Xin Q. Diesel Engine System Design
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842 Diesel engine system design
© Woodhead Publishing Limited, 2011
conditioning switched on. At part load or in a cold climate, the engine coolant
can be excessively cold and can adversely affect engine combustion and
performance. Moreover, overcooling in cooler design for certain operating
conditions requires additional measures to x the problem. For example, if
the charge air cooler outlet air temperature is lower than the dew temperature,
water is condensed in the cooler and may require a device to separate the
condensate. Another example is the fouling and corrosion problems of the
hydrocarbons and the acidic vapor condensate in the EGR cooler when the
EGR cooler outlet gas temperature is too low at part load.
To reach a target intake manifold gas temperature for emissions control,
there is a balance between the charge air cooler size (or effectiveness) and the
EGR cooler size within their allowable packaging constraints. Overcooling
the intake manifold mixture sometimes may be detrimental to NO
x
control.
The increase in the ignition delay with cold charge is accompanied by an
increase in the premixed portion of the fuel injection and NO
x
emissions.
Coolant temperature = 220°F, exhaust port equivalent
diameter=1.5 inches
2500
2000
1500
1000
500
0
Coolant heat transfer
0 W/m
2
.K (insulated)
Coolant heat transfer
1000 W/m
2
.K
Coolant heat transfer
2000 W/m
2
.K
Coolant heat transfer
4000 W/m
2
.K
0 1 2 3 4 5 6
Exhaust port length (inch)
Coolant heat transfer
500 W/m
2
.K
Coolant heat transfer
1500 W/m
2
.K
Coolant heat transfer
3000 W/m
2
.K
Exhaust port wall metal
temperature increases
Coolant heat rejection of six exhaust ports
(Btu/min)
12.9 Effect of exhaust port length on engine coolant heat rejection at
rated power.
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843Diesel engine heat rejection and cooling
© Woodhead Publishing Limited, 2011
EGR cooler heat transfer performance and ow restriction deteriorate
signicantly when soot and sulfate particulates deposit on the cooling tube
surface. In the design specication of cooler sizing, a sufcient margin of
effectiveness and pressure drop should be reserved to account for EGR cooler
fouling. The explanation of EGR cooler fouling and the related references are
12.10 Parametric simulation of design effects on engine coolant heat
rejection.
EGR rate = 15%
EGR rate = 18%
EGR rate = 21%
Compressor efficiency
= 74%
Turbine efficiency
= 67%
Exhaust restriction
= 8.2≤Hg
1020 1030 1040 1050 1060 1070 1080 1090 1100 1110 1120
Exhaust manifold gas temperature (°F)
Engine simulation at 2300 rpm (A/F ratio = 23)
500
Btu/min
300 hp
280 hp
260 hp
240 hp
Engine coolant heat rejection (including
EGR cooler heat rejection, Btu/min)
A/F ratio = 22
A/F ratio = 23
A/F ratio = 24
Compressor efficiency
= 74%
Turbine efficiency
= 67%
Exhaust restriction
= 8.2≤Hg
1000 1020 1040 1060 1080 1100 1120 1140
Exhaust manifold gas temperature (°F)
Engine simulation at 2300 rpm (EGR rate = 18%)
300 hp
280 hp
260 hp
240 hp
Engine coolant heat rejection (including
EGR cooler heat rejection, Btu/min)
500
Btu/min
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844 Diesel engine system design
© Woodhead Publishing Limited, 2011
provided in the durability discussions in Section 2.12. EGR cooler design and
cooling performance are elaborated by Ap (2000), Stolz et al. (2001), Chalgren
et al. (2002), Melgar et al. (2004), Honma et al. (2004), and Mosburger et al.
(2008). Air-cooled charge air cooler is widely used in diesel vehicles although
sometimes water-cooled charge air coolers are used (Kern and Wallner,
1986; Chalgren et al., 2004). Other vehicle cooling system design issues or
components (e.g., underhood thermal management, radiator, cooling fan) are
12.10 Continued
Compressor
efficiency = 65%
Compressor
efficiency = 70%
Compressor
efficiency = 75%
Turbine efficiency
= 67%
Exhaust restriction
= 8.2≤Hg
1040 1050 1060 1070 1080 1090 1100 1110 1120 1130
Exhaust manifold gas temperature (°F)
Engine simulation at 2300 rpm (A/F ratio = 23,
EGR rate = 18%)
280 hp
290 hp
260 hp
240 hp
220 hp
Engine coolant heat rejection (including
EGR cooler heat rejection, Btu/min)
500
Btu/min
Turbine
efficiency = 60%
Turbine
efficiency = 65%
Turbine
efficiency = 70%
Compressor efficiency
= 74%
Exhaust restriction
= 8.2≤Hg
1040 1050 1060 1070 1080 1090 1100 1110 1120
Exhaust manifold gas temperature (°F)
Engine simulation at 2300 rpm (A/F ratio = 23,
EGR rate = 18%)
280 hp
290 hp
260 hp
240 hp
Engine coolant heat rejection (including
EGR cooler heat rejection, Btu/min)
500
Btu/min
Diesel-Xin-12.indd 844 5/5/11 12:02:55 PM
845Diesel engine heat rejection and cooling
© Woodhead Publishing Limited, 2011
introduced by Habchi et al. (1994), Avequin et al. (2001), Muto et al. (2001),
Chang et al. (2003), Shah (2003), and Scott and McDonald (2005).
In coolant selection, forced convection or sub-cooled boiling should
be maintained, and saturated boiling should be avoided. With saturated
boiling, there is a risk of vapor blanket and lm boiling (see Section 2.12.2)
which can cause insulation overheating and thermal fatigue of the cooler
component. More information on engine coolant is provided by SAE J814
(2007), Hannigan (1993), and Brosel (1999).
In cooling system design, various congurations with different cooling
media and cooler arrangements may be proposed in order to control the heat
rejection under the vehicle front-end packaging constraints while achieving
the same target of intake manifold gas temperature. The hottest engine outlet
coolant temperature usually occurs at an intermediate speed between the peak
torque and the rated power due to the nature of the matching between the
engine heat rejection and the operating characteristics of the radiator and the
water pump. Engine system analysis needs to be conducted under the harshest
environmental conditions in order to cover the worst application scenarios of
the highest engine-outlet coolant temperature. The extreme conditions may
include sea-level altitude at 38°C or 100°F hot ambient, 1676 m or 5500 feet
altitude at 38°C, or 10,000 feet on a hot day. The elevated compressor inlet
air temperature due to in-vehicle underhood heating should be considered.
Moreover, the effect of using air conditioning and hot air recirculation around
the radiator and the charge air cooler should not be ignored when analyzing
the cooling medium (sink) temperature.
SAE J631 (2007), J1004 (2004), J1148 (2004), J1393 (2004), J2082
(1992), J1994 (2008), and J1339 (2009) provide fundamental information
on engine cooling systems.
Fundamentals of engine cooling system design are introduced by Bosch and
Real (1990) and Kanefsky et al. (1999). Engine cooling system performance
sensitivity is analyzed by Rahman and Sun (2003), Rahman et al. (2001),
and Savage et al. (2007). An analysis of radiator top tank temperature has
been conducted by Tang et al. (2008). Engine cooling system design and
optimization are reported by Valaszkai and Jouannet (2000), Koch and
Haubner (2000), Pantow et al. (2001), Hughes and Wiseman (2001), Chalgren
and Allen (2005), and Burke et al. (2010). Cooling system simulations have
been carried out by Sakai et al. (1994), Mohan et al. (1997), Ap (1999), and
Hughes et al. (2001). A simulation methodology of EGR and engine cooling
systems and their controls is given by Chalgren et al. (2002).
12.4.2 Cooler performance calculations
The cooler performance design specication includes effectiveness, heat
rejection, and pressure losses at both the gas side and the cooling medium
Diesel-Xin-12.indd 845 5/5/11 12:02:55 PM
846 Diesel engine system design
© Woodhead Publishing Limited, 2011
side. Cooler thermal performance calculations are basically based on two
formulas: (1) the de nition of cooler effectiveness and (2) the equation for
the heat transfer rate. Taking EGR cooler as an example, its heat transfer
calculation is illustrated below. The cooler effectiveness is de ned as:
e
cooler
=
Actu
al heat t
ra
al heat traal heat t
ns
fe
r
ra
te
Ma
x po
ssi
bl
e
heat t
ra
ns
fe
r
ra
te
=
(
,,
(
,,
(
mc
TT
– TT –
gas
mc
gas
mc
p
gas
,,gas,,
gas
,,gas,,
TT
gas
TT
in
TT
in
TT
ga
TT
ga
TT
sss
out
p
gas
in
coolant,i
n
co
TT
gas
TT
gas
in
TT
in
coolant,i
TT
coolant,i
m
,
,
)
()
p
()
p
mc()mc
(
TT – TT
)
=
(
()
()
mi
n
olant
oolanto
pc
oolant
coolant,
out
coolant,i
n
TT
coolant,
TT
coolant,
out
TT
out
coolant,i
TT
coolant,i
m
c
pc,pc
(
TT – TT
)
(
cT
ccTc
T
TT
p
cT
p
cT
gas
cT
gas
cT
in
coolant,i
T
coolant,i
T
n
gas
TT
gas
TT
in
TT
in
TT
gas
TT
gas
TT
gas
)(
cT)(cT
–
)
=
TT – TT
,
,,
in,,in
gas,,gas
mi
)(
mi
)(
cT)(cT
mi
cT)(cT
n
)(
n
)(
cT)(cT
n
cT)(cT
,
out
gas
in
coolant
,i
coolant,icoolant
n
TT
– TT –
gas
TT
gas
in
TT
in
coolant
TT
coolant
12.13
The cooler heat rejection is expressed as
QK
AT
cooler
QK
cooler
QK
hh
AT
hh
AT
me
AT
me
AT
an
QK= QK
·
hh
·
hh
AT · AT
D
ATDAT
12.14
where K
h
is the overall heat transfer coef cient, A
h
is the heat transfer area,
and the mean temperature difference of the heat exchanger is de ned as
D=
D=TD=
TT
TT
me
D=
me
D=
D=TD=
me
D=TD=
an
D=
an
D=
gas
TT
gas
TT
,i
TT
,i
TT
nc
TT
nc
TT
oolant
,i
oolant,ioolant
n
gas
TT
gas
TT
,
out
TT
out
TT
c
TT
c
TT
(
TT – TT
TT
nc
TT – TT
nc
TT
)
– (
TT – TT
oolant,
ooolant,o
out
gas
,i
nc
oolant
,i
oolant,ioolant
n
gas
,
out
TT
gas
TT
gas
,i
TT
,i
nc
TT
nc
T
gas
T
gas
)
ln
TT – TT
nc
TT
nc
–
nc
TT
nc
–
TTT
coolant,
TTT
coolant,
TTT
out
Ê
Ë
Á
Ê
Á
Ê
Ë
Á
Ë
ˆ
¯
˜
ˆ
˜
ˆ
¯
˜
¯
The cooler heat transfer rate can also be expressed as
Qm
Qm
cT
T
m
cooler
Qm
cooler
Qm
gas
p
cT
p
cT
gas
cT
gas
cT
gas
cT
gas
cT
,
gas
T
gas
T
,
out
co
Qm= Qm
(
cT(cT
–
)
=
,
in
olant
oolanto
pc
oolant
coolant,
out
coolant
,i
coolant,icoolant
n
cT
coolant,
cT
coolant,
cT
pc
cT
pc
oolant
cT
oolant
T
coolant
T
coolant
pc,pc
(
cT(cT
–
)
12.15
For parallel- ow cooling, the cooler effectiveness can be calculated by
e
cooler
hh
gas
p
gas
gas
pg
a
KA
hh
KA
hh
mc
gas
mc
gas
mc
gas
mc
gas
=
1 – exp
–
1 +
,
pg,pg
sss
coolant
pc
oolant
gas
pg
a
mc
coolant
mc
coolant
mc
gas
mc
gas
pc,pc
pg,pg
1 +
Ê
Ë
Á
Ê
Á
Ê
Ë
Á
Ë
ˆ
¯
˜
ˆ
˜
ˆ
¯
˜
¯
È
Î
Í
È
Í
È
Î
Í
Î
˘
˚
˙
˘
˙
˘
˚
˙
˚
sss
coolant
pc
oolant
f
mc
coolant
mc
coolant
pc,pc
–(
f–(f
1+
)
=
1 – e
1 +
NT
f
NT
f
–(
NT
–(
f–(f
NT
f–(f
Uc
–(
Uc
–(
1+
Uc
1+
c
t
Uc
t
Uc
t
12.16
For counter- ow cooling, the cooler effectiveness can be calculated by
e
t
t
t
cooler
f
f
=
1 – e
1 –
· e
–(
f–(f
1–
)
–(
f–(f
1–
)
NT
f
NT
f
–(
NT
–(
f–(f
NT
f–(f
Uc
t
Uc
t
–(
Uc
–(
1–
Uc
1–
NT
f
NT
f
–(
NT
–(
f–(f
NT
f–(f
Uc
t
Uc
t
–(
Uc
–(
1–
Uc
1–
c
12.17
where the number of transfer units (NTU) is de ned as
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847Diesel engine heat rejection and cooling
© Woodhead Publishing Limited, 2011
f
KA
mc
hh
KA
hh
KA
gas
mc
gas
mc
p
gas
NT
f
NT
f
U
=
,
12.18
and
t
c
=
,
mc
mc
gas
mc
gas
mc
p
gas
coolant
mc
coolant
mc
pc
,pc,
oolant
12.19
For the EGR cooler, the value of t
c
is very small (around 0.02). From
equation 12.16 or 12.17, it is observed that the EGR cooler effectiveness
is a function of EGR gas mass ow rate and cooler heat transfer capacity
K
h
A
h
. Note that cooler effectiveness does not depend on the cooler cooling
medium temperature. Figure 12.11 shows the calculated characteristics of
EGR cooler effectiveness. The steady-state performance of the charge air
cooler and vehicle radiator can be calculated in a similar way. In engine
cycle simulations, the engine coolant temperature and the cooler cooling
medium temperatures can be calculated by the above equations to couple
with the computation of engine coolant heat rejection.
As to the transient performance of the coolers, Pearson et al. (2000) provided
a theoretical analysis on the wave-action model of a charge air cooler’s
boundary, and a methodology to predict the instantaneous effectiveness and
heat transfer coef cient of the cooler as a function of air mass ow rate.
12.4.3 Cooler sink temperature and cooling capability
The calculation of cooler sink temperature is important for engine system
design because it affects cooling system design and the predictions of heat
rejection and engine air or gas temperatures at the cooler outlet. The sink
temperature refers to the cooling medium inlet temperature. For the charge
air cooler or the radiator, the sink temperature is the cooling air temperature
in front of the cooler or the radiator. For the EGR cooler or the liquid-cooled
inter-stage cooler, the sink temperature is the coolant inlet temperature of
the cooler. For the engine cylinder, the sink temperature is the radiator outlet
coolant temperature. It is obvious that the sink temperature is dependent on
the vehicle cooling system con guration (e.g., whether the charge air cooler
is placed in front of or behind the radiator). Figure 12.12 shows the effect
of EGR cooler sink temperature on EGR cooler sizing. It is observed from
this example that to reach the same intake manifold temperature of 167°F,
if the EGR cooler sink temperature increases by 10°F, the EGR cooler
effectiveness has to increase by 1% in order to maintain the same intake
manifold gas temperature.
One important parameter in engine system design is the radiator inlet
coolant temperature (i.e., the top tank temperature). Applying equations
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848 Diesel engine system design
© Woodhead Publishing Limited, 2011
Effect of EGR cooler K
h
A
h
value on EGR cooler effectiveness
Effect of EGR cooler fouling on EGR cooler effectiveness
Baseline K
h
A
h
value
2 times of baseline K
h
A
h
value
4 times of baseline K
h
A
h
value
8 times of baseline K
h
A
h
value
16 times of baseline K
h
A
h
value
24 times of baseline K
h
A
h
value
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
1
0.9
0.8
0.7
0.6
0.5
0.4
EGR cooler effectivenessEGR cooler effectiveness
0 2 4 6 8 10 12 14
EGR mass flow rate (lb/min)
0 2 4 6 8 10 12 14
EGR mass flow rate (lb/min)
Clean cooler
Heat transfer coefficient Kh reduced by 10%
Heat transfer coefficient Kh reduced by 20%
Heat transfer coefficient Kh reduced by 30%
Heat transfer coefficient Kh reduced by 40%
1 lb/min = 0.00756 kg/sec
12.11 Cooler effectiveness characteristics.
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849Diesel engine heat rejection and cooling
© Woodhead Publishing Limited, 2011
12.13 and 12.15 to the radiator, the following equation can be derived to
calculate this temperature:
T
Q
T
RAD
T
RAD
T
In
le
tC
oolant
RAD
,h
rj
RAD
pm
in
s
T
s
T
,
=
()
mc()mc
pm
()
pm
+
()
()
e
ink
iinki
RAD
,
12.20
If the radiator is placed behind a charge air cooler (as is usually the case),
T
sink,RAD
is equal to the hot cooling air temperature at the outlet of the charge
air cooler, and it can be calculated by
T
Q
m
CA
T
CA
T
CC
oolingAir
Ou
t
CAC,
hr
j
hrjhr
CoolingA
ir
pa
i
,
CC,CC
pa,pa
=
c
rrr
T
+
,
CA
T
CA
T
CC
,CC,
oolingAir
In
oolingAirInoolingAir
12.21
where T
CAC,CoolingAirIn
is the sink temperature of the charge air cooler and
T
CAC,CoolingAirIn
= T
AMB
+ DT
recir
12.22
DT
recir
is a temperature rise due to the recirculation effect in front of the
charge air cooler. Note that
m
CoolingA
ir
is dependent upon vehicle speed, fan
speed, and altitude level (due to ambient air density change). The radiator
outlet coolant temperature can be calculated after the radiator inlet coolant
temperature is obtained, provided the radiator heat rejection and the coolant
ow rate are known.
Denote
()
=
()
,
()
()
()
()
()mc()
()mc()
f
pm
()
pm
()
in
ca
()
ca
()
()mc()
ca
()mc()
lp
()
lp
()
()mc()
lp
()mc()
mi
nc
f
nc
f
m
where
m
ca
l
is the cooling or cooled
(whichever is minimum) ow rate at an engine speed used for model
EGR cooler coolant T = 221°F
EGR cooler coolant T = 188°F
EGR cooler coolant T = 152°F
EGR cooler coolant T = 116°F
A/F ratio = 22, EGR rate = 31%
80% 85% 90% 95% 100%
EGR cooler effectiveness
210
200
190
180
170
160
150
140
130
120
110
100
Intake manifold gas temperature (°F)
12.12 Relationship between EGR cooler heat transfer capacity
(effectiveness) and cooler coolant temperature (simulation at rated
power 2300 rpm 300 hp).
Diesel-Xin-12.indd 849 5/5/11 12:02:58 PM
850 Diesel engine system design
© Woodhead Publishing Limited, 2011
calibration/tuning, and f
cm
is a cooling capability multiplier for the ow rate
(to be detailed later). Also denote e
RAD
= e
RAD,cal
f
ce
, where e
RAD,cal
is the
radiator effectiveness at the model calibration condition, and f
ce
is a cooling
capability multiplier for the effectiveness. Moreover, de ne the cooling
capability of the radiator as
F
RAD
RAD
pm
in
RAD
ca
lc
ca
l
fm
lc
fm
lc
RAD
fm
RAD
=
)
RAD
)
RAD
pm
)
pm
fm · (fm
,,
ca,,ca
lc,,lc
fm
,,
fm
lc
fm
lc,,lc
fm
lc
ee
pm
ee
pm
in
ee
in
)
ee
)
pm
)
pm
ee
pm
)
pm
mc )mc
ee
mc )mc
)
ee
)
RAD
)
RAD
ee
RAD
)
RAD
=
ee
=
fm
e
fm
fm
,,
fm
e
fm
,,
fm
(
)( )
)
ee
)( )
ee
)
fm
fm
fm
fm
)
)
fm · (fm
fm · (fm
cf
ccfc
pm
cf
pm
cf
cf
in
cf
cm
cf
cm
cf
RAD
cf)cf
cf
pm
cf)cf
pm
cf
,
12.23
Substituting 12.23 into 12.20, the following are obtained:
F
RAD
RAD
hr
j
hrjhr
RAD
In
letCoolant
si
nk
RAD
Q
TT
RAD
TT
RAD
In
TT
In
letCoolant
TT
letCoolant
si
TT
si
=
TT – TT
,
,,
In,,In
letCoolant,,letCoolant
si,,si
nk,,nk
12.24
T
Q
T
RAD
T
RAD
T
In
letCoolant
RAD
hr
j
hrjhr
RAD
si
T
si
T
nk
RAD
,
,
,
=
+
F
F
12.25
T
Q
f
T
si
T
si
T
nk
RAD
CA
Ch
rj
ca
lp
mi
nc
f
nc
f
mC
AC
mCACmC
AM
T
AM
T
B
AMBAM
,
,
Ch,Ch
,
mC,mC
=
()
mc()mc
ca
()
ca
mc
ca
mc()mc
ca
mc
lp
()
lp
mc
lp
mc()mc
lp
mc
+
()
()
+
D
T
r
T
r
T
eci
r
12.26
Equation 12.24 is used to calibrate the model for cooling capability, for
example at one operating condition with a cooling air ow rate
m
ca
l
and
effectiveness e
cal
. At other operating conditions, the cooling air ow rate
changes to
mf
mf
mf
ca
mf
lc
mf
lc
mf
m
,
and the effectiveness changes to e
cal
f
ce
. The cooling
capability F
RAD
changes accordingly to F
RAD,cal
f
ce
f
cm
. The multiplier f
ce
f
cm
converts the cooling capability from that of the model calibration condition
to the capability at other engine speed or load mode, or other ambient
conditions such as high altitude. Therefore, if f
ce
and f
cm
are known, the
radiator coolant temperature at any other operating condition can be calculated
using equations 12.25 and 12.26.
De ne f
ce
f
ce1
f
ce2
f
ce3
and f
cm
f
cm1
f
cm2
f
cm3
f
cm4
. f
ce1
is an altitude
multiplier for cooler effectiveness. At sea-level altitude, f
ce1
1. At high
altitude,
f
c
f
c
f
ai
rS
eaLevel
ai
rS
e
e
rr
ai
rr
ai
ra
rr
ra
ltitude
rr
ltitude
r
1
,,
ai,,ai
rS,,rS
rr
,,
rr
ra
rr
ra,,ra
rr
ra
ltitude
rr
ltitude,,ltitude
rr
ltitude
,
rS,rS
= 1 +
rr
–
rr
aL
aaLa
evel
x
·
%
12.27
The air density is calculated by
r
ai
r
AM
B
AMBAM
ai
r
p
T
ai
T
ai
=
·
287
12.28
where r
air
is in kg/m
3
, p
AMB
is in Pa, and T
air
is in K. The model 12.27 is
based on an assumption that every 1% of the radiator effectiveness reduction
corresponds to x% of the reduction in cooling air mass ow rate or air
density. For example, if 35% of effectiveness reduction at high altitude
Diesel-Xin-12.indd 850 5/5/11 12:03:00 PM
851Diesel engine heat rejection and cooling
© Woodhead Publishing Limited, 2011
corresponds to 75% reduction in radiator’s cooling air mass ow rate ratio,
this means on average every 1% of effectiveness reduction corresponds
to 2.14% reduction in cooling air ow rate or density, i.e., x = 2.14. This
example gives roughly 3.6°F increase in the top tank temperature for every
1000 feet altitude increase.
The parameter f
ce2
is a multiplier for radiator or CAC cooling air ow
uniformity and mal-distribution. At the model calibration condition, f
ce2
1.
The parameter f
ce3
is a multiplier to account for the change in effectiveness
due to the variation in
()
()
()
()mc()
pm
()
pm
()
in
. As shown in Fig. 12.13, f
ce3
can be modeled
as
f
f
c
f
c
f
ca
lc
al
pc
f
pc
f
m
n
ca
l
e
e
e
3
=
1 – (
1 –
)[
lc
)[
lc
()
mc()mc
lc
()
lc
mc
lc
mc()mc
lc
mc
al
()
al
mc
al
mc()mc
al
mc
pc
()
pc
]
()
()
()
()
mi
pcmipc
pcnpc
12.29
where
m
ca
l
is the normalized cooling or cooled (whichever is minimum)
mass ow rate at the model calibration condition. The parameter e
cal
is a
known effectiveness term at the model calibration condition. The exponent
n in equation 12.29 can be adjusted to change the shape of the effectiveness
characteristic curve (e.g., n = 0.5).
The multiplier f
cm1
is a cooling fan speed multiplier for the cooling air
ow rate and is proportional to engine speed. The parameter f
cm2
is a vehicle
ram air speed multiplier and is proportional to vehicle speed. The parameter
f
cm3
is a water pump speed multiplier and is proportional to engine speed.
The parameter f
cm4
is a multiplier for vehicle underhood cooling air ow
restriction and any model calibration uncertainty. At the model calibration
condition, f
cm1
= f
cm2
= f
cm3
= f
cm4
1. If
()
()
()
()mc()
ca
()
ca
()
()mc()
ca
()mc()
lp
()
lp
()
()mc()
lp
()mc()
mi
n
refers to the coolant
ow (for the radiator) or the charge air ow (for the air-cooled CAC), f
cm1
= f
cm2
= f
cm4
= 1 because they do not apply in that case. For air-cooled CAC
or if
()
()
()
()mc()
ca
()
ca
()
()mc()
ca
()mc()
lp
()
lp
()
()mc()
lp
()mc()
mi
n
refers to the cooling air ow rate for the radiator, f
cm3
= 1
because it does not apply. It should be noted that when
()
()
()
()mc()
pm
()
pm
()
in
changes
between cooling air ow and liquid coolant ow at different engine speeds
or operating conditions, the equations 12.25 and 12.26 involving the term
()
,
()
()
()mc()
f
ca
()
ca
()
()mc()
ca
()mc()
lp
()
lp
()
()mc()
lp
()mc()
mi
nc
f
nc
f
m
RAD
cannot be used. In that case, the actual
()
()
()
()mc()
pm
()
pm
()
in
at each
speed or operating condition must be used as in equation 12.20.
Equation 12.25 shows that the radiator coolant temperature depends directly
on the cooling capability. In engine system design, a normal practice is to
estimate the required change in the normalized radiator cooling capability
(i.e., essentially effectiveness multiplied by cooling air ow rate) until the
engine outlet coolant temperature reaches the design target under the predicted
heat rejection. For example, a normalized cooling capability of 1.58 means
58% larger than the baseline cooling capability.
Engine simulation shows that although the coolant heat rejection reaches
the highest value at rated power, the radiator inlet coolant temperature usually
Diesel-Xin-12.indd 851 5/5/11 12:03:01 PM