4.2.1 Overview of engine thermodynamic cycle
calculations
Engine thermodynamic cycle analysis is the core of air system theory and
the foundation for static (steady state) and dynamic (transient) engine system
designs. An engine system model can be built with a modern commercial
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software package by putting the modeling elements together in a graphical
programming environment. A large amount of engine performance simulation
data can be produced by running the model to solve the differential equations
involved. The system analysis engineers need to understand the cause-
and-effect relationship between the relating parameters. They also need to
interpret and present the computed results in a correct, intuitive, and simple
fashion. For example, they need to explain what the reasons are for the
change in pumping loss after the values of hardware design parameters and
software calibration parameters are changed. The best way to understand
the fundamentals is to examine the governing equations that describe the
system behavior. Simplied forms of the equations are acceptable for this
purpose. The parametric dependency can be revealed from the equations
mathematically. This chapter presents the fundamental theory behind the
cycle simulation software. Both the differential equations of the engine in-
cylinder cycle process and the steady-state equations of the network system
of the turbocharged EGR engine are described. Their links are discussed.
The complementary sub-models of heat transfer, combustion and intake/
exhaust valve ows are also provided.
Extensive reviews of internal combustion engine thermodynamic cycles
have been provided by other researchers (Chow and Wyszynski, 1999; Ribeiro
and Martins, 2007; Silva, 1993; Veiásquez and Milanez, 1995; Júnior et al.,
2005; Primus, 1999; Proell, 1993; Makartchouk, 2002). The performance
of internal combustion engines is introduced in several classical textbooks
(Heywood, 1988; Stone, 1999; Pulkrabek, 2003; and Martyr and Plint, 2007)
and SAE procedures (SAE J228, J604, J1312, J1829, J2548, and J2723).
Turbocharging performance is reviewed in Watson (1999). System dynamics,
which is the foundation for transient performance and model-based electronic
controls, is introduced in Palm III (2005) and Ogata (2004). Diesel engine
transient performance modeling is addressed in Rakopoulos and Giakoumis
(2009).
4.2.2 Model assumptions of engine in-cylinder cycle
process
The engine in-cylinder cycle process is determined by gas temperature (T),
pressure (p) and mass (m). These parameters are solved by two ordinary
differential equations for energy and mass conservations respectively and
the ideal gas law equation. Initial conditions of in-cylinder p, T and m can
be estimated from the intake manifold parameters, and the computation is
conducted on a crank-angle basis with time-marching numerical integration
until cyclic convergence is achieved for all the gas state parameters inside
the entire engine. The assumptions for the in-cylinder thermodynamic model
described in this chapter include the following:
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• the in-cylinder single zone model (i.e., the burned and unburned mixture
has a uniform temperature)
• zero-dimensional state parameters (i.e., at each moment, the pressure,
temperature, or concentration in the cylinder are equal or homogeneous
everywhere; no condensed species)
• ideal gases (i.e., the gases obey the equation of state pV = mR
gas
T;
the speci c heat, internal energy, and enthalpy of the gases vary with
temperature and constituents but not with pressure)
• the quasi-steady-state process for the gas owing into and out of the
cylinder (i.e., within a small time step in numerical integration the ow
process is treated as steady state)
• ignoring the kinetic energy of the intake and exhaust gas ows.
4.2.3 Governing equations of the in-cylinder
instantaneous cycle process
The energy conservation equation of the in-cylinder gas can be expressed
as:
d
d
=
d
d
+
d
d
d
d
·
UW
dUWd
Q
h
m
i
i
j
j
j
ff
=
ff
=
d
ff
d
ff
d
ff
d
·
ff
·
h
ff
h
j
ff
j
j
ff
j
SS
SS
d
SS
d
d
SS
d
+SS +
Q
SS
Q
i
SS
i
ff
SS
ff
+
ff
+SS +
ff
+
4.1
where f is the crank angle (degrees), U is the internal energy of the in-cylinder
gas, W is the mechanical work acting on the piston, Q
i
is the heat exchanged
through the system boundary and fuel combustion, h
j
is the speci c enthalpy,
and h
j
m
j
is the energy brought into and out of the cylinder by the intake
and exhaust gas ow. The enthalpy can be calculated with a datum of zero
enthalpy de ned at 0 K or 298.15 K or any other arbitrary datum temperature.
Note that a positive value for the heat or mass ow means owing into the
cylinder and a negative value means owing out of the cylinder. Each term
in equation 4.1 is further expressed as:
d
d
=
d
d
=
d
d
+
d
d
U
u
m
m
u
ff
=
ff
=
d
ff
d
ff
+
ff
+
d
ff
d
m
ff
m
()
mu
()
mu
mu◊mu
()
mu◊mu
4.2
d
d
= –
d
d
W
p
V
ff
= –
ff
= –
d
ff
d
p
ff
p
4.3
S
i
i
fuel
wall
Q
Q
Q
d
d
=
d
d
+
d
d
ff
=
ff
=
d
ff
d
f
4.4
where V is the in-cylinder instantaneous volume, m is the in-cylinder gas mass,
Q
fuel
is the heat energy released from fuel combustion, and Q
wall
is the heat
transfer through the walls of the cylinder head, the piston and the liner. The
energy of the intake and exhaust gas exchange mass ows is given by:
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