02 Nov 2017
Eindhoven University of Technology, Netherlands
Copyright c 2013 Society of Automotive Engineers, Inc.
At the TU/e (Eindhoven University of Technology) a
Volvo T5 turbocharged engine set-up is built for research
purposes in the field of alternative fuels and
waste energy recovery. Originally, this Volvo engine
is equipped with an air-air intercooler. Due
to the absence of wind in the engine cell, a waterair
intercooler is used instead, which origins from a
Mercedes-Benz SL55 AMG. For research purposes,
it is desirable to be able to tune the intake air temperature
by means of a control system. This is e.g. interesting
for engine knock studies. As the cooling capacity
is decisive for the intake air temperature of the
combustion engine, the principle objective of this research
is to analyze the cooling capacity of the waterair
intercooler. The ultimate goal is to specify the lowest
intake air temperature at each rotational speed.
This theoretical analysis is based on heat transfer theory
from two different perspectives: the energy content
of the water- and air flow and the heat transfer
rate within the intercooler based on its geometry and
material properties. This analysis is fulfilled by means
of a physical model using the software package MATLAB.
The main result of this analysis is that the intake
air can be reduced with 22.9 K to an intake air temperature
of 310.5 K. From the performed sensitivity analysis
it can be concluded that the results of the initial
model are stable. Nevertheless, due to the assumption
of adiabatic heat transfer, this does not guarantee
the overall reliability of the solution. Hitherto, this
theoretical analysis is limited to one rotational speed,
namely 6000 rpm.
Since many years, intercoolers are used to cool down
compressed air before entering the intake manifold.
In most cases, air is compressed by means of a compressor
which is part of the turbocharger. Due to
irreversible operation of the compressor, air will not
only be compressed but some mechanical power is
converted into heat. This induces a temperature increase
of the air. An increased intake air temperature
increases the tendency for knock and deteriorates the
volumetric efficiency [1]. By cooling the intake air
through the intercooler, also the density is further increased.
The efficiency for an intercooler is defined as the ratio
of the actual heat transfer rate to the maximum possible
(potential) heat transfer rate. [2]
The research goal of this paper is to determine the
cooling capacity of the Mercedes-Benz SL55 AMG
water-air intercooler (Figure 1) and to analyze the influence
of different parameters on the intercooler outgoing
air temperature.
A physical model has been made using formulae
and correlations related to the specific intercooler
type. Using equation balances, the outgoing air temperature
can be calculated when input values are
given. Accordingly, a sensitivity analysis has been
1
Figure 1: Render of the Mercedes-Benz SL55 AMG
water-air intercooler
performed to validate the reliability and robustness of
the model.
An intercooler can be interpret as a heat exchanger.
Heat exchangers are usually classified by flow arrangement
and construction type. For modeling purposes,
it is important to distinct the different types of
heat exchangers for applying the right formulae and
correlations [3, 4, 5].
Figure 2: Intercooler classification by flow arrangement
In Figure 2 and 3 the intercooler is classified by flow
arrangement and construction respectively. From this
classification it is concluded that the heat transfer theory
applied must be applicable for a (recuperative indirect)
plate-fin-tube multi pass cross flow heat exchanger
(i.e. intercooler).
The analysis starts with a theoretical approach. In
Figure 4 below a schematic overview of the intercooler
with associated in- and outgoing flows is displayed
Figure 3: Intercooler classification by construction
T1 = Tin,air T2 = Tout,air
T3 = Tin,water T4 = Tout,water
Figure 4: Schematic overview intercooler and flows
In this heat exchanging process the heat is transferred
from the air flow to the water flow. Assumptions made
for this theoretical analysis are:
_ The heat exchange process is only between the
hot gas and cold fluid. This means there is no
heat loss to the surroundings, i.e. adiabatic heat
transfer process. The red line in Figure 4 indicates
the boundary of the heat exchange process.
_ Potential and kinetic energy changes are negligible.
The heat transfer rate q that occurs in the intercooler
can be described by its overall heat transfer coefficient
and the heat exchanging surface.
q = U _ A _ _Tlm (1)
In this relation U describes the overall heat transfer
coefficient, A the cooling surface, and _Tlm the logarithmic
mean temperature difference. Both factors,
2
U and A depend on the intercooler geometry and the
flow through the intercooler, while _Tlm exists as a
boundary condition. The analysis for the total heat
transfer rate q is divided in two parts. First the term
U _ A will be analyzed. Subsequently, the quantity
_Tlm will be regarded and finally, the fluid flows and
conservation of energy will be treated.
OVERALL HEAT TRANSFER COEFFICIENT
The product of U and A is used to describe the overall
thermal resistance.
Rtot =
X
Rt =
1
UA
(2)
For the specific heat exchanging process of the intercooler
this relation can be written as
1
UA
1
(_0hA)water
+ Rw +
1
(_0hA)air
(3)
in which the first term of the right hand side represents
the inverse of the convective heat transfer coefficient
between the intercooler and water flow and the
last term of the right hand side the inverse of the convective
heat transfer coefficient between the air flow
and the intercooler. Both terms are derived from the
relation for convective heat transfer for fin-equipped
applications.
q = _0 _ h _ A _ (Tb ô€€€ T1) (4)
In this relation Tb and T1 represent the base temperature
and the surroundings temperature respectively.
The quantity _0 is known as the overall surface efficiency,
which will be explained later on.
The middle term of the right hand side from Equation
3 represents the conductive heat transfer coefficient
of the wall that separates the air and the water flow
(the tube). All three terms can be regarded as a thermal
resistance for their specific mechanism of heat
transfer. The different mechanisms of heat transfer
are displayed in a schematic overview of a random
finned-pipe configuration.
In the lower right part of Figure 5 the convection from
the hot air to the outer tube wall is illustrated, in the
upper part the conduction from outer to inner tube
wall, and in the lower left part the convection from the
inner wall to the cooling water.
Figure 5: Schematic overview heat exchange for
finned tube configuration
During normal heat exchanger operation, surfaces
are often subject to pollution or fouling. Sources for
fouling can be reactions between the fluid and the
heat-exchanging wall material. Most common form is
rust formation. Also fluid impurities contribute to fouling
[2]. Fouling leads to a film on the surface which
can greatly increase the resistance to heat transfer
between the fluids. To include fouling in the model, an
additional thermal resistance is introduced in Equation
3, called the fouling factor Rf . This leads to
1
UA
1
(_0hA)water
R"
f;water
(_0A)water
+ Rw+ (5)
R"
f;air
(_0A)air
1
(_0hA)air
wherein the thermal conduction resistance term Rw
(for circular tubes) is defined as
Rw = Rt;cond =
ln (r2=r1)
2_Lk
(6)
in which r2 is the outer radius, r1 the inner radius, L
the length, and k the thermal conductivity of the tube.
As stated earlier, the quantity _0 in Equation 5 is the
overall efficiency of a finned surface. It is defined as
_0 = 1 ô€€€
Af
A
_ (1 ô€€€ _f ) (7)
where Af =A is the ratio between the fin surface and
3
total surface. The fin efficiency for rectangular fins is
defined as
_0 =
tanh (mL)
mL
(8)
where m = (2h=kt)1=2. In Equation 8 t is the fin thickness,
k the thermal conductivity of the fins, and h the
convection heat transfer coefficient from the flowing
air to the fins. The convection heat transfer coefficient
is now the only uncertain parameter in Equation 5.
To determine the value of this parameter the Sieder-
Tate and Dittus-B ¨ olter correlations must be used [6].
Both correlations calculate the Nusselt number. By
means of the Nusselt number the corresponding convection
heat transfer coefficient can be determined.
The above mentioned correlations must be applied to
a laminar and turbulent flow respectively. A laminar
flow is characterized by a Reynolds number smaller
than 2300 (Re < 2300) and a turbulent flow by a
Reynolds number larger than 10000 (Re > 10000).
After several manipulations and substitutions, which
can be read over in the Appendix, the correlations for
the convection heat transfer coefficient for both laminar
and turbulent case end up in
hlaminar =
k _ 1:86 _
De _ ReDe _ Pr
L
_1
3
=De
(9)
hturbulent =
n
k _ 0:023 _ Re
4
5D
e
_ Prn
o
=De:
From the Equations 2 up to 9 the factor U _ A can be
determined. In the following subsection, the logarithmic
mean temperature will be regarded.
LOGARITHMIC MEAN TEMPERATURE DIFFERENCE
The logarithmic mean temperature difference can be
expressed as
_Tlm = F _
_T1 ô€€€ _T2
ln (_T1=_T2)
(10)
= F _
T1 ô€€€ T3 ô€€€ T2 + T4
ln ([T1 ô€€€ T3] = [T2 ô€€€ T4])
More details about the derivation of Equation 10 can
be found in [2]. The correction factor in Equation 10
is the result of the fact that the initial correlation of
_Tlm (without correction factor) is derived from a parallel
flow arrangement. For a cross flow or other than
parallel configuration, the correction factor should be
used [6]. The correction factor can be determined
graphically from a correction factor chart. The factor
is dependent on temperatures of the in- and out flows
of the intercooler.
CONSERVATION OF ENERGY
For the prediction of the performance of a heat exchanger,
it is necessary to relate the total heat transfer
rate to quantities such as the overall heat transfer
coefficient, the inlet and outlet fluid temperatures, and
the total surface area for heat transfer. Partly this is
satisfied with equations above. However, those were
only applied to the equipment itself, not to the fluid
flows. The required relations can be obtained by applying
an overall energy balance to the hot and cold
fluids [2]. For the air and water flow this leads to
qair = m_ air (i1 ô€€€ i2) (11)
qwater = m_ water (i4 ô€€€ i3) :
In Equation 11, i denotes the specific enthalpy of the
fluid.
The specific enthalpy is the multiplication of the specific
heat capacity and temperature, which leads to
qair = m_ air (cp;1 _ T1 ô€€€ cp;2 _ T2) (12)
qwater = m_ water (cp;4 _ T4 ô€€€ cp;3 _ T3) :
According to the conservation of energy, the retained
heat of the ingoing air and water flow should be equal
to the retained heat of the outgoing air and water flow.
This means that
qin = qout (13)
m_ air _ cp;1 _ T1 + m_ water _ cp;3 _ T3 =
m_ air _ cp;2 _ T1 + m_ water _ cp;4 _ T4
m_ air _ (cp;1 _ T1 ô€€€ cp;2 _ T2) =
m_ water _ (cp;4 _ T4 ô€€€ cp;3 _ T3)
The difference in heat (i.e. energy) content, for each
4
of the fluids (air and water), between ingoing and outgoing
flow described in Equation 13 should equal the
heat transferred in the intercooler described in Equation
1.
qtransferred = _qair = _qwater (14)
U _ A _ _Tlm = m_ air _ (cp;1 _ T1 ô€€€ cp;2 _ T2)
With Equation 13 and 14 the heat transfer problem
can be solved for the outgoing temperatures T2 and
T4. The Equations were solved using the software
package MATLAB. However, many parameters required
to calculate U _ A are temperature dependent.
Therefore, fluid property data from the NIST (National
Institute of Standards and Technology) database was
used to implement the temperature dependence [7].
The intercooler ingoing air temperature is the compressor
outgoing air temperature and can be calculated
using the relation from the book of Hiereth [8].
The increase in temperature in the compressor depends
on the pressure ratio selected and on the compressor
efficiency which was estimated 0.7.
T1 = Tamb
1 +
1
_C
pamb + pover
pamb
_(_ô€€€1)=_
ô€€€ 1
(15)
In Equation 15, _C is the compressor efficiency, _ the
heat capacity ratio, and pover the over pressure with
respect to the ambient pressure pamb.
The heat capacity ratio is also dependent on temperature,
however its value ranges from 1.4035 to 1.3983
using the NIST database. Due to this insignificant
change its value is fixed at 1.4. Some other important
input parameters are listed in Table 1.
Table 1: Model input parameters
Value Unit
Cylinder volume 2.5x10ô€€€3 [m3]
Compressor efficiency 0.7 [-]
Maximum over pressure 0.38 [bar]
Heat capacity ratio 1.4 [-]
Ingoing water temperature 285 [K]
Mass flow water 0.7 [kg/s]
In the following section, the model results will be presented
and discussed.
First, model results will be presented using the input
parameters listed in Table 1. Accordingly, some of
these parameters will be varied to analyze the effect
on the outgoing air temperature and cooling capacity.
Finally, a sensitivity analysis will be performed on the
geometrical intercooler quantities.
MODEL RESULTS
The model results with above mentioned input parameters
are listed in Table 2.
Table 2: Model input parameters
Value Unit
T1= Tin;air 333.3 [K]
T2= Tout;air 310.5 [K]
T4= Tout;water 286.7 [K]
_Tair -22.9 [K]
_Twater +1.7 [K]
U _ A 156.5 [W/K]
q 4.58x103 [W]
It is obvious that the air temperature decrease of -22.9
K is obtained with a water temperature increase of
only +1.7 K. This has among other things to due with
the much higher heat capacity from water compared
to air. Furthermore, the maximum cooling capacity
from the intercooler reaches up to nearly 5 kW.
Compressor efficiency The compressor efficiency
is uncertain for the specific system to be
investigated. In literature it can be found that on
average this value is between 60 and 75 %. For this
reason the examined domain is set on the average
domain _ 10 %. This means between 50 and 85 %.
The results for the outgoing air temperature and the
associated _Tair are presented in Figure 6 and 7.
In Figure 6 it is obvious that the outgoing air temperature
decreases with increasing compressor efficiency.
This is not due to an increased _Tair over the
intercooler, as this quantity decreases for increasing
compressor efficiency (Figure 7). The reason can be
found in Figure 8. From this Figure it is obvious that
the outgoing air temperature of the compressor (ingoing
air temperature of the intercooler) decreases for
increasing compressor efficiency. This means that a
lower compressor efficiency results in a larger temperature
difference between the water and air flow
which results in a larger heat flux and thus cooling
capacity (Figure 9) .
5
0.5 0.55 0.6 0.65 0.7 0.75 0.8
308
310
312
314
316
318
Air Temperature Out Intercooler [K]
Compressor Efficiency [−]
Figure 6: Air temperature out intercooler as function
of compressor efficiency
0.5 0.55 0.6 0.65 0.7 0.75 0.8
−30
−28
−26
−24
−22
−20
Delta T Air Intercooler [K]
Compressor Efficiency [−]
Figure 7: Delta T air intercooler as function of compressor
efficiency
These two contradictory effects, however, do not compensate
each other. The net effect results in a lower
outgoing air temperature for a higher compressor efficiency.
Therefore, a higher compressor efficiency has
a positive effect on the intake air temperature of the
engine.
Ingoing temperature cooling water The ingoing
temperature of the cooling water ranges from 277 up
to 293 K depending on the season. In Figure 10 the
result of the variation in this temperature is presented.
From this result it can be concluded that an increase
in the water ingoing temperature results in a proportional
higher outgoing air temperature. In other words,
they are linear related. Due to the decrease of temperature
difference between the water and air flow the
cooling capacity becomes smaller too [Add Figure
0.5 0.55 0.6 0.65 0.7 0.75 0.8
330
335
340
345
Air Temperature In Intercooler [K]
Compressor Efficiency [−]
Figure 8: Air temperature in intercooler as function of
compressor efficiency
0.5 0.55 0.6 0.65 0.7 0.75 0.8
1.2
1.3
1.4
1.5
1.6
1.7
1.8
x 104
Cooling Capacity [W]
Compressor Efficiency [−]
Figure 9: Cooling capacity as function of compressor
efficiency [VERIFY FIGURE!!!]
Mass flow water The water mass flow is freely adjustable
in the engine set-up. However, the maximum
value of the water mass flow is unknown. This is dependent
on the head and the pressure drop of the integrated
cooling system. However, with the model the
variation of different quantities can be analyzed for a
varying water mass flow.
Looking at Figure 11, the most interesting phenomenon
in this analysis is the non linearity of the
trend lines. It can be seen that the _Tair tends to approach
an asymptote (for _Twater the same holds). In
other words from a certain mass flow (approximately
0.9 kg/s) the air temperature does not decrease significant
anymore regardless an increase of the water
6
280 285 290
308
309
310
311
312
313
Air Temperature Out Intercooler [K]
Water Temperature In Intercooler [K]
Figure 10: Air temperature out intercooler as function
of water temperature in
0.2 0.4 0.6 0.8 1 1.2
−24
−22
−20
−18
−16
−14
−12
Delta T Air Intercooler [K]
Mass Flow Water [kg/s]
Figure 11: Delta T air intercooler as function of mass
flow water
mass flow. The reason for this phenomenon is the increase
of the heat transfer convection coefficient for
an increasing mass flow of water.
As can be seen in Figure 12 this increase is linear.
However, the fifth factor of U _ A is inversely proportional
with h. This causes the _Tair to tend to an
asymptote. In Figure 13 and 14 this is plotted for both
the first factor of U _ A as for U _ A total (Equation 5).
SENSITIVITY ANALYSIS
To validate the reliability and robustness of the model
for the intercooler outgoing air temperature (i.e. intake
air temperature engine), the values for the geometrical
quantities of the intercooler (Table 3) are varied
with _10, _20, and _40 %. In this analysis only one
value is changed at a time, while all other parameters
0.2 0.4 0.6 0.8 1 1.2
0.5
1
1.5
2
2.5
x 104
Convection Heat Transfer Coefficient [W/m2K]
Mass Flow Water [kg/s]
Figure 12: Convection heat transfer coefficient as
function of mass flow water
0.2 0.4 0.6 0.8 1 1.2
0.5
1
1.5
2
x 10−3
1st factor U ïƒ—ï€ A [W/K]
Mass Flow Water [kg/s]
Figure 13: 1st factor U _ A as function of mass flow
water
0.2 0.4 0.6 0.8 1 1.2
125
130
135
140
145
150
155
160 U
A
W/K]
Mass Flow Water [kg/s]
Figure 14: U _ A as function of mass flow water
7
are kept fixed to the value of the initial model treated in
the first part of this section. In this way the sensitivity
of a specific quantity can be analyzed. An important
note is that some quantities are dependent on each
other (e.g. Aw is dependent on Lp and r1). Furthermore,
in reality a situation can occur that two changes
compensate each other due to opposite effects on the
outgoing air temperature. For this reason Aa and Aw
are considered separately from the other quantities in
Table 3.
Table 3: Model input parameters
Geometrical quantity Unit
t Fin thickness [m]
r1 Inner radius tube [m]
r2 Outer radius tube [m]
La Length air channel [m]
Lp Length water channel [m]
Lf Length fins [m]
Aa Air contact surface [m2]
Aw Water contact surface [m2]
Considering the results in Figure 15 from the above
described analysis it can be concluded that the initial
solution is rather stable.
t r1 r2 L_a L_p L_f A_a A_w
305
310
315
320
Changed Quantities
Air Temperature Out Intercooler [K]
+10%
+20%
+40%
−10%
−20%
−40%
Figure 15: Results sensitivity analysis on outgoing air
temperature intercooler
The absolute differences that occur in the outgoing air
temperature are maximum 1.5 K for a relative geometric
change of 10 %. This 1.5 K temperature change
holds for Aa. As said before, Aa and Aw are composed
of the quantities listed previously. This means
that theoretically a 10 % deviation for Aa and Aw is
harder to induce than for the other geometric quantities.
This means that a temperature difference of 1.5
K is not plausible.
It must be taken into account that a combination of deviations
is much more likely to occur than only value
at a time. It is also possible that a combination of
deviations for the assumed values leads to a larger
increase or decrease of the outgoing air temperature.
This leads to infinite many possibilities to analyze.
However, although not analyzed, larger deviations
than a few degrees should not be expected for
_10 %.
The results for _20 and _40 % show more or less
a similar trend than for _10 %. The quantities show
the same relative changes in output for different input
values. The most sensitive quantity is Aa, the total
contact surface of the air. The least sensitive quantity
is the outer radius r2. It hardly affects the outgoing air
temperature, even not for _40 %.
For _20 % the largest decrease in outgoing air temperature
is 2.6 K, the temperature increase amounts
3.3 K. For _40 % values of 4.6 and 7.9 K hold for
the maximum temperature decrease and increase respectively.
These maximum values occur for relative
changes for the most sensitive quantity Aa.
In Figure 16 the same results are presented for the
additional _T. It is the temperature difference between
the initial outgoing air temperature (310.5 K,
Table 2) and the acquired outgoing air temperature
following from the sensitivity analysis.
t r1 r2 L_a L_p L_f A_a A_w
−6
−4
−2
0
2
4
6
8
Changed Quantities
Delta T Air Intercooler [K]
plus 10%
plus 20%
plus 40%
minus 10%
minus 20%
minus 40%
Figure 16: Results sensitivity analysis on Delta T air
intercooler
It can be be concluded that the sensitivity analysis is
suitable to use for analyzing the effect of varying the
value of a single quantity on the outgoing air temperature.
However, in reality several quantities can change
simultaneously. This can amplify or cancel out the net
effect on the outgoing air temperature. This means
that in practise the outgoing air temperature can ex-
8
ceed the upper or lower values presented in Figure 16
and that this analysis can not be interpret as an error
analysis.
_ It is determined that the considered intercooler
can be classified as a (recuperative indirect)
plate-fin-tube multi pass cross-flow heat exchanger.
This classification is important because
it justifies the used formulae and correlations.
_ From the initial model parameters it can be concluded
that the cooling capacity is about 4.6 kW
and that the air temperature can be decreased
with 22.9 K to an outgoing air temperature of
310.5 K. However, the uncertainties concerning
the compressor efficiency (0.5 to 0.85), ingoing
water temperature (278 to 293 K), and water
mass flow (0.1 to 1.2 kg/s) result in outgoing air
temperatures of 318 to 307 K, 307 to 314 K, and
323 to 309 K respectively.
_ From the sensitivity analysis on the geometrical
quantities it can be concluded that the contact
surface on the air side is most sensitive, namely
_1.5 K for _10 %, -2.6 K and +3.3 K for _20
%, and -4.6 K and +7.9 K for _40 %. The least
certain geometrical quantity is the length of the
water tube inside the intercooler. The sensitivity
analysis shows that the outgoing air temperature
is rather insensitive to this quantity, only -1.3 K
and +2.2 K for a deviation of _40 %. In general,
it can be concluded that the solution is rather stable.
_ The assumption for adiabatic heat transfer is expected
to lead to a significant, non negligible error
in the estimation of the actual heat transfer or
cooling capacity. To improve the model accuracy,
heat transfer (i.e. radiation and convection) to the
surroundings should be incorporated.
_ In this analysis, the cooling capacity was determined
for one rotational speed. In further investigation
the full rotational speed domain should be
considered.
_ In future research, an experimental analysis
could be carried out to compare, validate and further
improve the model.
[1] J.B. Heywood. Internal Combustion Engine Fundamentals.
McGraw-Hill, 1988.
[2] F.P. Incropera, D.P. de Witt, T.L. Bergman, and
A.S. Lavine. Introduction to Heat Transfer, 5th edition.
John Wiley & Sons Inc: Hoboken, 2007.
[3] G. Walker. Industrial Heat Exchangers - A Basic
Guide. Hemisphere Publishing Corporation, 1982.
[4] W.M. Rohsenow and J.P. Hartnett. Handbook of
Heat Transfer. New York: McGraw-Hill Book Company,
1973.
[5] E.A.D. Saunders. Heat Exchangers - Selection,
Design and Construction. Longman Scientific and
Technical, 1988.
[6] B.P.M. van Esch and H.P. van Kemenade. Proces
technische constructies. Eindhoven University of
Technology, 2010.
[7] S.R. Turns. Thermodynamics - Concepts and
Applications, 6th edition. Cambridge University
Press: New York, 2006.
[8] H. Hiereth and P. Prenninger. Charging the internal
combustion engine. SpringWienNewYork:
New York, 2003.
Dr. ir. M.D. Boot (Director PI)
Progression Industry
Eindhoven, Den Dolech 2
m.d.boot@tue.nl
Ir. R. Dijkstra (Employee R&E)
University of Technology
Eindhoven, Den Dolech 2
r.dijkstra@tue.nl
T.H. Kingma BSc (Student)
University of Technology
Eindhoven, Den Dolech 2
t.h.kingma@student.tue.nl
The authors would like to express their gratitude towards...
NIST National Institute of Standards
and Technology
Re Reynolds number
Nu Nusselt number
9
Pr Prandtl number
De Deborah number
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